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| <a href="svdmf_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 svdmf.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 SVD Matrix Factorization</span></div> |
| <div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> * @date January 2011</span></div> |
| <div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> * @sa For a brief introduction to SVD Matrix Factorization, see the module</span></div> |
| <div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"> * description \ref grp_svdmf.</span></div> |
| <div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment"> */</span><span class="comment">/* ----------------------------------------------------------------------- */</span></div> |
| <div class="line"><a name="l00012"></a><span class="lineno"> 12</span> </div> |
| <div class="line"><a name="l00013"></a><span class="lineno"> 13</span> m4_include(`SQLCommon.m4<span class="stringliteral">')</span></div> |
| <div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment">@addtogroup grp_svdmf </span></div> |
| <div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment">@about</span></div> |
| <div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment">This module implements "partial SVD decomposition" method for representing a sparse matrix using a low-rank approximation.</span></div> |
| <div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment">Mathematically, this algorithm seeks to find matrices U and V that, for any given A, minimizes:\n</span></div> |
| <div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment">\f[ ||\boldsymbol A - \boldsymbol UV ||_2 </span></div> |
| <div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment">\f]</span></div> |
| <div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment">subject to \f$ rank(\boldsymbol UV) \leq k \f$, where \f$ ||\cdot||_2 \f$ denotes the Frobenius norm and \f$ k \leq rank(\boldsymbol A)\f$.</span></div> |
| <div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment">If A is \f$ m \times n \f$, then U will be \f$ m \times k \f$ and V will be \f$ k \times n \f$.</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">This algorithm is not intended to do the full decomposition, or to be used as part of</span></div> |
| <div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment">inverse procedure. It effectively computes the SVD of a low-rank approximation of A (preferably sparse), with the singular values absorbed in U and V. </span></div> |
| <div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment">Code is based on the write-up as appears at [1], with some modifications.</span></div> |
| <div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">@input</span></div> |
| <div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment">The <b>input matrix</b> is expected to be of the following form:</span></div> |
| <div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment"><pre>{TABLE|VIEW} <em>input_table</em> (</span></div> |
| <div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment"> <em>col_num</em> INTEGER,</span></div> |
| <div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment"> <em>row_num</em> INTEGER,</span></div> |
| <div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment"> <em>value</em> FLOAT </span></div> |
| <div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment">)</pre></span></div> |
| <div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment">Input is contained in a table where column number and row number for each cell</span></div> |
| <div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">are sequential; that is to say that if the data was written as a matrix, those values would be the</span></div> |
| <div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment">actual row and column numbers and not some random identifiers. All rows and columns must be associated with a value.</span></div> |
| <div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment">There should not be any missing row, columns or values.</span></div> |
| <div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="comment">@usage</span></div> |
| <div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="comment">The SVD function is called as follows:</span></div> |
| <div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment"><pre>SELECT \ref svdmf_run( '<em>input_table</em>', '<em>col_name</em>',</span></div> |
| <div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment"> '<em>row_name</em>', '<em>value</em>', <em>num_features</em>);</pre></span></div> |
| <div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment">The function returns two tables \c matrix_u and \c matrix_v, which represent the matrices U and V in table format.</span></div> |
| <div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment">@examp</span></div> |
| <div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="comment">-# Prepare an input table/view:</span></div> |
| <div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="comment">\code</span></div> |
| <div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment">CREATE TABLE svd_test (</span></div> |
| <div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="comment"> col INT,</span></div> |
| <div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="comment"> row INT,</span></div> |
| <div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="comment"> val FLOAT</span></div> |
| <div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="comment">);</span></div> |
| <div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="comment">\endcode </span></div> |
| <div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="comment">-# Populate the input table with some data. e.g.:</span></div> |
| <div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="comment">\code</span></div> |
| <div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="comment">sql> INSERT INTO svd_test SELECT (g.a%1000)+1, g.a/1000+1, random() FROM generate_series(1,1000) AS g(a);</span></div> |
| <div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="comment">\endcode </span></div> |
| <div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="comment">-# Call svdmf_run() stored procedure, e.g.: </span></div> |
| <div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="comment">\code</span></div> |
| <div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="comment">sql> select madlib.svdmf_run( 'svd_test', 'col', 'row', 'val', 3);</span></div> |
| <div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="comment">\endcode</span></div> |
| <div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="comment">-# Sample Output:</span></div> |
| <div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="comment">\code</span></div> |
| <div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="comment">INFO: ('Started svdmf_run() with parameters:',)</span></div> |
| <div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="comment">INFO: (' * input_matrix = madlib_svdsparse_test.test',)</span></div> |
| <div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="comment">INFO: (' * col_name = col_num',)</span></div> |
| <div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="comment">INFO: (' * row_name = row_num',)</span></div> |
| <div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="comment">INFO: (' * value = val',)</span></div> |
| <div class="line"><a name="l00076"></a><span class="lineno"> 76</span> <span class="comment">INFO: (' * num_features = 3',)</span></div> |
| <div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="comment">INFO: ('Copying the source data into a temporary table...',)</span></div> |
| <div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="comment">INFO: ('Estimating feature: 1',)</span></div> |
| <div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="comment">INFO: ('...Iteration 1: residual_error = 33345014611.1, step_size = 4.9997500125e-10, min_improvement = 1.0',)</span></div> |
| <div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="comment">INFO: ('...Iteration 2: residual_error = 33345014557.6, step_size = 5.49972501375e-10, min_improvement = 1.0',)</span></div> |
| <div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="comment">INFO: ('...Iteration 3: residual_error = 33345014054.3, step_size = 6.04969751512e-10, min_improvement = 1.0',)</span></div> |
| <div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="comment">...</span></div> |
| <div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="comment">INFO: ('...Iteration 78: residual_error = 2.02512133868, step_size = 5.78105354457e-10, min_improvement = 1.0',)</span></div> |
| <div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="comment">INFO: ('...Iteration 79: residual_error = 0.893810181282, step_size = 6.35915889903e-10, min_improvement = 1.0',)</span></div> |
| <div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="comment">INFO: ('...Iteration 80: residual_error = 0.34496773222, step_size = 6.99507478893e-10, min_improvement = 1.0',)</span></div> |
| <div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <span class="comment">INFO: ('Swapping residual error matrix...',)</span></div> |
| <div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="comment"> svdmf_run </span></div> |
| <div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="comment">--------------------------------------------------------------------------------------------</span></div> |
| <div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <span class="comment"> </span></div> |
| <div class="line"><a name="l00090"></a><span class="lineno"> 90</span> <span class="comment"> Finished SVD matrix factorisation for madlib_svdsparse_test.test (row_num, col_num, val). </span></div> |
| <div class="line"><a name="l00091"></a><span class="lineno"> 91</span> <span class="comment"> Results: </span></div> |
| <div class="line"><a name="l00092"></a><span class="lineno"> 92</span> <span class="comment"> * total error = 0.34496773222</span></div> |
| <div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="comment"> * number of estimated features = 1</span></div> |
| <div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="comment"> Output:</span></div> |
| <div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <span class="comment"> * table : madlib.matrix_u</span></div> |
| <div class="line"><a name="l00096"></a><span class="lineno"> 96</span> <span class="comment"> * table : madlib.matrix_v</span></div> |
| <div class="line"><a name="l00097"></a><span class="lineno"> 97</span> <span class="comment"> Time elapsed: 4 minutes 47.86839 seconds.</span></div> |
| <div class="line"><a name="l00098"></a><span class="lineno"> 98</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00099"></a><span class="lineno"> 99</span> <span class="comment">\endcode</span></div> |
| <div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00101"></a><span class="lineno"> 101</span> <span class="comment">@literature</span></div> |
| <div class="line"><a name="l00102"></a><span class="lineno"> 102</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00103"></a><span class="lineno"> 103</span> <span class="comment">[1] Simon Funk, Netflix Update: Try This at Home, December 11 2006,</span></div> |
| <div class="line"><a name="l00104"></a><span class="lineno"> 104</span> <span class="comment"> http://sifter.org/~simon/journal/20061211.html</span></div> |
| <div class="line"><a name="l00105"></a><span class="lineno"> 105</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00106"></a><span class="lineno"> 106</span> <span class="comment">@sa File svdmf.sql_in documenting the SQL functions.</span></div> |
| <div class="line"><a name="l00107"></a><span class="lineno"> 107</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00108"></a><span class="lineno"> 108</span> <span class="comment">@internal</span></div> |
| <div class="line"><a name="l00109"></a><span class="lineno"> 109</span> <span class="comment">@sa namespace svdmf (documenting the implementation in Python)</span></div> |
| <div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="comment">@endinternal </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">*/</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">/**</span></div> |
| <div class="line"><a name="l00115"></a><span class="lineno"> 115</span> <span class="comment"> * @brief Partial SVD decomposition of a sparse matrix into U and V components</span></div> |
| <div class="line"><a name="l00116"></a><span class="lineno"> 116</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00117"></a><span class="lineno"> 117</span> <span class="comment"> * This function takes as input the table representation of a sparse matrix and</span></div> |
| <div class="line"><a name="l00118"></a><span class="lineno"> 118</span> <span class="comment"> * decomposes it into the specified set of most significant features of matrices</span></div> |
| <div class="line"><a name="l00119"></a><span class="lineno"> 119</span> <span class="comment"> * of U and V matrix. </span></div> |
| <div class="line"><a name="l00120"></a><span class="lineno"> 120</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00121"></a><span class="lineno"> 121</span> <span class="comment"> * @param input_table Name of the table/view with the source data</span></div> |
| <div class="line"><a name="l00122"></a><span class="lineno"> 122</span> <span class="comment"> * @param col_name Name of the column containing cell column number</span></div> |
| <div class="line"><a name="l00123"></a><span class="lineno"> 123</span> <span class="comment"> * @param row_name Name of the column containing cell row number</span></div> |
| <div class="line"><a name="l00124"></a><span class="lineno"> 124</span> <span class="comment"> * @param value Name of the column containing cell value</span></div> |
| <div class="line"><a name="l00125"></a><span class="lineno"> 125</span> <span class="comment"> * @param num_features Rank of desired approximation</span></div> |
| <div class="line"><a name="l00126"></a><span class="lineno"> 126</span> <span class="comment"> * </span></div> |
| <div class="line"><a name="l00127"></a><span class="lineno"> 127</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00128"></a><span class="lineno"> 128</span> CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.svdmf_run(</div> |
| <div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  input_table TEXT, col_name TEXT, row_name TEXT, value TEXT, num_features INT</div> |
| <div class="line"><a name="l00130"></a><span class="lineno"> 130</span> )</div> |
| <div class="line"><a name="l00131"></a><span class="lineno"> 131</span> RETURNS TEXT</div> |
| <div class="line"><a name="l00132"></a><span class="lineno"> 132</span> AS $$</div> |
| <div class="line"><a name="l00133"></a><span class="lineno"> 133</span> </div> |
| <div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  PythonFunctionBodyOnly(`svd_mf', `svdmf<span class="stringliteral">')</span></div> |
| <div class="line"><a name="l00135"></a><span class="lineno"> 135</span> <span class="stringliteral"> </span></div> |
| <div class="line"><a name="l00136"></a><span class="lineno"> 136</span> <span class="stringliteral"> # schema_madlib comes from PythonFunctionBodyOnly</span></div> |
| <div class="line"><a name="l00137"></a><span class="lineno"> 137</span> <span class="stringliteral"> return svdmf.svdmf_run( schema_madlib, input_table, col_name, row_name, value, num_features);</span></div> |
| <div class="line"><a name="l00138"></a><span class="lineno"> 138</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00139"></a><span class="lineno"> 139</span> <span class="stringliteral">$$ LANGUAGE plpythonu;</span></div> |
| <div class="line"><a name="l00140"></a><span class="lineno"> 140</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00141"></a><span class="lineno"> 141</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00142"></a><span class="lineno"> 142</span> <span class="comment"> * @brief Partial SVD decomposition of a sparse matrix into U and V components</span></div> |
| <div class="line"><a name="l00143"></a><span class="lineno"> 143</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00144"></a><span class="lineno"> 144</span> <span class="comment"> * This function takes as input the table representation of a sparse matrix and</span></div> |
| <div class="line"><a name="l00145"></a><span class="lineno"> 145</span> <span class="comment"> * decomposes it into the specified set of most significant features of matrices</span></div> |
| <div class="line"><a name="l00146"></a><span class="lineno"> 146</span> <span class="comment"> * of U and V matrix. </span></div> |
| <div class="line"><a name="l00147"></a><span class="lineno"> 147</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00148"></a><span class="lineno"> 148</span> <span class="comment"> * @param input_table Name of the table/view with the source data</span></div> |
| <div class="line"><a name="l00149"></a><span class="lineno"> 149</span> <span class="comment"> * @param col_name Name of the column containing cell column number</span></div> |
| <div class="line"><a name="l00150"></a><span class="lineno"><a class="code" href="svdmf_8sql__in.html#a6cff34415cca23aa0a826cc08a6283f5"> 150</a></span> <span class="comment"> * @param row_name Name of the column containing cell row number</span></div> |
| <div class="line"><a name="l00151"></a><span class="lineno"> 151</span> <span class="comment"> * @param value Name of the column containing cell value</span></div> |
| <div class="line"><a name="l00152"></a><span class="lineno"> 152</span> <span class="comment"> * @param num_features Rank of desired approximation</span></div> |
| <div class="line"><a name="l00153"></a><span class="lineno"> 153</span> <span class="comment"> * @param num_iterations Maximum number if iterations to perform regardless of convergence</span></div> |
| <div class="line"><a name="l00154"></a><span class="lineno"> 154</span> <span class="comment"> * @param min_error Acceptable level of error in convergence.</span></div> |
| <div class="line"><a name="l00155"></a><span class="lineno"> 155</span> <span class="comment"> * </span></div> |
| <div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00157"></a><span class="lineno"> 157</span> </div> |
| <div class="line"><a name="l00158"></a><span class="lineno"> 158</span> CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.svdmf_run(</div> |
| <div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  input_table TEXT, col_name TEXT, row_name TEXT, value TEXT, num_features INT, num_iterations INT, min_error FLOAT</div> |
| <div class="line"><a name="l00160"></a><span class="lineno"> 160</span> )</div> |
| <div class="line"><a name="l00161"></a><span class="lineno"> 161</span> RETURNS TEXT</div> |
| <div class="line"><a name="l00162"></a><span class="lineno"> 162</span> AS $$</div> |
| <div class="line"><a name="l00163"></a><span class="lineno"> 163</span> </div> |
| <div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  PythonFunctionBodyOnly(`svd_mf', `svdmf<span class="stringliteral">')</span></div> |
| <div class="line"><a name="l00165"></a><span class="lineno"> 165</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00166"></a><span class="lineno"> 166</span> <span class="stringliteral"> # schema_madlib comes from PythonFunctionBodyOnly</span></div> |
| <div class="line"><a name="l00167"></a><span class="lineno"> 167</span> <span class="stringliteral"> return svdmf.svdmf_run_full( schema_madlib, input_table, col_name, row_name, value, num_features, num_iterations, min_error);</span></div> |
| <div class="line"><a name="l00168"></a><span class="lineno"> 168</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00169"></a><span class="lineno"> 169</span> <span class="stringliteral">$$ LANGUAGE plpythonu;</span></div> |
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