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<div class="title">lanczos.hpp</div> </div>
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<a href="lanczos_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_LANCZOS_HPP_</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="preprocessor">#define VIENNACL_LINALG_LANCZOS_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="l00027"></a><span class="lineno"> 27</span> <span class="preprocessor">#include <cmath></span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="preprocessor">#include <vector></span></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="preprocessor">#include "<a class="code" href="vector_8hpp.html">viennacl/vector.hpp</a>"</span></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="preprocessor">#include "<a class="code" href="compressed__matrix_8hpp.html">viennacl/compressed_matrix.hpp</a>"</span></div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="preprocessor">#include "<a class="code" href="prod_8hpp.html">viennacl/linalg/prod.hpp</a>"</span></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="preprocessor">#include "<a class="code" href="inner__prod_8hpp.html">viennacl/linalg/inner_prod.hpp</a>"</span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="preprocessor">#include "<a class="code" href="norm__2_8hpp.html">viennacl/linalg/norm_2.hpp</a>"</span></div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="preprocessor">#include "<a class="code" href="matrix__market_8hpp.html">viennacl/io/matrix_market.hpp</a>"</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="preprocessor">#include "<a class="code" href="bisect_8hpp.html">viennacl/linalg/bisect.hpp</a>"</span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="preprocessor">#include "<a class="code" href="random_8hpp.html">viennacl/tools/random.hpp</a>"</span></div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> </div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="keyword">namespace </span>viennacl</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> {</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="keyword">namespace </span>linalg</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> {</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> </div>
<div class="line"><a name="l00045"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1lanczos__tag.html"> 45</a></span> <span class="keyword">class </span><a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html">lanczos_tag</a></div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> {</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="keyword">public</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>  <span class="keyword">enum</span></div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  {</div>
<div class="line"><a name="l00051"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1lanczos__tag.html#a8a743b9f474124a0f779ed35c6f6a684a937ee8052e51309672b2bcdba4bb015e"> 51</a></span>  <a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#a8a743b9f474124a0f779ed35c6f6a684a937ee8052e51309672b2bcdba4bb015e">partial_reorthogonalization</a> = 0,</div>
<div class="line"><a name="l00052"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1lanczos__tag.html#a8a743b9f474124a0f779ed35c6f6a684a8ecf6c75a5bd6248e628651a83a9adf1"> 52</a></span>  <a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#a8a743b9f474124a0f779ed35c6f6a684a8ecf6c75a5bd6248e628651a83a9adf1">full_reorthogonalization</a>,</div>
<div class="line"><a name="l00053"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1lanczos__tag.html#a8a743b9f474124a0f779ed35c6f6a684a5a98f73ee4246c0d97c82917edeca27e"> 53</a></span>  <a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#a8a743b9f474124a0f779ed35c6f6a684a5a98f73ee4246c0d97c82917edeca27e">no_reorthogonalization</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> </div>
<div class="line"><a name="l00064"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1lanczos__tag.html#aa71eae96da7f83e2c510ae02a2c7dbce"> 64</a></span>  <a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#aa71eae96da7f83e2c510ae02a2c7dbce">lanczos_tag</a>(<span class="keywordtype">double</span> <a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#a47e14babee64097056526536b277dbae">factor</a> = 0.75,</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> numeig = 10,</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="keywordtype">int</span> met = 0,</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> krylov = 100) : factor_(<a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#a47e14babee64097056526536b277dbae">factor</a>), num_eigenvalues_(numeig), method_(met), krylov_size_(krylov) {}</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span> </div>
<div class="line"><a name="l00070"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1lanczos__tag.html#ae744c43467774ee300f5fab0c607aed1"> 70</a></span>  <span class="keywordtype">void</span> <a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#ae744c43467774ee300f5fab0c607aed1">num_eigenvalues</a>(<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> numeig){ num_eigenvalues_ = numeig; }</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span> </div>
<div class="line"><a name="l00073"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1lanczos__tag.html#abfff89303690a662fab2fbabcca2ee25"> 73</a></span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> <a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#abfff89303690a662fab2fbabcca2ee25">num_eigenvalues</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> num_eigenvalues_; }</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span> </div>
<div class="line"><a name="l00076"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1lanczos__tag.html#a3ce84b79a3ff77dd91a656232311cd52"> 76</a></span>  <span class="keywordtype">void</span> <a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#a3ce84b79a3ff77dd91a656232311cd52">factor</a>(<span class="keywordtype">double</span> fct) { factor_ = fct; }</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> </div>
<div class="line"><a name="l00079"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1lanczos__tag.html#a47e14babee64097056526536b277dbae"> 79</a></span>  <span class="keywordtype">double</span> <a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#a47e14babee64097056526536b277dbae">factor</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> factor_; }</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span> </div>
<div class="line"><a name="l00082"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1lanczos__tag.html#a4e07073e383c1f5ed160d007f05d6eb3"> 82</a></span>  <span class="keywordtype">void</span> <a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#a4e07073e383c1f5ed160d007f05d6eb3">krylov_size</a>(<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> <a class="code" href="namespaceviennacl_1_1linalg.html#adfd5b21910a692a78c547b22b9157c2e">max</a>) { krylov_size_ = <a class="code" href="namespaceviennacl_1_1linalg.html#adfd5b21910a692a78c547b22b9157c2e">max</a>; }</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span> </div>
<div class="line"><a name="l00085"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1lanczos__tag.html#aaad9aa2dc06eb4a5ca272d7fc78fb072"> 85</a></span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> <a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#aaad9aa2dc06eb4a5ca272d7fc78fb072">krylov_size</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> krylov_size_; }</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span> </div>
<div class="line"><a name="l00088"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1lanczos__tag.html#aad5c2c34a2b41e2a6a9b52dedd1d2ecf"> 88</a></span>  <span class="keywordtype">void</span> <a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#aad5c2c34a2b41e2a6a9b52dedd1d2ecf">method</a>(<span class="keywordtype">int</span> met){ method_ = met; }</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span> </div>
<div class="line"><a name="l00091"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1lanczos__tag.html#af2126adae7cd63d5c9c380066cdfabf1"> 91</a></span>  <span class="keywordtype">int</span> <a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#af2126adae7cd63d5c9c380066cdfabf1">method</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> method_; }</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span> </div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span> </div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="keyword">private</span>:</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keywordtype">double</span> factor_;</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> num_eigenvalues_;</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="keywordtype">int</span> method_; <span class="comment">// see enum defined above for possible values</span></div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> krylov_size_;</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span> };</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> </div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span> </div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span> <span class="keyword">namespace </span>detail</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span> {</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="keyword">template</span><<span class="keyword">typename</span> NumericT></div>
<div class="line"><a name="l00109"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#ab967b62c4a6c67c3e37623eac4cc4fc1"> 109</a></span>  <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#ab967b62c4a6c67c3e37623eac4cc4fc1">inverse_iteration</a>(std::vector<NumericT> <span class="keyword">const</span> & alphas, std::vector<NumericT> <span class="keyword">const</span> & betas,</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> & eigenvalue, std::vector<NumericT> & eigenvector)</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>  std::vector<NumericT> alpha_sweeped = alphas;</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=0; i<alpha_sweeped.size(); ++i)</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  alpha_sweeped[i] -= eigenvalue;</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> <a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>=1; <a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a> < alpha_sweeped.size(); ++<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>)</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  alpha_sweeped[<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>] -= betas[<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>] * betas[<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>] / alpha_sweeped[<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>-1];</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span> </div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="comment">// starting guess: ignore last equation</span></div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  eigenvector[alphas.size() - 1] = 1.0;</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span> </div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> iter=0; iter<1; ++iter)</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>  <span class="comment">// solve first n-1 equations (A - \lambda I) y = -beta[n]</span></div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  eigenvector[alphas.size() - 1] /= alpha_sweeped[alphas.size() - 1];</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> row2=1; row2 < alphas.size(); ++row2)</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>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> <a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a> = alphas.size() - row2 - 1;</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  eigenvector[<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>] -= eigenvector[row+1] * betas[row+1];</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  eigenvector[<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>] /= alpha_sweeped[<a class="code" href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">row</a>];</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  }</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span> </div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="comment">// normalize eigenvector:</span></div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> norm_vector = 0;</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=0; i<eigenvector.size(); ++i)</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  norm_vector += eigenvector[i] * eigenvector[i];</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  norm_vector = std::sqrt(norm_vector);</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=0; i<eigenvector.size(); ++i)</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  eigenvector[i] /= norm_vector;</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  }</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span> </div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <span class="comment">//eigenvalue = (alphas[0] * eigenvector[0] + betas[1] * eigenvector[1]) / eigenvector[0];</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="l00156"></a><span class="lineno"> 156</span>  <span class="keyword">template</span><<span class="keyword">typename</span> MatrixT, <span class="keyword">typename</span> DenseMatrixT, <span class="keyword">typename</span> NumericT></div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  std::vector<NumericT></div>
<div class="line"><a name="l00158"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#a07c896c3efe02f24adf912b1f89e5c07"> 158</a></span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a07c896c3efe02f24adf912b1f89e5c07">lanczosPRO</a> (MatrixT <span class="keyword">const</span>& A, <a class="code" href="classviennacl_1_1vector__base.html">vector_base<NumericT></a> & r, DenseMatrixT & eigenvectors_A, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> <a class="code" href="namespaceviennacl_1_1traits.html#aa2344ea20469f55fbc15a8e9526494d0">size</a>, <a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html">lanczos_tag</a> <span class="keyword">const</span> & tag, <span class="keywordtype">bool</span> compute_eigenvectors)</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  {</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <span class="comment">// generation of some random numbers, used for lanczos PRO algorithm</span></div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <a class="code" href="classviennacl_1_1tools_1_1normal__random__numbers.html">viennacl::tools::normal_random_numbers<NumericT></a> get_N;</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>  std::vector<vcl_size_t> l_bound(size/2), u_bound(size/2);</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> n = r.<a class="code" href="classviennacl_1_1vector__base.html#a15c47ae4326098aeaa4ed6b91fc6df9b">size</a>();</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  std::vector<NumericT> w(size), w_old(size); <span class="comment">//w_k, w_{k-1}</span></div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span> </div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> inner_rt;</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  std::vector<NumericT> alphas, betas;</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  <a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<NumericT, viennacl::column_major></a> Q(n, size); <span class="comment">//column-major matrix holding the Krylov basis vectors</span></div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span> </div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  <span class="keywordtype">bool</span> second_step = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> eps = std::numeric_limits<NumericT>::epsilon();</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> squ_eps = std::sqrt(eps);</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> eta = std::exp(std::log(eps) * tag.<a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#a3ce84b79a3ff77dd91a656232311cd52">factor</a>());</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span> </div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> beta = <a class="code" href="namespaceviennacl_1_1linalg.html#ae46f15d01c01f92a153b3f555a15096b">viennacl::linalg::norm_2</a>(r);</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>  r /= beta;</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span> </div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> q_0(Q.<a class="code" href="classviennacl_1_1matrix__base.html#a4082cd3586bc99deb68733257b30c51f">handle</a>(), Q.<a class="code" href="classviennacl_1_1matrix__base.html#a24e4f5fa27a1af5ad47e52a97c065d68">size1</a>(), 0, 1);</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  q_0 = r;</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span> </div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<NumericT></a> u = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>(A, r);</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> alpha = <a class="code" href="namespaceviennacl_1_1linalg.html#ab35950c4374eb3be08a03d852508c01a">viennacl::linalg::inner_prod</a>(u, r);</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  alphas.push_back(alpha);</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  w[0] = 1;</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  betas.push_back(beta);</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>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> batches = 0;</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i = 1; i < <a class="code" href="namespaceviennacl_1_1traits.html#aa2344ea20469f55fbc15a8e9526494d0">size</a>; i++) <span class="comment">// Main loop for setting up the Krylov space</span></div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  {</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> q_iminus1(Q.<a class="code" href="classviennacl_1_1matrix__base.html#a4082cd3586bc99deb68733257b30c51f">handle</a>(), Q.<a class="code" href="classviennacl_1_1matrix__base.html#a24e4f5fa27a1af5ad47e52a97c065d68">size1</a>(), (i-1) * Q.<a class="code" href="classviennacl_1_1matrix__base.html#a82018b4e169973bdfb9d3be68ceb5be0">internal_size1</a>(), 1);</div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  r = u - alpha * q_iminus1;</div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  beta = <a class="code" href="namespaceviennacl_1_1linalg.html#ae46f15d01c01f92a153b3f555a15096b">viennacl::linalg::norm_2</a>(r);</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span> </div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  betas.push_back(beta);</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  r = r / beta;</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span> </div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  <span class="comment">// Update recurrence relation for estimating orthogonality loss</span></div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  w_old = w;</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  w[0] = (betas[1] * w_old[1] + (alphas[0] - alpha) * w_old[0] - betas[i - 1] * w_old[0]) / beta + eps * 0.3 * get_N() * (betas[1] + beta);</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j = 1; j < i - 1; j++)</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  w[j] = (betas[j + 1] * w_old[j + 1] + (alphas[j] - alpha) * w_old[j] + betas[j] * w_old[j - 1] - betas[i - 1] * w_old[j]) / beta + eps * 0.3 * get_N() * (betas[j + 1] + beta);</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  w[i-1] = 0.6 * eps * <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a>(n) * get_N() * betas[1] / beta;</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="comment">//</span></div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  <span class="comment">// Check whether there has been a need for reorthogonalization detected in the previous iteration.</span></div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  <span class="comment">// If so, run the reorthogonalization for each batch</span></div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="keywordflow">if</span> (second_step)</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  {</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j = 0; j < batches; j++)</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  {</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k = l_bound[j] + 1; k < u_bound[j] - 1; k++)</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>  <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> q_k(Q.<a class="code" href="classviennacl_1_1matrix__base.html#a4082cd3586bc99deb68733257b30c51f">handle</a>(), Q.<a class="code" href="classviennacl_1_1matrix__base.html#a24e4f5fa27a1af5ad47e52a97c065d68">size1</a>(), k * Q.<a class="code" href="classviennacl_1_1matrix__base.html#a82018b4e169973bdfb9d3be68ceb5be0">internal_size1</a>(), 1);</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  inner_rt = <a class="code" href="namespaceviennacl_1_1linalg.html#ab35950c4374eb3be08a03d852508c01a">viennacl::linalg::inner_prod</a>(r, q_k);</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  r = r - inner_rt * q_k;</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  w[k] = 1.5 * eps * get_N();</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>  }</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> temp = <a class="code" href="namespaceviennacl_1_1linalg.html#ae46f15d01c01f92a153b3f555a15096b">viennacl::linalg::norm_2</a>(r);</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  r = r / temp;</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  beta = beta * temp;</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  second_step = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  }</div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  batches = 0;</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>  <span class="comment">//</span></div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  <span class="comment">// Check for semiorthogonality</span></div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j = 0; j < i; j++)</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  {</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <span class="keywordflow">if</span> (std::fabs(w[j]) >= squ_eps) <span class="comment">// tentative loss of orthonormality, hence reorthonomalize</span></div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  {</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> q_j(Q.<a class="code" href="classviennacl_1_1matrix__base.html#a4082cd3586bc99deb68733257b30c51f">handle</a>(), Q.<a class="code" href="classviennacl_1_1matrix__base.html#a24e4f5fa27a1af5ad47e52a97c065d68">size1</a>(), j * Q.<a class="code" href="classviennacl_1_1matrix__base.html#a82018b4e169973bdfb9d3be68ceb5be0">internal_size1</a>(), 1);</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  inner_rt = <a class="code" href="namespaceviennacl_1_1linalg.html#ab35950c4374eb3be08a03d852508c01a">viennacl::linalg::inner_prod</a>(r, q_j);</div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  r = r - inner_rt * q_j;</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  w[j] = 1.5 * eps * get_N();</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k = j - 1;</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span> </div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  <span class="comment">// orthogonalization with respect to earlier basis vectors</span></div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  <span class="keywordflow">while</span> (std::fabs(w[k]) > eta)</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>  <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> q_k(Q.<a class="code" href="classviennacl_1_1matrix__base.html#a4082cd3586bc99deb68733257b30c51f">handle</a>(), Q.<a class="code" href="classviennacl_1_1matrix__base.html#a24e4f5fa27a1af5ad47e52a97c065d68">size1</a>(), k * Q.<a class="code" href="classviennacl_1_1matrix__base.html#a82018b4e169973bdfb9d3be68ceb5be0">internal_size1</a>(), 1);</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  inner_rt = <a class="code" href="namespaceviennacl_1_1linalg.html#ab35950c4374eb3be08a03d852508c01a">viennacl::linalg::inner_prod</a>(r, q_k);</div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  r = r - inner_rt * q_k;</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  w[k] = 1.5 * eps * get_N();</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  <span class="keywordflow">if</span> (k == 0) <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  k--;</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>  l_bound[batches] = k;</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>  <span class="comment">// orthogonalization with respect to later basis vectors</span></div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  k = j + 1;</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  <span class="keywordflow">while</span> (k < i && std::fabs(w[k]) > eta)</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  {</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> q_k(Q.<a class="code" href="classviennacl_1_1matrix__base.html#a4082cd3586bc99deb68733257b30c51f">handle</a>(), Q.<a class="code" href="classviennacl_1_1matrix__base.html#a24e4f5fa27a1af5ad47e52a97c065d68">size1</a>(), k * Q.<a class="code" href="classviennacl_1_1matrix__base.html#a82018b4e169973bdfb9d3be68ceb5be0">internal_size1</a>(), 1);</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  inner_rt = <a class="code" href="namespaceviennacl_1_1linalg.html#ab35950c4374eb3be08a03d852508c01a">viennacl::linalg::inner_prod</a>(r, q_k);</div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  r = r - inner_rt * q_k;</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  w[k] = 1.5 * eps * get_N();</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  k++;</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  }</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  u_bound[batches] = k - 1;</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  batches++;</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span> </div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  j = k-1; <span class="comment">// go to end of current batch</span></div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  }</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  }</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span> </div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  <span class="comment">// Normalize basis vector and reorthogonalize as needed</span></div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  <span class="keywordflow">if</span> (batches > 0)</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>  <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> temp = <a class="code" href="namespaceviennacl_1_1linalg.html#ae46f15d01c01f92a153b3f555a15096b">viennacl::linalg::norm_2</a>(r);</div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  r = r / temp;</div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  beta = beta * temp;</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  second_step = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  }</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span> </div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  <span class="comment">// store Krylov vector in Q:</span></div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> q_i(Q.<a class="code" href="classviennacl_1_1matrix__base.html#a4082cd3586bc99deb68733257b30c51f">handle</a>(), Q.<a class="code" href="classviennacl_1_1matrix__base.html#a24e4f5fa27a1af5ad47e52a97c065d68">size1</a>(), i * Q.<a class="code" href="classviennacl_1_1matrix__base.html#a82018b4e169973bdfb9d3be68ceb5be0">internal_size1</a>(), 1);</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  q_i = r;</div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span> </div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <span class="comment">// determine and store alpha = <r, u> with u = A q_i - beta q_{i-1}</span></div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  u = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>(A, r);</div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  u += (-beta) * q_iminus1;</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  alpha = <a class="code" href="namespaceviennacl_1_1linalg.html#ab35950c4374eb3be08a03d852508c01a">viennacl::linalg::inner_prod</a>(u, r);</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  alphas.push_back(alpha);</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  }</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span> </div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  <span class="comment">// Step 2: Compute eigenvalues of tridiagonal matrix obtained during Lanczos iterations:</span></div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  std::vector<NumericT> eigenvalues = <a class="code" href="namespaceviennacl_1_1linalg.html#a54d70c731aed90556e228b7f14ac3a52">bisect</a>(alphas, betas);</div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span> </div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  <span class="comment">// Step 3: Compute eigenvectors via inverse iteration. Does not update eigenvalues, so only approximate by nature.</span></div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  <span class="keywordflow">if</span> (compute_eigenvectors)</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>  std::vector<NumericT> eigenvector_tridiag(alphas.size());</div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  <span class="keywordflow">for</span> (std::size_t i=0; i < tag.<a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#ae744c43467774ee300f5fab0c607aed1">num_eigenvalues</a>(); ++i)</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  {</div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  <span class="comment">// compute eigenvector of tridiagonal matrix via inverse:</span></div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#ab967b62c4a6c67c3e37623eac4cc4fc1">inverse_iteration</a>(alphas, betas, eigenvalues[eigenvalues.size() - i - 1], eigenvector_tridiag);</div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span> </div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  <span class="comment">// eigenvector w of full matrix A. Given as w = Q * u, where u is the eigenvector of the tridiagonal matrix</span></div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<NumericT></a> eigenvector_u(eigenvector_tridiag.size());</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(eigenvector_tridiag, eigenvector_u);</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span> </div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> eigenvector_A(eigenvectors_A.handle(),</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  eigenvectors_A.size1(),</div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  eigenvectors_A.row_major() ? i : i * eigenvectors_A.internal_size1(),</div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  eigenvectors_A.row_major() ? eigenvectors_A.internal_size2() : 1);</div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  eigenvector_A = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>(<a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(Q,</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0, Q.<a class="code" href="classviennacl_1_1matrix__base.html#a24e4f5fa27a1af5ad47e52a97c065d68">size1</a>()),</div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0, eigenvector_u.size())),</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  eigenvector_u);</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  }</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  }</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span> </div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  <span class="keywordflow">return</span> eigenvalues;</div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  }</div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span> </div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span> </div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  <span class="keyword">template</span>< <span class="keyword">typename</span> MatrixT, <span class="keyword">typename</span> DenseMatrixT, <span class="keyword">typename</span> NumericT></div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  std::vector<NumericT></div>
<div class="line"><a name="l00345"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#a26da2e5971bed8094c415bd6ced7ac48"> 345</a></span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a26da2e5971bed8094c415bd6ced7ac48">lanczos</a>(MatrixT <span class="keyword">const</span>& A, <a class="code" href="classviennacl_1_1vector__base.html">vector_base<NumericT></a> & r, DenseMatrixT & eigenvectors_A, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> krylov_dim, <a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html">lanczos_tag</a> <span class="keyword">const</span> & tag, <span class="keywordtype">bool</span> compute_eigenvectors)</div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  {</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  std::vector<NumericT> alphas, betas;</div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<NumericT></a> Aq(r.<a class="code" href="classviennacl_1_1vector__base.html#a15c47ae4326098aeaa4ed6b91fc6df9b">size</a>());</div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  <a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<NumericT, viennacl::column_major></a> Q(r.<a class="code" href="classviennacl_1_1vector__base.html#a15c47ae4326098aeaa4ed6b91fc6df9b">size</a>(), krylov_dim + 1); <span class="comment">// Krylov basis (each Krylov vector is one column)</span></div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span> </div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> norm_r = <a class="code" href="namespaceviennacl_1_1linalg.html#ae46f15d01c01f92a153b3f555a15096b">norm_2</a>(r);</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> beta = norm_r;</div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  r /= norm_r;</div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span> </div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  <span class="comment">// first Krylov vector:</span></div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> q0(Q.handle(), Q.size1(), 0, 1);</div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  q0 = r;</div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span> </div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  <span class="comment">// Step 1: Run Lanczos' method to obtain tridiagonal matrix</span></div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i = 0; i < krylov_dim; i++)</div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  {</div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  betas.push_back(beta);</div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  <span class="comment">// last available vector from Krylov basis:</span></div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> q_i(Q.handle(), Q.size1(), i * Q.internal_size1(), 1);</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>  <span class="comment">// Lanczos algorithm:</span></div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  <span class="comment">// - Compute A * q:</span></div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  Aq = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>(A, q_i);</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">// - Form Aq <- Aq - <Aq, q_i> * q_i - beta * q_{i-1}, where beta is ||q_i|| before normalization in previous iteration</span></div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> alpha = <a class="code" href="namespaceviennacl_1_1linalg.html#ab35950c4374eb3be08a03d852508c01a">viennacl::linalg::inner_prod</a>(Aq, q_i);</div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  Aq -= alpha * q_i;</div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span> </div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  <span class="keywordflow">if</span> (i > 0)</div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  {</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> q_iminus1(Q.handle(), Q.size1(), (i-1) * Q.internal_size1(), 1);</div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  Aq -= beta * q_iminus1;</div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span> </div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  <span class="comment">// Extra measures for improved numerical stability?</span></div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  <span class="keywordflow">if</span> (tag.<a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#aad5c2c34a2b41e2a6a9b52dedd1d2ecf">method</a>() == <a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#a8a743b9f474124a0f779ed35c6f6a684a8ecf6c75a5bd6248e628651a83a9adf1">lanczos_tag::full_reorthogonalization</a>)</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">// Gram-Schmidt (re-)orthogonalization:</span></div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  <span class="comment">// TODO: Reuse fast (pipelined) routines from GMRES or GEMV</span></div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j = 0; j < i; j++)</div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  {</div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> q_j(Q.handle(), Q.size1(), j * Q.internal_size1(), 1);</div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> inner_rq = <a class="code" href="namespaceviennacl_1_1linalg.html#ab35950c4374eb3be08a03d852508c01a">viennacl::linalg::inner_prod</a>(Aq, q_j);</div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  Aq -= inner_rq * q_j;</div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  }</div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  }</div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  }</div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span> </div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  <span class="comment">// normalize Aq and add to Krylov basis at column i+1 in Q:</span></div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  beta = <a class="code" href="namespaceviennacl_1_1linalg.html#ae46f15d01c01f92a153b3f555a15096b">viennacl::linalg::norm_2</a>(Aq);</div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> q_iplus1(Q.handle(), Q.size1(), (i+1) * Q.internal_size1(), 1);</div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  q_iplus1 = Aq / beta;</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>  alphas.push_back(alpha);</div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  }</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">//</span></div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  <span class="comment">// Step 2: Compute eigenvalues of tridiagonal matrix obtained during Lanczos iterations:</span></div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  std::vector<NumericT> eigenvalues = <a class="code" href="namespaceviennacl_1_1linalg.html#a54d70c731aed90556e228b7f14ac3a52">bisect</a>(alphas, betas);</div>
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span> </div>
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  <span class="comment">// Step 3: Compute eigenvectors via inverse iteration. Does not update eigenvalues, so only approximate by nature.</span></div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  <span class="keywordflow">if</span> (compute_eigenvectors)</div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  {</div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  std::vector<NumericT> eigenvector_tridiag(alphas.size());</div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  <span class="keywordflow">for</span> (std::size_t i=0; i < tag.<a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#ae744c43467774ee300f5fab0c607aed1">num_eigenvalues</a>(); ++i)</div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  {</div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  <span class="comment">// compute eigenvector of tridiagonal matrix via inverse:</span></div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#ab967b62c4a6c67c3e37623eac4cc4fc1">inverse_iteration</a>(alphas, betas, eigenvalues[eigenvalues.size() - i - 1], eigenvector_tridiag);</div>
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span> </div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  <span class="comment">// eigenvector w of full matrix A. Given as w = Q * u, where u is the eigenvector of the tridiagonal matrix</span></div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<NumericT></a> eigenvector_u(eigenvector_tridiag.size());</div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(eigenvector_tridiag, eigenvector_u);</div>
<div class="line"><a name="l00422"></a><span class="lineno"> 422</span> </div>
<div class="line"><a name="l00423"></a><span class="lineno"> 423</span>  <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> eigenvector_A(eigenvectors_A.handle(),</div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  eigenvectors_A.size1(),</div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span>  eigenvectors_A.row_major() ? i : i * eigenvectors_A.internal_size1(),</div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span>  eigenvectors_A.row_major() ? eigenvectors_A.internal_size2() : 1);</div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span>  eigenvector_A = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>(<a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(Q,</div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0, Q.size1()),</div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0, eigenvector_u.size())),</div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  eigenvector_u);</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>  }</div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span> </div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  <span class="keywordflow">return</span> eigenvalues;</div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span>  }</div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span> </div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span> } <span class="comment">// end namespace detail</span></div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span> </div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixT, <span class="keyword">typename</span> DenseMatrixT></div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span> std::vector< typename viennacl::result_of::cpu_value_type<typename MatrixT::value_type>::type ></div>
<div class="line"><a name="l00452"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg.html#af5002a88fa4cc3fbe65a904797a0ecba"> 452</a></span> <a class="code" href="namespaceviennacl_1_1linalg.html#af5002a88fa4cc3fbe65a904797a0ecba">eig</a>(MatrixT <span class="keyword">const</span> & <a class="code" href="classviennacl_1_1matrix.html">matrix</a>, DenseMatrixT & eigenvectors_A, <a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html">lanczos_tag</a> <span class="keyword">const</span> & tag, <span class="keywordtype">bool</span> compute_eigenvectors = <span class="keyword">true</span>)</div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span> {</div>
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structviennacl_1_1result__of_1_1value__type.html#a1fccdddb6d57eaba8f19506cea2051a3">viennacl::result_of::value_type<MatrixT>::type</a> NumericType;</div>
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structviennacl_1_1result__of_1_1cpu__value__type.html#aa015d93f419985879a7c13b09633c5c6">viennacl::result_of::cpu_value_type<NumericType>::type</a> CPU_NumericType;</div>
<div class="line"><a name="l00456"></a><span class="lineno"> 456</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> viennacl::result_of::vector_for_matrix<MatrixT>::type VectorT;</div>
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span> </div>
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  <a class="code" href="classviennacl_1_1tools_1_1uniform__random__numbers.html">viennacl::tools::uniform_random_numbers<CPU_NumericType></a> random_gen;</div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span> </div>
<div class="line"><a name="l00460"></a><span class="lineno"> 460</span>  std::vector<CPU_NumericType> eigenvalues;</div>
<div class="line"><a name="l00461"></a><span class="lineno"> 461</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> matrix_size = matrix.size1();</div>
<div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  VectorT r(matrix_size);</div>
<div class="line"><a name="l00463"></a><span class="lineno"> 463</span>  std::vector<CPU_NumericType> s(matrix_size);</div>
<div class="line"><a name="l00464"></a><span class="lineno"> 464</span> </div>
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=0; i<s.size(); ++i)</div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  s[i] = CPU_NumericType(0.5) + random_gen();</div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span> </div>
<div class="line"><a name="l00468"></a><span class="lineno"> 468</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a182fc6f710cc79252cebd332b480fe27">detail::copy_vec_to_vec</a>(s,r);</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>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> size_krylov = (matrix_size < tag.<a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#a4e07073e383c1f5ed160d007f05d6eb3">krylov_size</a>()) ? matrix_size</div>
<div class="line"><a name="l00471"></a><span class="lineno"> 471</span>  : tag.<a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#a4e07073e383c1f5ed160d007f05d6eb3">krylov_size</a>();</div>
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span> </div>
<div class="line"><a name="l00473"></a><span class="lineno"> 473</span>  <span class="keywordflow">switch</span> (tag.<a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#aad5c2c34a2b41e2a6a9b52dedd1d2ecf">method</a>())</div>
<div class="line"><a name="l00474"></a><span class="lineno"> 474</span>  {</div>
<div class="line"><a name="l00475"></a><span class="lineno"> 475</span>  <span class="keywordflow">case</span> <a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#a8a743b9f474124a0f779ed35c6f6a684a937ee8052e51309672b2bcdba4bb015e">lanczos_tag::partial_reorthogonalization</a>:</div>
<div class="line"><a name="l00476"></a><span class="lineno"> 476</span>  eigenvalues = <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a07c896c3efe02f24adf912b1f89e5c07">detail::lanczosPRO</a>(matrix, r, eigenvectors_A, size_krylov, tag, compute_eigenvectors);</div>
<div class="line"><a name="l00477"></a><span class="lineno"> 477</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00478"></a><span class="lineno"> 478</span>  <span class="keywordflow">case</span> <a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#a8a743b9f474124a0f779ed35c6f6a684a8ecf6c75a5bd6248e628651a83a9adf1">lanczos_tag::full_reorthogonalization</a>:</div>
<div class="line"><a name="l00479"></a><span class="lineno"> 479</span>  <span class="keywordflow">case</span> <a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#a8a743b9f474124a0f779ed35c6f6a684a5a98f73ee4246c0d97c82917edeca27e">lanczos_tag::no_reorthogonalization</a>:</div>
<div class="line"><a name="l00480"></a><span class="lineno"> 480</span>  eigenvalues = <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a26da2e5971bed8094c415bd6ced7ac48">detail::lanczos</a>(matrix, r, eigenvectors_A, size_krylov, tag, compute_eigenvectors);</div>
<div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  <span class="keywordflow">break</span>;</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> </div>
<div class="line"><a name="l00484"></a><span class="lineno"> 484</span>  std::vector<CPU_NumericType> largest_eigenvalues;</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>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i = 1; i<=tag.<a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#ae744c43467774ee300f5fab0c607aed1">num_eigenvalues</a>(); i++)</div>
<div class="line"><a name="l00487"></a><span class="lineno"> 487</span>  largest_eigenvalues.push_back(eigenvalues[size_krylov-i]);</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> </div>
<div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  <span class="keywordflow">return</span> largest_eigenvalues;</div>
<div class="line"><a name="l00491"></a><span class="lineno"> 491</span> }</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="l00503"></a><span class="lineno"> 503</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixT></div>
<div class="line"><a name="l00504"></a><span class="lineno"> 504</span> std::vector< typename viennacl::result_of::cpu_value_type<typename MatrixT::value_type>::type ></div>
<div class="line"><a name="l00505"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg.html#a7afda6c5b14466eaec9b3bd9db81d988"> 505</a></span> <a class="code" href="namespaceviennacl_1_1linalg.html#af5002a88fa4cc3fbe65a904797a0ecba">eig</a>(MatrixT <span class="keyword">const</span> & <a class="code" href="classviennacl_1_1matrix.html">matrix</a>, <a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html">lanczos_tag</a> <span class="keyword">const</span> & tag)</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>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structviennacl_1_1result__of_1_1cpu__value__type.html#aa015d93f419985879a7c13b09633c5c6">viennacl::result_of::cpu_value_type<typename MatrixT::value_type>::type</a> NumericType;</div>
<div class="line"><a name="l00508"></a><span class="lineno"> 508</span> </div>
<div class="line"><a name="l00509"></a><span class="lineno"> 509</span>  <a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<NumericType></a> eigenvectors(matrix.size1(), tag.<a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#ae744c43467774ee300f5fab0c607aed1">num_eigenvalues</a>());</div>
<div class="line"><a name="l00510"></a><span class="lineno"> 510</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceviennacl_1_1linalg.html#af5002a88fa4cc3fbe65a904797a0ecba">eig</a>(matrix, eigenvectors, tag, <span class="keyword">false</span>);</div>
<div class="line"><a name="l00511"></a><span class="lineno"> 511</span> }</div>
<div class="line"><a name="l00512"></a><span class="lineno"> 512</span> </div>
<div class="line"><a name="l00513"></a><span class="lineno"> 513</span> } <span class="comment">// end namespace linalg</span></div>
<div class="line"><a name="l00514"></a><span class="lineno"> 514</span> } <span class="comment">// end namespace viennacl</span></div>
<div class="line"><a name="l00515"></a><span class="lineno"> 515</span> <span class="preprocessor">#endif</span></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1lanczos__tag_html_af2126adae7cd63d5c9c380066cdfabf1"><div class="ttname"><a href="classviennacl_1_1linalg_1_1lanczos__tag.html#af2126adae7cd63d5c9c380066cdfabf1">viennacl::linalg::lanczos_tag::method</a></div><div class="ttdeci">int method() const </div><div class="ttdoc">Returns the reorthogonalization method. </div><div class="ttdef"><b>Definition:</b> <a href="lanczos_8hpp_source.html#l00091">lanczos.hpp:91</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_ae46f15d01c01f92a153b3f555a15096b"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#ae46f15d01c01f92a153b3f555a15096b">viennacl::linalg::norm_2</a></div><div class="ttdeci">T norm_2(std::vector< T, A > const &v1)</div><div class="ttdef"><b>Definition:</b> <a href="norm__2_8hpp_source.html#l00096">norm_2.hpp:96</a></div></div>
<div class="ttc" id="matrix__market_8hpp_html"><div class="ttname"><a href="matrix__market_8hpp.html">matrix_market.hpp</a></div><div class="ttdoc">A reader and writer for the matrix market format is implemented here. </div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1lanczos__tag_html_aaad9aa2dc06eb4a5ca272d7fc78fb072"><div class="ttname"><a href="classviennacl_1_1linalg_1_1lanczos__tag.html#aaad9aa2dc06eb4a5ca272d7fc78fb072">viennacl::linalg::lanczos_tag::krylov_size</a></div><div class="ttdeci">vcl_size_t krylov_size() const </div><div class="ttdoc">Returns the size of the kylov space. </div><div class="ttdef"><b>Definition:</b> <a href="lanczos_8hpp_source.html#l00085">lanczos.hpp:85</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_af5002a88fa4cc3fbe65a904797a0ecba"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#af5002a88fa4cc3fbe65a904797a0ecba">viennacl::linalg::eig</a></div><div class="ttdeci">std::vector< typename viennacl::result_of::cpu_value_type< typename MatrixT::value_type >::type > eig(MatrixT const &matrix, DenseMatrixT &eigenvectors_A, lanczos_tag const &tag, bool compute_eigenvectors=true)</div><div class="ttdoc">Implementation of the calculation of eigenvalues using lanczos (with and without reorthogonalization)...</div><div class="ttdef"><b>Definition:</b> <a href="lanczos_8hpp_source.html#l00452">lanczos.hpp:452</a></div></div>
<div class="ttc" id="norm__2_8hpp_html"><div class="ttname"><a href="norm__2_8hpp.html">norm_2.hpp</a></div><div class="ttdoc">Generic interface for the l^2-norm. See viennacl/linalg/vector_operations.hpp for implementations...</div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1lanczos__tag_html_aad5c2c34a2b41e2a6a9b52dedd1d2ecf"><div class="ttname"><a href="classviennacl_1_1linalg_1_1lanczos__tag.html#aad5c2c34a2b41e2a6a9b52dedd1d2ecf">viennacl::linalg::lanczos_tag::method</a></div><div class="ttdeci">void method(int met)</div><div class="ttdoc">Sets the reorthogonalization method. </div><div class="ttdef"><b>Definition:</b> <a href="lanczos_8hpp_source.html#l00088">lanczos.hpp:88</a></div></div>
<div class="ttc" id="prod_8hpp_html"><div class="ttname"><a href="prod_8hpp.html">prod.hpp</a></div><div class="ttdoc">Generic interface for matrix-vector and matrix-matrix products. See viennacl/linalg/vector_operations...</div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_a07c896c3efe02f24adf912b1f89e5c07"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#a07c896c3efe02f24adf912b1f89e5c07">viennacl::linalg::detail::lanczosPRO</a></div><div class="ttdeci">std::vector< NumericT > lanczosPRO(MatrixT const &A, vector_base< NumericT > &r, DenseMatrixT &eigenvectors_A, vcl_size_t size, lanczos_tag const &tag, bool compute_eigenvectors)</div><div class="ttdoc">Implementation of the Lanczos PRO algorithm (partial reorthogonalization) </div><div class="ttdef"><b>Definition:</b> <a href="lanczos_8hpp_source.html#l00158">lanczos.hpp:158</a></div></div>
<div class="ttc" id="classviennacl_1_1tools_1_1normal__random__numbers_html"><div class="ttname"><a href="classviennacl_1_1tools_1_1normal__random__numbers.html">viennacl::tools::normal_random_numbers</a></div><div class="ttdoc">Random number generator for returning normally distributed values. </div><div class="ttdef"><b>Definition:</b> <a href="random_8hpp_source.html#l00057">random.hpp:57</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1lanczos__tag_html_aa71eae96da7f83e2c510ae02a2c7dbce"><div class="ttname"><a href="classviennacl_1_1linalg_1_1lanczos__tag.html#aa71eae96da7f83e2c510ae02a2c7dbce">viennacl::linalg::lanczos_tag::lanczos_tag</a></div><div class="ttdeci">lanczos_tag(double factor=0.75, vcl_size_t numeig=10, int met=0, vcl_size_t krylov=100)</div><div class="ttdoc">The constructor. </div><div class="ttdef"><b>Definition:</b> <a href="lanczos_8hpp_source.html#l00064">lanczos.hpp:64</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_html_ab35950c4374eb3be08a03d852508c01a"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#ab35950c4374eb3be08a03d852508c01a">viennacl::linalg::inner_prod</a></div><div class="ttdeci">viennacl::enable_if< viennacl::is_stl< typename viennacl::traits::tag_of< VectorT1 >::type >::value, typename VectorT1::value_type >::type inner_prod(VectorT1 const &v1, VectorT2 const &v2)</div><div class="ttdef"><b>Definition:</b> <a href="inner__prod_8hpp_source.html#l00100">inner_prod.hpp:100</a></div></div>
<div class="ttc" id="structviennacl_1_1result__of_1_1value__type_html_a1fccdddb6d57eaba8f19506cea2051a3"><div class="ttname"><a href="structviennacl_1_1result__of_1_1value__type.html#a1fccdddb6d57eaba8f19506cea2051a3">viennacl::result_of::value_type::type</a></div><div class="ttdeci">T::value_type type</div><div class="ttdef"><b>Definition:</b> <a href="result__of_8hpp_source.html#l00213">result_of.hpp:213</a></div></div>
<div class="ttc" id="inner__prod_8hpp_html"><div class="ttname"><a href="inner__prod_8hpp.html">inner_prod.hpp</a></div><div class="ttdoc">Generic interface for the computation of inner products. See viennacl/linalg/vector_operations.hpp for implementations. </div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1lanczos__tag_html_a8a743b9f474124a0f779ed35c6f6a684a937ee8052e51309672b2bcdba4bb015e"><div class="ttname"><a href="classviennacl_1_1linalg_1_1lanczos__tag.html#a8a743b9f474124a0f779ed35c6f6a684a937ee8052e51309672b2bcdba4bb015e">viennacl::linalg::lanczos_tag::partial_reorthogonalization</a></div><div class="ttdef"><b>Definition:</b> <a href="lanczos_8hpp_source.html#l00051">lanczos.hpp:51</a></div></div>
<div class="ttc" id="tests_2src_2bisect_8cpp_html_a52b5d30a2d7b064678644a3bf49b7f6c"><div class="ttname"><a href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a></div><div class="ttdeci">float NumericT</div><div class="ttdef"><b>Definition:</b> <a href="tests_2src_2bisect_8cpp_source.html#l00040">bisect.cpp:40</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_a54d70c731aed90556e228b7f14ac3a52"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#a54d70c731aed90556e228b7f14ac3a52">viennacl::linalg::bisect</a></div><div class="ttdeci">std::vector< typename viennacl::result_of::cpu_value_type< typename VectorT::value_type >::type > bisect(VectorT const &alphas, VectorT const &betas)</div><div class="ttdoc">Implementation of the bisect-algorithm for the calculation of the eigenvalues of a tridiagonal matrix...</div><div class="ttdef"><b>Definition:</b> <a href="bisect_8hpp_source.html#l00078">bisect.hpp:78</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1lanczos__tag_html_a8a743b9f474124a0f779ed35c6f6a684a5a98f73ee4246c0d97c82917edeca27e"><div class="ttname"><a href="classviennacl_1_1linalg_1_1lanczos__tag.html#a8a743b9f474124a0f779ed35c6f6a684a5a98f73ee4246c0d97c82917edeca27e">viennacl::linalg::lanczos_tag::no_reorthogonalization</a></div><div class="ttdef"><b>Definition:</b> <a href="lanczos_8hpp_source.html#l00053">lanczos.hpp:53</a></div></div>
<div class="ttc" id="namespaceviennacl_html_ae92c62d9fd59870c1f6b881e391d32aa"><div class="ttname"><a href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">viennacl::range</a></div><div class="ttdeci">basic_range range</div><div class="ttdef"><b>Definition:</b> <a href="forwards_8h_source.html#l00424">forwards.h:424</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1lanczos__tag_html_a8a743b9f474124a0f779ed35c6f6a684a8ecf6c75a5bd6248e628651a83a9adf1"><div class="ttname"><a href="classviennacl_1_1linalg_1_1lanczos__tag.html#a8a743b9f474124a0f779ed35c6f6a684a8ecf6c75a5bd6248e628651a83a9adf1">viennacl::linalg::lanczos_tag::full_reorthogonalization</a></div><div class="ttdef"><b>Definition:</b> <a href="lanczos_8hpp_source.html#l00052">lanczos.hpp:52</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_aa18d10f8a90e38bd9ff43c650fc670ef"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a></div><div class="ttdeci">VectorT prod(std::vector< std::vector< T, A1 >, A2 > const &matrix, VectorT const &vector)</div><div class="ttdef"><b>Definition:</b> <a href="prod_8hpp_source.html#l00102">prod.hpp:102</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1traits_html_aa2344ea20469f55fbc15a8e9526494d0"><div class="ttname"><a href="namespaceviennacl_1_1traits.html#aa2344ea20469f55fbc15a8e9526494d0">viennacl::traits::size</a></div><div class="ttdeci">vcl_size_t size(VectorType const &vec)</div><div class="ttdoc">Generic routine for obtaining the size of a vector (ViennaCL, uBLAS, etc.) </div><div class="ttdef"><b>Definition:</b> <a href="size_8hpp_source.html#l00239">size.hpp:239</a></div></div>
<div class="ttc" id="classviennacl_1_1tools_1_1uniform__random__numbers_html"><div class="ttname"><a href="classviennacl_1_1tools_1_1uniform__random__numbers.html">viennacl::tools::uniform_random_numbers</a></div><div class="ttdoc">Random number generator for returning uniformly distributed values in the closed interval [0...</div><div class="ttdef"><b>Definition:</b> <a href="random_8hpp_source.html#l00044">random.hpp:44</a></div></div>
<div class="ttc" id="compressed__matrix_8hpp_html"><div class="ttname"><a href="compressed__matrix_8hpp.html">compressed_matrix.hpp</a></div><div class="ttdoc">Implementation of the compressed_matrix class. </div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_a182fc6f710cc79252cebd332b480fe27"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#a182fc6f710cc79252cebd332b480fe27">viennacl::linalg::detail::copy_vec_to_vec</a></div><div class="ttdeci">void copy_vec_to_vec(viennacl::vector< NumericT > const &src, OtherVectorT &dest)</div><div class="ttdoc">overloaded function for copying vectors </div><div class="ttdef"><b>Definition:</b> <a href="bisect_8hpp_source.html#l00044">bisect.hpp:44</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< NumericT ></a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_a26da2e5971bed8094c415bd6ced7ac48"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#a26da2e5971bed8094c415bd6ced7ac48">viennacl::linalg::detail::lanczos</a></div><div class="ttdeci">std::vector< NumericT > lanczos(MatrixT const &A, vector_base< NumericT > &r, DenseMatrixT &eigenvectors_A, vcl_size_t krylov_dim, lanczos_tag const &tag, bool compute_eigenvectors)</div><div class="ttdoc">Implementation of the Lanczos FRO algorithm. </div><div class="ttdef"><b>Definition:</b> <a href="lanczos_8hpp_source.html#l00345">lanczos.hpp:345</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1lanczos__tag_html_ae744c43467774ee300f5fab0c607aed1"><div class="ttname"><a href="classviennacl_1_1linalg_1_1lanczos__tag.html#ae744c43467774ee300f5fab0c607aed1">viennacl::linalg::lanczos_tag::num_eigenvalues</a></div><div class="ttdeci">void num_eigenvalues(vcl_size_t numeig)</div><div class="ttdoc">Sets the number of eigenvalues. </div><div class="ttdef"><b>Definition:</b> <a href="lanczos_8hpp_source.html#l00070">lanczos.hpp:70</a></div></div>
<div class="ttc" id="namespaceviennacl_html_adc45a895937fe299100e2b235a442748"><div class="ttname"><a href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">viennacl::project</a></div><div class="ttdeci">matrix_range< MatrixType > project(MatrixType const &A, viennacl::range const &r1, viennacl::range const &r2)</div><div class="ttdef"><b>Definition:</b> <a href="matrix__proxy_8hpp_source.html#l00326">matrix_proxy.hpp:326</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1lanczos__tag_html_abfff89303690a662fab2fbabcca2ee25"><div class="ttname"><a href="classviennacl_1_1linalg_1_1lanczos__tag.html#abfff89303690a662fab2fbabcca2ee25">viennacl::linalg::lanczos_tag::num_eigenvalues</a></div><div class="ttdeci">vcl_size_t num_eigenvalues() const </div><div class="ttdoc">Returns the number of eigenvalues. </div><div class="ttdef"><b>Definition:</b> <a href="lanczos_8hpp_source.html#l00073">lanczos.hpp:73</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_a4082cd3586bc99deb68733257b30c51f"><div class="ttname"><a href="classviennacl_1_1matrix__base.html#a4082cd3586bc99deb68733257b30c51f">viennacl::matrix_base< NumericT >::handle</a></div><div class="ttdeci">handle_type & handle()</div><div class="ttdoc">Returns the OpenCL handle, non-const-version. </div><div class="ttdef"><b>Definition:</b> <a href="matrix__def_8hpp_source.html#l00244">matrix_def.hpp:244</a></div></div>
<div class="ttc" id="classviennacl_1_1vector_html"><div class="ttname"><a href="classviennacl_1_1vector.html">viennacl::vector< NumericT ></a></div></div>
<div class="ttc" id="structviennacl_1_1result__of_1_1cpu__value__type_html_aa015d93f419985879a7c13b09633c5c6"><div class="ttname"><a href="structviennacl_1_1result__of_1_1cpu__value__type.html#aa015d93f419985879a7c13b09633c5c6">viennacl::result_of::cpu_value_type::type</a></div><div class="ttdeci">T::ERROR_CANNOT_DEDUCE_CPU_SCALAR_TYPE_FOR_T type</div><div class="ttdef"><b>Definition:</b> <a href="result__of_8hpp_source.html#l00271">result_of.hpp:271</a></div></div>
<div class="ttc" id="classviennacl_1_1matrix__base_html_a24e4f5fa27a1af5ad47e52a97c065d68"><div class="ttname"><a href="classviennacl_1_1matrix__base.html#a24e4f5fa27a1af5ad47e52a97c065d68">viennacl::matrix_base< NumericT >::size1</a></div><div class="ttdeci">size_type size1() const</div><div class="ttdoc">Returns the number of rows. </div><div class="ttdef"><b>Definition:</b> <a href="matrix__def_8hpp_source.html#l00224">matrix_def.hpp:224</a></div></div>
<div class="ttc" id="namespaceviennacl_html_a0a574e6cd04ca0e42298b4ab845700e4"><div class="ttname"><a href="namespaceviennacl.html#a0a574e6cd04ca0e42298b4ab845700e4">viennacl::row</a></div><div class="ttdeci">vector_expression< const matrix_base< NumericT, F >, const unsigned int, op_row > row(const matrix_base< NumericT, F > &A, unsigned int i)</div><div class="ttdef"><b>Definition:</b> <a href="matrix_8hpp_source.html#l00910">matrix.hpp:910</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="namespaceviennacl_1_1linalg_html_adfd5b21910a692a78c547b22b9157c2e"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#adfd5b21910a692a78c547b22b9157c2e">viennacl::linalg::max</a></div><div class="ttdeci">NumericT max(std::vector< NumericT > const &v1)</div><div class="ttdef"><b>Definition:</b> <a href="maxmin_8hpp_source.html#l00047">maxmin.hpp:47</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="random_8hpp_html"><div class="ttname"><a href="random_8hpp.html">random.hpp</a></div><div class="ttdoc">A small collection of sequential random number generators. </div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1lanczos__tag_html_a4e07073e383c1f5ed160d007f05d6eb3"><div class="ttname"><a href="classviennacl_1_1linalg_1_1lanczos__tag.html#a4e07073e383c1f5ed160d007f05d6eb3">viennacl::linalg::lanczos_tag::krylov_size</a></div><div class="ttdeci">void krylov_size(vcl_size_t max)</div><div class="ttdoc">Sets the size of the kylov space. Must be larger than number of eigenvalues to compute. </div><div class="ttdef"><b>Definition:</b> <a href="lanczos_8hpp_source.html#l00082">lanczos.hpp:82</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="classviennacl_1_1matrix__base_html_a82018b4e169973bdfb9d3be68ceb5be0"><div class="ttname"><a href="classviennacl_1_1matrix__base.html#a82018b4e169973bdfb9d3be68ceb5be0">viennacl::matrix_base< NumericT >::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="bisect_8hpp_html"><div class="ttname"><a href="bisect_8hpp.html">bisect.hpp</a></div><div class="ttdoc">Implementation of the algorithm for finding eigenvalues of a tridiagonal matrix. </div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1lanczos__tag_html_a47e14babee64097056526536b277dbae"><div class="ttname"><a href="classviennacl_1_1linalg_1_1lanczos__tag.html#a47e14babee64097056526536b277dbae">viennacl::linalg::lanczos_tag::factor</a></div><div class="ttdeci">double factor() const </div><div class="ttdoc">Returns the exponent. </div><div class="ttdef"><b>Definition:</b> <a href="lanczos_8hpp_source.html#l00079">lanczos.hpp:79</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_ab967b62c4a6c67c3e37623eac4cc4fc1"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#ab967b62c4a6c67c3e37623eac4cc4fc1">viennacl::linalg::detail::inverse_iteration</a></div><div class="ttdeci">void inverse_iteration(std::vector< NumericT > const &alphas, std::vector< NumericT > const &betas, NumericT &eigenvalue, std::vector< NumericT > &eigenvector)</div><div class="ttdoc">Inverse iteration for finding an eigenvector for an eigenvalue. </div><div class="ttdef"><b>Definition:</b> <a href="lanczos_8hpp_source.html#l00109">lanczos.hpp:109</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1lanczos__tag_html_a3ce84b79a3ff77dd91a656232311cd52"><div class="ttname"><a href="classviennacl_1_1linalg_1_1lanczos__tag.html#a3ce84b79a3ff77dd91a656232311cd52">viennacl::linalg::lanczos_tag::factor</a></div><div class="ttdeci">void factor(double fct)</div><div class="ttdoc">Sets the exponent of epsilon. Values between 0.6 and 0.9 usually give best results. </div><div class="ttdef"><b>Definition:</b> <a href="lanczos_8hpp_source.html#l00076">lanczos.hpp:76</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1lanczos__tag_html"><div class="ttname"><a href="classviennacl_1_1linalg_1_1lanczos__tag.html">viennacl::linalg::lanczos_tag</a></div><div class="ttdoc">A tag for the lanczos algorithm. </div><div class="ttdef"><b>Definition:</b> <a href="lanczos_8hpp_source.html#l00045">lanczos.hpp:45</a></div></div>
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