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<div class="title">fspai.hpp</div> </div>
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<a href="fspai_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_DETAIL_SPAI_FSPAI_HPP</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="preprocessor">#define VIENNACL_LINALG_DETAIL_SPAI_FSPAI_HPP</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> </div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">/* =========================================================================</span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> Copyright (c) 2010-2016, Institute for Microelectronics,</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> Institute for Analysis and Scientific Computing,</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> TU Wien.</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> Portions of this software are copyright by UChicago Argonne, LLC.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"></span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment"> -----------------</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment"> ViennaCL - The Vienna Computing Library</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment"> -----------------</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment"></span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment"> Project Head: Karl Rupp rupp@iue.tuwien.ac.at</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment"></span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment"> (A list of authors and contributors can be found in the manual)</span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment"></span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment"> License: MIT (X11), see file LICENSE in the base directory</span></div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment">============================================================================= */</span></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> </div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#include <utility></span></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor">#include <iostream></span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="preprocessor">#include <fstream></span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="preprocessor">#include <string></span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="preprocessor">#include <algorithm></span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="preprocessor">#include <vector></span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="preprocessor">#include <math.h></span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="preprocessor">#include <map></span></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> </div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment">//boost includes</span></div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="preprocessor">#include "boost/numeric/ublas/vector.hpp"</span></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="preprocessor">#include "boost/numeric/ublas/matrix.hpp"</span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="preprocessor">#include "boost/numeric/ublas/matrix_proxy.hpp"</span></div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="preprocessor">#include "boost/numeric/ublas/vector_proxy.hpp"</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="preprocessor">#include "boost/numeric/ublas/storage.hpp"</span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="preprocessor">#include "boost/numeric/ublas/io.hpp"</span></div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="preprocessor">#include "boost/numeric/ublas/lu.hpp"</span></div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="preprocessor">#include "boost/numeric/ublas/triangular.hpp"</span></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="preprocessor">#include "boost/numeric/ublas/matrix_expression.hpp"</span></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> </div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// ViennaCL includes</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="preprocessor">#include "<a class="code" href="prod_8hpp.html">viennacl/linalg/prod.hpp</a>"</span></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="preprocessor">#include "<a class="code" href="matrix_8hpp.html">viennacl/matrix.hpp</a>"</span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</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="l00045"></a><span class="lineno"> 45</span> <span class="preprocessor">#include "<a class="code" href="sparse__matrix__operations_8hpp.html">viennacl/linalg/sparse_matrix_operations.hpp</a>"</span></div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="preprocessor">#include "<a class="code" href="matrix__operations_8hpp.html">viennacl/linalg/matrix_operations.hpp</a>"</span></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="preprocessor">#include "<a class="code" href="scalar_8hpp.html">viennacl/scalar.hpp</a>"</span></div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="preprocessor">#include "<a class="code" href="cg_8hpp.html">viennacl/linalg/cg.hpp</a>"</span></div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</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="l00050"></a><span class="lineno"> 50</span> <span class="preprocessor">#include "<a class="code" href="ilu_8hpp.html">viennacl/linalg/ilu.hpp</a>"</span></div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment">//#include <omp.h></span></div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> </div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="keyword">namespace </span>viennacl</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> {</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="keyword">namespace </span>linalg</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span> {</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="keyword">namespace </span>detail</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span> {</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="keyword">namespace </span>spai</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span> {</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span> </div>
<div class="line"><a name="l00071"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html"> 71</a></span> <span class="keyword">class </span><a class="code" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html">fspai_tag</a></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span> {</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="keyword">public</span>:</div>
<div class="line"><a name="l00081"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#a71bd4d8f9e2b2530c4ac0aa9f220fb4d"> 81</a></span>  <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#a71bd4d8f9e2b2530c4ac0aa9f220fb4d">fspai_tag</a>(</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="keywordtype">double</span> residual_norm_threshold = 1e-3,</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> iteration_limit = 5,</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="keywordtype">bool</span> is_static = <span class="keyword">false</span>,</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keywordtype">bool</span> is_right = <span class="keyword">false</span>)</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  : residual_norm_threshold_(residual_norm_threshold),</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  iteration_limit_(iteration_limit),</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  is_static_(is_static),</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  is_right_(is_right) {}</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span> </div>
<div class="line"><a name="l00091"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#a343d50ea020c9858992c2b9998de029d"> 91</a></span>  <span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#a343d50ea020c9858992c2b9998de029d">getResidualNormThreshold</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> residual_norm_threshold_; }</div>
<div class="line"><a name="l00092"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#adac97317085425dccccd17b1101b48b5"> 92</a></span>  <span class="keyword">inline</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#adac97317085425dccccd17b1101b48b5">getIterationLimit</a> ()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> iteration_limit_; }</div>
<div class="line"><a name="l00093"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#ac6a4e2817d41685c01dbd3288fa2040b"> 93</a></span>  <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#ac6a4e2817d41685c01dbd3288fa2040b">getIsStatic</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> is_static_; }</div>
<div class="line"><a name="l00094"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#abc6969227f20fe566a6facb9c4c6c92a"> 94</a></span>  <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#abc6969227f20fe566a6facb9c4c6c92a">getIsRight</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> is_right_; }</div>
<div class="line"><a name="l00095"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#a5527a30c629f794f13da007a4aee9270"> 95</a></span>  <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#a5527a30c629f794f13da007a4aee9270">setResidualNormThreshold</a>(<span class="keywordtype">double</span> residual_norm_threshold)</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  {</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="keywordflow">if</span> (residual_norm_threshold > 0)</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  residual_norm_threshold_ = residual_norm_threshold;</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  }</div>
<div class="line"><a name="l00100"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#a3a77ab82209b48986e7259e0caf0d15b"> 100</a></span>  <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#a3a77ab82209b48986e7259e0caf0d15b">setIterationLimit</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> iteration_limit)</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="keywordflow">if</span> (iteration_limit > 0)</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  iteration_limit_ = iteration_limit;</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  }</div>
<div class="line"><a name="l00105"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#a9e946a528617beee32177ec12ba13a75"> 105</a></span>  <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#a9e946a528617beee32177ec12ba13a75">setIsRight</a>(<span class="keywordtype">bool</span> is_right) { is_right_ = is_right; }</div>
<div class="line"><a name="l00106"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#a168c2ef94e9bb8b5e110a4b50102c32e"> 106</a></span>  <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#a168c2ef94e9bb8b5e110a4b50102c32e">setIsStatic</a>(<span class="keywordtype">bool</span> is_static) { is_static_ = is_static; }</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span> </div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span> <span class="keyword">private</span>:</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="keywordtype">double</span> residual_norm_threshold_;</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> iteration_limit_;</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="keywordtype">bool</span> is_static_;</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keywordtype">bool</span> is_right_;</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span> };</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span> </div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span> </div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span> <span class="comment">//</span></div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span> <span class="comment">// Helper: Store A in an STL container of type, exploiting symmetry</span></div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span> <span class="comment">// Reason: ublas interface does not allow to iterate over nonzeros of a particular row without starting an iterator1 from the very beginning of the matrix...</span></div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span> <span class="comment">//</span></div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixT, <span class="keyword">typename</span> NumericT></div>
<div class="line"><a name="l00121"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#af1ff03eb8bd6bd2f78f4738731394f7d"> 121</a></span> <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#af1ff03eb8bd6bd2f78f4738731394f7d">sym_sparse_matrix_to_stl</a>(MatrixT <span class="keyword">const</span> & A, std::vector<std::map<unsigned int, NumericT> > & STL_A)</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>  STL_A.resize(A.size1());</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="keywordflow">for</span> (<span class="keyword">typename</span> MatrixT::const_iterator1 row_it = A.begin1();</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  row_it != A.end1();</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  ++row_it)</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  {</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="keywordflow">for</span> (<span class="keyword">typename</span> MatrixT::const_iterator2 col_it = row_it.begin();</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  col_it != row_it.end();</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  ++col_it)</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="keywordflow">if</span> (col_it.index1() >= col_it.index2())</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  STL_A[col_it.index1()][<span class="keyword">static_cast<</span><span class="keywordtype">unsigned</span> <span class="keywordtype">int</span><span class="keyword">></span>(col_it.index2())] = *col_it;</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="keywordflow">break</span>; <span class="comment">//go to next row</span></div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  }</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  }</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span> }</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">//</span></div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span> <span class="comment">// Generate index sets J_k, k=0,...,N-1</span></div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span> <span class="comment">//</span></div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixT></div>
<div class="line"><a name="l00145"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#ae5f2c2a17a35ffa9682589bc3bd692dc"> 145</a></span> <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#ae5f2c2a17a35ffa9682589bc3bd692dc">generateJ</a>(MatrixT <span class="keyword">const</span> & A, std::vector<std::vector<vcl_size_t> > & J)</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span> {</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  <span class="keywordflow">for</span> (<span class="keyword">typename</span> MatrixT::const_iterator1 row_it = A.begin1();</div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  row_it != A.end1();</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  ++row_it)</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  {</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  <span class="keywordflow">for</span> (<span class="keyword">typename</span> MatrixT::const_iterator2 col_it = row_it.begin();</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  col_it != row_it.end();</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  ++col_it)</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  {</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="keywordflow">if</span> (col_it.index1() > col_it.index2()) <span class="comment">//Matrix is symmetric, thus only work on lower triangular part</span></div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  {</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  J[col_it.index2()].push_back(col_it.index1());</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  J[col_it.index1()].push_back(col_it.index2());</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="keywordflow">else</span></div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <span class="keywordflow">break</span>; <span class="comment">//go to next row</span></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>  }</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span> }</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span> </div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span> </div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span> <span class="comment">//</span></div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span> <span class="comment">// Extracts the blocks A(\tilde{J}_k, \tilde{J}_k) from A</span></div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span> <span class="comment">// Sets up y_k = A(\tilde{J}_k, k) for the inplace-solution after Cholesky-factoriation</span></div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span> <span class="comment">//</span></div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span> <span class="keyword">template</span><<span class="keyword">typename</span> NumericT, <span class="keyword">typename</span> MatrixT, <span class="keyword">typename</span> VectorT></div>
<div class="line"><a name="l00172"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#acd198c046af39cfe38f1aad62c0580ae"> 172</a></span> <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#acd198c046af39cfe38f1aad62c0580ae">fill_blocks</a>(std::vector< std::map<unsigned int, NumericT> > & A,</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  std::vector<MatrixT> & blocks,</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  std::vector<std::vector<vcl_size_t> > <span class="keyword">const</span> & J,</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  std::vector<VectorT> & Y)</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span> {</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k=0; k<A.size(); ++k)</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  {</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  std::vector<vcl_size_t> <span class="keyword">const</span> & Jk = J[k];</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  VectorT & yk = Y[k];</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  MatrixT & block_k = blocks[k];</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>  yk.resize(Jk.size());</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  block_k.resize(Jk.size(), Jk.size());</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  block_k.clear();</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span> </div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=0; i<Jk.size(); ++i)</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> row_index = Jk[i];</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  std::map<unsigned int, NumericT> & A_row = A[row_index];</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>  <span class="comment">//fill y_k:</span></div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  yk[i] = A_row[<span class="keyword">static_cast<</span><span class="keywordtype">unsigned</span> <span class="keywordtype">int</span><span class="keyword">></span>(k)];</div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span> </div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j=0; j<Jk.size(); ++j)</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  {</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> col_index = Jk[j];</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="keywordflow">if</span> (col_index <= row_index && A_row.find(static_cast<unsigned int>(col_index)) != A_row.end()) <span class="comment">//block is symmetric, thus store only lower triangular part</span></div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  block_k(i, j) = A_row[<span class="keyword">static_cast<</span><span class="keywordtype">unsigned</span> <span class="keywordtype">int</span><span class="keyword">></span>(col_index)];</div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  }</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  }</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  }</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span> }</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span> </div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span> </div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span> <span class="comment">//</span></div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span> <span class="comment">// Perform Cholesky factorization of A inplace. Cf. Schwarz: Numerische Mathematik, vol 5, p. 58</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="keyword">template</span><<span class="keyword">typename</span> MatrixT></div>
<div class="line"><a name="l00210"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#ac3aaf276d63d5442f2f95d060912c4ab"> 210</a></span> <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#ac3aaf276d63d5442f2f95d060912c4ab">cholesky_decompose</a>(MatrixT & A)</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span> {</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k=0; k<A.size2(); ++k)</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">if</span> (A(k,k) <= 0)</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>  std::cout << <span class="stringliteral">"k: "</span> << k << std::endl;</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  std::cout << <span class="stringliteral">"A(k,k): "</span> << A(k,k) << std::endl;</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  }</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span> </div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  assert(A(k,k) > 0 && <span class="keywordtype">bool</span>(<span class="stringliteral">"Matrix not positive definite in Cholesky factorization."</span>));</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span> </div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  A(k,k) = std::sqrt(A(k,k));</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>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=k+1; i<A.size1(); ++i)</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  {</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  A(i,k) /= A(k,k);</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j=k+1; j<=i; ++j)</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  A(i,j) -= A(i,k) * A(j,k);</div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  }</div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  }</div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span> }</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span> </div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span> </div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span> <span class="comment">//</span></div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span> <span class="comment">// Compute x in Ax = b, where A is already Cholesky factored (A = L L^T)</span></div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span> <span class="comment">//</span></div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixT, <span class="keyword">typename</span> VectorT></div>
<div class="line"><a name="l00238"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#a097e316b51cf3854abec362e6a6d1d47"> 238</a></span> <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#a097e316b51cf3854abec362e6a6d1d47">cholesky_solve</a>(MatrixT <span class="keyword">const</span> & L, VectorT & b)</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span> {</div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  <span class="comment">// inplace forward solve L x = b</span></div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=0; i<L.size1(); ++i)</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  {</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="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="l00244"></a><span class="lineno"> 244</span>  b[i] -= L(i,j) * b[j];</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  b[i] /= L(i,i);</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> </div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  <span class="comment">// inplace backward solve L^T x = b:</span></div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=L.size1()-1;; --i)</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  {</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k=i+1; k<L.size1(); ++k)</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  b[i] -= L(k,i) * b[k];</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  b[i] /= L(i,i);</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span> </div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  <span class="keywordflow">if</span> (i==0) <span class="comment">//vcl_size_t might be unsigned, therefore manual check for equality with zero here</span></div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  }</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span> }</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span> </div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span> </div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span> </div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span> <span class="comment">//</span></div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span> <span class="comment">// Compute the Cholesky factor L from the sparse vectors y_k</span></div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span> <span class="comment">//</span></div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixT, <span class="keyword">typename</span> VectorT></div>
<div class="line"><a name="l00266"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#aeac5736cf32d6afbea570aa683dbe115"> 266</a></span> <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#aeac5736cf32d6afbea570aa683dbe115">computeL</a>(MatrixT <span class="keyword">const</span> & A,</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  MatrixT & L,</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  MatrixT & L_trans,</div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  std::vector<VectorT> & Y,</div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  std::vector<std::vector<vcl_size_t> > & J)</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>  <span class="keyword">typedef</span> <span class="keyword">typename</span> VectorT::value_type NumericType;</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  <span class="keyword">typedef</span> std::vector<std::map<unsigned int, NumericType> > STLSparseMatrixType;</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span> </div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  STLSparseMatrixType L_temp(A.size1());</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span> </div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k=0; k<A.size1(); ++k)</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  {</div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  std::vector<vcl_size_t> <span class="keyword">const</span> & Jk = J[k];</div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  VectorT <span class="keyword">const</span> & yk = Y[k];</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span> </div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  <span class="comment">//compute L(k,k):</span></div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  NumericType Lkk = A(k,k);</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=0; i<Jk.size(); ++i)</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  Lkk -= A(Jk[i],k) * yk[i];</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span> </div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  Lkk = NumericType(1) / std::sqrt(Lkk);</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  L_temp[k][<span class="keyword">static_cast<</span><span class="keywordtype">unsigned</span> <span class="keywordtype">int</span><span class="keyword">></span>(k)] = Lkk;</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  L_trans(k,k) = Lkk;</div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span> </div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  <span class="comment">//write lower diagonal entries:</span></div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=0; i<Jk.size(); ++i)</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  {</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  L_temp[Jk[i]][<span class="keyword">static_cast<</span><span class="keywordtype">unsigned</span> <span class="keywordtype">int</span><span class="keyword">></span>(k)] = -Lkk * yk[i];</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  L_trans(k, Jk[i]) = -Lkk * yk[i];</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">//for k</span></div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span> </div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span> </div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  <span class="comment">//build L from L_temp</span></div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=0; i<L_temp.size(); ++i)</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  <span class="keywordflow">for</span> (<span class="keyword">typename</span> std::map<unsigned int, NumericType>::const_iterator it = L_temp[i].begin();</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  it != L_temp[i].end();</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  ++it)</div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  L(i, it->first) = it->second;</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span> }</div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span> </div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span> </div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span> <span class="comment">//</span></div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span> <span class="comment">// Top level FSPAI function</span></div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span> <span class="comment">//</span></div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixT></div>
<div class="line"><a name="l00313"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#a23b282bb53b72b43e7f76d9aeb3df64b"> 313</a></span> <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#a23b282bb53b72b43e7f76d9aeb3df64b">computeFSPAI</a>(MatrixT <span class="keyword">const</span> & A,</div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  MatrixT <span class="keyword">const</span> & PatternA,</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  MatrixT & L,</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  MatrixT & L_trans,</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html">fspai_tag</a>)</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span> {</div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixT::value_type <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a>;</div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  <span class="keyword">typedef</span> boost::numeric::ublas::matrix<NumericT> DenseMatrixType;</div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  <span class="keyword">typedef</span> std::vector<std::map<unsigned int, NumericT> > SparseMatrixType;</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span> </div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  <span class="comment">// preprocessing: Store A in a STL container:</span></div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  <span class="comment">//std::cout << "Transferring to STL container:" << std::endl;</span></div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  std::vector<std::vector<NumericT> > y_k(A.size1());</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  SparseMatrixType STL_A(A.size1());</div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#af1ff03eb8bd6bd2f78f4738731394f7d">sym_sparse_matrix_to_stl</a>(A, STL_A);</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="l00332"></a><span class="lineno"> 332</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  <span class="comment">// Step 1: Generate pattern indices</span></div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  <span class="comment">//std::cout << "computeFSPAI(): Generating pattern..." << std::endl;</span></div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  std::vector<std::vector<vcl_size_t> > J(A.size1());</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#ae5f2c2a17a35ffa9682589bc3bd692dc">generateJ</a>(PatternA, J);</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span> </div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  <span class="comment">// Step 2: Set up matrix blocks</span></div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  <span class="comment">//std::cout << "computeFSPAI(): Setting up matrix blocks..." << std::endl;</span></div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  std::vector<DenseMatrixType> subblocks_A(A.size1());</div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#acd198c046af39cfe38f1aad62c0580ae">fill_blocks</a>(STL_A, subblocks_A, J, y_k);</div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  STL_A.clear(); <span class="comment">//not needed anymore</span></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>  <span class="comment">//</span></div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  <span class="comment">// Step 3: Cholesky-factor blocks</span></div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  <span class="comment">//std::cout << "computeFSPAI(): Cholesky-factorization..." << std::endl;</span></div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=0; i<subblocks_A.size(); ++i)</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  {</div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  <span class="comment">//std::cout << "Block before: " << subblocks_A[i] << std::endl;</span></div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#ac3aaf276d63d5442f2f95d060912c4ab">cholesky_decompose</a>(subblocks_A[i]);</div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  <span class="comment">//std::cout << "Block after: " << subblocks_A[i] << std::endl;</span></div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  }</div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span> </div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span> </div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  <span class="comment">/*vcl_size_t num_bytes = 0;</span></div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span> <span class="comment"> for (vcl_size_t i=0; i<subblocks_A.size(); ++i)</span></div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span> <span class="comment"> num_bytes += 8*subblocks_A[i].size1()*subblocks_A[i].size2();*/</span></div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  <span class="comment">//std::cout << "Memory for FSPAI matrix: " << num_bytes / (1024.0 * 1024.0) << " MB" << std::endl;</span></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>  <span class="comment">//</span></div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  <span class="comment">// Step 4: Solve for y_k</span></div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  <span class="comment">//std::cout << "computeFSPAI(): Cholesky-solve..." << std::endl;</span></div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=0; i<y_k.size(); ++i)</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  {</div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  <span class="keywordflow">if</span> (subblocks_A[i].<a class="code" href="namespaceviennacl_1_1traits.html#aa756f5d6820722094cae0d8b9bb6d5e2">size1</a>() > 0) <span class="comment">//block might be empty...</span></div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  {</div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  <span class="comment">//y_k[i].resize(subblocks_A[i].size1());</span></div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  <span class="comment">//std::cout << "y_k[" << i << "]: ";</span></div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  <span class="comment">//for (vcl_size_t j=0; j<y_k[i].size(); ++j)</span></div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  <span class="comment">// std::cout << y_k[i][j] << " ";</span></div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  <span class="comment">//std::cout << std::endl;</span></div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#a097e316b51cf3854abec362e6a6d1d47">cholesky_solve</a>(subblocks_A[i], y_k[i]);</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  }</div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  }</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> </div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  <span class="comment">// Step 5: Set up Cholesky factors L and L_trans</span></div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  <span class="comment">//std::cout << "computeFSPAI(): Computing L..." << std::endl;</span></div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  L.resize(A.size1(), A.size2(), <span class="keyword">false</span>);</div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  L.reserve(A.nnz(), <span class="keyword">false</span>);</div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  L_trans.resize(A.size1(), A.size2(), <span class="keyword">false</span>);</div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  L_trans.reserve(A.nnz(), <span class="keyword">false</span>);</div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#aeac5736cf32d6afbea570aa683dbe115">computeL</a>(A, L, L_trans, y_k, 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>  <span class="comment">//std::cout << "L: " << L << std::endl;</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> </div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span> </div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span> }</div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span> }</div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span> }</div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span> }</div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span> </div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span> <span class="preprocessor">#endif</span></div>
<div class="ttc" id="matrix__operations_8hpp_html"><div class="ttname"><a href="matrix__operations_8hpp.html">matrix_operations.hpp</a></div><div class="ttdoc">Implementations of dense matrix related operations including matrix-vector products. </div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_1_1spai_html_ac3aaf276d63d5442f2f95d060912c4ab"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#ac3aaf276d63d5442f2f95d060912c4ab">viennacl::linalg::detail::spai::cholesky_decompose</a></div><div class="ttdeci">void cholesky_decompose(MatrixT &A)</div><div class="ttdef"><b>Definition:</b> <a href="fspai_8hpp_source.html#l00210">fspai.hpp:210</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_1_1spai_html_af1ff03eb8bd6bd2f78f4738731394f7d"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#af1ff03eb8bd6bd2f78f4738731394f7d">viennacl::linalg::detail::spai::sym_sparse_matrix_to_stl</a></div><div class="ttdeci">void sym_sparse_matrix_to_stl(MatrixT const &A, std::vector< std::map< unsigned int, NumericT > > &STL_A)</div><div class="ttdef"><b>Definition:</b> <a href="fspai_8hpp_source.html#l00121">fspai.hpp:121</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="matrix_8hpp_html"><div class="ttname"><a href="matrix_8hpp.html">matrix.hpp</a></div><div class="ttdoc">Implementation of the dense matrix class. </div></div>
<div class="ttc" id="namespaceviennacl_1_1traits_html_aa756f5d6820722094cae0d8b9bb6d5e2"><div class="ttname"><a href="namespaceviennacl_1_1traits.html#aa756f5d6820722094cae0d8b9bb6d5e2">viennacl::traits::size1</a></div><div class="ttdeci">vcl_size_t size1(MatrixType const &mat)</div><div class="ttdoc">Generic routine for obtaining the number of rows of a matrix (ViennaCL, uBLAS, etc.) </div><div class="ttdef"><b>Definition:</b> <a href="size_8hpp_source.html#l00163">size.hpp:163</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag_html_abc6969227f20fe566a6facb9c4c6c92a"><div class="ttname"><a href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#abc6969227f20fe566a6facb9c4c6c92a">viennacl::linalg::detail::spai::fspai_tag::getIsRight</a></div><div class="ttdeci">bool getIsRight() const </div><div class="ttdef"><b>Definition:</b> <a href="fspai_8hpp_source.html#l00094">fspai.hpp:94</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="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_1_1detail_1_1spai_html_a097e316b51cf3854abec362e6a6d1d47"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#a097e316b51cf3854abec362e6a6d1d47">viennacl::linalg::detail::spai::cholesky_solve</a></div><div class="ttdeci">void cholesky_solve(MatrixT const &L, VectorT &b)</div><div class="ttdef"><b>Definition:</b> <a href="fspai_8hpp_source.html#l00238">fspai.hpp:238</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag_html"><div class="ttname"><a href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html">viennacl::linalg::detail::spai::fspai_tag</a></div><div class="ttdoc">A tag for FSPAI. Experimental. </div><div class="ttdef"><b>Definition:</b> <a href="fspai_8hpp_source.html#l00071">fspai.hpp:71</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag_html_a3a77ab82209b48986e7259e0caf0d15b"><div class="ttname"><a href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#a3a77ab82209b48986e7259e0caf0d15b">viennacl::linalg::detail::spai::fspai_tag::setIterationLimit</a></div><div class="ttdeci">void setIterationLimit(unsigned long iteration_limit)</div><div class="ttdef"><b>Definition:</b> <a href="fspai_8hpp_source.html#l00100">fspai.hpp:100</a></div></div>
<div class="ttc" id="ilu_8hpp_html"><div class="ttname"><a href="ilu_8hpp.html">ilu.hpp</a></div><div class="ttdoc">Implementations of incomplete factorization preconditioners. Convenience header file. </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="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag_html_a343d50ea020c9858992c2b9998de029d"><div class="ttname"><a href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#a343d50ea020c9858992c2b9998de029d">viennacl::linalg::detail::spai::fspai_tag::getResidualNormThreshold</a></div><div class="ttdeci">double getResidualNormThreshold() const </div><div class="ttdef"><b>Definition:</b> <a href="fspai_8hpp_source.html#l00091">fspai.hpp:91</a></div></div>
<div class="ttc" id="sparse__matrix__operations_8hpp_html"><div class="ttname"><a href="sparse__matrix__operations_8hpp.html">sparse_matrix_operations.hpp</a></div><div class="ttdoc">Implementations of operations using sparse matrices. </div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag_html_adac97317085425dccccd17b1101b48b5"><div class="ttname"><a href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#adac97317085425dccccd17b1101b48b5">viennacl::linalg::detail::spai::fspai_tag::getIterationLimit</a></div><div class="ttdeci">unsigned long getIterationLimit() const </div><div class="ttdef"><b>Definition:</b> <a href="fspai_8hpp_source.html#l00092">fspai.hpp:92</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="cg_8hpp_html"><div class="ttname"><a href="cg_8hpp.html">cg.hpp</a></div><div class="ttdoc">The conjugate gradient method is implemented here. </div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_1_1spai_html_aeac5736cf32d6afbea570aa683dbe115"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#aeac5736cf32d6afbea570aa683dbe115">viennacl::linalg::detail::spai::computeL</a></div><div class="ttdeci">void computeL(MatrixT const &A, MatrixT &L, MatrixT &L_trans, std::vector< VectorT > &Y, std::vector< std::vector< vcl_size_t > > &J)</div><div class="ttdef"><b>Definition:</b> <a href="fspai_8hpp_source.html#l00266">fspai.hpp:266</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag_html_a168c2ef94e9bb8b5e110a4b50102c32e"><div class="ttname"><a href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#a168c2ef94e9bb8b5e110a4b50102c32e">viennacl::linalg::detail::spai::fspai_tag::setIsStatic</a></div><div class="ttdeci">void setIsStatic(bool is_static)</div><div class="ttdef"><b>Definition:</b> <a href="fspai_8hpp_source.html#l00106">fspai.hpp:106</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag_html_ac6a4e2817d41685c01dbd3288fa2040b"><div class="ttname"><a href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#ac6a4e2817d41685c01dbd3288fa2040b">viennacl::linalg::detail::spai::fspai_tag::getIsStatic</a></div><div class="ttdeci">bool getIsStatic() const </div><div class="ttdef"><b>Definition:</b> <a href="fspai_8hpp_source.html#l00093">fspai.hpp:93</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_1_1spai_html_ae5f2c2a17a35ffa9682589bc3bd692dc"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#ae5f2c2a17a35ffa9682589bc3bd692dc">viennacl::linalg::detail::spai::generateJ</a></div><div class="ttdeci">void generateJ(MatrixT const &A, std::vector< std::vector< vcl_size_t > > &J)</div><div class="ttdef"><b>Definition:</b> <a href="fspai_8hpp_source.html#l00145">fspai.hpp:145</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_1_1spai_html_a23b282bb53b72b43e7f76d9aeb3df64b"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#a23b282bb53b72b43e7f76d9aeb3df64b">viennacl::linalg::detail::spai::computeFSPAI</a></div><div class="ttdeci">void computeFSPAI(MatrixT const &A, MatrixT const &PatternA, MatrixT &L, MatrixT &L_trans, fspai_tag)</div><div class="ttdef"><b>Definition:</b> <a href="fspai_8hpp_source.html#l00313">fspai.hpp:313</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_1_1spai_html_acd198c046af39cfe38f1aad62c0580ae"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#acd198c046af39cfe38f1aad62c0580ae">viennacl::linalg::detail::spai::fill_blocks</a></div><div class="ttdeci">void fill_blocks(std::vector< std::map< unsigned int, NumericT > > &A, std::vector< MatrixT > &blocks, std::vector< std::vector< vcl_size_t > > const &J, std::vector< VectorT > &Y)</div><div class="ttdef"><b>Definition:</b> <a href="fspai_8hpp_source.html#l00172">fspai.hpp:172</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag_html_a9e946a528617beee32177ec12ba13a75"><div class="ttname"><a href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#a9e946a528617beee32177ec12ba13a75">viennacl::linalg::detail::spai::fspai_tag::setIsRight</a></div><div class="ttdeci">void setIsRight(bool is_right)</div><div class="ttdef"><b>Definition:</b> <a href="fspai_8hpp_source.html#l00105">fspai.hpp:105</a></div></div>
<div class="ttc" id="scalar_8hpp_html"><div class="ttname"><a href="scalar_8hpp.html">scalar.hpp</a></div><div class="ttdoc">Implementation of the ViennaCL scalar class. </div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag_html_a71bd4d8f9e2b2530c4ac0aa9f220fb4d"><div class="ttname"><a href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#a71bd4d8f9e2b2530c4ac0aa9f220fb4d">viennacl::linalg::detail::spai::fspai_tag::fspai_tag</a></div><div class="ttdeci">fspai_tag(double residual_norm_threshold=1e-3, unsigned int iteration_limit=5, bool is_static=false, bool is_right=false)</div><div class="ttdoc">Constructor. </div><div class="ttdef"><b>Definition:</b> <a href="fspai_8hpp_source.html#l00081">fspai.hpp:81</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag_html_a5527a30c629f794f13da007a4aee9270"><div class="ttname"><a href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html#a5527a30c629f794f13da007a4aee9270">viennacl::linalg::detail::spai::fspai_tag::setResidualNormThreshold</a></div><div class="ttdeci">void setResidualNormThreshold(double residual_norm_threshold)</div><div class="ttdef"><b>Definition:</b> <a href="fspai_8hpp_source.html#l00095">fspai.hpp:95</a></div></div>
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