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 <span id="projectnumber">1.7.1</span>
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<div id="projectbrief">Free open-source GPU-accelerated linear algebra and solver library.</div>
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<div class="title">qr.cpp</div> </div>
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<a href="tutorial_2qr_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="l00025"></a><span class="lineno"> 25</span> <span class="comment">// Activate ublas support in ViennaCL</span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="preprocessor">#define VIENNACL_WITH_UBLAS</span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</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> <span class="comment">// Include necessary system headers</span></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment">//</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> <span class="comment">//</span></div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment">// ViennaCL includes</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment">//</span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="preprocessor">#include "<a class="code" href="matrix_8hpp.html">viennacl/matrix.hpp</a>"</span></div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="preprocessor">#include "<a class="code" href="prod_8hpp.html">viennacl/linalg/prod.hpp</a>"</span></div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="preprocessor">#include "<a class="code" href="qr_8hpp.html">viennacl/linalg/qr.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="comment">//</span></div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// Boost includes</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment">//</span></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="preprocessor">#include <boost/numeric/ublas/vector.hpp></span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="preprocessor">#include <boost/numeric/ublas/matrix.hpp></span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="preprocessor">#include <boost/numeric/ublas/io.hpp></span></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> </div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="keywordtype">double</span> <a class="code" href="libviennacl__blas1_8cpp.html#ade615bbf93f6f668af70fb8e6b427d17">check</a>(MatrixType <span class="keyword">const</span> & qr, MatrixType <span class="keyword">const</span> & ref)</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="keywordtype">bool</span> do_break = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="keywordtype">double</span> max_error = 0;</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="keywordflow">for</span> (std::size_t i=0; i<ref.size1(); ++i)</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<ref.size2(); ++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="keywordflow">if</span> (qr(i,j) != 0.0 && ref(i,j) != 0.0)</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  {</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="keywordtype">double</span> rel_err = fabs(qr(i,j) - ref(i,j)) / fabs(ref(i,j) );</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>  <span class="keywordflow">if</span> (rel_err > max_error)</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  max_error = rel_err;</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  }</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> </div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="comment">/* Uncomment the following if you also want to check for NaNs.</span></div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="comment"> if (qr(i,j) != qr(i,j))</span></div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="comment"> {</span></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="comment"> std::cout << "!!!" << std::endl;</span></div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="comment"> std::cout << "!!! NaN detected at i=" << i << " and j=" << j << std::endl;</span></div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="comment"> std::cout << "!!!" << std::endl;</span></div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="comment"> do_break = true;</span></div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span> <span class="comment"> break;</span></div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="comment"> }*/</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>  <span class="keywordflow">if</span> (do_break)</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="keywordflow">break</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="keywordflow">return</span> max_error;</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span> }</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span> </div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <span class="keywordtype">int</span> <a class="code" href="benchmarks_2qr_8cpp.html#ac0f2228420376f4db7e1274f2b41667c">main</a> (<span class="keywordtype">int</span>, <span class="keyword">const</span> <span class="keywordtype">char</span> **)</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="keyword">typedef</span> <span class="keywordtype">double</span> <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>; <span class="comment">//feel free to change this to 'double' if supported by your hardware</span></div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <span class="keyword">typedef</span> boost::numeric::ublas::matrix<ScalarType> MatrixType;</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="keyword">typedef</span> <a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<ScalarType, viennacl::column_major></a> VCLMatrixType;</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::size_t rows = 113; <span class="comment">// number of rows in the matrix</span></div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  std::size_t cols = 54; <span class="comment">// number of columns</span></div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span> </div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  MatrixType ublas_A(rows, cols);</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  MatrixType Q(rows, rows);</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  MatrixType R(rows, cols);</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>  <span class="comment">// Some random data with a bit of extra weight on the diagonal</span></div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keywordflow">for</span> (std::size_t i=0; i<rows; ++i)</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="keywordflow">for</span> (std::size_t j=0; j<cols; ++j)</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>  ublas_A(i,j) = <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(-1.0) + <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>((i+1)*(j+1))</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  + <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>( (rand() % 1000) - 500.0) / <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(1000.0);</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="keywordflow">if</span> (i == j)</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  ublas_A(i,j) += <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(10.0);</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>  R(i,j) = 0.0;</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"> 119</span>  <span class="keywordflow">for</span> (std::size_t j=0; j<rows; ++j)</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  Q(i,j) = <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(0.0);</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> </div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="comment">// keep initial input matrix for comparison</span></div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  MatrixType ublas_A_backup(ublas_A);</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> </div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  VCLMatrixType vcl_A(ublas_A.size1(), ublas_A.size2());</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>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(ublas_A, vcl_A);</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span> </div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  std::cout << <span class="stringliteral">"--- Boost.uBLAS ---"</span> << std::endl;</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  std::vector<ScalarType> ublas_betas = <a class="code" href="namespaceviennacl_1_1linalg.html#a83f573386903bae3a5379ab4cbfc5e2d">viennacl::linalg::inplace_qr</a>(ublas_A); <span class="comment">//computes the QR factorization</span></div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span> </div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <a class="code" href="namespaceviennacl_1_1linalg.html#a76fc8bf8f5a20c576b7ddbad32d3e56d">viennacl::linalg::recoverQ</a>(ublas_A, ublas_betas, Q, R);</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  MatrixType ublas_QR = <a class="code" href="sparse__prod_8cpp.html#a2c8637b3d6a972d1d8fd85fb3089c6da">prod</a>(Q, R);</div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  <span class="keywordtype">double</span> ublas_error = <a class="code" href="libviennacl__blas1_8cpp.html#ade615bbf93f6f668af70fb8e6b427d17">check</a>(ublas_QR, ublas_A_backup);</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  std::cout << <span class="stringliteral">"Maximum relative error (ublas): "</span> << ublas_error << std::endl;</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span> </div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  std::cout << <span class="stringliteral">"--- Hybrid (default) ---"</span> << std::endl;</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(ublas_A_backup, vcl_A);</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  std::vector<ScalarType> <a class="code" href="least-squares_8cpp.html#ac887df28e24b43a0bda14bd218659c78">hybrid_betas</a> = <a class="code" href="namespaceviennacl_1_1linalg.html#a83f573386903bae3a5379ab4cbfc5e2d">viennacl::linalg::inplace_qr</a>(vcl_A);</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span> </div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(vcl_A, ublas_A);</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  Q.clear(); R.clear();</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  <a class="code" href="namespaceviennacl_1_1linalg.html#a76fc8bf8f5a20c576b7ddbad32d3e56d">viennacl::linalg::recoverQ</a>(ublas_A, hybrid_betas, Q, R);</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <span class="keywordtype">double</span> hybrid_error = <a class="code" href="libviennacl__blas1_8cpp.html#ade615bbf93f6f668af70fb8e6b427d17">check</a>(ublas_QR, ublas_A_backup);</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  std::cout << <span class="stringliteral">"Maximum relative error (hybrid): "</span> << hybrid_error << std::endl;</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span> </div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span> </div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  std::cout << <span class="stringliteral">"!!!! TUTORIAL COMPLETED SUCCESSFULLY !!!!"</span> << std::endl;</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span> </div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  <span class="keywordflow">return</span> EXIT_SUCCESS;</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span> }</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span> </div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_a83f573386903bae3a5379ab4cbfc5e2d"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#a83f573386903bae3a5379ab4cbfc5e2d">viennacl::linalg::inplace_qr</a></div><div class="ttdeci">std::vector< T > inplace_qr(viennacl::matrix< T, F, ALIGNMENT > &A, vcl_size_t block_size=16)</div><div class="ttdoc">Overload of inplace-QR factorization of a ViennaCL matrix A. </div><div class="ttdef"><b>Definition:</b> <a href="qr_8hpp_source.html#l00647">qr.hpp:647</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="benchmarks_2qr_8cpp_html_ac0f2228420376f4db7e1274f2b41667c"><div class="ttname"><a href="benchmarks_2qr_8cpp.html#ac0f2228420376f4db7e1274f2b41667c">main</a></div><div class="ttdeci">int main(int argc, const char *argv[])</div><div class="ttdef"><b>Definition:</b> <a href="benchmarks_2qr_8cpp_source.html#l00053">qr.cpp:53</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="least-squares_8cpp_html_ac887df28e24b43a0bda14bd218659c78"><div class="ttname"><a href="least-squares_8cpp.html#ac887df28e24b43a0bda14bd218659c78">hybrid_betas</a></div><div class="ttdeci">std::cout<< "--- ViennaCL (hybrid implementation) ---"<< std::endl;std::vector< ScalarType > hybrid_betas</div><div class="ttdef"><b>Definition:</b> <a href="least-squares_8cpp_source.html#l00134">least-squares.cpp:134</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_a76fc8bf8f5a20c576b7ddbad32d3e56d"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#a76fc8bf8f5a20c576b7ddbad32d3e56d">viennacl::linalg::recoverQ</a></div><div class="ttdeci">void recoverQ(MatrixType const &A, VectorType const &betas, MatrixType &Q, MatrixType &R)</div><div class="ttdef"><b>Definition:</b> <a href="qr_8hpp_source.html#l00564">qr.hpp:564</a></div></div>
<div class="ttc" id="qr_8hpp_html"><div class="ttname"><a href="qr_8hpp.html">qr.hpp</a></div><div class="ttdoc">Provides a QR factorization using a block-based approach. </div></div>
<div class="ttc" id="sparse__prod_8cpp_html_a2c8637b3d6a972d1d8fd85fb3089c6da"><div class="ttname"><a href="sparse__prod_8cpp.html#a2c8637b3d6a972d1d8fd85fb3089c6da">prod</a></div><div class="ttdeci">void prod(std::vector< std::map< IndexT, NumericT > > const &stl_A, std::vector< std::map< IndexT, NumericT > > const &stl_B, std::vector< std::map< IndexT, NumericT > > &stl_C)</div><div class="ttdef"><b>Definition:</b> <a href="sparse__prod_8cpp_source.html#l00114">sparse_prod.cpp:114</a></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="libviennacl__blas1_8cpp_html_ade615bbf93f6f668af70fb8e6b427d17"><div class="ttname"><a href="libviennacl__blas1_8cpp.html#ade615bbf93f6f668af70fb8e6b427d17">check</a></div><div class="ttdeci">void check(T const &t, U const &u, EpsilonT eps)</div><div class="ttdef"><b>Definition:</b> <a href="libviennacl__blas1_8cpp_source.html#l00066">libviennacl_blas1.cpp:66</a></div></div>
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