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<div class="title">tql2.cpp</div> </div>
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<a href="tql2_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="l00025"></a><span class="lineno"> 25</span> <span class="comment">// include necessary system headers</span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="preprocessor">#include <iostream></span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="preprocessor">#include <fstream></span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="preprocessor">#include <limits></span></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="preprocessor">#include <string></span></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="preprocessor">#include <iomanip></span></div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> </div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="preprocessor">#define VIENNACL_WITH_UBLAS</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="compressed__matrix_8hpp.html">viennacl/compressed_matrix.hpp</a>"</span></div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="preprocessor">#include "<a class="code" href="matrix__market_8hpp.html">viennacl/io/matrix_market.hpp</a>"</span></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> </div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="preprocessor">#include "<a class="code" href="qr-method_8hpp.html">viennacl/linalg/qr-method.hpp</a>"</span></div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="preprocessor">#include "<a class="code" href="qr-method-common_8hpp.html">viennacl/linalg/qr-method-common.hpp</a>"</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="preprocessor">#include "<a class="code" href="host__based_2matrix__operations_8hpp.html">viennacl/linalg/host_based/matrix_operations.hpp</a>"</span></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> <span class="comment">// Use the shortcut 'ublas::' instead of 'boost::numeric::ublas::'</span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="keyword">namespace </span>ublas = boost::numeric::ublas;</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> </div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// Run in single precision. Change to double precision if provided by your GPU.</span></div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="keyword">typedef</span> <span class="keywordtype">float</span> <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>;</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> </div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="keywordtype">int</span> <a class="code" href="tests_2src_2bisect_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>()</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> {</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  std::size_t sz = 10;</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  std::cout << <span class="stringliteral">"Compute eigenvalues and eigenvectors of matrix of size "</span> << sz << <span class="stringliteral">"-by-"</span> << sz << std::endl << std::endl;</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>  std::vector<ScalarType> d(sz), e(sz);</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="comment">// Initialize diagonal and superdiagonal elements of the tridiagonal matrix</span></div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  d[0] = 1; e[0] = 0;</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  d[1] = 2; e[1] = 4;</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  d[2] =-4; e[2] = 5;</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  d[3] = 6; e[3] = 1;</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  d[4] = 3; e[4] = 2;</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  d[5] = 4; e[5] =-3;</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  d[6] = 7; e[6] = 5;</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  d[7] = 9; e[7] = 1;</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  d[8] = 3; e[8] = 5;</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  d[9] = 8; e[9] = 2;</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span> </div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<ScalarType></a> Q = <a class="code" href="classviennacl_1_1identity__matrix.html">viennacl::identity_matrix<ScalarType></a>(sz);</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span> </div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <a class="code" href="namespaceviennacl_1_1linalg.html#a3fe3eb20d4dcda794259fd6a6d30afb6">viennacl::linalg::tql2</a>(Q, d, e);</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span> </div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  std::cout << <span class="stringliteral">"Eigenvalues: "</span> << std::endl;</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i < d.size(); i++)</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  std::cout << std::setprecision(6) << std::fixed << d[i] << <span class="stringliteral">" "</span>;</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  std::cout << std::endl;</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::cout << std::endl;</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  std::cout << <span class="stringliteral">"Eigenvectors corresponding to the eigenvalues above are the columns: "</span> << std::endl << std::endl;</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  std::cout << Q << std::endl;</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span> </div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  std::cout << std::endl <<<span class="stringliteral">"--------TUTORIAL COMPLETED----------"</span> << std::endl;</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span> </div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="keywordflow">return</span> EXIT_SUCCESS;</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span> }</div>
<div class="ttc" id="host__based_2matrix__operations_8hpp_html"><div class="ttname"><a href="host__based_2matrix__operations_8hpp.html">matrix_operations.hpp</a></div><div class="ttdoc">Implementations of dense matrix related operations, including matrix-vector products, using a plain single-threaded or OpenMP-enabled execution on CPU. </div></div>
<div class="ttc" id="matrix__market_8hpp_html"><div class="ttname"><a href="matrix__market_8hpp.html">matrix_market.hpp</a></div><div class="ttdoc">A reader and writer for the matrix market format is implemented here. </div></div>
<div class="ttc" id="tests_2src_2bisect_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="tests_2src_2bisect_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> <a href="tests_2src_2bisect_8cpp_source.html#l00091">bisect.cpp:91</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_a3fe3eb20d4dcda794259fd6a6d30afb6"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#a3fe3eb20d4dcda794259fd6a6d30afb6">viennacl::linalg::tql2</a></div><div class="ttdeci">void tql2(matrix_base< SCALARTYPE, F > &Q, VectorType &d, VectorType &e)</div><div class="ttdef"><b>Definition:</b> <a href="tql2_8hpp_source.html#l00131">tql2.hpp:131</a></div></div>
<div class="ttc" id="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="qr-method-common_8hpp_html"><div class="ttname"><a href="qr-method-common_8hpp.html">qr-method-common.hpp</a></div><div class="ttdoc">Common routines used for the QR method and SVD. Experimental. </div></div>
<div class="ttc" id="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="qr-method_8hpp_html"><div class="ttname"><a href="qr-method_8hpp.html">qr-method.hpp</a></div><div class="ttdoc">Implementation of the QR method for eigenvalue computations. Experimental. </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="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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