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<div class="title">lanczos.cpp</div> </div>
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<a href="lanczos_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="l00028"></a><span class="lineno"> 28</span> <span class="comment">// include necessary system headers</span></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="preprocessor">#include <iostream></span></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> </div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment">//include basic scalar and vector types of ViennaCL</span></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="preprocessor">#include "<a class="code" href="scalar_8hpp.html">viennacl/scalar.hpp</a>"</span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="preprocessor">#include "<a class="code" href="vector_8hpp.html">viennacl/vector.hpp</a>"</span></div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="preprocessor">#include "<a class="code" href="matrix_8hpp.html">viennacl/matrix.hpp</a>"</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="preprocessor">#include "<a class="code" href="matrix__proxy_8hpp.html">viennacl/matrix_proxy.hpp</a>"</span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</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="l00037"></a><span class="lineno"> 37</span> </div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="preprocessor">#include "<a class="code" href="lanczos_8hpp.html">viennacl/linalg/lanczos.hpp</a>"</span></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</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="l00040"></a><span class="lineno"> 40</span> </div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// Some helper functions for this tutorial:</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="preprocessor">#include <iostream></span></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="preprocessor">#include <string></span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="preprocessor">#include <iomanip></span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> </div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="keywordtype">int</span> <a class="code" href="tests_2src_2bisect_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>()</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="comment">// If you GPU does not support double precision, use `float` instead of `double`:</span></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="keyword">typedef</span> <span class="keywordtype">double</span> <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>;</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> </div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  std::vector< std::map<unsigned int, ScalarType> > host_A;</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="keywordflow">if</span> (!<a class="code" href="namespaceviennacl_1_1io.html#ad934125ed3dbe661e264bcd7d62b1048">viennacl::io::read_matrix_market_file</a>(host_A, <span class="stringliteral">"../examples/testdata/mat65k.mtx"</span>))</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>  std::cout << <span class="stringliteral">"Error reading Matrix file"</span> << std::endl;</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="keywordflow">return</span> EXIT_FAILURE;</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</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>  <a class="code" href="classviennacl_1_1compressed__matrix.html">viennacl::compressed_matrix<ScalarType></a> A;</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(host_A, A);</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span> </div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html">viennacl::linalg::lanczos_tag</a> ltag(0.75, <span class="comment">// Select a power of 0.75 as the tolerance for the machine precision.</span></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  10, <span class="comment">// Compute (approximations to) the 10 largest eigenvalues</span></div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <a class="code" href="classviennacl_1_1linalg_1_1lanczos__tag.html#a8a743b9f474124a0f779ed35c6f6a684a937ee8052e51309672b2bcdba4bb015e">viennacl::linalg::lanczos_tag::partial_reorthogonalization</a>, <span class="comment">// use partial reorthogonalization</span></div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  30); <span class="comment">// Maximum size of the Krylov space</span></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>  std::cout << <span class="stringliteral">"Running Lanczos algorithm (eigenvalues only). This might take a while..."</span> << std::endl;</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  std::vector<ScalarType> lanczos_eigenvalues = <a class="code" href="namespaceviennacl_1_1linalg.html#af5002a88fa4cc3fbe65a904797a0ecba">viennacl::linalg::eig</a>(A, ltag);</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>  std::cout << <span class="stringliteral">"Running Lanczos algorithm (with eigenvectors). This might take a while..."</span> << std::endl;</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<ScalarType></a> approx_eigenvectors_A(A.<a class="code" href="classviennacl_1_1compressed__matrix.html#a463cf1739f9cdd387aa185cb574db183">size1</a>(), ltag.num_eigenvalues());</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  lanczos_eigenvalues = <a class="code" href="namespaceviennacl_1_1linalg.html#af5002a88fa4cc3fbe65a904797a0ecba">viennacl::linalg::eig</a>(A, approx_eigenvectors_A, ltag);</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span> </div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="keywordflow">for</span> (std::size_t i = 0; i< lanczos_eigenvalues.size(); i++)</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>  std::cout << <span class="stringliteral">"Approx. eigenvalue "</span> << std::setprecision(7) << lanczos_eigenvalues[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="comment">// test approximated eigenvector by computing A*v:</span></div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> approx_eigenvector = <a class="code" href="namespaceviennacl.html#a7fca08f4a83edffe7f47666d298ca87d">viennacl::column</a>(approx_eigenvectors_A, static_cast<unsigned int>(i));</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> Aq = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>(A, approx_eigenvector);</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  std::cout << <span class="stringliteral">" ("</span> << <a class="code" href="namespaceviennacl_1_1linalg.html#ab35950c4374eb3be08a03d852508c01a">viennacl::linalg::inner_prod</a>(Aq, approx_eigenvector) << <span class="stringliteral">" for <Av,v> with approx. eigenvector v)"</span> << std::endl;</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">return</span> EXIT_SUCCESS;</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span> }</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span> </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="namespaceviennacl_1_1linalg_html_af5002a88fa4cc3fbe65a904797a0ecba"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#af5002a88fa4cc3fbe65a904797a0ecba">viennacl::linalg::eig</a></div><div class="ttdeci">std::vector< typename viennacl::result_of::cpu_value_type< typename MatrixT::value_type >::type > eig(MatrixT const &matrix, DenseMatrixT &eigenvectors_A, lanczos_tag const &tag, bool compute_eigenvectors=true)</div><div class="ttdoc">Implementation of the calculation of eigenvalues using lanczos (with and without reorthogonalization)...</div><div class="ttdef"><b>Definition:</b> <a href="lanczos_8hpp_source.html#l00452">lanczos.hpp:452</a></div></div>
<div class="ttc" id="classviennacl_1_1compressed__matrix_html_a463cf1739f9cdd387aa185cb574db183"><div class="ttname"><a href="classviennacl_1_1compressed__matrix.html#a463cf1739f9cdd387aa185cb574db183">viennacl::compressed_matrix::size1</a></div><div class="ttdeci">const vcl_size_t & size1() const </div><div class="ttdoc">Returns the number of rows. </div><div class="ttdef"><b>Definition:</b> <a href="compressed__matrix_8hpp_source.html#l00927">compressed_matrix.hpp:927</a></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="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="classviennacl_1_1matrix_html"><div class="ttname"><a href="classviennacl_1_1matrix.html">viennacl::matrix</a></div><div class="ttdoc">A dense matrix class. </div><div class="ttdef"><b>Definition:</b> <a href="forwards_8h_source.html#l00375">forwards.h:375</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_ab35950c4374eb3be08a03d852508c01a"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#ab35950c4374eb3be08a03d852508c01a">viennacl::linalg::inner_prod</a></div><div class="ttdeci">viennacl::enable_if< viennacl::is_stl< typename viennacl::traits::tag_of< VectorT1 >::type >::value, typename VectorT1::value_type >::type inner_prod(VectorT1 const &v1, VectorT2 const &v2)</div><div class="ttdef"><b>Definition:</b> <a href="inner__prod_8hpp_source.html#l00100">inner_prod.hpp:100</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1lanczos__tag_html_a8a743b9f474124a0f779ed35c6f6a684a937ee8052e51309672b2bcdba4bb015e"><div class="ttname"><a href="classviennacl_1_1linalg_1_1lanczos__tag.html#a8a743b9f474124a0f779ed35c6f6a684a937ee8052e51309672b2bcdba4bb015e">viennacl::linalg::lanczos_tag::partial_reorthogonalization</a></div><div class="ttdef"><b>Definition:</b> <a href="lanczos_8hpp_source.html#l00051">lanczos.hpp:51</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_aa18d10f8a90e38bd9ff43c650fc670ef"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a></div><div class="ttdeci">VectorT prod(std::vector< std::vector< T, A1 >, A2 > const &matrix, VectorT const &vector)</div><div class="ttdef"><b>Definition:</b> <a href="prod_8hpp_source.html#l00102">prod.hpp:102</a></div></div>
<div class="ttc" id="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_1vector_html"><div class="ttname"><a href="classviennacl_1_1vector.html">viennacl::vector< ScalarType ></a></div></div>
<div class="ttc" id="matrix__proxy_8hpp_html"><div class="ttname"><a href="matrix__proxy_8hpp.html">matrix_proxy.hpp</a></div><div class="ttdoc">Proxy classes for matrices. </div></div>
<div class="ttc" id="vector_8hpp_html"><div class="ttname"><a href="vector_8hpp.html">vector.hpp</a></div><div class="ttdoc">The vector type with operator-overloads and proxy classes is defined here. Linear algebra operations ...</div></div>
<div class="ttc" id="namespaceviennacl_html_a10b7f8cf6b8864a7aa196d670481a453"><div class="ttname"><a href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a></div><div class="ttdeci">void copy(std::vector< NumericT > &cpu_vec, circulant_matrix< NumericT, AlignmentV > &gpu_mat)</div><div class="ttdoc">Copies a circulant matrix from the std::vector to the OpenCL device (either GPU or multi-core CPU) ...</div><div class="ttdef"><b>Definition:</b> <a href="circulant__matrix_8hpp_source.html#l00150">circulant_matrix.hpp:150</a></div></div>
<div class="ttc" id="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="classviennacl_1_1compressed__matrix_html"><div class="ttname"><a href="classviennacl_1_1compressed__matrix.html">viennacl::compressed_matrix</a></div><div class="ttdoc">A sparse square matrix in compressed sparse rows format. </div><div class="ttdef"><b>Definition:</b> <a href="compressed__matrix_8hpp_source.html#l00559">compressed_matrix.hpp:559</a></div></div>
<div class="ttc" id="namespaceviennacl_html_a7fca08f4a83edffe7f47666d298ca87d"><div class="ttname"><a href="namespaceviennacl.html#a7fca08f4a83edffe7f47666d298ca87d">viennacl::column</a></div><div class="ttdeci">vector_expression< const matrix_base< NumericT, F >, const unsigned int, op_column > column(const matrix_base< NumericT, F > &A, unsigned int j)</div><div class="ttdef"><b>Definition:</b> <a href="matrix_8hpp_source.html#l00918">matrix.hpp:918</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1io_html_ad934125ed3dbe661e264bcd7d62b1048"><div class="ttname"><a href="namespaceviennacl_1_1io.html#ad934125ed3dbe661e264bcd7d62b1048">viennacl::io::read_matrix_market_file</a></div><div class="ttdeci">long read_matrix_market_file(MatrixT &mat, const char *file, long index_base=1)</div><div class="ttdoc">Reads a sparse matrix from a file (MatrixMarket format) </div><div class="ttdef"><b>Definition:</b> <a href="matrix__market_8hpp_source.html#l00339">matrix_market.hpp:339</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_1lanczos__tag_html"><div class="ttname"><a href="classviennacl_1_1linalg_1_1lanczos__tag.html">viennacl::linalg::lanczos_tag</a></div><div class="ttdoc">A tag for the lanczos algorithm. </div><div class="ttdef"><b>Definition:</b> <a href="lanczos_8hpp_source.html#l00045">lanczos.hpp:45</a></div></div>
<div class="ttc" id="lanczos_8hpp_html"><div class="ttname"><a href="lanczos_8hpp.html">lanczos.hpp</a></div><div class="ttdoc">Generic interface for the Lanczos algorithm. </div></div>
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