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<div class="title">small_matrix.hpp</div> </div>
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<a href="small__matrix_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_SMALL_MATRIX_HPP</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="preprocessor">#define VIENNACL_LINALG_DETAIL_SPAI_SMALL_MATRIX_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 <utility></span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="preprocessor">#include <iostream></span></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="preprocessor">#include <fstream></span></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="preprocessor">#include <string></span></div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="preprocessor">#include <algorithm></span></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="preprocessor">#include <vector></span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="preprocessor">#include <math.h></span></div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="preprocessor">#include <map></span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="preprocessor">#include "boost/numeric/ublas/vector.hpp"</span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="preprocessor">#include "boost/numeric/ublas/matrix.hpp"</span></div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="preprocessor">#include "boost/numeric/ublas/matrix_proxy.hpp"</span></div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="preprocessor">#include "boost/numeric/ublas/vector_proxy.hpp"</span></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="preprocessor">#include "boost/numeric/ublas/storage.hpp"</span></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="preprocessor">#include "boost/numeric/ublas/io.hpp"</span></div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="preprocessor">#include "boost/numeric/ublas/lu.hpp"</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="preprocessor">#include "boost/numeric/ublas/triangular.hpp"</span></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="preprocessor">#include "boost/numeric/ublas/matrix_expression.hpp"</span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="preprocessor">#include "boost/numeric/ublas/detail/matrix_assign.hpp"</span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> </div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="preprocessor">#include "<a class="code" href="forwards_8h.html">viennacl/forwards.h</a>"</span></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> </div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="keyword">namespace </span>viennacl</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> {</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="keyword">namespace </span>linalg</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> {</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="keyword">namespace </span>detail</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> {</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="keyword">namespace </span>spai</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span> {</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> </div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="comment">//</span></div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="comment">// Constructs an orthonormal sparse matrix M (with M^T M = Id). Is composed of elementary 2x2 rotation matrices with suitable renumbering.</span></div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="comment">//</span></div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixT></div>
<div class="line"><a name="l00061"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#a75d03e25caf5c1957fab6334c0d91c31"> 61</a></span> <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#a75d03e25caf5c1957fab6334c0d91c31">make_rotation_matrix</a>(MatrixT & mat,</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> new_size,</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> off_diagonal_distance = 4)</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>  mat.resize(new_size, new_size, <span class="keyword">false</span>);</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  mat.clear();</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span> </div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keywordtype">double</span> val = 1.0 / std::sqrt(2.0);</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> </div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=0; i<new_size; ++i)</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  mat(i,i) = val;</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="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=off_diagonal_distance; i<new_size; ++i)</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  {</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  mat(i-off_diagonal_distance, i) = val;</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  mat(i, i-off_diagonal_distance) = -val;</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  }</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> </div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span> }</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span> </div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span> </div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="comment">//calcualtes matrix determinant</span></div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixT></div>
<div class="line"><a name="l00084"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#ad6543d2795df36b19080b431aca258b1"> 84</a></span> <span class="keywordtype">double</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#ad6543d2795df36b19080b431aca258b1">determinant</a>(boost::numeric::ublas::matrix_expression<MatrixT> <span class="keyword">const</span> & mat_r)</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span> {</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keywordtype">double</span> det = 1.0;</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span> </div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  MatrixT mLu(mat_r());</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  boost::numeric::ublas::permutation_matrix<vcl_size_t> pivots(mat_r().<a class="code" href="namespaceviennacl_1_1traits.html#aa756f5d6820722094cae0d8b9bb6d5e2">size1</a>());</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span> </div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="keywordtype">int</span> is_singular = <span class="keyword">static_cast<</span><span class="keywordtype">int</span><span class="keyword">></span>(<a class="code" href="namespaceviennacl_1_1linalg.html#a1050039fb153ae8ad818390a30f96bc4">lu_factorize</a>(mLu, pivots));</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>  <span class="keywordflow">if</span> (!is_singular)</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  {</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=0; i < pivots.size(); ++i)</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> (pivots(i) != i)</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  det *= -1.0;</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>  det *= mLu(i,i);</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>  }</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  det = 0.0;</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span> </div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keywordflow">return</span> det;</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> </div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span> }</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span> }</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> }</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span> <span class="preprocessor">#endif</span></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="forwards_8h_html"><div class="ttname"><a href="forwards_8h.html">forwards.h</a></div><div class="ttdoc">This file provides the forward declarations for the main types used within ViennaCL. </div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_1_1spai_html_a75d03e25caf5c1957fab6334c0d91c31"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#a75d03e25caf5c1957fab6334c0d91c31">viennacl::linalg::detail::spai::make_rotation_matrix</a></div><div class="ttdeci">void make_rotation_matrix(MatrixT &mat, vcl_size_t new_size, vcl_size_t off_diagonal_distance=4)</div><div class="ttdef"><b>Definition:</b> <a href="small__matrix_8hpp_source.html#l00061">small_matrix.hpp:61</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="namespaceviennacl_1_1linalg_1_1detail_1_1spai_html_ad6543d2795df36b19080b431aca258b1"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#ad6543d2795df36b19080b431aca258b1">viennacl::linalg::detail::spai::determinant</a></div><div class="ttdeci">double determinant(boost::numeric::ublas::matrix_expression< MatrixT > const &mat_r)</div><div class="ttdef"><b>Definition:</b> <a href="small__matrix_8hpp_source.html#l00084">small_matrix.hpp:84</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_a1050039fb153ae8ad818390a30f96bc4"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#a1050039fb153ae8ad818390a30f96bc4">viennacl::linalg::lu_factorize</a></div><div class="ttdeci">void lu_factorize(matrix< NumericT, viennacl::row_major > &A)</div><div class="ttdoc">LU factorization of a row-major dense matrix. </div><div class="ttdef"><b>Definition:</b> <a href="lu_8hpp_source.html#l00042">lu.hpp:42</a></div></div>
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