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| <div class="title">linalg.sql_in</div> </div> |
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| <div class="contents"> |
| <a href="linalg_8sql__in.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/* ----------------------------------------------------------------------- */</span><span class="comment">/**</span></div> |
| <div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment"> * @file linalg.sql_in</span></div> |
| <div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> * @brief SQL functions for linear algebra</span></div> |
| <div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> * @sa For an overview of linear-algebra functions, see the module</span></div> |
| <div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> * description \ref grp_linalg.</span></div> |
| <div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment"> */</span><span class="comment">/* ----------------------------------------------------------------------- */</span></div> |
| <div class="line"><a name="l00011"></a><span class="lineno"> 11</span> </div> |
| <div class="line"><a name="l00012"></a><span class="lineno"> 12</span> m4_include(`SQLCommon.m4<span class="stringliteral">')</span></div> |
| <div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment">@addtogroup grp_linalg</span></div> |
| <div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment">\warning <em> This MADlib method is still in early stage development. There may be some </span></div> |
| <div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment">issues that will be addressed in a future version. Interface and implementation</span></div> |
| <div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment">is subject to change. </em></span></div> |
| <div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment">@about</span></div> |
| <div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment">The linalg module consists of useful utility functions for basic linear </span></div> |
| <div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment">algebra operations. Several of these functions can be used</span></div> |
| <div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment">while implementing new algorithms.</span></div> |
| <div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment">Refer to the file for documentation on each of the utlity functions.</span></div> |
| <div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment">Linear-algebra functions.</span></div> |
| <div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">@sa File linalg.sql_in documenting the SQL functions.</span></div> |
| <div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment">*/</span></div> |
| <div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment"> * @brief 1-norm of a vector</span></div> |
| <div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment"> * @param x Vector \f$ \vec x = (x_1, \dots, x_n) \f$</span></div> |
| <div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment"> * @return \f$ \| x \|_1 = \sum_{i=1}^n |x_i| \f$</span></div> |
| <div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00041"></a><span class="lineno"> 41</span> CREATE FUNCTION MADLIB_SCHEMA.norm1(</div> |
| <div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  x DOUBLE PRECISION[]</div> |
| <div class="line"><a name="l00043"></a><span class="lineno"> 43</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00044"></a><span class="lineno"> 44</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="stringliteral">IMMUTABLE</span></div> |
| <div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="stringliteral">STRICT;</span></div> |
| <div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment"> * @brief 2-norm of a vector</span></div> |
| <div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="comment"> * @param x Vector \f$ \vec x = (x_1, \dots, x_n) \f$</span></div> |
| <div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="comment"> * @return \f$ \| x \|_2 = \sqrt{\sum_{i=1}^n x_i^2} \f$</span></div> |
| <div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00055"></a><span class="lineno"> 55</span> CREATE FUNCTION MADLIB_SCHEMA.norm2(</div> |
| <div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  x DOUBLE PRECISION[]</div> |
| <div class="line"><a name="l00057"></a><span class="lineno"> 57</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00058"></a><span class="lineno"> 58</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="stringliteral">IMMUTABLE</span></div> |
| <div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="stringliteral">STRICT;</span></div> |
| <div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00063"></a><span class="lineno"><a class="code" href="linalg_8sql__in.html#a300300fe4b8576ba0b97b95d8dea3057"> 63</a></span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="comment"> * @brief 1-norm of the difference between two vectors</span></div> |
| <div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="comment"> * @param x Vector \f$ \vec x = (x_1, \dots, x_n) \f$</span></div> |
| <div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="comment"> * @param y Vector \f$ \vec y = (y_1, \dots, y_n) \f$</span></div> |
| <div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="comment"> * @return \f$ \| x - y \|_1 = \sum_{i=1}^n |x_i - y_i| \f$</span></div> |
| <div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00070"></a><span class="lineno"> 70</span> CREATE FUNCTION MADLIB_SCHEMA.dist_norm1(</div> |
| <div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  x DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  y DOUBLE PRECISION[]</div> |
| <div class="line"><a name="l00073"></a><span class="lineno"> 73</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00074"></a><span class="lineno"> 74</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00076"></a><span class="lineno"> 76</span> <span class="stringliteral">IMMUTABLE</span></div> |
| <div class="line"><a name="l00077"></a><span class="lineno"><a class="code" href="linalg_8sql__in.html#a50fdfe30cc0edc6888a909dbb4b4c239"> 77</a></span> <span class="stringliteral">STRICT;</span></div> |
| <div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="comment"> * @brief 2-norm of the difference between two vectors</span></div> |
| <div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="comment"> * @param x Vector \f$ \vec x = (x_1, \dots, x_n) \f$</span></div> |
| <div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="comment"> * @param y Vector \f$ \vec y = (y_1, \dots, y_n) \f$</span></div> |
| <div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="comment"> * @return \f$ \| x - y \|_2 = \sqrt{\sum_{i=1}^n (x_i - y_i)^2} \f$</span></div> |
| <div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00086"></a><span class="lineno"> 86</span> CREATE FUNCTION MADLIB_SCHEMA.dist_norm2(</div> |
| <div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  x DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  y DOUBLE PRECISION[]</div> |
| <div class="line"><a name="l00089"></a><span class="lineno"> 89</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00090"></a><span class="lineno"> 90</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00091"></a><span class="lineno"> 91</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00092"></a><span class="lineno"><a class="code" href="linalg_8sql__in.html#aad193850e79c4b9d811ca9bc53e13476"> 92</a></span> <span class="stringliteral">IMMUTABLE</span></div> |
| <div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="stringliteral">STRICT;</span></div> |
| <div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00096"></a><span class="lineno"> 96</span> <span class="comment"> * @brief Squared 2-norm of the difference between two vectors</span></div> |
| <div class="line"><a name="l00097"></a><span class="lineno"> 97</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00098"></a><span class="lineno"> 98</span> <span class="comment"> * @param x Vector \f$ \vec x = (x_1, \dots, x_n) \f$</span></div> |
| <div class="line"><a name="l00099"></a><span class="lineno"> 99</span> <span class="comment"> * @param y Vector \f$ \vec y = (y_1, \dots, y_n) \f$</span></div> |
| <div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="comment"> * @return \f$ \| x - y \|_2^2 = \sum_{i=1}^n (x_i - y_i)^2 \f$</span></div> |
| <div class="line"><a name="l00101"></a><span class="lineno"> 101</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00102"></a><span class="lineno"> 102</span> CREATE FUNCTION MADLIB_SCHEMA.squared_dist_norm2(</div> |
| <div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  x DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  y DOUBLE PRECISION[]</div> |
| <div class="line"><a name="l00105"></a><span class="lineno"> 105</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00106"></a><span class="lineno"> 106</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00107"></a><span class="lineno"> 107</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00108"></a><span class="lineno"><a class="code" href="linalg_8sql__in.html#aa58e51526edea6ea98db30b6f250adb4"> 108</a></span> <span class="stringliteral">IMMUTABLE</span></div> |
| <div class="line"><a name="l00109"></a><span class="lineno"> 109</span> <span class="stringliteral">STRICT;</span></div> |
| <div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00111"></a><span class="lineno"> 111</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00112"></a><span class="lineno"> 112</span> <span class="comment"> * @brief Angle between two vectors</span></div> |
| <div class="line"><a name="l00113"></a><span class="lineno"> 113</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00114"></a><span class="lineno"> 114</span> <span class="comment"> * @param x Vector \f$ \vec x = (x_1, \dots, x_n) \f$</span></div> |
| <div class="line"><a name="l00115"></a><span class="lineno"> 115</span> <span class="comment"> * @param y Vector \f$ \vec y = (y_1, \dots, y_n) \f$</span></div> |
| <div class="line"><a name="l00116"></a><span class="lineno"> 116</span> <span class="comment"> * @return \f$ \arccos\left(\frac{\langle \vec x, \vec y \rangle}</span></div> |
| <div class="line"><a name="l00117"></a><span class="lineno"> 117</span> <span class="comment"> * {\| \vec x \| \cdot \| \vec y \|}\right) \f$</span></div> |
| <div class="line"><a name="l00118"></a><span class="lineno"> 118</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00119"></a><span class="lineno"> 119</span> CREATE FUNCTION MADLIB_SCHEMA.dist_angle(</div> |
| <div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  x DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  y DOUBLE PRECISION[]</div> |
| <div class="line"><a name="l00122"></a><span class="lineno"> 122</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00123"></a><span class="lineno"> 123</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00124"></a><span class="lineno"><a class="code" href="linalg_8sql__in.html#a00a08e69f27524f2096032214e15b668"> 124</a></span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00125"></a><span class="lineno"> 125</span> <span class="stringliteral">IMMUTABLE</span></div> |
| <div class="line"><a name="l00126"></a><span class="lineno"> 126</span> <span class="stringliteral">STRICT;</span></div> |
| <div class="line"><a name="l00127"></a><span class="lineno"> 127</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00128"></a><span class="lineno"> 128</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00129"></a><span class="lineno"> 129</span> <span class="comment"> * @brief Tanimoto distance between two vectors</span></div> |
| <div class="line"><a name="l00130"></a><span class="lineno"> 130</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00131"></a><span class="lineno"> 131</span> <span class="comment"> * @param x Vector \f$ \vec x = (x_1, \dots, x_n) \f$</span></div> |
| <div class="line"><a name="l00132"></a><span class="lineno"> 132</span> <span class="comment"> * @param y Vector \f$ \vec y = (y_1, \dots, y_n) \f$</span></div> |
| <div class="line"><a name="l00133"></a><span class="lineno"> 133</span> <span class="comment"> * @return \f$ 1 - \frac{\langle \vec x, \vec y \rangle}</span></div> |
| <div class="line"><a name="l00134"></a><span class="lineno"> 134</span> <span class="comment"> * {\| \vec x \|^2 \cdot \| \vec y \|^2</span></div> |
| <div class="line"><a name="l00135"></a><span class="lineno"> 135</span> <span class="comment"> * - \langle \vec x, \vec y \rangle} \f$</span></div> |
| <div class="line"><a name="l00136"></a><span class="lineno"> 136</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00137"></a><span class="lineno"> 137</span> CREATE FUNCTION MADLIB_SCHEMA.dist_tanimoto(</div> |
| <div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  x DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  y DOUBLE PRECISION[]</div> |
| <div class="line"><a name="l00140"></a><span class="lineno"> 140</span> ) RETURNS DOUBLE PRECISION</div> |
| <div class="line"><a name="l00141"></a><span class="lineno"><a class="code" href="linalg_8sql__in.html#a8c7b9281a72ff22caf06161701b27e84"> 141</a></span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00142"></a><span class="lineno"> 142</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00143"></a><span class="lineno"> 143</span> <span class="stringliteral">IMMUTABLE</span></div> |
| <div class="line"><a name="l00144"></a><span class="lineno"> 144</span> <span class="stringliteral">STRICT;</span></div> |
| <div class="line"><a name="l00145"></a><span class="lineno"> 145</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00146"></a><span class="lineno"> 146</span> <span class="stringliteral">/*</span></div> |
| <div class="line"><a name="l00147"></a><span class="lineno"> 147</span> <span class="stringliteral"> * @brief closest_column return type</span></div> |
| <div class="line"><a name="l00148"></a><span class="lineno"> 148</span> <span class="stringliteral"> */</span></div> |
| <div class="line"><a name="l00149"></a><span class="lineno"> 149</span> <span class="stringliteral">CREATE TYPE MADLIB_SCHEMA.closest_column_result AS (</span></div> |
| <div class="line"><a name="l00150"></a><span class="lineno"> 150</span> <span class="stringliteral"> column_id INTEGER,</span></div> |
| <div class="line"><a name="l00151"></a><span class="lineno"> 151</span> <span class="stringliteral"> distance DOUBLE PRECISION</span></div> |
| <div class="line"><a name="l00152"></a><span class="lineno"> 152</span> <span class="stringliteral">);</span></div> |
| <div class="line"><a name="l00153"></a><span class="lineno"> 153</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00154"></a><span class="lineno"> 154</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00155"></a><span class="lineno"> 155</span> <span class="comment"> * @brief Given matrix \f$ M \f$ and vector \f$ \vec x \f$ compute the column</span></div> |
| <div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="comment"> * of \f$ M \f$ that is closest to \f$ \vec x \f$</span></div> |
| <div class="line"><a name="l00157"></a><span class="lineno"> 157</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00158"></a><span class="lineno"> 158</span> <span class="comment"> * @param M Matrix \f$ M = (\vec{m_0} \dots \vec{m_{l-1}})</span></div> |
| <div class="line"><a name="l00159"></a><span class="lineno"><a class="code" href="linalg_8sql__in.html#afa13b4c6122b99422d666dedea136c18"> 159</a></span> <span class="comment"> * \in \mathbb{R}^{k \times l} \f$</span></div> |
| <div class="line"><a name="l00160"></a><span class="lineno"> 160</span> <span class="comment"> * @param x Vector \f$ \vec x \in \mathbb R^k \f$</span></div> |
| <div class="line"><a name="l00161"></a><span class="lineno"> 161</span> <span class="comment"> * @param dist The metric \f$ \operatorname{dist} \f$. This needs to be a</span></div> |
| <div class="line"><a name="l00162"></a><span class="lineno"> 162</span> <span class="comment"> * function with signature</span></div> |
| <div class="line"><a name="l00163"></a><span class="lineno"> 163</span> <span class="comment"> * <tt>DOUBLE PRECISION[] x DOUBLE PRECISION[] -> DOUBLE PRECISION</tt>.</span></div> |
| <div class="line"><a name="l00164"></a><span class="lineno"> 164</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00165"></a><span class="lineno"> 165</span> <span class="comment"> * @returns A composite value:</span></div> |
| <div class="line"><a name="l00166"></a><span class="lineno"> 166</span> <span class="comment"> * - <tt>columns_id INTEGER</tt> - The 0-based index of the column of \f$ M \f$</span></div> |
| <div class="line"><a name="l00167"></a><span class="lineno"> 167</span> <span class="comment"> * that is closest to \f$ x \f$. In case of ties, the first such index is</span></div> |
| <div class="line"><a name="l00168"></a><span class="lineno"> 168</span> <span class="comment"> * returned. That is, \c columns_id is the minimum element in the set</span></div> |
| <div class="line"><a name="l00169"></a><span class="lineno"> 169</span> <span class="comment"> * \f$ \arg\min_{i=0,\dots,l-1} \operatorname{dist}(\vec{m_i}, \vec x) \f$.</span></div> |
| <div class="line"><a name="l00170"></a><span class="lineno"> 170</span> <span class="comment"> * - <tt>distance DOUBLE PRECISION</tt> - The minimum distance between any</span></div> |
| <div class="line"><a name="l00171"></a><span class="lineno"> 171</span> <span class="comment"> * column of \f$ M \f$ and \f$ x \f$. That is,</span></div> |
| <div class="line"><a name="l00172"></a><span class="lineno"> 172</span> <span class="comment"> * \f$ \min_{i=0,\dots,l-1} \operatorname{dist}(\vec{m_i}, \vec x) \f$.</span></div> |
| <div class="line"><a name="l00173"></a><span class="lineno"> 173</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00174"></a><span class="lineno"> 174</span> CREATE FUNCTION MADLIB_SCHEMA.closest_column(</div> |
| <div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  M DOUBLE PRECISION[][],</div> |
| <div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  x DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  dist REGPROC /*+ DEFAULT '<a class="code" href="linalg_8sql__in.html#a00a08e69f27524f2096032214e15b668" title="Squared 2-norm of the difference between two vectors. ">squared_dist_norm2</a><span class="stringliteral">' */</span></div> |
| <div class="line"><a name="l00178"></a><span class="lineno"> 178</span> <span class="stringliteral">) RETURNS MADLIB_SCHEMA.closest_column_result</span></div> |
| <div class="line"><a name="l00179"></a><span class="lineno"> 179</span> <span class="stringliteral">IMMUTABLE</span></div> |
| <div class="line"><a name="l00180"></a><span class="lineno"> 180</span> <span class="stringliteral">STRICT</span></div> |
| <div class="line"><a name="l00181"></a><span class="lineno"> 181</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00182"></a><span class="lineno"> 182</span> <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00183"></a><span class="lineno"> 183</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00184"></a><span class="lineno"> 184</span> <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.closest_column(</span></div> |
| <div class="line"><a name="l00185"></a><span class="lineno"> 185</span> <span class="stringliteral"> M DOUBLE PRECISION[][],</span></div> |
| <div class="line"><a name="l00186"></a><span class="lineno"> 186</span> <span class="stringliteral"> x DOUBLE PRECISION[]</span></div> |
| <div class="line"><a name="l00187"></a><span class="lineno"> 187</span> <span class="stringliteral">) RETURNS MADLIB_SCHEMA.closest_column_result</span></div> |
| <div class="line"><a name="l00188"></a><span class="lineno"> 188</span> <span class="stringliteral">IMMUTABLE</span></div> |
| <div class="line"><a name="l00189"></a><span class="lineno"> 189</span> <span class="stringliteral">STRICT</span></div> |
| <div class="line"><a name="l00190"></a><span class="lineno"> 190</span> <span class="stringliteral">LANGUAGE sql</span></div> |
| <div class="line"><a name="l00191"></a><span class="lineno"> 191</span> <span class="stringliteral">AS $$</span></div> |
| <div class="line"><a name="l00192"></a><span class="lineno"> 192</span> <span class="stringliteral"> SELECT MADLIB_SCHEMA.closest_column($1, $2,</span></div> |
| <div class="line"><a name="l00193"></a><span class="lineno"> 193</span> <span class="stringliteral"> '</span>MADLIB_SCHEMA.squared_dist_norm2<span class="stringliteral">')</span></div> |
| <div class="line"><a name="l00194"></a><span class="lineno"> 194</span> <span class="stringliteral">$$;</span></div> |
| <div class="line"><a name="l00195"></a><span class="lineno"> 195</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00196"></a><span class="lineno"><a class="code" href="linalg_8sql__in.html#aa2856d10fa6cb12a5b168bab217197ed"> 196</a></span> <span class="stringliteral">/*</span></div> |
| <div class="line"><a name="l00197"></a><span class="lineno"> 197</span> <span class="stringliteral"> * @brief closest_columns return type</span></div> |
| <div class="line"><a name="l00198"></a><span class="lineno"> 198</span> <span class="stringliteral"> */</span></div> |
| <div class="line"><a name="l00199"></a><span class="lineno"> 199</span> <span class="stringliteral">CREATE TYPE MADLIB_SCHEMA.closest_columns_result AS (</span></div> |
| <div class="line"><a name="l00200"></a><span class="lineno"> 200</span> <span class="stringliteral"> column_ids INTEGER[],</span></div> |
| <div class="line"><a name="l00201"></a><span class="lineno"> 201</span> <span class="stringliteral"> distances DOUBLE PRECISION[]</span></div> |
| <div class="line"><a name="l00202"></a><span class="lineno"> 202</span> <span class="stringliteral">);</span></div> |
| <div class="line"><a name="l00203"></a><span class="lineno"> 203</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00204"></a><span class="lineno"> 204</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00205"></a><span class="lineno"> 205</span> <span class="comment"> * @brief Given matrix \f$ M \f$ and vector \f$ \vec x \f$ compute the columns</span></div> |
| <div class="line"><a name="l00206"></a><span class="lineno"> 206</span> <span class="comment"> * of \f$ M \f$ that are closest to \f$ \vec x \f$</span></div> |
| <div class="line"><a name="l00207"></a><span class="lineno"> 207</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00208"></a><span class="lineno"> 208</span> <span class="comment"> * This function does essentially the same as \ref closest_column(), except that</span></div> |
| <div class="line"><a name="l00209"></a><span class="lineno"> 209</span> <span class="comment"> * it allows to specify the number of closest columns to return. The return</span></div> |
| <div class="line"><a name="l00210"></a><span class="lineno"> 210</span> <span class="comment"> * value is a composite value:</span></div> |
| <div class="line"><a name="l00211"></a><span class="lineno"> 211</span> <span class="comment"> * - <tt>columns_ids INTEGER[]</tt> - The 0-based indices of the \c num columns</span></div> |
| <div class="line"><a name="l00212"></a><span class="lineno"> 212</span> <span class="comment"> * of \f$ M \f$ that are closest to \f$ x \f$. In case of ties, the first</span></div> |
| <div class="line"><a name="l00213"></a><span class="lineno"> 213</span> <span class="comment"> * such indices are returned.</span></div> |
| <div class="line"><a name="l00214"></a><span class="lineno"> 214</span> <span class="comment"> * - <tt>distances DOUBLE PRECISION[]</tt> - The distances between the columns</span></div> |
| <div class="line"><a name="l00215"></a><span class="lineno"> 215</span> <span class="comment"> * of \f$ M \f$ with indices in \c columns_ids and \f$ x \f$. That is,</span></div> |
| <div class="line"><a name="l00216"></a><span class="lineno"> 216</span> <span class="comment"> * <tt>distances[i]</tt> contains</span></div> |
| <div class="line"><a name="l00217"></a><span class="lineno"> 217</span> <span class="comment"> * \f$ \operatorname{dist}(\vec{m_j}, \vec x) \f$, where \f$ j = \f$</span></div> |
| <div class="line"><a name="l00218"></a><span class="lineno"> 218</span> <span class="comment"> * <tt>columns_ids[i]</tt>.</span></div> |
| <div class="line"><a name="l00219"></a><span class="lineno"> 219</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00220"></a><span class="lineno"> 220</span> CREATE FUNCTION MADLIB_SCHEMA.closest_columns(</div> |
| <div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  M DOUBLE PRECISION[][],</div> |
| <div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  x DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  num INTEGER,</div> |
| <div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  dist REGPROC /*+ DEFAULT '<a class="code" href="linalg_8sql__in.html#a00a08e69f27524f2096032214e15b668" title="Squared 2-norm of the difference between two vectors. ">squared_dist_norm2</a><span class="stringliteral">' */</span></div> |
| <div class="line"><a name="l00225"></a><span class="lineno"> 225</span> <span class="stringliteral">) RETURNS MADLIB_SCHEMA.closest_columns_result</span></div> |
| <div class="line"><a name="l00226"></a><span class="lineno"> 226</span> <span class="stringliteral">IMMUTABLE</span></div> |
| <div class="line"><a name="l00227"></a><span class="lineno"> 227</span> <span class="stringliteral">STRICT</span></div> |
| <div class="line"><a name="l00228"></a><span class="lineno"> 228</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00229"></a><span class="lineno"> 229</span> <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00230"></a><span class="lineno"> 230</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00231"></a><span class="lineno"> 231</span> <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.closest_columns(</span></div> |
| <div class="line"><a name="l00232"></a><span class="lineno"> 232</span> <span class="stringliteral"> M DOUBLE PRECISION[][],</span></div> |
| <div class="line"><a name="l00233"></a><span class="lineno"> 233</span> <span class="stringliteral"> x DOUBLE PRECISION[],</span></div> |
| <div class="line"><a name="l00234"></a><span class="lineno"> 234</span> <span class="stringliteral"> num INTEGER</span></div> |
| <div class="line"><a name="l00235"></a><span class="lineno"> 235</span> <span class="stringliteral">) RETURNS MADLIB_SCHEMA.closest_columns_result</span></div> |
| <div class="line"><a name="l00236"></a><span class="lineno"> 236</span> <span class="stringliteral">IMMUTABLE</span></div> |
| <div class="line"><a name="l00237"></a><span class="lineno"> 237</span> <span class="stringliteral">STRICT</span></div> |
| <div class="line"><a name="l00238"></a><span class="lineno"> 238</span> <span class="stringliteral">LANGUAGE sql</span></div> |
| <div class="line"><a name="l00239"></a><span class="lineno"> 239</span> <span class="stringliteral">AS $$</span></div> |
| <div class="line"><a name="l00240"></a><span class="lineno"> 240</span> <span class="stringliteral"> SELECT MADLIB_SCHEMA.closest_columns($1, $2, $3,</span></div> |
| <div class="line"><a name="l00241"></a><span class="lineno"> 241</span> <span class="stringliteral"> '</span>MADLIB_SCHEMA.squared_dist_norm2<span class="stringliteral">')</span></div> |
| <div class="line"><a name="l00242"></a><span class="lineno"><a class="code" href="linalg_8sql__in.html#ad3e16fc5435474b96b182ba20905461e"> 242</a></span> <span class="stringliteral">$$;</span></div> |
| <div class="line"><a name="l00243"></a><span class="lineno"> 243</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00244"></a><span class="lineno"> 244</span> <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.avg_vector_transition(</span></div> |
| <div class="line"><a name="l00245"></a><span class="lineno"> 245</span> <span class="stringliteral"> state DOUBLE PRECISION[],</span></div> |
| <div class="line"><a name="l00246"></a><span class="lineno"> 246</span> <span class="stringliteral"> x DOUBLE PRECISION[]</span></div> |
| <div class="line"><a name="l00247"></a><span class="lineno"> 247</span> <span class="stringliteral">) RETURNS DOUBLE PRECISION[]</span></div> |
| <div class="line"><a name="l00248"></a><span class="lineno"> 248</span> <span class="stringliteral">LANGUAGE c</span></div> |
| <div class="line"><a name="l00249"></a><span class="lineno"> 249</span> <span class="stringliteral">IMMUTABLE</span></div> |
| <div class="line"><a name="l00250"></a><span class="lineno"> 250</span> <span class="stringliteral">CALLED ON NULL INPUT</span></div> |
| <div class="line"><a name="l00251"></a><span class="lineno"> 251</span> <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00252"></a><span class="lineno"> 252</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00253"></a><span class="lineno"> 253</span> <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.avg_vector_merge(</span></div> |
| <div class="line"><a name="l00254"></a><span class="lineno"> 254</span> <span class="stringliteral"> state_left DOUBLE PRECISION[],</span></div> |
| <div class="line"><a name="l00255"></a><span class="lineno"> 255</span> <span class="stringliteral"> state_right DOUBLE PRECISION[]</span></div> |
| <div class="line"><a name="l00256"></a><span class="lineno"> 256</span> <span class="stringliteral">) RETURNS DOUBLE PRECISION[]</span></div> |
| <div class="line"><a name="l00257"></a><span class="lineno"> 257</span> <span class="stringliteral">LANGUAGE c</span></div> |
| <div class="line"><a name="l00258"></a><span class="lineno"> 258</span> <span class="stringliteral">IMMUTABLE</span></div> |
| <div class="line"><a name="l00259"></a><span class="lineno"> 259</span> <span class="stringliteral">STRICT</span></div> |
| <div class="line"><a name="l00260"></a><span class="lineno"> 260</span> <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00261"></a><span class="lineno"> 261</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00262"></a><span class="lineno"> 262</span> <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.avg_vector_final(</span></div> |
| <div class="line"><a name="l00263"></a><span class="lineno"> 263</span> <span class="stringliteral"> state DOUBLE PRECISION[]</span></div> |
| <div class="line"><a name="l00264"></a><span class="lineno"> 264</span> <span class="stringliteral">) RETURNS DOUBLE PRECISION[]</span></div> |
| <div class="line"><a name="l00265"></a><span class="lineno"> 265</span> <span class="stringliteral">LANGUAGE c</span></div> |
| <div class="line"><a name="l00266"></a><span class="lineno"> 266</span> <span class="stringliteral">IMMUTABLE</span></div> |
| <div class="line"><a name="l00267"></a><span class="lineno"> 267</span> <span class="stringliteral">STRICT</span></div> |
| <div class="line"><a name="l00268"></a><span class="lineno"> 268</span> <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00269"></a><span class="lineno"> 269</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00270"></a><span class="lineno"> 270</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00271"></a><span class="lineno"> 271</span> <span class="comment"> * @brief Compute the average of vectors</span></div> |
| <div class="line"><a name="l00272"></a><span class="lineno"> 272</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00273"></a><span class="lineno"> 273</span> <span class="comment"> * Given vectors \f$ x_1, \dots, x_n \f$, compute the average</span></div> |
| <div class="line"><a name="l00274"></a><span class="lineno"> 274</span> <span class="comment"> * \f$ \frac 1n \sum_{i=1}^n x_i \f$.</span></div> |
| <div class="line"><a name="l00275"></a><span class="lineno"> 275</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00276"></a><span class="lineno"> 276</span> <span class="comment"> * @param x Point \f$ x_i \f$</span></div> |
| <div class="line"><a name="l00277"></a><span class="lineno"> 277</span> <span class="comment"> * @returns Average \f$ \frac 1n \sum_{i=1}^n x_i \f$</span></div> |
| <div class="line"><a name="l00278"></a><span class="lineno"> 278</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00279"></a><span class="lineno"> 279</span> CREATE AGGREGATE MADLIB_SCHEMA.avg(</div> |
| <div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  /*+ x */ DOUBLE PRECISION[]</div> |
| <div class="line"><a name="l00281"></a><span class="lineno"> 281</span> ) (</div> |
| <div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  STYPE=DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  SFUNC=MADLIB_SCHEMA.avg_vector_transition,</div> |
| <div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  m4_ifdef(`__GREENPLUM__', `PREFUNC=MADLIB_SCHEMA.avg_vector_merge,<span class="stringliteral">')</span></div> |
| <div class="line"><a name="l00285"></a><span class="lineno"> 285</span> <span class="stringliteral"> FINALFUNC=MADLIB_SCHEMA.avg_vector_final,</span></div> |
| <div class="line"><a name="l00286"></a><span class="lineno"> 286</span> <span class="stringliteral"> INITCOND='</span>{0,0,0}<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00287"></a><span class="lineno"> 287</span> <span class="stringliteral">);</span></div> |
| <div class="line"><a name="l00288"></a><span class="lineno"> 288</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00289"></a><span class="lineno"> 289</span> <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.normalized_avg_vector_transition(</span></div> |
| <div class="line"><a name="l00290"></a><span class="lineno"> 290</span> <span class="stringliteral"> state DOUBLE PRECISION[],</span></div> |
| <div class="line"><a name="l00291"></a><span class="lineno"> 291</span> <span class="stringliteral"> x DOUBLE PRECISION[]</span></div> |
| <div class="line"><a name="l00292"></a><span class="lineno"> 292</span> <span class="stringliteral">) RETURNS DOUBLE PRECISION[]</span></div> |
| <div class="line"><a name="l00293"></a><span class="lineno"> 293</span> <span class="stringliteral">LANGUAGE c</span></div> |
| <div class="line"><a name="l00294"></a><span class="lineno"> 294</span> <span class="stringliteral">IMMUTABLE</span></div> |
| <div class="line"><a name="l00295"></a><span class="lineno"> 295</span> <span class="stringliteral">CALLED ON NULL INPUT</span></div> |
| <div class="line"><a name="l00296"></a><span class="lineno"> 296</span> <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00297"></a><span class="lineno"> 297</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00298"></a><span class="lineno"> 298</span> <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.normalized_avg_vector_final(</span></div> |
| <div class="line"><a name="l00299"></a><span class="lineno"> 299</span> <span class="stringliteral"> state DOUBLE PRECISION[]</span></div> |
| <div class="line"><a name="l00300"></a><span class="lineno"> 300</span> <span class="stringliteral">) RETURNS DOUBLE PRECISION[]</span></div> |
| <div class="line"><a name="l00301"></a><span class="lineno"><a class="code" href="linalg_8sql__in.html#a1aa37f73fb1cd8d7d106aa518dd8c0b4"> 301</a></span> <span class="stringliteral">LANGUAGE c</span></div> |
| <div class="line"><a name="l00302"></a><span class="lineno"> 302</span> <span class="stringliteral">IMMUTABLE</span></div> |
| <div class="line"><a name="l00303"></a><span class="lineno"> 303</span> <span class="stringliteral">STRICT</span></div> |
| <div class="line"><a name="l00304"></a><span class="lineno"> 304</span> <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00305"></a><span class="lineno"> 305</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00306"></a><span class="lineno"> 306</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00307"></a><span class="lineno"> 307</span> <span class="comment"> * @brief Compute the normalized average of vectors</span></div> |
| <div class="line"><a name="l00308"></a><span class="lineno"> 308</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00309"></a><span class="lineno"> 309</span> <span class="comment"> * Given vectors \f$ x_1, \dots, x_n \f$, define</span></div> |
| <div class="line"><a name="l00310"></a><span class="lineno"> 310</span> <span class="comment"> * \f$ \widetilde{x} := \frac 1n \sum_{i=1}^n \frac{x_i}{\| x_i \|} \f$, and</span></div> |
| <div class="line"><a name="l00311"></a><span class="lineno"> 311</span> <span class="comment"> * compute the normalized average</span></div> |
| <div class="line"><a name="l00312"></a><span class="lineno"> 312</span> <span class="comment"> * \f$ \frac{\widetilde{x}}{\| \widetilde{x} \|} \f$.</span></div> |
| <div class="line"><a name="l00313"></a><span class="lineno"> 313</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00314"></a><span class="lineno"> 314</span> <span class="comment"> * @param x Point \f$ x_i \f$</span></div> |
| <div class="line"><a name="l00315"></a><span class="lineno"> 315</span> <span class="comment"> * @returns Normalized average \f$ \frac{\widetilde{x}}{\| \widetilde{x} \|} \f$</span></div> |
| <div class="line"><a name="l00316"></a><span class="lineno"> 316</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00317"></a><span class="lineno"> 317</span> CREATE AGGREGATE MADLIB_SCHEMA.normalized_avg(</div> |
| <div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  /*+ x */ DOUBLE PRECISION[]</div> |
| <div class="line"><a name="l00319"></a><span class="lineno"> 319</span> ) (</div> |
| <div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  STYPE=DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  SFUNC=MADLIB_SCHEMA.normalized_avg_vector_transition,</div> |
| <div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  m4_ifdef(`__GREENPLUM__', `PREFUNC=MADLIB_SCHEMA.avg_vector_merge,<span class="stringliteral">')</span></div> |
| <div class="line"><a name="l00323"></a><span class="lineno"> 323</span> <span class="stringliteral"> FINALFUNC=MADLIB_SCHEMA.normalized_avg_vector_final,</span></div> |
| <div class="line"><a name="l00324"></a><span class="lineno"> 324</span> <span class="stringliteral"> INITCOND='</span>{0,0,0}<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00325"></a><span class="lineno"> 325</span> <span class="stringliteral">);</span></div> |
| <div class="line"><a name="l00326"></a><span class="lineno"> 326</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00327"></a><span class="lineno"> 327</span> <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.matrix_agg_transition(</span></div> |
| <div class="line"><a name="l00328"></a><span class="lineno"> 328</span> <span class="stringliteral"> state DOUBLE PRECISION[],</span></div> |
| <div class="line"><a name="l00329"></a><span class="lineno"> 329</span> <span class="stringliteral"> x DOUBLE PRECISION[]</span></div> |
| <div class="line"><a name="l00330"></a><span class="lineno"> 330</span> <span class="stringliteral">) RETURNS DOUBLE PRECISION[]</span></div> |
| <div class="line"><a name="l00331"></a><span class="lineno"> 331</span> <span class="stringliteral">LANGUAGE c</span></div> |
| <div class="line"><a name="l00332"></a><span class="lineno"> 332</span> <span class="stringliteral">IMMUTABLE</span></div> |
| <div class="line"><a name="l00333"></a><span class="lineno"> 333</span> <span class="stringliteral">STRICT</span></div> |
| <div class="line"><a name="l00334"></a><span class="lineno"> 334</span> <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00335"></a><span class="lineno"> 335</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00336"></a><span class="lineno"> 336</span> <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.matrix_agg_final(</span></div> |
| <div class="line"><a name="l00337"></a><span class="lineno"> 337</span> <span class="stringliteral"> state DOUBLE PRECISION[]</span></div> |
| <div class="line"><a name="l00338"></a><span class="lineno"> 338</span> <span class="stringliteral">) RETURNS DOUBLE PRECISION[]</span></div> |
| <div class="line"><a name="l00339"></a><span class="lineno"><a class="code" href="linalg_8sql__in.html#a0b04663ca206f03e66aed5ea2b4cc461"> 339</a></span> <span class="stringliteral">LANGUAGE c</span></div> |
| <div class="line"><a name="l00340"></a><span class="lineno"> 340</span> <span class="stringliteral">IMMUTABLE</span></div> |
| <div class="line"><a name="l00341"></a><span class="lineno"> 341</span> <span class="stringliteral">STRICT</span></div> |
| <div class="line"><a name="l00342"></a><span class="lineno"> 342</span> <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00343"></a><span class="lineno"> 343</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00344"></a><span class="lineno"> 344</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00345"></a><span class="lineno"> 345</span> <span class="comment"> * @brief Combine vectors to a matrix</span></div> |
| <div class="line"><a name="l00346"></a><span class="lineno"> 346</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00347"></a><span class="lineno"> 347</span> <span class="comment"> * Given vectors \f$ \vec x_1, \dots, \vec x_n \in \mathbb R^m \f$,</span></div> |
| <div class="line"><a name="l00348"></a><span class="lineno"> 348</span> <span class="comment"> * return matrix \f$ ( \vec x_1 \dots \vec x_n ) \in \mathbb R^{m \times n}\f$.</span></div> |
| <div class="line"><a name="l00349"></a><span class="lineno"> 349</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00350"></a><span class="lineno"> 350</span> <span class="comment"> * @param x Vector \f$ x_i \f$</span></div> |
| <div class="line"><a name="l00351"></a><span class="lineno"> 351</span> <span class="comment"> * @returns Matrix with columns \f$ x_1, \dots, x_n \f$</span></div> |
| <div class="line"><a name="l00352"></a><span class="lineno"> 352</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00353"></a><span class="lineno"> 353</span> CREATE</div> |
| <div class="line"><a name="l00354"></a><span class="lineno"> 354</span> m4_ifdef(`__GREENPLUM__', m4_ifdef(`__HAS_ORDERED_AGGREGATES__<span class="stringliteral">', `ORDERED'</span>))</div> |
| <div class="line"><a name="l00355"></a><span class="lineno"> 355</span> AGGREGATE MADLIB_SCHEMA.matrix_agg(</div> |
| <div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  <span class="comment">/*+ x */</span> DOUBLE PRECISION[]</div> |
| <div class="line"><a name="l00357"></a><span class="lineno"> 357</span> ) (</div> |
| <div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  STYPE=DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  SFUNC=MADLIB_SCHEMA.matrix_agg_transition,</div> |
| <div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  FINALFUNC=MADLIB_SCHEMA.matrix_agg_final,</div> |
| <div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  INITCOND=<span class="stringliteral">'{0,0,0}'</span></div> |
| <div class="line"><a name="l00362"></a><span class="lineno"> 362</span> );</div> |
| <div class="line"><a name="l00363"></a><span class="lineno"> 363</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00364"></a><span class="lineno"> 364</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00365"></a><span class="lineno"> 365</span> <span class="comment"> * @brief Return the column of a matrix</span></div> |
| <div class="line"><a name="l00366"></a><span class="lineno"> 366</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00367"></a><span class="lineno"> 367</span> <span class="comment"> * @param matrix Two-dimensional matrix</span></div> |
| <div class="line"><a name="l00368"></a><span class="lineno"> 368</span> <span class="comment"> * @param col Column of the matrix to return (0-based index)</span></div> |
| <div class="line"><a name="l00369"></a><span class="lineno"> 369</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00370"></a><span class="lineno"> 370</span> CREATE FUNCTION MADLIB_SCHEMA.matrix_column(</div> |
| <div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  matrix DOUBLE PRECISION[][],</div> |
| <div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  col INTEGER</div> |
| <div class="line"><a name="l00373"></a><span class="lineno"> 373</span> ) RETURNS DOUBLE PRECISION[]</div> |
| <div class="line"><a name="l00374"></a><span class="lineno"> 374</span> LANGUAGE c</div> |
| <div class="line"><a name="l00375"></a><span class="lineno"><a class="code" href="linalg_8sql__in.html#a9c439706f35d6cac89f151d553a5f111"> 375</a></span> IMMUTABLE</div> |
| <div class="line"><a name="l00376"></a><span class="lineno"> 376</span> STRICT</div> |
| <div class="line"><a name="l00377"></a><span class="lineno"> 377</span> AS <span class="stringliteral">'MODULE_PATHNAME'</span>;</div> |
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