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<div class="title">blas2.cpp</div> </div>
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<a href="examples_2tutorial_2blas2_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">// 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> </div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment">// uBLAS headers</span></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="preprocessor">#include <boost/numeric/ublas/io.hpp></span></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="preprocessor">#include <boost/numeric/ublas/triangular.hpp></span></div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="preprocessor">#include <boost/numeric/ublas/matrix_sparse.hpp></span></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="preprocessor">#include <boost/numeric/ublas/matrix.hpp></span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="preprocessor">#include <boost/numeric/ublas/matrix_proxy.hpp></span></div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="preprocessor">#include <boost/numeric/ublas/vector_proxy.hpp></span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="preprocessor">#include <boost/numeric/ublas/lu.hpp></span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="preprocessor">#include <boost/numeric/ublas/io.hpp></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> </div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment">// Must be set if you want to use ViennaCL algorithms on ublas objects</span></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="preprocessor">#define VIENNACL_WITH_UBLAS 1</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"> 42</span> <span class="comment">// ViennaCL headers</span></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="preprocessor">#include "<a class="code" href="scalar_8hpp.html">viennacl/scalar.hpp</a>"</span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="preprocessor">#include "<a class="code" href="vector_8hpp.html">viennacl/vector.hpp</a>"</span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="preprocessor">#include "<a class="code" href="matrix_8hpp.html">viennacl/matrix.hpp</a>"</span></div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="preprocessor">#include "<a class="code" href="direct__solve_8hpp.html">viennacl/linalg/direct_solve.hpp</a>"</span></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="preprocessor">#include "<a class="code" href="prod_8hpp.html">viennacl/linalg/prod.hpp</a>"</span> <span class="comment">//generic matrix-vector product</span></div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="preprocessor">#include "<a class="code" href="norm__2_8hpp.html">viennacl/linalg/norm_2.hpp</a>"</span> <span class="comment">//generic l2-norm for vectors</span></div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="preprocessor">#include "<a class="code" href="lu_8hpp.html">viennacl/linalg/lu.hpp</a>"</span> <span class="comment">//LU substitution routines</span></div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="preprocessor">#include "<a class="code" href="random_8hpp.html">viennacl/tools/random.hpp</a>"</span></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">// Make `boost::numeric::ublas` available under the shortcut `ublas`:</span></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="keyword">using namespace </span>boost::numeric;</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> <span class="keywordtype">int</span> <a class="code" href="tests_2src_2bisect_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>()</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="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="l00061"></a><span class="lineno"> 61</span> </div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <a class="code" href="classviennacl_1_1tools_1_1uniform__random__numbers.html">viennacl::tools::uniform_random_numbers<ScalarType></a> randomNumber;</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span> </div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  ublas::vector<ScalarType> rhs(12);</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i < rhs.size(); ++i)</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  rhs(i) = randomNumber();</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  ublas::vector<ScalarType> rhs2 = rhs;</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  ublas::vector<ScalarType> result = ublas::zero_vector<ScalarType>(10);</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  ublas::vector<ScalarType> result2 = result;</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  ublas::vector<ScalarType> rhs_trans = rhs;</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  rhs_trans.resize(result.size(), <span class="keyword">true</span>);</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  ublas::vector<ScalarType> result_trans = ublas::zero_vector<ScalarType>(rhs.size());</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>  ublas::matrix<ScalarType> matrix(result.size(),rhs.size());</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span> </div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i < matrix.size1(); ++i)</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j = 0; j < matrix.size2(); ++j)</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  matrix(i,j) = randomNumber();</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span> </div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  std::vector< ScalarType > stl_result(result.size());</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  std::vector< ScalarType > stl_rhs(rhs.size());</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  std::vector< std::vector<ScalarType> > stl_matrix(result.size());</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i < result.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>  stl_matrix[i].resize(rhs.size());</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j = 0; j < matrix.size2(); ++j)</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>  stl_rhs[j] = rhs[j];</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  stl_matrix[i][j] = matrix(i,j);</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  }</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="l00106"></a><span class="lineno"> 106</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> vcl_rhs(rhs.size());</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> vcl_result(result.size());</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<ScalarType></a> vcl_matrix(result.size(), rhs.size());</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<ScalarType></a> vcl_matrix2(result.size(), rhs.size());</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>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(rhs.begin(), rhs.end(), vcl_rhs.begin());</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(matrix, vcl_matrix); <span class="comment">//copy from ublas dense matrix type to ViennaCL type</span></div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span> </div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  vcl_matrix2 = vcl_matrix;</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  vcl_matrix2 += vcl_matrix;</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  vcl_matrix2 -= vcl_matrix;</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  vcl_matrix2 = vcl_matrix2 + vcl_matrix;</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  vcl_matrix2 = vcl_matrix2 - vcl_matrix;</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>  <a class="code" href="classviennacl_1_1scalar.html">viennacl::scalar<ScalarType></a> vcl_3(3.0);</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  vcl_matrix2 *= <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(2.0);</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  vcl_matrix2 /= <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(2.0);</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  vcl_matrix2 *= vcl_3;</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  vcl_matrix2 /= vcl_3;</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span> </div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  vcl_matrix.clear();</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span> </div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(stl_matrix, vcl_matrix); <span class="comment">//alternative: copy from STL vector< vector<> > type to ViennaCL type</span></div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span> </div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  <span class="comment">//for demonstration purposes (no effect):</span></div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(vcl_matrix, matrix); <span class="comment">//copy back from ViennaCL to ublas type.</span></div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(vcl_matrix, stl_matrix); <span class="comment">//copy back from ViennaCL to STL type.</span></div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span> </div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  std::cout << <span class="stringliteral">"----- Matrix-Vector product -----"</span> << std::endl;</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  result = <a class="code" href="sparse__prod_8cpp.html#a2c8637b3d6a972d1d8fd85fb3089c6da">ublas::prod</a>(matrix, rhs); <span class="comment">//the ublas way</span></div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  stl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>(stl_matrix, stl_rhs); <span class="comment">//using STL</span></div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  vcl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>(vcl_matrix, vcl_rhs); <span class="comment">//the ViennaCL way</span></div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span> </div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  std::cout << <span class="stringliteral">"----- Transposed Matrix-Vector product -----"</span> << std::endl;</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  result_trans = <a class="code" href="sparse__prod_8cpp.html#a2c8637b3d6a972d1d8fd85fb3089c6da">prod</a>(<a class="code" href="blas3__solve_8cpp.html#ad8f94754a20a0c6dc74fd3cb5eb675b3">trans</a>(matrix), rhs_trans);</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span> </div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> vcl_rhs_trans(rhs_trans.size());</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> vcl_result_trans(result_trans.size());</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(rhs_trans.begin(), rhs_trans.end(), vcl_rhs_trans.begin());</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  vcl_result_trans = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>(<a class="code" href="blas3__solve_8cpp.html#ad8f94754a20a0c6dc74fd3cb5eb675b3">trans</a>(vcl_matrix), vcl_rhs_trans);</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span> </div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span> </div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span> </div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  ublas::matrix<ScalarType> tri_matrix(10,10);</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <span class="keywordflow">for</span> (std::size_t i=0; i<tri_matrix.size1(); ++i)</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  {</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  <span class="keywordflow">for</span> (std::size_t j=0; j<i; ++j)</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  tri_matrix(i,j) = 0.0;</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span> </div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  <span class="keywordflow">for</span> (std::size_t j=i; j<tri_matrix.size2(); ++j)</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  tri_matrix(i,j) = matrix(i,j);</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  }</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span> </div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<ScalarType></a> vcl_tri_matrix = <a class="code" href="classviennacl_1_1identity__matrix.html">viennacl::identity_matrix<ScalarType></a>(tri_matrix.size1());</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(tri_matrix, vcl_tri_matrix);</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span> </div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  <span class="comment">// Bring vectors to correct size:</span></div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  rhs.resize(tri_matrix.size1(), <span class="keyword">true</span>);</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  rhs2.resize(tri_matrix.size1(), <span class="keyword">true</span>);</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  vcl_rhs.resize(tri_matrix.size1(), <span class="keyword">true</span>);</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span> </div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(rhs.begin(), rhs.end(), vcl_rhs.begin());</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  vcl_result.resize(10);</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span> </div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span> </div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  std::cout << <span class="stringliteral">"----- Upper Triangular solve -----"</span> << std::endl;</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">ublas::solve</a>(tri_matrix, rhs, ublas::upper_tag()); <span class="comment">//ublas</span></div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  vcl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(vcl_tri_matrix, vcl_rhs, <a class="code" href="structviennacl_1_1linalg_1_1upper__tag.html">viennacl::linalg::upper_tag</a>()); <span class="comment">//ViennaCL</span></div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span> </div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1cuda.html#acb0b34e3ac22c72081eceaabeab80f22">ublas::inplace_solve</a>(tri_matrix, rhs, ublas::upper_tag()); <span class="comment">//ublas</span></div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  <a class="code" href="namespaceviennacl_1_1linalg.html#adf06f61be9418e5817eed66004f9dd2b">viennacl::linalg::inplace_solve</a>(vcl_tri_matrix, vcl_rhs, <a class="code" href="structviennacl_1_1linalg_1_1upper__tag.html">viennacl::linalg::upper_tag</a>()); <span class="comment">//ViennaCL</span></div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span> </div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span> </div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  std::cout << <span class="stringliteral">"----- LU factorization -----"</span> << std::endl;</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  std::size_t lu_dim = 300;</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  ublas::matrix<ScalarType> square_matrix(lu_dim, lu_dim);</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  ublas::vector<ScalarType> lu_rhs(lu_dim);</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<ScalarType></a> vcl_square_matrix(lu_dim, lu_dim);</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> vcl_lu_rhs(lu_dim);</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span> </div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="keywordflow">for</span> (std::size_t i=0; i<lu_dim; ++i)</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="keywordflow">for</span> (std::size_t j=0; j<lu_dim; ++j)</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  square_matrix(i,j) = randomNumber();</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span> </div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  <span class="comment">//put some more weight on diagonal elements:</span></div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  <span class="keywordflow">for</span> (std::size_t j=0; j<lu_dim; ++j)</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  {</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  square_matrix(j,j) += <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(10.0);</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  lu_rhs(j) = randomNumber();</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  }</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span> </div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(square_matrix, vcl_square_matrix);</div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(lu_rhs, vcl_lu_rhs);</div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  <a class="code" href="namespaceviennacl_1_1linalg.html#a1050039fb153ae8ad818390a30f96bc4">viennacl::linalg::lu_factorize</a>(vcl_square_matrix);</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  <a class="code" href="namespaceviennacl_1_1linalg.html#a118a9164bc965f8ec728eda73a5e2450">viennacl::linalg::lu_substitute</a>(vcl_square_matrix, vcl_lu_rhs);</div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(square_matrix, vcl_square_matrix);</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(lu_rhs, vcl_lu_rhs);</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span> </div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span> </div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  <a class="code" href="namespaceviennacl_1_1linalg.html#a1050039fb153ae8ad818390a30f96bc4">ublas::lu_factorize</a>(square_matrix);</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1cuda.html#acb0b34e3ac22c72081eceaabeab80f22">ublas::inplace_solve</a> (square_matrix, lu_rhs, ublas::unit_lower_tag ());</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1cuda.html#acb0b34e3ac22c72081eceaabeab80f22">ublas::inplace_solve</a> (square_matrix, lu_rhs, ublas::upper_tag ());</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span> </div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span> </div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  <a class="code" href="namespaceviennacl_1_1linalg.html#a1050039fb153ae8ad818390a30f96bc4">viennacl::linalg::lu_factorize</a>(vcl_square_matrix);</div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <a class="code" href="namespaceviennacl_1_1linalg.html#a118a9164bc965f8ec728eda73a5e2450">viennacl::linalg::lu_substitute</a>(vcl_square_matrix, vcl_lu_rhs);</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span> </div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  std::cout << <span class="stringliteral">"!!!! TUTORIAL COMPLETED SUCCESSFULLY !!!!"</span> << std::endl;</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span> </div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  <span class="keywordflow">return</span> EXIT_SUCCESS;</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span> }</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span> </div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1cuda_html_acb0b34e3ac22c72081eceaabeab80f22"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1cuda.html#acb0b34e3ac22c72081eceaabeab80f22">viennacl::linalg::cuda::inplace_solve</a></div><div class="ttdeci">void inplace_solve(matrix_base< NumericT > const &A, matrix_base< NumericT > &B, SolverTagT tag)</div><div class="ttdoc">Direct inplace solver for triangular systems with multiple right hand sides, i.e. A \ B (MATLAB notat...</div><div class="ttdef"><b>Definition:</b> <a href="cuda_2direct__solve_8hpp_source.html#l00253">direct_solve.hpp:253</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_adf06f61be9418e5817eed66004f9dd2b"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#adf06f61be9418e5817eed66004f9dd2b">viennacl::linalg::inplace_solve</a></div><div class="ttdeci">void inplace_solve(const matrix_base< NumericT > &A, matrix_base< NumericT > &B, SolverTagT)</div><div class="ttdoc">Direct inplace solver for triangular systems with multiple right hand sides, i.e. A \ B (MATLAB notat...</div><div class="ttdef"><b>Definition:</b> <a href="direct__solve_8hpp_source.html#l00217">direct_solve.hpp:217</a></div></div>
<div class="ttc" id="classviennacl_1_1scalar_html"><div class="ttname"><a href="classviennacl_1_1scalar.html">viennacl::scalar</a></div><div class="ttdoc">This class represents a single scalar value on the GPU and behaves mostly like a built-in scalar type...</div><div class="ttdef"><b>Definition:</b> <a href="forwards_8h_source.html#l00227">forwards.h:227</a></div></div>
<div class="ttc" id="norm__2_8hpp_html"><div class="ttname"><a href="norm__2_8hpp.html">norm_2.hpp</a></div><div class="ttdoc">Generic interface for the l^2-norm. See viennacl/linalg/vector_operations.hpp for implementations...</div></div>
<div class="ttc" id="blas3__solve_8cpp_html_ad8f94754a20a0c6dc74fd3cb5eb675b3"><div class="ttname"><a href="blas3__solve_8cpp.html#ad8f94754a20a0c6dc74fd3cb5eb675b3">trans</a></div><div class="ttdeci">std::vector< std::vector< NumericT > > trans(std::vector< std::vector< NumericT > > const &A)</div><div class="ttdef"><b>Definition:</b> <a href="blas3__solve_8cpp_source.html#l00195">blas3_solve.cpp:195</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="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_a118a9164bc965f8ec728eda73a5e2450"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#a118a9164bc965f8ec728eda73a5e2450">viennacl::linalg::lu_substitute</a></div><div class="ttdeci">void lu_substitute(matrix< NumericT, F1, AlignmentV1 > const &A, matrix< NumericT, F2, AlignmentV2 > &B)</div><div class="ttdoc">LU substitution for the system LU = rhs. </div><div class="ttdef"><b>Definition:</b> <a href="lu_8hpp_source.html#l00201">lu.hpp:201</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="namespaceviennacl_1_1linalg_html_a6e9b329b64ac782e6a5687ad2fc47a2a"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a></div><div class="ttdeci">VectorT solve(MatrixT const &matrix, VectorT const &rhs, bicgstab_tag const &tag, PreconditionerT const &precond)</div><div class="ttdef"><b>Definition:</b> <a href="bicgstab_8hpp_source.html#l00496">bicgstab.hpp:496</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="classviennacl_1_1tools_1_1uniform__random__numbers_html"><div class="ttname"><a href="classviennacl_1_1tools_1_1uniform__random__numbers.html">viennacl::tools::uniform_random_numbers</a></div><div class="ttdoc">Random number generator for returning uniformly distributed values in the closed interval [0...</div><div class="ttdef"><b>Definition:</b> <a href="random_8hpp_source.html#l00044">random.hpp:44</a></div></div>
<div class="ttc" id="structviennacl_1_1linalg_1_1upper__tag_html"><div class="ttname"><a href="structviennacl_1_1linalg_1_1upper__tag.html">viennacl::linalg::upper_tag</a></div><div class="ttdoc">A tag class representing an upper triangular matrix. </div><div class="ttdef"><b>Definition:</b> <a href="forwards_8h_source.html#l00854">forwards.h:854</a></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="lu_8hpp_html"><div class="ttname"><a href="lu_8hpp.html">lu.hpp</a></div><div class="ttdoc">Implementations of LU factorization for row-major and column-major dense matrices. </div></div>
<div class="ttc" id="direct__solve_8hpp_html"><div class="ttname"><a href="direct__solve_8hpp.html">direct_solve.hpp</a></div><div class="ttdoc">Implementations of dense direct solvers are found here. </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="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="random_8hpp_html"><div class="ttname"><a href="random_8hpp.html">random.hpp</a></div><div class="ttdoc">A small collection of sequential random number generators. </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>
<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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