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<div class="title">tql.cpp</div> </div>
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<a href="tql_8cpp.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="comment">/* =========================================================================</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment"> Copyright (c) 2010-2016, Institute for Microelectronics,</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment"> Institute for Analysis and Scientific Computing,</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment"> TU Wien.</span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> Portions of this software are copyright by UChicago Argonne, LLC.</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"></span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> -----------------</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> ViennaCL - The Vienna Computing Library</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"> Project Head: Karl Rupp rupp@iue.tuwien.ac.at</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"> (A list of authors and contributors can be found in the PDF manual)</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment"></span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment"> License: MIT (X11), see file LICENSE in the base directory</span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment">============================================================================= */</span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> </div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> </div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> </div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment">/*</span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment">*</span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment">* Test file for tql-algorithm</span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment">*</span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment">*/</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">// include necessary system headers</span></div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="preprocessor">#include <iostream></span></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> </div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> </div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment">//include basic scalar and vector types of ViennaCL</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="preprocessor">#include "<a class="code" href="scalar_8hpp.html">viennacl/scalar.hpp</a>"</span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="preprocessor">#include "<a class="code" href="vector_8hpp.html">viennacl/vector.hpp</a>"</span></div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="preprocessor">#include "<a class="code" href="tql2_8hpp.html">viennacl/linalg/tql2.hpp</a>"</span></div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> </div>
<div class="line"><a name="l00039"></a><span class="lineno"><a class="line" href="tql_8cpp.html#a6ebf6899d6c1c8b7b9d09be872c05aae"> 39</a></span> <span class="preprocessor">#define EPS 10.0e-5</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> </div>
<div class="line"><a name="l00042"></a><span class="lineno"><a class="line" href="tql_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5"> 42</a></span> <span class="keyword">typedef</span> <span class="keywordtype">float</span> <a class="code" href="tql_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>;</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> </div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> </div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="comment">// Test the eigenvectors</span></div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="comment">// Perform the multiplication (T - lambda * I) * Q, with the original tridiagonal matrx T, the</span></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// eigenvalues lambda and the eigenvectors in Q. Result has to be 0.</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">template</span> <<span class="keyword">typename</span> MatrixLayout></div>
<div class="line"><a name="l00050"></a><span class="lineno"><a class="line" href="tql_8cpp.html#addc3b5bf488c68ee7b156e7554638126"> 50</a></span> <span class="keywordtype">bool</span> <a class="code" href="tql_8cpp.html#addc3b5bf488c68ee7b156e7554638126">test_eigen_val_vec</a>(<a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<ScalarType, MatrixLayout></a> & Q,</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  std::vector<ScalarType> & eigenvalues,</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  std::vector<ScalarType> & d,</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  std::vector<ScalarType> & e)</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>  std::size_t Q_size = Q.<a class="code" href="classviennacl_1_1matrix__base.html#a4348766b3b9cb049f7acd6a795272dbe">size2</a>();</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> value = 0;</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> </div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="keywordflow">for</span>(std::size_t j = 0; j < Q_size; j++)</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  {</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="comment">// calculate first row</span></div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  value = (d[0]- eigenvalues[j]) * Q(0, j) + e[1] * Q(1, j);</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="keywordflow">if</span> (value > <a class="code" href="tql_8cpp.html#a6ebf6899d6c1c8b7b9d09be872c05aae">EPS</a>)</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</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>  <span class="comment">// calcuate inner rows</span></div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="keywordflow">for</span>(std::size_t i = 1; i < Q_size - 1; i++)</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>  value = e[i] * Q(i - 1, j) + (d[i]- eigenvalues[j]) * Q(i, j) + e[i + 1] * Q(i + 1, j);</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="keywordflow">if</span> (value > <a class="code" href="tql_8cpp.html#a6ebf6899d6c1c8b7b9d09be872c05aae">EPS</a>)</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  }</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="comment">// calculate last row</span></div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  value = e[Q_size - 1] * Q(Q_size - 2, j) + (d[Q_size - 1] - eigenvalues[j]) * Q(Q_size - 1, j);</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="keywordflow">if</span> (value > <a class="code" href="tql_8cpp.html#a6ebf6899d6c1c8b7b9d09be872c05aae">EPS</a>)</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  }</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <span class="keywordflow">return</span> <span class="keyword">true</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="l00086"></a><span class="lineno"> 86</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixLayout></div>
<div class="line"><a name="l00087"></a><span class="lineno"><a class="line" href="tql_8cpp.html#a8204a5a8d4b9cbed559875cb65848656"> 87</a></span> <span class="keywordtype">void</span> <a class="code" href="tql_8cpp.html#a8204a5a8d4b9cbed559875cb65848656">test_qr_method_sym</a>()</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span> {</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  std::size_t sz = 220;</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>  <a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<ScalarType, MatrixLayout></a> Q = <a class="code" href="classviennacl_1_1identity__matrix.html">viennacl::identity_matrix<ScalarType></a>(sz);</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  std::vector<ScalarType> d(sz), e(sz), d_ref(sz), e_ref(sz);</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>  std::cout << <span class="stringliteral">"Testing matrix of size "</span> << sz << <span class="stringliteral">"-by-"</span> << sz << std::endl << std::endl;</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span> </div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="comment">// Initialize diagonal and superdiagonal elements</span></div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="keywordflow">for</span>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i < sz; ++i)</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  {</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  d[i] = ((float)(i % 9)) - 4.5f;</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  e[i] = ((float)(i % 5)) - 4.5f;</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>  e[0] = 0.0f;</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  d_ref = d;</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  e_ref = e;</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="comment">//---Run the tql2 algorithm-----------------------------------</span></div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <a class="code" href="namespaceviennacl_1_1linalg.html#a3fe3eb20d4dcda794259fd6a6d30afb6">viennacl::linalg::tql2</a>(Q, d, e);</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span> </div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span> </div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="comment">// ---Test the computed eigenvalues and eigenvectors</span></div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="keywordflow">if</span>(!test_eigen_val_vec<MatrixLayout>(Q, d, d_ref, e_ref))</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  exit(EXIT_FAILURE);</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span> <span class="comment">/*</span></div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span> <span class="comment"> for( unsigned int i = 0; i < sz; ++i)</span></div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span> <span class="comment"> std::cout << "Eigenvalue " << i << "= " << d[i] << std::endl;</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> }</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span> </div>
<div class="line"><a name="l00119"></a><span class="lineno"><a class="line" href="tql_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 119</a></span> <span class="keywordtype">int</span> <a class="code" href="tql_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>()</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> </div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  std::cout << std::endl << <span class="stringliteral">"COMPUTATION OF EIGENVALUES AND EIGENVECTORS"</span> << std::endl;</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  std::cout << std::endl << <span class="stringliteral">"Testing QL algorithm for symmetric tridiagonal row-major matrices..."</span> << std::endl;</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  test_qr_method_sym<viennacl::row_major>();</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span> </div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  std::cout << std::endl << <span class="stringliteral">"Testing QL algorithm for symmetric tridiagonal column-major matrices..."</span> << std::endl;</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  test_qr_method_sym<viennacl::column_major>();</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span> </div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  std::cout << std::endl <<<span class="stringliteral">"--------TEST SUCCESSFULLY COMPLETED----------"</span> << std::endl;</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span> }</div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_a3fe3eb20d4dcda794259fd6a6d30afb6"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#a3fe3eb20d4dcda794259fd6a6d30afb6">viennacl::linalg::tql2</a></div><div class="ttdeci">void tql2(matrix_base< SCALARTYPE, F > &Q, VectorType &d, VectorType &e)</div><div class="ttdef"><b>Definition:</b> <a href="tql2_8hpp_source.html#l00131">tql2.hpp:131</a></div></div>
<div class="ttc" id="tql2_8hpp_html"><div class="ttname"><a href="tql2_8hpp.html">tql2.hpp</a></div><div class="ttdoc">Implementation of the tql2-algorithm for eigenvalue computations. </div></div>
<div class="ttc" id="classviennacl_1_1matrix_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="classviennacl_1_1identity__matrix_html"><div class="ttname"><a href="classviennacl_1_1identity__matrix.html">viennacl::identity_matrix</a></div><div class="ttdoc">Represents a vector consisting of 1 at a given index and zeros otherwise. To be used as an initialize...</div><div class="ttdef"><b>Definition:</b> <a href="matrix__def_8hpp_source.html#l00069">matrix_def.hpp:69</a></div></div>
<div class="ttc" id="tql_8cpp_html_a8204a5a8d4b9cbed559875cb65848656"><div class="ttname"><a href="tql_8cpp.html#a8204a5a8d4b9cbed559875cb65848656">test_qr_method_sym</a></div><div class="ttdeci">void test_qr_method_sym()</div><div class="ttdef"><b>Definition:</b> <a href="tql_8cpp_source.html#l00087">tql.cpp:87</a></div></div>
<div class="ttc" id="tql_8cpp_html_addc3b5bf488c68ee7b156e7554638126"><div class="ttname"><a href="tql_8cpp.html#addc3b5bf488c68ee7b156e7554638126">test_eigen_val_vec</a></div><div class="ttdeci">bool test_eigen_val_vec(viennacl::matrix< ScalarType, MatrixLayout > &Q, std::vector< ScalarType > &eigenvalues, std::vector< ScalarType > &d, std::vector< ScalarType > &e)</div><div class="ttdef"><b>Definition:</b> <a href="tql_8cpp_source.html#l00050">tql.cpp:50</a></div></div>
<div class="ttc" id="tql_8cpp_html_ad5c19ca4f47d3f8ec21232a5af2624e5"><div class="ttname"><a href="tql_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a></div><div class="ttdeci">float ScalarType</div><div class="ttdef"><b>Definition:</b> <a href="tql_8cpp_source.html#l00042">tql.cpp:42</a></div></div>
<div class="ttc" id="classviennacl_1_1matrix__base_html_a4348766b3b9cb049f7acd6a795272dbe"><div class="ttname"><a href="classviennacl_1_1matrix__base.html#a4348766b3b9cb049f7acd6a795272dbe">viennacl::matrix_base< NumericT >::size2</a></div><div class="ttdeci">size_type size2() const</div><div class="ttdoc">Returns the number of columns. </div><div class="ttdef"><b>Definition:</b> <a href="matrix__def_8hpp_source.html#l00226">matrix_def.hpp:226</a></div></div>
<div class="ttc" id="tql_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="tql_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> <a href="tql_8cpp_source.html#l00119">tql.cpp:119</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="fft__1d_8cpp_html_ad5c19ca4f47d3f8ec21232a5af2624e5"><div class="ttname"><a href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a></div><div class="ttdeci">float ScalarType</div><div class="ttdef"><b>Definition:</b> <a href="fft__1d_8cpp_source.html#l00042">fft_1d.cpp:42</a></div></div>
<div class="ttc" id="tql_8cpp_html_a6ebf6899d6c1c8b7b9d09be872c05aae"><div class="ttname"><a href="tql_8cpp.html#a6ebf6899d6c1c8b7b9d09be872c05aae">EPS</a></div><div class="ttdeci">#define EPS</div><div class="ttdef"><b>Definition:</b> <a href="tql_8cpp_source.html#l00039">tql.cpp:39</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>
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