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<div class="header">
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<div class="title">spai.hpp</div>  </div>
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<div class="contents">
<a href="opencl_2kernels_2spai_8hpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="preprocessor">#ifndef VIENNACL_LINALG_OPENCL_KERNELS_SPAI_HPP</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="preprocessor">#define VIENNACL_LINALG_OPENCL_KERNELS_SPAI_HPP</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;</div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">/* =========================================================================</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">   Copyright (c) 2010-2016, Institute for Microelectronics,</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">                            Institute for Analysis and Scientific Computing,</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">                            TU Wien.</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">   Portions of this software are copyright by UChicago Argonne, LLC.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment">                            -----------------</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="comment">                  ViennaCL - The Vienna Computing Library</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="comment">                            -----------------</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="comment">   Project Head:    Karl Rupp                   rupp@iue.tuwien.ac.at</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="comment">   (A list of authors and contributors can be found in the manual)</span></div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="comment">   License:         MIT (X11), see file LICENSE in the base directory</span></div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="comment">============================================================================= */</span></div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;</div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="tools_8hpp.html">viennacl/tools/tools.hpp</a>&quot;</span></div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="kernel_8hpp.html">viennacl/ocl/kernel.hpp</a>&quot;</span></div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="platform_8hpp.html">viennacl/ocl/platform.hpp</a>&quot;</span></div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="ocl_2utils_8hpp.html">viennacl/ocl/utils.hpp</a>&quot;</span></div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="keyword">namespace </span>viennacl</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;{</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;<span class="keyword">namespace </span>linalg</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;{</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;<span class="keyword">namespace </span>opencl</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;{</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;<span class="keyword">namespace </span>kernels</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;{</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> StringT&gt;</div>
<div class="line"><a name="l00040"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a6fc75b18244da56426784cbf789c030c">   40</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a6fc75b18244da56426784cbf789c030c">generate_spai_assemble_blocks</a>(StringT &amp; source, std::string <span class="keyword">const</span> &amp; numeric_string)</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;{</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;  source.append(<span class="stringliteral">&quot;float get_element(__global const unsigned int * row_indices, \n&quot;</span>);</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;  source.append(<span class="stringliteral">&quot;           __global const unsigned int * column_indices, \n&quot;</span>);</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;  source.append(<span class="stringliteral">&quot;           __global const &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * elements, \n&quot;</span>);</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;  source.append(<span class="stringliteral">&quot;           unsigned int row, \n&quot;</span>);</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;  source.append(<span class="stringliteral">&quot;           unsigned int col) \n&quot;</span>);</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;  source.append(<span class="stringliteral">&quot;{ \n&quot;</span>);</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;  source.append(<span class="stringliteral">&quot;  unsigned int row_end = row_indices[row+1]; \n&quot;</span>);</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;  source.append(<span class="stringliteral">&quot;  for (unsigned int i = row_indices[row]; i &lt; row_end; ++i){ \n&quot;</span>);</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;  source.append(<span class="stringliteral">&quot;    if (column_indices[i] == col) \n&quot;</span>);</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;  source.append(<span class="stringliteral">&quot;      return elements[i]; \n&quot;</span>);</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;  source.append(<span class="stringliteral">&quot;    if (column_indices[i] &gt; col) \n&quot;</span>);</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;  source.append(<span class="stringliteral">&quot;      return 0; \n&quot;</span>);</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;  source.append(<span class="stringliteral">&quot;  } \n&quot;</span>);</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;  source.append(<span class="stringliteral">&quot;  return 0; \n&quot;</span>);</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;  source.append(<span class="stringliteral">&quot;void block_assembly(__global const unsigned int * row_indices, \n&quot;</span>);</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;  source.append(<span class="stringliteral">&quot;          __global const unsigned int * column_indices, \n&quot;</span>);</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;  source.append(<span class="stringliteral">&quot;          __global const &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * elements, \n&quot;</span>);</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;  source.append(<span class="stringliteral">&quot;          __global const unsigned int * matrix_dimensions, \n&quot;</span>);</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;  source.append(<span class="stringliteral">&quot;          __global const unsigned int * set_I, \n&quot;</span>);</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;  source.append(<span class="stringliteral">&quot;          __global const unsigned int * set_J, \n&quot;</span>);</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;  source.append(<span class="stringliteral">&quot;          unsigned int matrix_ind, \n&quot;</span>);</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;  source.append(<span class="stringliteral">&quot;          __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * com_A_I_J) \n&quot;</span>);</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;  source.append(<span class="stringliteral">&quot;{ \n&quot;</span>);</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;  source.append(<span class="stringliteral">&quot;  unsigned int row_n = matrix_dimensions[2*matrix_ind]; \n&quot;</span>);</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;  source.append(<span class="stringliteral">&quot;  unsigned int col_n = matrix_dimensions[2*matrix_ind + 1]; \n&quot;</span>);</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;  source.append(<span class="stringliteral">&quot;  for (unsigned int i = 0; i &lt; col_n; ++i){ \n&quot;</span>);</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;          <span class="comment">//start row index</span></div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;  source.append(<span class="stringliteral">&quot;        for (unsigned int j = 0; j &lt; row_n; j++){ \n&quot;</span>);</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;  source.append(<span class="stringliteral">&quot;          com_A_I_J[ i*row_n + j] = get_element(row_indices, column_indices, elements, set_I[j], set_J[i]); \n&quot;</span>);</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;  source.append(<span class="stringliteral">&quot;        } \n&quot;</span>);</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;  source.append(<span class="stringliteral">&quot;      } \n&quot;</span>);</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;  source.append(<span class="stringliteral">&quot;__kernel void assemble_blocks( \n&quot;</span>);</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;  source.append(<span class="stringliteral">&quot;          __global const unsigned int * row_indices, \n&quot;</span>);</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;  source.append(<span class="stringliteral">&quot;          __global const unsigned int * column_indices, \n&quot;</span>);</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;  source.append(<span class="stringliteral">&quot;          __global const &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * elements, \n&quot;</span>);</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;  source.append(<span class="stringliteral">&quot;          __global const unsigned int * set_I, \n&quot;</span>);</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;  source.append(<span class="stringliteral">&quot;        __global const unsigned int * set_J, \n&quot;</span>);</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;  source.append(<span class="stringliteral">&quot;      __global const unsigned int * i_ind, \n&quot;</span>);</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;  source.append(<span class="stringliteral">&quot;      __global const unsigned int * j_ind, \n&quot;</span>);</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;  source.append(<span class="stringliteral">&quot;        __global const unsigned int * block_ind, \n&quot;</span>);</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;  source.append(<span class="stringliteral">&quot;        __global const unsigned int * matrix_dimensions, \n&quot;</span>);</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;  source.append(<span class="stringliteral">&quot;      __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * com_A_I_J, \n&quot;</span>);</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;  source.append(<span class="stringliteral">&quot;      __global unsigned int * g_is_update, \n&quot;</span>);</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;  source.append(<span class="stringliteral">&quot;                   unsigned int  block_elems_num) \n&quot;</span>);</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;  source.append(<span class="stringliteral">&quot;{ \n&quot;</span>);</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;  source.append(<span class="stringliteral">&quot;    for (unsigned int i  = get_global_id(0); i &lt; block_elems_num; i += get_global_size(0)){ \n&quot;</span>);</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;  source.append(<span class="stringliteral">&quot;        if ((matrix_dimensions[2*i] &gt; 0) &amp;&amp; (matrix_dimensions[2*i + 1] &gt; 0) &amp;&amp; g_is_update[i] &gt; 0){ \n&quot;</span>);</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;  source.append(<span class="stringliteral">&quot;            block_assembly(row_indices, column_indices, elements, matrix_dimensions, set_I + i_ind[i], set_J + j_ind[i], i, com_A_I_J + block_ind[i]); \n&quot;</span>);</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;  source.append(<span class="stringliteral">&quot;        } \n&quot;</span>);</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;  source.append(<span class="stringliteral">&quot;  } \n&quot;</span>);</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;}</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> StringT&gt;</div>
<div class="line"><a name="l00101"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a947e6322493e8087cfd86d03fd858189">  101</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a947e6322493e8087cfd86d03fd858189">generate_spai_block_bv_assembly</a>(StringT &amp; source, std::string <span class="keyword">const</span> &amp; numeric_string)</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;{</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;  source.append(<span class="stringliteral">&quot;  void assemble_bv(__global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * g_bv_r, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * g_bv, unsigned int col_n){ \n&quot;</span>);</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;  source.append(<span class="stringliteral">&quot;    for (unsigned int i = 0; i &lt; col_n; ++i){ \n&quot;</span>);</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;  source.append(<span class="stringliteral">&quot;      g_bv_r[i] = g_bv[ i]; \n&quot;</span>);</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;  source.append(<span class="stringliteral">&quot;  } \n&quot;</span>);</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;  source.append(<span class="stringliteral">&quot;  void assemble_bv_block(__global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * g_bv_r, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * g_bv, unsigned int col_n, \n&quot;</span>);</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;  source.append(<span class="stringliteral">&quot;               __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * g_bv_u, unsigned int col_n_u) \n&quot;</span>);</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;  source.append(<span class="stringliteral">&quot;  { \n&quot;</span>);</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;  source.append(<span class="stringliteral">&quot;    assemble_bv(g_bv_r, g_bv, col_n); \n&quot;</span>);</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;  source.append(<span class="stringliteral">&quot;    assemble_bv(g_bv_r + col_n, g_bv_u, col_n_u); \n&quot;</span>);</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;  source.append(<span class="stringliteral">&quot;  } \n&quot;</span>);</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;  source.append(<span class="stringliteral">&quot;  __kernel void block_bv_assembly(__global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * g_bv, \n&quot;</span>);</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;  source.append(<span class="stringliteral">&quot;              __global unsigned int * start_bv_ind, \n&quot;</span>);</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;  source.append(<span class="stringliteral">&quot;              __global unsigned int * matrix_dimensions, \n&quot;</span>);</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;  source.append(<span class="stringliteral">&quot;              __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * g_bv_u, \n&quot;</span>);</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;  source.append(<span class="stringliteral">&quot;              __global unsigned int * start_bv_u_ind, \n&quot;</span>);</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;  source.append(<span class="stringliteral">&quot;              __global unsigned int * matrix_dimensions_u, \n&quot;</span>);</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;  source.append(<span class="stringliteral">&quot;              __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * g_bv_r, \n&quot;</span>);</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;  source.append(<span class="stringliteral">&quot;              __global unsigned int * start_bv_r_ind, \n&quot;</span>);</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;  source.append(<span class="stringliteral">&quot;              __global unsigned int * matrix_dimensions_r, \n&quot;</span>);</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;  source.append(<span class="stringliteral">&quot;              __global unsigned int * g_is_update, \n&quot;</span>);</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;  source.append(<span class="stringliteral">&quot;              //__local  &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * local_gb, \n&quot;</span>);</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;  source.append(<span class="stringliteral">&quot;              unsigned int  block_elems_num) \n&quot;</span>);</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;  source.append(<span class="stringliteral">&quot;  { \n&quot;</span>);</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;  source.append(<span class="stringliteral">&quot;    for (unsigned int i  = get_global_id(0); i &lt; block_elems_num; i += get_global_size(0)){ \n&quot;</span>);</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;  source.append(<span class="stringliteral">&quot;      if ((matrix_dimensions[2*i] &gt; 0) &amp;&amp; (matrix_dimensions[2*i + 1] &gt; 0) &amp;&amp; g_is_update[i] &gt; 0){ \n&quot;</span>);</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;  source.append(<span class="stringliteral">&quot;        assemble_bv_block(g_bv_r + start_bv_r_ind[i], g_bv + start_bv_ind[i], matrix_dimensions[2*i + 1], g_bv_u + start_bv_u_ind[i], matrix_dimensions_u[2*i + 1]); \n&quot;</span>);</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;  source.append(<span class="stringliteral">&quot;      } \n&quot;</span>);</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;  source.append(<span class="stringliteral">&quot;  } \n&quot;</span>);</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;}</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> StringT&gt;</div>
<div class="line"><a name="l00138"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a8aa3b4bed4795a77017bf4419fd3b180">  138</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a8aa3b4bed4795a77017bf4419fd3b180">generate_spai_block_least_squares</a>(StringT &amp; source, std::string <span class="keyword">const</span> &amp; numeric_string)</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;{</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;  source.append(<span class="stringliteral">&quot;void custom_dot_prod_ls(__global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * A, unsigned int row_n, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * v, unsigned int ind, &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; *res){ \n&quot;</span>);</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;  source.append(<span class="stringliteral">&quot;  *res = 0.0; \n&quot;</span>);</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;  source.append(<span class="stringliteral">&quot;  for (unsigned int j = ind; j &lt; row_n; ++j){ \n&quot;</span>);</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;  source.append(<span class="stringliteral">&quot;    if (j == ind){ \n&quot;</span>);</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;  source.append(<span class="stringliteral">&quot;      *res += v[ j]; \n&quot;</span>);</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;  source.append(<span class="stringliteral">&quot;    }else{ \n&quot;</span>);</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;  source.append(<span class="stringliteral">&quot;      *res += A[ j + ind*row_n]*v[ j]; \n&quot;</span>);</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;  source.append(<span class="stringliteral">&quot;  } \n&quot;</span>);</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;  source.append(<span class="stringliteral">&quot;void backwardSolve(__global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R,  unsigned int row_n, unsigned int col_n, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * y, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * x){ \n&quot;</span>);</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;  source.append(<span class="stringliteral">&quot;  for (int i = col_n-1; i &gt;= 0; i--) { \n&quot;</span>);</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;  source.append(<span class="stringliteral">&quot;    x[ i] = y[ i]; \n&quot;</span>);</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;  source.append(<span class="stringliteral">&quot;    for (int j = i+1; j &lt; col_n; ++j) { \n&quot;</span>);</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;  source.append(<span class="stringliteral">&quot;      x[ i] -= R[ i + j*row_n]*x[ j]; \n&quot;</span>);</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;  source.append(<span class="stringliteral">&quot;    x[i] /= R[ i + i*row_n]; \n&quot;</span>);</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;  source.append(<span class="stringliteral">&quot;  } \n&quot;</span>);</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;  source.append(<span class="stringliteral">&quot;void apply_q_trans_vec_ls(__global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R, unsigned int row_n, unsigned int col_n, __global const &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * b_v,  __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * y){ \n&quot;</span>);</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;  source.append(<span class="stringliteral">&quot;            &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; inn_prod = 0; \n&quot;</span>);</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;  source.append(<span class="stringliteral">&quot;            for (unsigned int i = 0; i &lt; col_n; ++i){ \n&quot;</span>);</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;  source.append(<span class="stringliteral">&quot;                custom_dot_prod_ls(R, row_n, y, i, &amp;inn_prod); \n&quot;</span>);</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;  source.append(<span class="stringliteral">&quot;                for (unsigned int j = i; j &lt; row_n; ++j){ \n&quot;</span>);</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;  source.append(<span class="stringliteral">&quot;                    if (i == j){ \n&quot;</span>);</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;  source.append(<span class="stringliteral">&quot;                        y[ j] -= b_v[ i]*inn_prod; \n&quot;</span>);</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;  source.append(<span class="stringliteral">&quot;                    } \n&quot;</span>);</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;  source.append(<span class="stringliteral">&quot;                    else{ \n&quot;</span>);</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;  source.append(<span class="stringliteral">&quot;                        y[j] -= b_v[ i]*inn_prod*R[ j +i*row_n]; \n&quot;</span>);</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;  source.append(<span class="stringliteral">&quot;                    } \n&quot;</span>);</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;  source.append(<span class="stringliteral">&quot;                } \n&quot;</span>);</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;  source.append(<span class="stringliteral">&quot;            } \n&quot;</span>);</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;  source.append(<span class="stringliteral">&quot;        } \n&quot;</span>);</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;  source.append(<span class="stringliteral">&quot;void ls(__global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R, unsigned int row_n, unsigned int col_n, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * b_v, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * m_v, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * y_v){ \n&quot;</span>);</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;  source.append(<span class="stringliteral">&quot;  apply_q_trans_vec_ls(R, row_n, col_n, b_v, y_v); \n&quot;</span>);</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;  source.append(<span class="stringliteral">&quot;  //m_new - is m_v now \n&quot;</span>);</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;  source.append(<span class="stringliteral">&quot;  backwardSolve(R, row_n, col_n, y_v, m_v); \n&quot;</span>);</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;  source.append(<span class="stringliteral">&quot;__kernel void block_least_squares( \n&quot;</span>);</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;  source.append(<span class="stringliteral">&quot;      __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * global_R, \n&quot;</span>);</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;  source.append(<span class="stringliteral">&quot;      __global unsigned int * block_ind, \n&quot;</span>);</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;  source.append(<span class="stringliteral">&quot;      __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * b_v, \n&quot;</span>);</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;  source.append(<span class="stringliteral">&quot;      __global unsigned int * start_bv_inds, \n&quot;</span>);</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;  source.append(<span class="stringliteral">&quot;      __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * m_v, \n&quot;</span>);</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;  source.append(<span class="stringliteral">&quot;      __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * y_v, \n&quot;</span>);</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;  source.append(<span class="stringliteral">&quot;      __global unsigned int * start_y_inds, \n&quot;</span>);</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;  source.append(<span class="stringliteral">&quot;      __global unsigned int * matrix_dimensions, \n&quot;</span>);</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;  source.append(<span class="stringliteral">&quot;      __global unsigned int * g_is_update, \n&quot;</span>);</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;  source.append(<span class="stringliteral">&quot;      unsigned int  block_elems_num) \n&quot;</span>);</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;  source.append(<span class="stringliteral">&quot;{ \n&quot;</span>);</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;  source.append(<span class="stringliteral">&quot;    for (unsigned int i  = get_global_id(0); i &lt; block_elems_num; i += get_global_size(0)){ \n&quot;</span>);</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;  source.append(<span class="stringliteral">&quot;        if ((matrix_dimensions[2*i] &gt; 0) &amp;&amp; (matrix_dimensions[2*i + 1] &gt; 0) &amp;&amp; g_is_update[i] &gt; 0){ \n&quot;</span>);</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;  source.append(<span class="stringliteral">&quot;            ls(global_R + block_ind[i], matrix_dimensions[2*i], matrix_dimensions[2*i + 1], b_v +start_bv_inds[i], m_v + start_bv_inds[i], y_v + start_y_inds[i] ); \n&quot;</span>);</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;  source.append(<span class="stringliteral">&quot;        } \n&quot;</span>);</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;}</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> StringT&gt;</div>
<div class="line"><a name="l00204"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a59c4e99f39339ce7adfbb4793ec9a90f">  204</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a59c4e99f39339ce7adfbb4793ec9a90f">generate_spai_block_q_mult</a>(StringT &amp; source, std::string <span class="keyword">const</span> &amp; numeric_string)</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;{</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;  source.append(<span class="stringliteral">&quot;void custom_dot_prod(__global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * A, unsigned int row_n, __local &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * v, unsigned int ind, &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; *res){ \n&quot;</span>);</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;  source.append(<span class="stringliteral">&quot;  *res = 0.0; \n&quot;</span>);</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;  source.append(<span class="stringliteral">&quot;  for (unsigned int j = ind; j &lt; row_n; ++j){ \n&quot;</span>);</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;  source.append(<span class="stringliteral">&quot;    if (j == ind){ \n&quot;</span>);</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;  source.append(<span class="stringliteral">&quot;      *res += v[j]; \n&quot;</span>);</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;  source.append(<span class="stringliteral">&quot;    }else{ \n&quot;</span>);</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;  source.append(<span class="stringliteral">&quot;      *res += A[j + ind*row_n]*v[j]; \n&quot;</span>);</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;  source.append(<span class="stringliteral">&quot;  } \n&quot;</span>);</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;</div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;  source.append(<span class="stringliteral">&quot;void apply_q_trans_vec(__global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R, unsigned int row_n, unsigned int col_n, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * b_v, __local &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * y){ \n&quot;</span>);</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;  source.append(<span class="stringliteral">&quot;  &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; inn_prod = 0; \n&quot;</span>);</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;  source.append(<span class="stringliteral">&quot;  for (unsigned int i = 0; i &lt; col_n; ++i){ \n&quot;</span>);</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;  source.append(<span class="stringliteral">&quot;    custom_dot_prod(R, row_n, y, i, &amp;inn_prod); \n&quot;</span>);</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;  source.append(<span class="stringliteral">&quot;    for (unsigned int j = i; j &lt; row_n; ++j){ \n&quot;</span>);</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;  source.append(<span class="stringliteral">&quot;      if (i == j){ \n&quot;</span>);</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;  source.append(<span class="stringliteral">&quot;        y[j] -= b_v[ i]*inn_prod; \n&quot;</span>);</div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;  source.append(<span class="stringliteral">&quot;      } \n&quot;</span>);</div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;  source.append(<span class="stringliteral">&quot;      else{ \n&quot;</span>);</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;  source.append(<span class="stringliteral">&quot;        y[j] -= b_v[ i]*inn_prod*R[ j + i*row_n]; \n&quot;</span>);</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;  source.append(<span class="stringliteral">&quot;      } \n&quot;</span>);</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;  source.append(<span class="stringliteral">&quot;  } \n&quot;</span>);</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;</div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;  source.append(<span class="stringliteral">&quot;void q_mult(__global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R, unsigned int row_n, unsigned int col_n, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * b_v, __local &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R_u, unsigned int col_n_u){ \n&quot;</span>);</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;  source.append(<span class="stringliteral">&quot;        for (unsigned int i = get_local_id(0); i &lt; col_n_u; i+= get_local_size(0)){ \n&quot;</span>);</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;  source.append(<span class="stringliteral">&quot;          apply_q_trans_vec(R, row_n, col_n, b_v, R_u + row_n*i); \n&quot;</span>);</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;  source.append(<span class="stringliteral">&quot;        } \n&quot;</span>);</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;  source.append(<span class="stringliteral">&quot;void matrix_from_global_to_local(__global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* g_M, __local &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* l_M, unsigned int row_n, unsigned int col_n, unsigned int mat_start_ind){ \n&quot;</span>);</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;  source.append(<span class="stringliteral">&quot;  for (unsigned int i = get_local_id(0); i &lt; col_n; i+= get_local_size(0)){ \n&quot;</span>);</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;  source.append(<span class="stringliteral">&quot;    for (unsigned int j = 0; j &lt; row_n; ++j){ \n&quot;</span>);</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;  source.append(<span class="stringliteral">&quot;      l_M[i*row_n + j] = g_M[mat_start_ind + i*row_n + j]; \n&quot;</span>);</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;  source.append(<span class="stringliteral">&quot;  } \n&quot;</span>);</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;</div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;  source.append(<span class="stringliteral">&quot;void matrix_from_local_to_global(__global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* g_M, __local &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* l_M, unsigned int row_n, unsigned int col_n, unsigned int mat_start_ind){ \n&quot;</span>);</div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;  source.append(<span class="stringliteral">&quot;  for (unsigned int i = get_local_id(0); i &lt; col_n; i+= get_local_size(0)){ \n&quot;</span>);</div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;  source.append(<span class="stringliteral">&quot;    for (unsigned int j = 0; j &lt; row_n; ++j){ \n&quot;</span>);</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;  source.append(<span class="stringliteral">&quot;      g_M[mat_start_ind + i*row_n + j] = l_M[i*row_n + j]; \n&quot;</span>);</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;  source.append(<span class="stringliteral">&quot;  } \n&quot;</span>);</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;  source.append(<span class="stringliteral">&quot;__kernel void block_q_mult(__global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * global_R, \n&quot;</span>);</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;  source.append(<span class="stringliteral">&quot;  __global unsigned int * block_ind, \n&quot;</span>);</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;  source.append(<span class="stringliteral">&quot;  __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * global_R_u, \n&quot;</span>);</div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;  source.append(<span class="stringliteral">&quot;  __global unsigned int *block_ind_u, \n&quot;</span>);</div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;  source.append(<span class="stringliteral">&quot;  __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * b_v, \n&quot;</span>);</div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;  source.append(<span class="stringliteral">&quot;  __global unsigned int * start_bv_inds, \n&quot;</span>);</div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;  source.append(<span class="stringliteral">&quot;  __global unsigned int * matrix_dimensions, \n&quot;</span>);</div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;  source.append(<span class="stringliteral">&quot;  __global unsigned int * matrix_dimensions_u, \n&quot;</span>);</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;  source.append(<span class="stringliteral">&quot;  __global unsigned int * g_is_update, \n&quot;</span>);</div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;  source.append(<span class="stringliteral">&quot;  __local  &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * local_R_u, \n&quot;</span>);</div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;  source.append(<span class="stringliteral">&quot;    unsigned int  block_elems_num){ \n&quot;</span>);</div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;  source.append(<span class="stringliteral">&quot;    for (unsigned int i  = get_group_id(0); i &lt; block_elems_num; i += get_num_groups(0)){ \n&quot;</span>);</div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;  source.append(<span class="stringliteral">&quot;          if ((matrix_dimensions[2*i] &gt; 0) &amp;&amp; (matrix_dimensions[2*i + 1] &gt; 0) &amp;&amp; (g_is_update[i] &gt; 0)){ \n&quot;</span>);</div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;          <span class="comment">//matrix_from_global_to_local(R, local_buff_R, matrix_dimensions[2*i], matrix_dimensions[2*i + 1], start_matrix_inds[i]); \n&quot;);</span></div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;  source.append(<span class="stringliteral">&quot;        matrix_from_global_to_local(global_R_u, local_R_u, matrix_dimensions_u[2*i], matrix_dimensions_u[2*i+ 1], block_ind_u[i]); \n&quot;</span>);</div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;  source.append(<span class="stringliteral">&quot;        barrier(CLK_LOCAL_MEM_FENCE); \n&quot;</span>);</div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;  source.append(<span class="stringliteral">&quot;              q_mult(global_R + block_ind[i], matrix_dimensions[2*i], matrix_dimensions[2*i + 1], b_v + start_bv_inds[i], local_R_u, \n&quot;</span>);</div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;  source.append(<span class="stringliteral">&quot;             matrix_dimensions_u[2*i + 1]); \n&quot;</span>);</div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;  source.append(<span class="stringliteral">&quot;        barrier(CLK_LOCAL_MEM_FENCE); \n&quot;</span>);</div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;  source.append(<span class="stringliteral">&quot;              matrix_from_local_to_global(global_R_u, local_R_u, matrix_dimensions_u[2*i], matrix_dimensions_u[2*i + 1], block_ind_u[i]); \n&quot;</span>);</div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;  source.append(<span class="stringliteral">&quot;          } \n&quot;</span>);</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;  source.append(<span class="stringliteral">&quot;      } \n&quot;</span>);</div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;}</div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> StringT&gt;</div>
<div class="line"><a name="l00280"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a46c06e71a895b596b14c63ebc30d6da0">  280</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a46c06e71a895b596b14c63ebc30d6da0">generate_spai_block_qr</a>(StringT &amp; source, std::string <span class="keyword">const</span> &amp; numeric_string)</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;{</div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;  source.append(<span class="stringliteral">&quot;void dot_prod(__local const &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* A, unsigned int n, unsigned int beg_ind, &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* res){ \n&quot;</span>);</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;  source.append(<span class="stringliteral">&quot;    *res = 0; \n&quot;</span>);</div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;  source.append(<span class="stringliteral">&quot;    for (unsigned int i = beg_ind; i &lt; n; ++i){ \n&quot;</span>);</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;  source.append(<span class="stringliteral">&quot;        *res += A[(beg_ind-1)*n + i]*A[(beg_ind-1)*n + i]; \n&quot;</span>);</div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;</div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;  source.append(<span class="stringliteral">&quot;void vector_div(__global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* v, unsigned int beg_ind, &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; b, unsigned int n){ \n&quot;</span>);</div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;  source.append(<span class="stringliteral">&quot;    for (unsigned int i = beg_ind; i &lt; n; ++i){ \n&quot;</span>);</div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;  source.append(<span class="stringliteral">&quot;        v[i] /= b; \n&quot;</span>);</div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;</div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;  source.append(<span class="stringliteral">&quot;void copy_vector(__local const &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* A, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* v, const unsigned int beg_ind, const unsigned int n){ \n&quot;</span>);</div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;  source.append(<span class="stringliteral">&quot;    for (unsigned int i = beg_ind; i &lt; n; ++i){ \n&quot;</span>);</div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;  source.append(<span class="stringliteral">&quot;        v[i] = A[(beg_ind-1)*n + i]; \n&quot;</span>);</div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;</div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;</div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;  source.append(<span class="stringliteral">&quot;void householder_vector(__local const &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* A, unsigned int j, unsigned int n, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* v, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* b){ \n&quot;</span>);</div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;  source.append(<span class="stringliteral">&quot;    &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; sg; \n&quot;</span>);</div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;  source.append(<span class="stringliteral">&quot;    dot_prod(A, n, j+1, &amp;sg); \n&quot;</span>);</div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;  source.append(<span class="stringliteral">&quot;    copy_vector(A, v, j+1, n); \n&quot;</span>);</div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;  source.append(<span class="stringliteral">&quot;    &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; mu; \n&quot;</span>);</div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;  source.append(<span class="stringliteral">&quot;    v[j] = 1.0; \n&quot;</span>);</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;      <span class="comment">//print_contigious_vector(v, v_start_ind, n);</span></div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;  source.append(<span class="stringliteral">&quot;    if (sg == 0){ \n&quot;</span>);</div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;  source.append(<span class="stringliteral">&quot;        *b = 0; \n&quot;</span>);</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;  source.append(<span class="stringliteral">&quot;    else{ \n&quot;</span>);</div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;  source.append(<span class="stringliteral">&quot;        mu = sqrt(A[j*n + j]*A[ j*n + j] + sg); \n&quot;</span>);</div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;  source.append(<span class="stringliteral">&quot;        if (A[ j*n + j] &lt;= 0){ \n&quot;</span>);</div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;  source.append(<span class="stringliteral">&quot;            v[j] = A[ j*n + j] - mu; \n&quot;</span>);</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;  source.append(<span class="stringliteral">&quot;        }else{ \n&quot;</span>);</div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;  source.append(<span class="stringliteral">&quot;            v[j] = -sg/(A[ j*n + j] + mu); \n&quot;</span>);</div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;  source.append(<span class="stringliteral">&quot;        } \n&quot;</span>);</div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;  source.append(<span class="stringliteral">&quot;    *b = 2*(v[j]*v[j])/(sg + v[j]*v[j]); \n&quot;</span>);</div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;          <span class="comment">//*b = (2*v[j]*v[j])/(sg + (v[j])*(v[j]));</span></div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;  source.append(<span class="stringliteral">&quot;        vector_div(v, j, v[j], n); \n&quot;</span>);</div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;          <span class="comment">//print_contigious_vector(v, v_start_ind, n);</span></div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;</div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;  source.append(<span class="stringliteral">&quot;void custom_inner_prod(__local const &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* A, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* v, unsigned int col_ind, unsigned int row_num, unsigned int start_ind, &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* res){ \n&quot;</span>);</div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;  source.append(<span class="stringliteral">&quot;    for (unsigned int i = start_ind; i &lt; row_num; ++i){ \n&quot;</span>);</div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;  source.append(<span class="stringliteral">&quot;        *res += A[col_ind*row_num + i]*v[i]; \n&quot;</span>);</div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;  <span class="comment">//</span></div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;  source.append(<span class="stringliteral">&quot;void apply_householder_reflection(__local &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* A,  unsigned int row_n, unsigned int col_n, unsigned int iter_cnt, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* v, &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; b){ \n&quot;</span>);</div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;  source.append(<span class="stringliteral">&quot;    &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; in_prod_res; \n&quot;</span>);</div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;  source.append(<span class="stringliteral">&quot;    for (unsigned int i= iter_cnt + get_local_id(0); i &lt; col_n; i+=get_local_size(0)){ \n&quot;</span>);</div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;  source.append(<span class="stringliteral">&quot;        in_prod_res = 0.0; \n&quot;</span>);</div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;  source.append(<span class="stringliteral">&quot;        custom_inner_prod(A, v, i, row_n, iter_cnt, &amp;in_prod_res); \n&quot;</span>);</div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;  source.append(<span class="stringliteral">&quot;        for (unsigned int j = iter_cnt; j &lt; row_n; ++j){ \n&quot;</span>);</div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;  source.append(<span class="stringliteral">&quot;            A[ i*row_n + j] -= b*in_prod_res* v[j]; \n&quot;</span>);</div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;  source.append(<span class="stringliteral">&quot;        } \n&quot;</span>);</div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;</div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;  source.append(<span class="stringliteral">&quot;void store_householder_vector(__local &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* A,  unsigned int ind, unsigned int n, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* v){ \n&quot;</span>);</div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;  source.append(<span class="stringliteral">&quot;    for (unsigned int i = ind; i &lt; n; ++i){ \n&quot;</span>);</div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;  source.append(<span class="stringliteral">&quot;        A[ (ind-1)*n + i] = v[i]; \n&quot;</span>);</div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;</div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;  source.append(<span class="stringliteral">&quot;void single_qr( __local &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* R, __global unsigned int* matrix_dimensions, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* b_v, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* v, unsigned int matrix_ind){ \n&quot;</span>);</div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;              <span class="comment">//matrix_dimensions[0] - number of rows</span></div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;                <span class="comment">//matrix_dimensions[1] - number of columns</span></div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;  source.append(<span class="stringliteral">&quot;  unsigned int col_n = matrix_dimensions[2*matrix_ind + 1]; \n&quot;</span>);</div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;  source.append(<span class="stringliteral">&quot;  unsigned int row_n = matrix_dimensions[2*matrix_ind]; \n&quot;</span>);</div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;</div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;  source.append(<span class="stringliteral">&quot;  if ((col_n == row_n)&amp;&amp;(row_n == 1)){ \n&quot;</span>);</div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;  source.append(<span class="stringliteral">&quot;    b_v[0] = 0.0; \n&quot;</span>);</div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;  source.append(<span class="stringliteral">&quot;      return; \n&quot;</span>);</div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;  source.append(<span class="stringliteral">&quot;  } \n&quot;</span>);</div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;  source.append(<span class="stringliteral">&quot;  for (unsigned int i = 0; i &lt; col_n; ++i){ \n&quot;</span>);</div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;  source.append(<span class="stringliteral">&quot;    if (get_local_id(0) == 0){ \n&quot;</span>);</div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;  source.append(<span class="stringliteral">&quot;      householder_vector(R, i, row_n, v, b_v + i); \n&quot;</span>);</div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;  source.append(<span class="stringliteral">&quot;    barrier(CLK_LOCAL_MEM_FENCE); \n&quot;</span>);</div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;  source.append(<span class="stringliteral">&quot;    apply_householder_reflection(R, row_n, col_n, i, v, b_v[i]); \n&quot;</span>);</div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;  source.append(<span class="stringliteral">&quot;    barrier(CLK_LOCAL_MEM_FENCE); \n&quot;</span>);</div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;  source.append(<span class="stringliteral">&quot;    if (get_local_id(0) == 0){ \n&quot;</span>);</div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;  source.append(<span class="stringliteral">&quot;      if (i &lt; matrix_dimensions[2*matrix_ind]){ \n&quot;</span>);</div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;  source.append(<span class="stringliteral">&quot;        store_householder_vector(R, i+1, row_n, v); \n&quot;</span>);</div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;  source.append(<span class="stringliteral">&quot;      } \n&quot;</span>);</div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;  source.append(<span class="stringliteral">&quot;  } \n&quot;</span>);</div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;</div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;  source.append(<span class="stringliteral">&quot;void matrix_from_global_to_local_qr(__global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* g_M, __local &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* l_M, unsigned int row_n, unsigned int col_n, unsigned int mat_start_ind){ \n&quot;</span>);</div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;  source.append(<span class="stringliteral">&quot;  for (unsigned int i = get_local_id(0); i &lt; col_n; i+= get_local_size(0)){ \n&quot;</span>);</div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;  source.append(<span class="stringliteral">&quot;    for (unsigned int j = 0; j &lt; row_n; ++j){ \n&quot;</span>);</div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;  source.append(<span class="stringliteral">&quot;      l_M[i*row_n + j] = g_M[mat_start_ind + i*row_n + j]; \n&quot;</span>);</div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;  source.append(<span class="stringliteral">&quot;  } \n&quot;</span>);</div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;  source.append(<span class="stringliteral">&quot;void matrix_from_local_to_global_qr(__global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* g_M, __local &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* l_M, unsigned int row_n, unsigned int col_n, unsigned int mat_start_ind){ \n&quot;</span>);</div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;  source.append(<span class="stringliteral">&quot;  for (unsigned int i = get_local_id(0); i &lt; col_n; i+= get_local_size(0)){ \n&quot;</span>);</div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;  source.append(<span class="stringliteral">&quot;    for (unsigned int j = 0; j &lt; row_n; ++j){ \n&quot;</span>);</div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;  source.append(<span class="stringliteral">&quot;      g_M[mat_start_ind + i*row_n + j] = l_M[i*row_n + j]; \n&quot;</span>);</div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;  source.append(<span class="stringliteral">&quot;  } \n&quot;</span>);</div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;</div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;</div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;  source.append(<span class="stringliteral">&quot;__kernel void block_qr( \n&quot;</span>);</div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;  source.append(<span class="stringliteral">&quot;      __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* R, \n&quot;</span>);</div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;  source.append(<span class="stringliteral">&quot;      __global unsigned int* matrix_dimensions, \n&quot;</span>);</div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;  source.append(<span class="stringliteral">&quot;      __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* b_v, \n&quot;</span>);</div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;  source.append(<span class="stringliteral">&quot;      __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* v, \n&quot;</span>);</div>
<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;  source.append(<span class="stringliteral">&quot;      __global unsigned int* start_matrix_inds, \n&quot;</span>);</div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;  source.append(<span class="stringliteral">&quot;      __global unsigned int* start_bv_inds, \n&quot;</span>);</div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;  source.append(<span class="stringliteral">&quot;      __global unsigned int* start_v_inds, \n&quot;</span>);</div>
<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;  source.append(<span class="stringliteral">&quot;      __global unsigned int * g_is_update, \n&quot;</span>);</div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;  source.append(<span class="stringliteral">&quot;      __local &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot;* local_buff_R, \n&quot;</span>);</div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;  source.append(<span class="stringliteral">&quot;      unsigned int block_elems_num){ \n&quot;</span>);</div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;  source.append(<span class="stringliteral">&quot;    for (unsigned int i  = get_group_id(0); i &lt; block_elems_num; i += get_num_groups(0)){ \n&quot;</span>);</div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;  source.append(<span class="stringliteral">&quot;        if ((matrix_dimensions[2*i] &gt; 0) &amp;&amp; (matrix_dimensions[2*i + 1] &gt; 0) &amp;&amp; g_is_update[i] &gt; 0){ \n&quot;</span>);</div>
<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;  source.append(<span class="stringliteral">&quot;      matrix_from_global_to_local_qr(R, local_buff_R, matrix_dimensions[2*i], matrix_dimensions[2*i + 1], start_matrix_inds[i]); \n&quot;</span>);</div>
<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;  source.append(<span class="stringliteral">&quot;      barrier(CLK_LOCAL_MEM_FENCE); \n&quot;</span>);</div>
<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;  source.append(<span class="stringliteral">&quot;            single_qr(local_buff_R, matrix_dimensions, b_v + start_bv_inds[i], v + start_v_inds[i], i); \n&quot;</span>);</div>
<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;  source.append(<span class="stringliteral">&quot;      barrier(CLK_LOCAL_MEM_FENCE); \n&quot;</span>);</div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;  source.append(<span class="stringliteral">&quot;            matrix_from_local_to_global_qr(R, local_buff_R, matrix_dimensions[2*i], matrix_dimensions[2*i + 1], start_matrix_inds[i]); \n&quot;</span>);</div>
<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160;  source.append(<span class="stringliteral">&quot;        } \n&quot;</span>);</div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;}</div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;</div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> StringT&gt;</div>
<div class="line"><a name="l00414"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a0ef446958eadb7566af5af164c42d753">  414</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a0ef446958eadb7566af5af164c42d753">generate_spai_block_qr_assembly</a>(StringT &amp; source, std::string <span class="keyword">const</span> &amp; numeric_string)</div>
<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;{</div>
<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;  source.append(<span class="stringliteral">&quot;void assemble_upper_part(__global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R_q, \n&quot;</span>);</div>
<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;  source.append(<span class="stringliteral">&quot;            unsigned int row_n_q, unsigned int col_n_q, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R_u, \n&quot;</span>);</div>
<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;  source.append(<span class="stringliteral">&quot;            unsigned int row_n_u, unsigned int col_n_u, \n&quot;</span>);</div>
<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;  source.append(<span class="stringliteral">&quot;            unsigned int col_n, unsigned int diff){ \n&quot;</span>);</div>
<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;  source.append(<span class="stringliteral">&quot;            for (unsigned int i = 0; i &lt; col_n_q; ++i){ \n&quot;</span>);</div>
<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160;  source.append(<span class="stringliteral">&quot;                for (unsigned int j = 0; j &lt; diff; ++j){ \n&quot;</span>);</div>
<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;  source.append(<span class="stringliteral">&quot;          R_q[ i*row_n_q + j] = R_u[ i*row_n_u + j + col_n ]; \n&quot;</span>);</div>
<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;  source.append(<span class="stringliteral">&quot;                } \n&quot;</span>);</div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;  source.append(<span class="stringliteral">&quot;            } \n&quot;</span>);</div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;  source.append(<span class="stringliteral">&quot;        } \n&quot;</span>);</div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;</div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;  source.append(<span class="stringliteral">&quot;void assemble_lower_part(__global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R_q, unsigned int row_n_q, unsigned int col_n_q, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R_u_u, \n&quot;</span>);</div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;  source.append(<span class="stringliteral">&quot;             unsigned int row_n_u_u, unsigned int col_n_u_u, \n&quot;</span>);</div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;  source.append(<span class="stringliteral">&quot;             unsigned int diff){ \n&quot;</span>);</div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;  source.append(<span class="stringliteral">&quot;  for (unsigned int i = 0; i &lt; col_n_u_u; ++i){ \n&quot;</span>);</div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;  source.append(<span class="stringliteral">&quot;    for (unsigned int j = 0; j &lt; row_n_u_u; ++j){ \n&quot;</span>);</div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;  source.append(<span class="stringliteral">&quot;      R_q[i*row_n_q + j + diff] = R_u_u[i*row_n_u_u + j]; \n&quot;</span>);</div>
<div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160;  source.append(<span class="stringliteral">&quot;  } \n&quot;</span>);</div>
<div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;</div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;  source.append(<span class="stringliteral">&quot;void assemble_qr_block(__global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R_q, unsigned int row_n_q, unsigned int col_n_q, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R_u, unsigned int row_n_u, \n&quot;</span>);</div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;  source.append(<span class="stringliteral">&quot;            unsigned int col_n_u, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R_u_u, unsigned int row_n_u_u, unsigned int col_n_u_u, unsigned int col_n){ \n&quot;</span>);</div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;  source.append(<span class="stringliteral">&quot;            unsigned int diff = row_n_u - col_n; \n&quot;</span>);</div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;  source.append(<span class="stringliteral">&quot;            assemble_upper_part(R_q, row_n_q, col_n_q, R_u, row_n_u, col_n_u, col_n, diff); \n&quot;</span>);</div>
<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;  source.append(<span class="stringliteral">&quot;            if (diff &gt; 0){ \n&quot;</span>);</div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;  source.append(<span class="stringliteral">&quot;              assemble_lower_part(R_q, row_n_q, col_n_q, R_u_u, row_n_u_u, col_n_u_u, diff); \n&quot;</span>);</div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;  source.append(<span class="stringliteral">&quot;            } \n&quot;</span>);</div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;</div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;  source.append(<span class="stringliteral">&quot;__kernel void block_qr_assembly( \n&quot;</span>);</div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;  source.append(<span class="stringliteral">&quot;      __global unsigned int * matrix_dimensions, \n&quot;</span>);</div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;  source.append(<span class="stringliteral">&quot;      __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R_u, \n&quot;</span>);</div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;  source.append(<span class="stringliteral">&quot;      __global unsigned int * block_ind_u, \n&quot;</span>);</div>
<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;  source.append(<span class="stringliteral">&quot;      __global unsigned int * matrix_dimensions_u, \n&quot;</span>);</div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;  source.append(<span class="stringliteral">&quot;      __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R_u_u, \n&quot;</span>);</div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;  source.append(<span class="stringliteral">&quot;      __global unsigned int * block_ind_u_u, \n&quot;</span>);</div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;  source.append(<span class="stringliteral">&quot;      __global unsigned int * matrix_dimensions_u_u, \n&quot;</span>);</div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;  source.append(<span class="stringliteral">&quot;      __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R_q, \n&quot;</span>);</div>
<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;  source.append(<span class="stringliteral">&quot;      __global unsigned int * block_ind_q, \n&quot;</span>);</div>
<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;  source.append(<span class="stringliteral">&quot;      __global unsigned int * matrix_dimensions_q, \n&quot;</span>);</div>
<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160;  source.append(<span class="stringliteral">&quot;      __global unsigned int * g_is_update, \n&quot;</span>);</div>
<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160;  source.append(<span class="stringliteral">&quot;          //__local  &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * local_R_q, \n&quot;</span>);</div>
<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;  source.append(<span class="stringliteral">&quot;      unsigned int  block_elems_num) \n&quot;</span>);</div>
<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160;  source.append(<span class="stringliteral">&quot;{ \n&quot;</span>);</div>
<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;  source.append(<span class="stringliteral">&quot;    for (unsigned int i  = get_global_id(0); i &lt; block_elems_num; i += get_global_size(0)){ \n&quot;</span>);</div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;  source.append(<span class="stringliteral">&quot;        if ((matrix_dimensions[2*i] &gt; 0) &amp;&amp; (matrix_dimensions[2*i + 1] &gt; 0) &amp;&amp; g_is_update[i] &gt; 0){ \n&quot;</span>);</div>
<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;  source.append(<span class="stringliteral">&quot;           assemble_qr_block(R_q + block_ind_q[i], matrix_dimensions_q[2*i], matrix_dimensions_q[2*i + 1], R_u + block_ind_u[i], matrix_dimensions_u[2*i], \n&quot;</span>);</div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;  source.append(<span class="stringliteral">&quot;             matrix_dimensions_u[2*i + 1], R_u_u + block_ind_u_u[i], matrix_dimensions_u_u[2*i], matrix_dimensions_u_u[2*i + 1], matrix_dimensions[2*i + 1]); \n&quot;</span>);</div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;  source.append(<span class="stringliteral">&quot;       } \n&quot;</span>);</div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;  source.append(<span class="stringliteral">&quot;   } \n&quot;</span>);</div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160;}</div>
<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;</div>
<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> StringT&gt;</div>
<div class="line"><a name="l00471"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#af432061aaf6283a75ec3b81ac0ab0f48">  471</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#af432061aaf6283a75ec3b81ac0ab0f48">generate_spai_block_qr_assembly_1</a>(StringT &amp; source, std::string <span class="keyword">const</span> &amp; numeric_string)</div>
<div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160;{</div>
<div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;  source.append(<span class="stringliteral">&quot;void assemble_upper_part_1(__global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R_q, unsigned int row_n_q, unsigned int col_n_q, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R_u, \n&quot;</span>);</div>
<div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160;  source.append(<span class="stringliteral">&quot;             unsigned int row_n_u, unsigned int col_n_u, \n&quot;</span>);</div>
<div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160;  source.append(<span class="stringliteral">&quot;             unsigned int col_n, unsigned int diff){ \n&quot;</span>);</div>
<div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;  source.append(<span class="stringliteral">&quot;            for (unsigned int i = 0; i &lt; col_n_q; ++i){ \n&quot;</span>);</div>
<div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;  source.append(<span class="stringliteral">&quot;                for (unsigned int j = 0; j &lt; diff; ++j){ \n&quot;</span>);</div>
<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;  source.append(<span class="stringliteral">&quot;          R_q[ i*row_n_q + j] = R_u[i*row_n_u + j + col_n ]; \n&quot;</span>);</div>
<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;  source.append(<span class="stringliteral">&quot;                } \n&quot;</span>);</div>
<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;  source.append(<span class="stringliteral">&quot;            } \n&quot;</span>);</div>
<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;  source.append(<span class="stringliteral">&quot;        } \n&quot;</span>);</div>
<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;</div>
<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;</div>
<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;  source.append(<span class="stringliteral">&quot;void assemble_qr_block_1(__global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R_q,  unsigned int row_n_q, unsigned int col_n_q, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R_u, unsigned int row_n_u, \n&quot;</span>);</div>
<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160;  source.append(<span class="stringliteral">&quot;            unsigned int col_n_u, unsigned int col_n){ \n&quot;</span>);</div>
<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;  source.append(<span class="stringliteral">&quot;            unsigned int diff = row_n_u - col_n; \n&quot;</span>);</div>
<div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160;  source.append(<span class="stringliteral">&quot;            assemble_upper_part_1(R_q, row_n_q, col_n_q, R_u, row_n_u, col_n_u, col_n, diff); \n&quot;</span>);</div>
<div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160;</div>
<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;  source.append(<span class="stringliteral">&quot;__kernel void block_qr_assembly_1( \n&quot;</span>);</div>
<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160;  source.append(<span class="stringliteral">&quot;  __global unsigned int * matrix_dimensions, \n&quot;</span>);</div>
<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;  source.append(<span class="stringliteral">&quot;  __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R_u, \n&quot;</span>);</div>
<div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160;  source.append(<span class="stringliteral">&quot;  __global unsigned int * block_ind_u, \n&quot;</span>);</div>
<div class="line"><a name="l00494"></a><span class="lineno">  494</span>&#160;  source.append(<span class="stringliteral">&quot;  __global unsigned int * matrix_dimensions_u, \n&quot;</span>);</div>
<div class="line"><a name="l00495"></a><span class="lineno">  495</span>&#160;  source.append(<span class="stringliteral">&quot;  __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R_q, \n&quot;</span>);</div>
<div class="line"><a name="l00496"></a><span class="lineno">  496</span>&#160;  source.append(<span class="stringliteral">&quot;  __global unsigned int * block_ind_q, \n&quot;</span>);</div>
<div class="line"><a name="l00497"></a><span class="lineno">  497</span>&#160;  source.append(<span class="stringliteral">&quot;  __global unsigned int * matrix_dimensions_q, \n&quot;</span>);</div>
<div class="line"><a name="l00498"></a><span class="lineno">  498</span>&#160;  source.append(<span class="stringliteral">&quot;  __global unsigned int * g_is_update, \n&quot;</span>);</div>
<div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160;  source.append(<span class="stringliteral">&quot;  unsigned int  block_elems_num) \n&quot;</span>);</div>
<div class="line"><a name="l00500"></a><span class="lineno">  500</span>&#160;  source.append(<span class="stringliteral">&quot;{ \n&quot;</span>);</div>
<div class="line"><a name="l00501"></a><span class="lineno">  501</span>&#160;  source.append(<span class="stringliteral">&quot;    for (unsigned int i  = get_global_id(0); i &lt; block_elems_num; i += get_global_size(0)){ \n&quot;</span>);</div>
<div class="line"><a name="l00502"></a><span class="lineno">  502</span>&#160;  source.append(<span class="stringliteral">&quot;        if ((matrix_dimensions[2*i] &gt; 0) &amp;&amp; (matrix_dimensions[2*i + 1] &gt; 0) &amp;&amp; g_is_update[i] &gt; 0){ \n&quot;</span>);</div>
<div class="line"><a name="l00503"></a><span class="lineno">  503</span>&#160;  source.append(<span class="stringliteral">&quot;            assemble_qr_block_1(R_q + block_ind_q[i], matrix_dimensions_q[2*i], matrix_dimensions_q[2*i + 1], R_u + block_ind_u[i], matrix_dimensions_u[2*i], \n&quot;</span>);</div>
<div class="line"><a name="l00504"></a><span class="lineno">  504</span>&#160;  source.append(<span class="stringliteral">&quot;              matrix_dimensions_u[2*i + 1], matrix_dimensions[2*i + 1]); \n&quot;</span>);</div>
<div class="line"><a name="l00505"></a><span class="lineno">  505</span>&#160;  source.append(<span class="stringliteral">&quot;        } \n&quot;</span>);</div>
<div class="line"><a name="l00506"></a><span class="lineno">  506</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00507"></a><span class="lineno">  507</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00508"></a><span class="lineno">  508</span>&#160;}</div>
<div class="line"><a name="l00509"></a><span class="lineno">  509</span>&#160;</div>
<div class="line"><a name="l00510"></a><span class="lineno">  510</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> StringT&gt;</div>
<div class="line"><a name="l00511"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a684d46d7a6d25da9315a650389a6b9a6">  511</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a684d46d7a6d25da9315a650389a6b9a6">generate_spai_block_r_assembly</a>(StringT &amp; source, std::string <span class="keyword">const</span> &amp; numeric_string)</div>
<div class="line"><a name="l00512"></a><span class="lineno">  512</span>&#160;{</div>
<div class="line"><a name="l00513"></a><span class="lineno">  513</span>&#160;  source.append(<span class="stringliteral">&quot;void assemble_r(__global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * gR, unsigned int row_n_r, unsigned int col_n_r, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R, \n&quot;</span>);</div>
<div class="line"><a name="l00514"></a><span class="lineno">  514</span>&#160;  source.append(<span class="stringliteral">&quot;        unsigned int row_n, unsigned int col_n) \n&quot;</span>);</div>
<div class="line"><a name="l00515"></a><span class="lineno">  515</span>&#160;  source.append(<span class="stringliteral">&quot;{ \n&quot;</span>);</div>
<div class="line"><a name="l00516"></a><span class="lineno">  516</span>&#160;  source.append(<span class="stringliteral">&quot;  for (unsigned int i = 0; i &lt; col_n; ++i){ \n&quot;</span>);</div>
<div class="line"><a name="l00517"></a><span class="lineno">  517</span>&#160;  source.append(<span class="stringliteral">&quot;     for (unsigned int j = 0; j &lt; row_n; ++j){ \n&quot;</span>);</div>
<div class="line"><a name="l00518"></a><span class="lineno">  518</span>&#160;  source.append(<span class="stringliteral">&quot;    gR[i*row_n_r + j] = R[i*row_n + j ]; \n&quot;</span>);</div>
<div class="line"><a name="l00519"></a><span class="lineno">  519</span>&#160;  source.append(<span class="stringliteral">&quot;     } \n&quot;</span>);</div>
<div class="line"><a name="l00520"></a><span class="lineno">  520</span>&#160;  source.append(<span class="stringliteral">&quot;  } \n&quot;</span>);</div>
<div class="line"><a name="l00521"></a><span class="lineno">  521</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00522"></a><span class="lineno">  522</span>&#160;</div>
<div class="line"><a name="l00523"></a><span class="lineno">  523</span>&#160;  source.append(<span class="stringliteral">&quot;void assemble_r_u(__global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * gR, \n&quot;</span>);</div>
<div class="line"><a name="l00524"></a><span class="lineno">  524</span>&#160;  source.append(<span class="stringliteral">&quot;          unsigned int row_n_r, unsigned int col_n_r, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R_u, unsigned int row_n_u, unsigned int col_n_u, \n&quot;</span>);</div>
<div class="line"><a name="l00525"></a><span class="lineno">  525</span>&#160;  source.append(<span class="stringliteral">&quot;          unsigned int col_n) \n&quot;</span>);</div>
<div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160;  source.append(<span class="stringliteral">&quot;{ \n&quot;</span>);</div>
<div class="line"><a name="l00527"></a><span class="lineno">  527</span>&#160;  source.append(<span class="stringliteral">&quot;  for (unsigned int i = 0; i &lt; col_n_u; ++i){ \n&quot;</span>);</div>
<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160;  source.append(<span class="stringliteral">&quot;    for (unsigned int j = 0; j &lt; col_n; ++j){ \n&quot;</span>);</div>
<div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160;  source.append(<span class="stringliteral">&quot;      gR[ (i+col_n)*row_n_r + j] = R_u[ i*row_n_u + j]; \n&quot;</span>);</div>
<div class="line"><a name="l00530"></a><span class="lineno">  530</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00531"></a><span class="lineno">  531</span>&#160;  source.append(<span class="stringliteral">&quot;  } \n&quot;</span>);</div>
<div class="line"><a name="l00532"></a><span class="lineno">  532</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00533"></a><span class="lineno">  533</span>&#160;</div>
<div class="line"><a name="l00534"></a><span class="lineno">  534</span>&#160;</div>
<div class="line"><a name="l00535"></a><span class="lineno">  535</span>&#160;  source.append(<span class="stringliteral">&quot;void assemble_r_u_u(__global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * gR,  unsigned int row_n_r, unsigned int col_n_r, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R_u_u, unsigned int row_n_u_u, \n&quot;</span>);</div>
<div class="line"><a name="l00536"></a><span class="lineno">  536</span>&#160;  source.append(<span class="stringliteral">&quot;          unsigned int col_n_u_u, unsigned int col_n) \n&quot;</span>);</div>
<div class="line"><a name="l00537"></a><span class="lineno">  537</span>&#160;  source.append(<span class="stringliteral">&quot;{ \n&quot;</span>);</div>
<div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160;  source.append(<span class="stringliteral">&quot;  for (unsigned int i = 0; i &lt; col_n_u_u; ++i){ \n&quot;</span>);</div>
<div class="line"><a name="l00539"></a><span class="lineno">  539</span>&#160;  source.append(<span class="stringliteral">&quot;    for (unsigned int j = 0; j &lt; row_n_u_u; ++j){ \n&quot;</span>);</div>
<div class="line"><a name="l00540"></a><span class="lineno">  540</span>&#160;  source.append(<span class="stringliteral">&quot;      gR[(col_n+i)*row_n_r + j + col_n] = R_u_u[i*row_n_u_u + j]; \n&quot;</span>);</div>
<div class="line"><a name="l00541"></a><span class="lineno">  541</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00542"></a><span class="lineno">  542</span>&#160;  source.append(<span class="stringliteral">&quot;  } \n&quot;</span>);</div>
<div class="line"><a name="l00543"></a><span class="lineno">  543</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00544"></a><span class="lineno">  544</span>&#160;</div>
<div class="line"><a name="l00545"></a><span class="lineno">  545</span>&#160;  source.append(<span class="stringliteral">&quot;void assemble_r_block(__global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * gR, unsigned int row_n_r, unsigned int col_n_r, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R, unsigned int row_n, \n&quot;</span>);</div>
<div class="line"><a name="l00546"></a><span class="lineno">  546</span>&#160;  source.append(<span class="stringliteral">&quot;        unsigned int col_n, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R_u, unsigned int row_n_u, unsigned int col_n_u, __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R_u_u, \n&quot;</span>);</div>
<div class="line"><a name="l00547"></a><span class="lineno">  547</span>&#160;  source.append(<span class="stringliteral">&quot;        unsigned int row_n_u_u, unsigned int col_n_u_u){ \n&quot;</span>);</div>
<div class="line"><a name="l00548"></a><span class="lineno">  548</span>&#160;  source.append(<span class="stringliteral">&quot;        assemble_r(gR, row_n_r, col_n_r, R, row_n, col_n); \n&quot;</span>);</div>
<div class="line"><a name="l00549"></a><span class="lineno">  549</span>&#160;  source.append(<span class="stringliteral">&quot;        assemble_r_u(gR, row_n_r, col_n_r, R_u, row_n_u, col_n_u, col_n); \n&quot;</span>);</div>
<div class="line"><a name="l00550"></a><span class="lineno">  550</span>&#160;  source.append(<span class="stringliteral">&quot;        assemble_r_u_u(gR, row_n_r, col_n_r, R_u_u, row_n_u_u, col_n_u_u, col_n); \n&quot;</span>);</div>
<div class="line"><a name="l00551"></a><span class="lineno">  551</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00552"></a><span class="lineno">  552</span>&#160;</div>
<div class="line"><a name="l00553"></a><span class="lineno">  553</span>&#160;</div>
<div class="line"><a name="l00554"></a><span class="lineno">  554</span>&#160;  source.append(<span class="stringliteral">&quot;__kernel void block_r_assembly( \n&quot;</span>);</div>
<div class="line"><a name="l00555"></a><span class="lineno">  555</span>&#160;  source.append(<span class="stringliteral">&quot;  __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R, \n&quot;</span>);</div>
<div class="line"><a name="l00556"></a><span class="lineno">  556</span>&#160;  source.append(<span class="stringliteral">&quot;  __global unsigned int * block_ind, \n&quot;</span>);</div>
<div class="line"><a name="l00557"></a><span class="lineno">  557</span>&#160;  source.append(<span class="stringliteral">&quot;  __global unsigned int * matrix_dimensions, \n&quot;</span>);</div>
<div class="line"><a name="l00558"></a><span class="lineno">  558</span>&#160;  source.append(<span class="stringliteral">&quot;  __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R_u, \n&quot;</span>);</div>
<div class="line"><a name="l00559"></a><span class="lineno">  559</span>&#160;  source.append(<span class="stringliteral">&quot;  __global unsigned int * block_ind_u, \n&quot;</span>);</div>
<div class="line"><a name="l00560"></a><span class="lineno">  560</span>&#160;  source.append(<span class="stringliteral">&quot;  __global unsigned int * matrix_dimensions_u, \n&quot;</span>);</div>
<div class="line"><a name="l00561"></a><span class="lineno">  561</span>&#160;  source.append(<span class="stringliteral">&quot;  __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * R_u_u, \n&quot;</span>);</div>
<div class="line"><a name="l00562"></a><span class="lineno">  562</span>&#160;  source.append(<span class="stringliteral">&quot;  __global unsigned int * block_ind_u_u, \n&quot;</span>);</div>
<div class="line"><a name="l00563"></a><span class="lineno">  563</span>&#160;  source.append(<span class="stringliteral">&quot;  __global unsigned int * matrix_dimensions_u_u, \n&quot;</span>);</div>
<div class="line"><a name="l00564"></a><span class="lineno">  564</span>&#160;  source.append(<span class="stringliteral">&quot;  __global &quot;</span>); source.append(numeric_string); source.append(<span class="stringliteral">&quot; * g_R, \n&quot;</span>);</div>
<div class="line"><a name="l00565"></a><span class="lineno">  565</span>&#160;  source.append(<span class="stringliteral">&quot;  __global unsigned int * block_ind_r, \n&quot;</span>);</div>
<div class="line"><a name="l00566"></a><span class="lineno">  566</span>&#160;  source.append(<span class="stringliteral">&quot;  __global unsigned int * matrix_dimensions_r, \n&quot;</span>);</div>
<div class="line"><a name="l00567"></a><span class="lineno">  567</span>&#160;  source.append(<span class="stringliteral">&quot;  __global unsigned int * g_is_update, \n&quot;</span>);</div>
<div class="line"><a name="l00568"></a><span class="lineno">  568</span>&#160;  source.append(<span class="stringliteral">&quot;  unsigned int  block_elems_num) \n&quot;</span>);</div>
<div class="line"><a name="l00569"></a><span class="lineno">  569</span>&#160;  source.append(<span class="stringliteral">&quot;{ \n&quot;</span>);</div>
<div class="line"><a name="l00570"></a><span class="lineno">  570</span>&#160;  source.append(<span class="stringliteral">&quot;    for (unsigned int i  = get_global_id(0); i &lt; block_elems_num; i += get_global_size(0)){ \n&quot;</span>);</div>
<div class="line"><a name="l00571"></a><span class="lineno">  571</span>&#160;  source.append(<span class="stringliteral">&quot;        if ((matrix_dimensions[2*i] &gt; 0) &amp;&amp; (matrix_dimensions[2*i + 1] &gt; 0) &amp;&amp; g_is_update[i] &gt; 0){ \n&quot;</span>);</div>
<div class="line"><a name="l00572"></a><span class="lineno">  572</span>&#160;</div>
<div class="line"><a name="l00573"></a><span class="lineno">  573</span>&#160;  source.append(<span class="stringliteral">&quot;            assemble_r_block(g_R + block_ind_r[i], matrix_dimensions_r[2*i], matrix_dimensions_r[2*i + 1], R + block_ind[i], matrix_dimensions[2*i], \n&quot;</span>);</div>
<div class="line"><a name="l00574"></a><span class="lineno">  574</span>&#160;  source.append(<span class="stringliteral">&quot;              matrix_dimensions[2*i + 1], R_u + block_ind_u[i], matrix_dimensions_u[2*i], matrix_dimensions_u[2*i + 1], \n&quot;</span>);</div>
<div class="line"><a name="l00575"></a><span class="lineno">  575</span>&#160;  source.append(<span class="stringliteral">&quot;              R_u_u + block_ind_u_u[i], matrix_dimensions_u_u[2*i], matrix_dimensions_u_u[2*i + 1]); \n&quot;</span>);</div>
<div class="line"><a name="l00576"></a><span class="lineno">  576</span>&#160;</div>
<div class="line"><a name="l00577"></a><span class="lineno">  577</span>&#160;  source.append(<span class="stringliteral">&quot;        } \n&quot;</span>);</div>
<div class="line"><a name="l00578"></a><span class="lineno">  578</span>&#160;  source.append(<span class="stringliteral">&quot;    } \n&quot;</span>);</div>
<div class="line"><a name="l00579"></a><span class="lineno">  579</span>&#160;  source.append(<span class="stringliteral">&quot;} \n&quot;</span>);</div>
<div class="line"><a name="l00580"></a><span class="lineno">  580</span>&#160;}</div>
<div class="line"><a name="l00581"></a><span class="lineno">  581</span>&#160;</div>
<div class="line"><a name="l00583"></a><span class="lineno">  583</span>&#160;</div>
<div class="line"><a name="l00584"></a><span class="lineno">  584</span>&#160;<span class="comment">// main kernel class</span></div>
<div class="line"><a name="l00586"></a><span class="lineno">  586</span>&#160;<span class="comment"></span><span class="keyword">template</span>&lt;<span class="keyword">typename</span> NumericT&gt;</div>
<div class="line"><a name="l00587"></a><span class="lineno"><a class="line" href="structviennacl_1_1linalg_1_1opencl_1_1kernels_1_1spai.html">  587</a></span>&#160;<span class="keyword">struct </span><a class="code" href="structviennacl_1_1linalg_1_1opencl_1_1kernels_1_1spai.html">spai</a></div>
<div class="line"><a name="l00588"></a><span class="lineno">  588</span>&#160;{</div>
<div class="line"><a name="l00589"></a><span class="lineno"><a class="line" href="structviennacl_1_1linalg_1_1opencl_1_1kernels_1_1spai.html#ad8f7e68d4451f8c928f310a24a206464">  589</a></span>&#160;  <span class="keyword">static</span> std::string <a class="code" href="structviennacl_1_1linalg_1_1opencl_1_1kernels_1_1spai.html#ad8f7e68d4451f8c928f310a24a206464">program_name</a>()</div>
<div class="line"><a name="l00590"></a><span class="lineno">  590</span>&#160;  {</div>
<div class="line"><a name="l00591"></a><span class="lineno">  591</span>&#160;    <span class="keywordflow">return</span> <a class="code" href="structviennacl_1_1ocl_1_1type__to__string.html">viennacl::ocl::type_to_string&lt;NumericT&gt;::apply</a>() + <span class="stringliteral">&quot;_spai&quot;</span>;</div>
<div class="line"><a name="l00592"></a><span class="lineno">  592</span>&#160;  }</div>
<div class="line"><a name="l00593"></a><span class="lineno">  593</span>&#160;</div>
<div class="line"><a name="l00594"></a><span class="lineno"><a class="line" href="structviennacl_1_1linalg_1_1opencl_1_1kernels_1_1spai.html#acc7e921176d6dffe6cad7a796413b6b5">  594</a></span>&#160;  <span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code" href="structviennacl_1_1linalg_1_1opencl_1_1kernels_1_1spai.html#acc7e921176d6dffe6cad7a796413b6b5">init</a>(<a class="code" href="classviennacl_1_1ocl_1_1context.html">viennacl::ocl::context</a> &amp; ctx)</div>
<div class="line"><a name="l00595"></a><span class="lineno">  595</span>&#160;  {</div>
<div class="line"><a name="l00596"></a><span class="lineno">  596</span>&#160;    <span class="keyword">static</span> std::map&lt;cl_context, bool&gt; init_done;</div>
<div class="line"><a name="l00597"></a><span class="lineno">  597</span>&#160;    <span class="keywordflow">if</span> (!init_done[ctx.<a class="code" href="classviennacl_1_1ocl_1_1context.html#a611d95b11db04230f63e37bfeae911db">handle</a>().<a class="code" href="classviennacl_1_1ocl_1_1handle.html#a5074caaee700015fc2d3b03540b01673">get</a>()])</div>
<div class="line"><a name="l00598"></a><span class="lineno">  598</span>&#160;    {</div>
<div class="line"><a name="l00599"></a><span class="lineno">  599</span>&#160;      <a class="code" href="structviennacl_1_1ocl_1_1_d_o_u_b_l_e___p_r_e_c_i_s_i_o_n___c_h_e_c_k_e_r.html#ae23d18c854e1df43cd329a5c1fdd6d9f">viennacl::ocl::DOUBLE_PRECISION_CHECKER&lt;NumericT&gt;::apply</a>(ctx);</div>
<div class="line"><a name="l00600"></a><span class="lineno">  600</span>&#160;      std::string numeric_string = <a class="code" href="structviennacl_1_1ocl_1_1type__to__string.html">viennacl::ocl::type_to_string&lt;NumericT&gt;::apply</a>();</div>
<div class="line"><a name="l00601"></a><span class="lineno">  601</span>&#160;</div>
<div class="line"><a name="l00602"></a><span class="lineno">  602</span>&#160;      std::string source;</div>
<div class="line"><a name="l00603"></a><span class="lineno">  603</span>&#160;      source.reserve(1024);</div>
<div class="line"><a name="l00604"></a><span class="lineno">  604</span>&#160;</div>
<div class="line"><a name="l00605"></a><span class="lineno">  605</span>&#160;      viennacl::ocl::append_double_precision_pragma&lt;NumericT&gt;(ctx, source);</div>
<div class="line"><a name="l00606"></a><span class="lineno">  606</span>&#160;</div>
<div class="line"><a name="l00607"></a><span class="lineno">  607</span>&#160;      <a class="code" href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a6fc75b18244da56426784cbf789c030c">generate_spai_assemble_blocks</a>(source, numeric_string);</div>
<div class="line"><a name="l00608"></a><span class="lineno">  608</span>&#160;      <a class="code" href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a947e6322493e8087cfd86d03fd858189">generate_spai_block_bv_assembly</a>(source, numeric_string);</div>
<div class="line"><a name="l00609"></a><span class="lineno">  609</span>&#160;      <a class="code" href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a8aa3b4bed4795a77017bf4419fd3b180">generate_spai_block_least_squares</a>(source, numeric_string);</div>
<div class="line"><a name="l00610"></a><span class="lineno">  610</span>&#160;      <a class="code" href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a59c4e99f39339ce7adfbb4793ec9a90f">generate_spai_block_q_mult</a>(source, numeric_string);</div>
<div class="line"><a name="l00611"></a><span class="lineno">  611</span>&#160;      <a class="code" href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a46c06e71a895b596b14c63ebc30d6da0">generate_spai_block_qr</a>(source, numeric_string);</div>
<div class="line"><a name="l00612"></a><span class="lineno">  612</span>&#160;      <a class="code" href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a0ef446958eadb7566af5af164c42d753">generate_spai_block_qr_assembly</a>(source, numeric_string);</div>
<div class="line"><a name="l00613"></a><span class="lineno">  613</span>&#160;      <a class="code" href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#af432061aaf6283a75ec3b81ac0ab0f48">generate_spai_block_qr_assembly_1</a>(source, numeric_string);</div>
<div class="line"><a name="l00614"></a><span class="lineno">  614</span>&#160;      <a class="code" href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a684d46d7a6d25da9315a650389a6b9a6">generate_spai_block_r_assembly</a>(source, numeric_string);</div>
<div class="line"><a name="l00615"></a><span class="lineno">  615</span>&#160;</div>
<div class="line"><a name="l00616"></a><span class="lineno">  616</span>&#160;      std::string prog_name = <a class="code" href="structviennacl_1_1linalg_1_1opencl_1_1kernels_1_1spai.html#ad8f7e68d4451f8c928f310a24a206464">program_name</a>();</div>
<div class="line"><a name="l00617"></a><span class="lineno">  617</span>&#160;<span class="preprocessor">      #ifdef VIENNACL_BUILD_INFO</span></div>
<div class="line"><a name="l00618"></a><span class="lineno">  618</span>&#160;      std::cout &lt;&lt; <span class="stringliteral">&quot;Creating program &quot;</span> &lt;&lt; prog_name &lt;&lt; std::endl;</div>
<div class="line"><a name="l00619"></a><span class="lineno">  619</span>&#160;<span class="preprocessor">      #endif</span></div>
<div class="line"><a name="l00620"></a><span class="lineno">  620</span>&#160;      ctx.add_program(source, prog_name);</div>
<div class="line"><a name="l00621"></a><span class="lineno">  621</span>&#160;      init_done[ctx.handle().get()] = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00622"></a><span class="lineno">  622</span>&#160;    } <span class="comment">//if</span></div>
<div class="line"><a name="l00623"></a><span class="lineno">  623</span>&#160;  } <span class="comment">//init</span></div>
<div class="line"><a name="l00624"></a><span class="lineno">  624</span>&#160;};</div>
<div class="line"><a name="l00625"></a><span class="lineno">  625</span>&#160;</div>
<div class="line"><a name="l00626"></a><span class="lineno">  626</span>&#160;}  <span class="comment">// namespace kernels</span></div>
<div class="line"><a name="l00627"></a><span class="lineno">  627</span>&#160;}  <span class="comment">// namespace opencl</span></div>
<div class="line"><a name="l00628"></a><span class="lineno">  628</span>&#160;}  <span class="comment">// namespace linalg</span></div>
<div class="line"><a name="l00629"></a><span class="lineno">  629</span>&#160;}  <span class="comment">// namespace viennacl</span></div>
<div class="line"><a name="l00630"></a><span class="lineno">  630</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00631"></a><span class="lineno">  631</span>&#160;</div>
<div class="ttc" id="structviennacl_1_1linalg_1_1opencl_1_1kernels_1_1spai_html"><div class="ttname"><a href="structviennacl_1_1linalg_1_1opencl_1_1kernels_1_1spai.html">viennacl::linalg::opencl::kernels::spai</a></div><div class="ttdoc">Main kernel class for generating OpenCL kernels for the sparse approximate inverse preconditioners...</div><div class="ttdef"><b>Definition:</b> <a href="opencl_2kernels_2spai_8hpp_source.html#l00587">spai.hpp:587</a></div></div>
<div class="ttc" id="platform_8hpp_html"><div class="ttname"><a href="platform_8hpp.html">platform.hpp</a></div><div class="ttdoc">Implements a OpenCL platform within ViennaCL. </div></div>
<div class="ttc" id="tools_8hpp_html"><div class="ttname"><a href="tools_8hpp.html">tools.hpp</a></div><div class="ttdoc">Various little tools used here and there in ViennaCL. </div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels_html_a684d46d7a6d25da9315a650389a6b9a6"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a684d46d7a6d25da9315a650389a6b9a6">viennacl::linalg::opencl::kernels::generate_spai_block_r_assembly</a></div><div class="ttdeci">void generate_spai_block_r_assembly(StringT &amp;source, std::string const &amp;numeric_string)</div><div class="ttdef"><b>Definition:</b> <a href="opencl_2kernels_2spai_8hpp_source.html#l00511">spai.hpp:511</a></div></div>
<div class="ttc" id="classviennacl_1_1ocl_1_1context_html"><div class="ttname"><a href="classviennacl_1_1ocl_1_1context.html">viennacl::ocl::context</a></div><div class="ttdoc">Manages an OpenCL context and provides the respective convenience functions for creating buffers...</div><div class="ttdef"><b>Definition:</b> <a href="ocl_2context_8hpp_source.html#l00055">context.hpp:55</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels_html_a0ef446958eadb7566af5af164c42d753"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a0ef446958eadb7566af5af164c42d753">viennacl::linalg::opencl::kernels::generate_spai_block_qr_assembly</a></div><div class="ttdeci">void generate_spai_block_qr_assembly(StringT &amp;source, std::string const &amp;numeric_string)</div><div class="ttdef"><b>Definition:</b> <a href="opencl_2kernels_2spai_8hpp_source.html#l00414">spai.hpp:414</a></div></div>
<div class="ttc" id="ocl_2utils_8hpp_html"><div class="ttname"><a href="ocl_2utils_8hpp.html">utils.hpp</a></div><div class="ttdoc">Provides OpenCL-related utilities. </div></div>
<div class="ttc" id="classviennacl_1_1ocl_1_1context_html_a611d95b11db04230f63e37bfeae911db"><div class="ttname"><a href="classviennacl_1_1ocl_1_1context.html#a611d95b11db04230f63e37bfeae911db">viennacl::ocl::context::handle</a></div><div class="ttdeci">const viennacl::ocl::handle&lt; cl_context &gt; &amp; handle() const </div><div class="ttdoc">Returns the context handle. </div><div class="ttdef"><b>Definition:</b> <a href="ocl_2context_8hpp_source.html#l00611">context.hpp:611</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels_html_a59c4e99f39339ce7adfbb4793ec9a90f"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a59c4e99f39339ce7adfbb4793ec9a90f">viennacl::linalg::opencl::kernels::generate_spai_block_q_mult</a></div><div class="ttdeci">void generate_spai_block_q_mult(StringT &amp;source, std::string const &amp;numeric_string)</div><div class="ttdef"><b>Definition:</b> <a href="opencl_2kernels_2spai_8hpp_source.html#l00204">spai.hpp:204</a></div></div>
<div class="ttc" id="structviennacl_1_1ocl_1_1_d_o_u_b_l_e___p_r_e_c_i_s_i_o_n___c_h_e_c_k_e_r_html_ae23d18c854e1df43cd329a5c1fdd6d9f"><div class="ttname"><a href="structviennacl_1_1ocl_1_1_d_o_u_b_l_e___p_r_e_c_i_s_i_o_n___c_h_e_c_k_e_r.html#ae23d18c854e1df43cd329a5c1fdd6d9f">viennacl::ocl::DOUBLE_PRECISION_CHECKER::apply</a></div><div class="ttdeci">static void apply(viennacl::ocl::context const &amp;)</div><div class="ttdef"><b>Definition:</b> <a href="ocl_2utils_8hpp_source.html#l00040">utils.hpp:40</a></div></div>
<div class="ttc" id="classviennacl_1_1ocl_1_1handle_html_a5074caaee700015fc2d3b03540b01673"><div class="ttname"><a href="classviennacl_1_1ocl_1_1handle.html#a5074caaee700015fc2d3b03540b01673">viennacl::ocl::handle::get</a></div><div class="ttdeci">const OCL_TYPE &amp; get() const </div><div class="ttdef"><b>Definition:</b> <a href="ocl_2handle_8hpp_source.html#l00191">handle.hpp:191</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels_html_a6fc75b18244da56426784cbf789c030c"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a6fc75b18244da56426784cbf789c030c">viennacl::linalg::opencl::kernels::generate_spai_assemble_blocks</a></div><div class="ttdeci">void generate_spai_assemble_blocks(StringT &amp;source, std::string const &amp;numeric_string)</div><div class="ttdef"><b>Definition:</b> <a href="opencl_2kernels_2spai_8hpp_source.html#l00040">spai.hpp:40</a></div></div>
<div class="ttc" id="structviennacl_1_1linalg_1_1opencl_1_1kernels_1_1spai_html_ad8f7e68d4451f8c928f310a24a206464"><div class="ttname"><a href="structviennacl_1_1linalg_1_1opencl_1_1kernels_1_1spai.html#ad8f7e68d4451f8c928f310a24a206464">viennacl::linalg::opencl::kernels::spai::program_name</a></div><div class="ttdeci">static std::string program_name()</div><div class="ttdef"><b>Definition:</b> <a href="opencl_2kernels_2spai_8hpp_source.html#l00589">spai.hpp:589</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels_html_a46c06e71a895b596b14c63ebc30d6da0"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a46c06e71a895b596b14c63ebc30d6da0">viennacl::linalg::opencl::kernels::generate_spai_block_qr</a></div><div class="ttdeci">void generate_spai_block_qr(StringT &amp;source, std::string const &amp;numeric_string)</div><div class="ttdef"><b>Definition:</b> <a href="opencl_2kernels_2spai_8hpp_source.html#l00280">spai.hpp:280</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels_html_a8aa3b4bed4795a77017bf4419fd3b180"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a8aa3b4bed4795a77017bf4419fd3b180">viennacl::linalg::opencl::kernels::generate_spai_block_least_squares</a></div><div class="ttdeci">void generate_spai_block_least_squares(StringT &amp;source, std::string const &amp;numeric_string)</div><div class="ttdef"><b>Definition:</b> <a href="opencl_2kernels_2spai_8hpp_source.html#l00138">spai.hpp:138</a></div></div>
<div class="ttc" id="kernel_8hpp_html"><div class="ttname"><a href="kernel_8hpp.html">kernel.hpp</a></div><div class="ttdoc">Representation of an OpenCL kernel in ViennaCL. </div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels_html_af432061aaf6283a75ec3b81ac0ab0f48"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#af432061aaf6283a75ec3b81ac0ab0f48">viennacl::linalg::opencl::kernels::generate_spai_block_qr_assembly_1</a></div><div class="ttdeci">void generate_spai_block_qr_assembly_1(StringT &amp;source, std::string const &amp;numeric_string)</div><div class="ttdef"><b>Definition:</b> <a href="opencl_2kernels_2spai_8hpp_source.html#l00471">spai.hpp:471</a></div></div>
<div class="ttc" id="structviennacl_1_1linalg_1_1opencl_1_1kernels_1_1spai_html_acc7e921176d6dffe6cad7a796413b6b5"><div class="ttname"><a href="structviennacl_1_1linalg_1_1opencl_1_1kernels_1_1spai.html#acc7e921176d6dffe6cad7a796413b6b5">viennacl::linalg::opencl::kernels::spai::init</a></div><div class="ttdeci">static void init(viennacl::ocl::context &amp;ctx)</div><div class="ttdef"><b>Definition:</b> <a href="opencl_2kernels_2spai_8hpp_source.html#l00594">spai.hpp:594</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels_html_a947e6322493e8087cfd86d03fd858189"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1opencl_1_1kernels.html#a947e6322493e8087cfd86d03fd858189">viennacl::linalg::opencl::kernels::generate_spai_block_bv_assembly</a></div><div class="ttdeci">void generate_spai_block_bv_assembly(StringT &amp;source, std::string const &amp;numeric_string)</div><div class="ttdef"><b>Definition:</b> <a href="opencl_2kernels_2spai_8hpp_source.html#l00101">spai.hpp:101</a></div></div>
<div class="ttc" id="structviennacl_1_1ocl_1_1type__to__string_html"><div class="ttname"><a href="structviennacl_1_1ocl_1_1type__to__string.html">viennacl::ocl::type_to_string</a></div><div class="ttdoc">Helper class for converting a type to its string representation. </div><div class="ttdef"><b>Definition:</b> <a href="ocl_2utils_8hpp_source.html#l00057">utils.hpp:57</a></div></div>
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