| <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> |
| <html xmlns="http://www.w3.org/1999/xhtml"> |
| <head> |
| <meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/> |
| <title>MADlib: linalg.sql_in Source File</title> |
| |
| <link href="tabs.css" rel="stylesheet" type="text/css"/> |
| <link href="doxygen.css" rel="stylesheet" type="text/css" /> |
| <link href="navtree.css" rel="stylesheet" type="text/css"/> |
| <script type="text/javascript" src="jquery.js"></script> |
| <script type="text/javascript" src="resize.js"></script> |
| <script type="text/javascript" src="navtree.js"></script> |
| <script type="text/javascript"> |
| $(document).ready(initResizable); |
| </script> |
| <link href="search/search.css" rel="stylesheet" type="text/css"/> |
| <script type="text/javascript" src="search/search.js"></script> |
| <script type="text/javascript"> |
| $(document).ready(function() { searchBox.OnSelectItem(0); }); |
| </script> |
| <script src="../mathjax/MathJax.js"> |
| MathJax.Hub.Config({ |
| extensions: ["tex2jax.js", "TeX/AMSmath.js", "TeX/AMSsymbols.js"], |
| jax: ["input/TeX","output/HTML-CSS"], |
| }); |
| </script> |
| </head> |
| <body> |
| <div id="top"><!-- do not remove this div! --> |
| |
| |
| <div id="titlearea"> |
| <table cellspacing="0" cellpadding="0"> |
| <tbody> |
| <tr style="height: 56px;"> |
| |
| |
| <td style="padding-left: 0.5em;"> |
| <div id="projectname">MADlib |
|  <span id="projectnumber">0.6</span> <span style="font-size:10pt; font-style:italic"><a href="../latest/./linalg_8sql__in_source.html"> A newer version is available</a></span> |
| </div> |
| <div id="projectbrief">User Documentation</div> |
| </td> |
| |
| |
| |
| </tr> |
| </tbody> |
| </table> |
| </div> |
| |
| <!-- Generated by Doxygen 1.7.5.1 --> |
| <script type="text/javascript"> |
| var searchBox = new SearchBox("searchBox", "search",false,'Search'); |
| </script> |
| <script type="text/javascript" src="dynsections.js"></script> |
| <div id="navrow1" class="tabs"> |
| <ul class="tablist"> |
| <li><a href="index.html"><span>Main Page</span></a></li> |
| <li><a href="modules.html"><span>Modules</span></a></li> |
| <li class="current"><a href="files.html"><span>Files</span></a></li> |
| <li> |
| <div id="MSearchBox" class="MSearchBoxInactive"> |
| <span class="left"> |
| <img id="MSearchSelect" src="search/mag_sel.png" |
| onmouseover="return searchBox.OnSearchSelectShow()" |
| onmouseout="return searchBox.OnSearchSelectHide()" |
| alt=""/> |
| <input type="text" id="MSearchField" value="Search" accesskey="S" |
| onfocus="searchBox.OnSearchFieldFocus(true)" |
| onblur="searchBox.OnSearchFieldFocus(false)" |
| onkeyup="searchBox.OnSearchFieldChange(event)"/> |
| </span><span class="right"> |
| <a id="MSearchClose" href="javascript:searchBox.CloseResultsWindow()"><img id="MSearchCloseImg" border="0" src="search/close.png" alt=""/></a> |
| </span> |
| </div> |
| </li> |
| </ul> |
| </div> |
| <div id="navrow2" class="tabs2"> |
| <ul class="tablist"> |
| <li><a href="files.html"><span>File List</span></a></li> |
| <li><a href="globals.html"><span>File Members</span></a></li> |
| </ul> |
| </div> |
| </div> |
| <div id="side-nav" class="ui-resizable side-nav-resizable"> |
| <div id="nav-tree"> |
| <div id="nav-tree-contents"> |
| </div> |
| </div> |
| <div id="splitbar" style="-moz-user-select:none;" |
| class="ui-resizable-handle"> |
| </div> |
| </div> |
| <script type="text/javascript"> |
| initNavTree('linalg_8sql__in.html',''); |
| </script> |
| <div id="doc-content"> |
| <div class="header"> |
| <div class="headertitle"> |
| <div class="title">linalg.sql_in</div> </div> |
| </div> |
| <div class="contents"> |
| <a href="linalg_8sql__in.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">/* ----------------------------------------------------------------------- */</span><span class="comment">/**</span> |
| <a name="l00002"></a>00002 <span class="comment"> *</span> |
| <a name="l00003"></a>00003 <span class="comment"> * @file linalg.sql_in</span> |
| <a name="l00004"></a>00004 <span class="comment"> *</span> |
| <a name="l00005"></a>00005 <span class="comment"> * @brief SQL functions for linear algebra</span> |
| <a name="l00006"></a>00006 <span class="comment"> *</span> |
| <a name="l00007"></a>00007 <span class="comment"> * @sa For an overview of linear-algebra functions, see the module</span> |
| <a name="l00008"></a>00008 <span class="comment"> * description \ref grp_linalg.</span> |
| <a name="l00009"></a>00009 <span class="comment"> *</span> |
| <a name="l00010"></a>00010 <span class="comment"> */</span><span class="comment">/* ----------------------------------------------------------------------- */</span> |
| <a name="l00011"></a>00011 |
| <a name="l00012"></a>00012 m4_include(`SQLCommon.m4<span class="stringliteral">')</span> |
| <a name="l00013"></a>00013 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00014"></a>00014 <span class="comment">/**</span> |
| <a name="l00015"></a>00015 <span class="comment">@internal</span> |
| <a name="l00016"></a>00016 <span class="comment">@addtogroup grp_linalg</span> |
| <a name="l00017"></a>00017 <span class="comment"></span> |
| <a name="l00018"></a>00018 <span class="comment">@about</span> |
| <a name="l00019"></a>00019 <span class="comment"></span> |
| <a name="l00020"></a>00020 <span class="comment">Linear-algebra functions.</span> |
| <a name="l00021"></a>00021 <span class="comment"></span> |
| <a name="l00022"></a>00022 <span class="comment">@sa File linalg.sql_in documenting the SQL functions.</span> |
| <a name="l00023"></a>00023 <span class="comment">*/</span> |
| <a name="l00024"></a>00024 <span class="comment"></span> |
| <a name="l00025"></a>00025 <span class="comment">/**</span> |
| <a name="l00026"></a>00026 <span class="comment"> * @brief 1-norm of a vector</span> |
| <a name="l00027"></a>00027 <span class="comment"> *</span> |
| <a name="l00028"></a>00028 <span class="comment"> * @param x Vector \f$ \vec x = (x_1, \dots, x_n) \f$</span> |
| <a name="l00029"></a>00029 <span class="comment"> * @return \f$ \| x \|_1 = \sum_{i=1}^n |x_i| \f$</span> |
| <a name="l00030"></a>00030 <span class="comment"> */</span> |
| <a name="l00031"></a>00031 CREATE FUNCTION MADLIB_SCHEMA.norm1( |
| <a name="l00032"></a>00032 x DOUBLE PRECISION[] |
| <a name="l00033"></a>00033 ) RETURNS DOUBLE PRECISION |
| <a name="l00034"></a>00034 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00035"></a>00035 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00036"></a>00036 <span class="stringliteral">IMMUTABLE</span> |
| <a name="l00037"></a>00037 <span class="stringliteral">STRICT;</span> |
| <a name="l00038"></a>00038 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00039"></a>00039 <span class="comment">/**</span> |
| <a name="l00040"></a>00040 <span class="comment"> * @brief 2-norm of a vector</span> |
| <a name="l00041"></a>00041 <span class="comment"> *</span> |
| <a name="l00042"></a>00042 <span class="comment"> * @param x Vector \f$ \vec x = (x_1, \dots, x_n) \f$</span> |
| <a name="l00043"></a>00043 <span class="comment"> * @return \f$ \| x \|_2 = \sqrt{\sum_{i=1}^n x_i^2} \f$</span> |
| <a name="l00044"></a>00044 <span class="comment"> */</span> |
| <a name="l00045"></a>00045 CREATE FUNCTION MADLIB_SCHEMA.norm2( |
| <a name="l00046"></a>00046 x DOUBLE PRECISION[] |
| <a name="l00047"></a>00047 ) RETURNS DOUBLE PRECISION |
| <a name="l00048"></a>00048 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00049"></a>00049 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00050"></a>00050 <span class="stringliteral">IMMUTABLE</span> |
| <a name="l00051"></a>00051 <span class="stringliteral">STRICT;</span> |
| <a name="l00052"></a>00052 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00053"></a><a class="code" href="linalg_8sql__in.html#a300300fe4b8576ba0b97b95d8dea3057">00053</a> <span class="comment">/**</span> |
| <a name="l00054"></a>00054 <span class="comment"> * @brief 1-norm of the difference between two vectors</span> |
| <a name="l00055"></a>00055 <span class="comment"> *</span> |
| <a name="l00056"></a>00056 <span class="comment"> * @param x Vector \f$ \vec x = (x_1, \dots, x_n) \f$</span> |
| <a name="l00057"></a>00057 <span class="comment"> * @param y Vector \f$ \vec y = (y_1, \dots, y_n) \f$</span> |
| <a name="l00058"></a>00058 <span class="comment"> * @return \f$ \| x - y \|_1 = \sum_{i=1}^n |x_i - y_i| \f$</span> |
| <a name="l00059"></a>00059 <span class="comment"> */</span> |
| <a name="l00060"></a>00060 CREATE FUNCTION MADLIB_SCHEMA.dist_norm1( |
| <a name="l00061"></a>00061 x DOUBLE PRECISION[], |
| <a name="l00062"></a>00062 y DOUBLE PRECISION[] |
| <a name="l00063"></a>00063 ) RETURNS DOUBLE PRECISION |
| <a name="l00064"></a>00064 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00065"></a>00065 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00066"></a>00066 <span class="stringliteral">IMMUTABLE</span> |
| <a name="l00067"></a><a class="code" href="linalg_8sql__in.html#a50fdfe30cc0edc6888a909dbb4b4c239">00067</a> <span class="stringliteral">STRICT;</span> |
| <a name="l00068"></a>00068 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00069"></a>00069 <span class="comment">/**</span> |
| <a name="l00070"></a>00070 <span class="comment"> * @brief 2-norm of the difference between two vectors</span> |
| <a name="l00071"></a>00071 <span class="comment"> *</span> |
| <a name="l00072"></a>00072 <span class="comment"> * @param x Vector \f$ \vec x = (x_1, \dots, x_n) \f$</span> |
| <a name="l00073"></a>00073 <span class="comment"> * @param y Vector \f$ \vec y = (y_1, \dots, y_n) \f$</span> |
| <a name="l00074"></a>00074 <span class="comment"> * @return \f$ \| x - y \|_2 = \sqrt{\sum_{i=1}^n (x_i - y_i)^2} \f$</span> |
| <a name="l00075"></a>00075 <span class="comment"> */</span> |
| <a name="l00076"></a>00076 CREATE FUNCTION MADLIB_SCHEMA.dist_norm2( |
| <a name="l00077"></a>00077 x DOUBLE PRECISION[], |
| <a name="l00078"></a>00078 y DOUBLE PRECISION[] |
| <a name="l00079"></a>00079 ) RETURNS DOUBLE PRECISION |
| <a name="l00080"></a>00080 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00081"></a>00081 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00082"></a><a class="code" href="linalg_8sql__in.html#aad193850e79c4b9d811ca9bc53e13476">00082</a> <span class="stringliteral">IMMUTABLE</span> |
| <a name="l00083"></a>00083 <span class="stringliteral">STRICT;</span> |
| <a name="l00084"></a>00084 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00085"></a>00085 <span class="comment">/**</span> |
| <a name="l00086"></a>00086 <span class="comment"> * @brief Squared 2-norm of the difference between two vectors</span> |
| <a name="l00087"></a>00087 <span class="comment"> *</span> |
| <a name="l00088"></a>00088 <span class="comment"> * @param x Vector \f$ \vec x = (x_1, \dots, x_n) \f$</span> |
| <a name="l00089"></a>00089 <span class="comment"> * @param y Vector \f$ \vec y = (y_1, \dots, y_n) \f$</span> |
| <a name="l00090"></a>00090 <span class="comment"> * @return \f$ \| x - y \|_2^2 = \sum_{i=1}^n (x_i - y_i)^2 \f$</span> |
| <a name="l00091"></a>00091 <span class="comment"> */</span> |
| <a name="l00092"></a>00092 CREATE FUNCTION MADLIB_SCHEMA.squared_dist_norm2( |
| <a name="l00093"></a>00093 x DOUBLE PRECISION[], |
| <a name="l00094"></a>00094 y DOUBLE PRECISION[] |
| <a name="l00095"></a>00095 ) RETURNS DOUBLE PRECISION |
| <a name="l00096"></a>00096 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00097"></a>00097 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00098"></a><a class="code" href="linalg_8sql__in.html#aa58e51526edea6ea98db30b6f250adb4">00098</a> <span class="stringliteral">IMMUTABLE</span> |
| <a name="l00099"></a>00099 <span class="stringliteral">STRICT;</span> |
| <a name="l00100"></a>00100 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00101"></a>00101 <span class="comment">/**</span> |
| <a name="l00102"></a>00102 <span class="comment"> * @brief Angle between two vectors</span> |
| <a name="l00103"></a>00103 <span class="comment"> *</span> |
| <a name="l00104"></a>00104 <span class="comment"> * @param x Vector \f$ \vec x = (x_1, \dots, x_n) \f$</span> |
| <a name="l00105"></a>00105 <span class="comment"> * @param y Vector \f$ \vec y = (y_1, \dots, y_n) \f$</span> |
| <a name="l00106"></a>00106 <span class="comment"> * @return \f$ \arccos\left(\frac{\langle \vec x, \vec y \rangle}</span> |
| <a name="l00107"></a>00107 <span class="comment"> * {\| \vec x \| \cdot \| \vec y \|}\right) \f$</span> |
| <a name="l00108"></a>00108 <span class="comment"> */</span> |
| <a name="l00109"></a>00109 CREATE FUNCTION MADLIB_SCHEMA.dist_angle( |
| <a name="l00110"></a>00110 x DOUBLE PRECISION[], |
| <a name="l00111"></a>00111 y DOUBLE PRECISION[] |
| <a name="l00112"></a>00112 ) RETURNS DOUBLE PRECISION |
| <a name="l00113"></a>00113 AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00114"></a><a class="code" href="linalg_8sql__in.html#a00a08e69f27524f2096032214e15b668">00114</a> <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00115"></a>00115 <span class="stringliteral">IMMUTABLE</span> |
| <a name="l00116"></a>00116 <span class="stringliteral">STRICT;</span> |
| <a name="l00117"></a>00117 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00118"></a>00118 <span class="comment">/**</span> |
| <a name="l00119"></a>00119 <span class="comment"> * @brief Tanimoto distance between two vectors</span> |
| <a name="l00120"></a>00120 <span class="comment"> *</span> |
| <a name="l00121"></a>00121 <span class="comment"> * @param x Vector \f$ \vec x = (x_1, \dots, x_n) \f$</span> |
| <a name="l00122"></a>00122 <span class="comment"> * @param y Vector \f$ \vec y = (y_1, \dots, y_n) \f$</span> |
| <a name="l00123"></a>00123 <span class="comment"> * @return \f$ 1 - \frac{\langle \vec x, \vec y \rangle}</span> |
| <a name="l00124"></a>00124 <span class="comment"> * {\| \vec x \|^2 \cdot \| \vec y \|^2</span> |
| <a name="l00125"></a>00125 <span class="comment"> * - \langle \vec x, \vec y \rangle} \f$</span> |
| <a name="l00126"></a>00126 <span class="comment"> */</span> |
| <a name="l00127"></a>00127 CREATE FUNCTION MADLIB_SCHEMA.dist_tanimoto( |
| <a name="l00128"></a>00128 x DOUBLE PRECISION[], |
| <a name="l00129"></a>00129 y DOUBLE PRECISION[] |
| <a name="l00130"></a>00130 ) RETURNS DOUBLE PRECISION |
| <a name="l00131"></a><a class="code" href="linalg_8sql__in.html#a8c7b9281a72ff22caf06161701b27e84">00131</a> AS 'MODULE_PATHNAME<span class="stringliteral">'</span> |
| <a name="l00132"></a>00132 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00133"></a>00133 <span class="stringliteral">IMMUTABLE</span> |
| <a name="l00134"></a>00134 <span class="stringliteral">STRICT;</span> |
| <a name="l00135"></a>00135 <span class="stringliteral"></span> |
| <a name="l00136"></a>00136 <span class="stringliteral">/*</span> |
| <a name="l00137"></a>00137 <span class="stringliteral"> * @brief closest_column return type</span> |
| <a name="l00138"></a>00138 <span class="stringliteral"> */</span> |
| <a name="l00139"></a>00139 <span class="stringliteral">CREATE TYPE MADLIB_SCHEMA.closest_column_result AS (</span> |
| <a name="l00140"></a>00140 <span class="stringliteral"> column_id INTEGER,</span> |
| <a name="l00141"></a>00141 <span class="stringliteral"> distance DOUBLE PRECISION</span> |
| <a name="l00142"></a>00142 <span class="stringliteral">);</span> |
| <a name="l00143"></a>00143 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00144"></a>00144 <span class="comment">/**</span> |
| <a name="l00145"></a>00145 <span class="comment"> * @brief Given matrix \f$ M \f$ and vector \f$ \vec x \f$ compute the column</span> |
| <a name="l00146"></a>00146 <span class="comment"> * of \f$ M \f$ that is closest to \f$ \vec x \f$</span> |
| <a name="l00147"></a>00147 <span class="comment"> *</span> |
| <a name="l00148"></a>00148 <span class="comment"> * @param M Matrix \f$ M = (\vec{m_0} \dots \vec{m_{l-1}})</span> |
| <a name="l00149"></a><a class="code" href="linalg_8sql__in.html#afa13b4c6122b99422d666dedea136c18">00149</a> <span class="comment"> * \in \mathbb{R}^{k \times l} \f$</span> |
| <a name="l00150"></a>00150 <span class="comment"> * @param x Vector \f$ \vec x \in \mathbb R^k \f$</span> |
| <a name="l00151"></a>00151 <span class="comment"> * @param dist The metric \f$ \operatorname{dist} \f$. This needs to be a</span> |
| <a name="l00152"></a>00152 <span class="comment"> * function with signature</span> |
| <a name="l00153"></a>00153 <span class="comment"> * <tt>DOUBLE PRECISION[] x DOUBLE PRECISION[] -> DOUBLE PRECISION</tt>.</span> |
| <a name="l00154"></a>00154 <span class="comment"> *</span> |
| <a name="l00155"></a>00155 <span class="comment"> * @returns A composite value:</span> |
| <a name="l00156"></a>00156 <span class="comment"> * - <tt>columns_id INTEGER</tt> - The 0-based index of the column of \f$ M \f$</span> |
| <a name="l00157"></a>00157 <span class="comment"> * that is closest to \f$ x \f$. In case of ties, the first such index is</span> |
| <a name="l00158"></a>00158 <span class="comment"> * returned. That is, \c columns_id is the minimum element in the set</span> |
| <a name="l00159"></a>00159 <span class="comment"> * \f$ \arg\min_{i=0,\dots,l-1} \operatorname{dist}(\vec{m_i}, \vec x) \f$.</span> |
| <a name="l00160"></a>00160 <span class="comment"> * - <tt>distance DOUBLE PRECISION</tt> - The minimum distance between any</span> |
| <a name="l00161"></a>00161 <span class="comment"> * column of \f$ M \f$ and \f$ x \f$. That is,</span> |
| <a name="l00162"></a>00162 <span class="comment"> * \f$ \min_{i=0,\dots,l-1} \operatorname{dist}(\vec{m_i}, \vec x) \f$.</span> |
| <a name="l00163"></a>00163 <span class="comment"> */</span> |
| <a name="l00164"></a>00164 CREATE FUNCTION MADLIB_SCHEMA.closest_column( |
| <a name="l00165"></a>00165 M DOUBLE PRECISION[][], |
| <a name="l00166"></a>00166 x DOUBLE PRECISION[], |
| <a name="l00167"></a>00167 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> |
| <a name="l00168"></a>00168 <span class="stringliteral">) RETURNS MADLIB_SCHEMA.closest_column_result</span> |
| <a name="l00169"></a>00169 <span class="stringliteral">IMMUTABLE</span> |
| <a name="l00170"></a>00170 <span class="stringliteral">STRICT</span> |
| <a name="l00171"></a>00171 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00172"></a>00172 <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">';</span> |
| <a name="l00173"></a>00173 <span class="stringliteral"></span> |
| <a name="l00174"></a>00174 <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.closest_column(</span> |
| <a name="l00175"></a>00175 <span class="stringliteral"> M DOUBLE PRECISION[][],</span> |
| <a name="l00176"></a>00176 <span class="stringliteral"> x DOUBLE PRECISION[]</span> |
| <a name="l00177"></a>00177 <span class="stringliteral">) RETURNS MADLIB_SCHEMA.closest_column_result</span> |
| <a name="l00178"></a>00178 <span class="stringliteral">IMMUTABLE</span> |
| <a name="l00179"></a>00179 <span class="stringliteral">STRICT</span> |
| <a name="l00180"></a>00180 <span class="stringliteral">LANGUAGE sql</span> |
| <a name="l00181"></a>00181 <span class="stringliteral">AS $$</span> |
| <a name="l00182"></a>00182 <span class="stringliteral"> SELECT MADLIB_SCHEMA.closest_column($1, $2,</span> |
| <a name="l00183"></a>00183 <span class="stringliteral"> '</span>MADLIB_SCHEMA.squared_dist_norm2<span class="stringliteral">')</span> |
| <a name="l00184"></a>00184 <span class="stringliteral">$$;</span> |
| <a name="l00185"></a>00185 <span class="stringliteral"></span> |
| <a name="l00186"></a><a class="code" href="linalg_8sql__in.html#aa2856d10fa6cb12a5b168bab217197ed">00186</a> <span class="stringliteral">/*</span> |
| <a name="l00187"></a>00187 <span class="stringliteral"> * @brief closest_columns return type</span> |
| <a name="l00188"></a>00188 <span class="stringliteral"> */</span> |
| <a name="l00189"></a>00189 <span class="stringliteral">CREATE TYPE MADLIB_SCHEMA.closest_columns_result AS (</span> |
| <a name="l00190"></a>00190 <span class="stringliteral"> column_ids INTEGER[],</span> |
| <a name="l00191"></a>00191 <span class="stringliteral"> distances DOUBLE PRECISION[]</span> |
| <a name="l00192"></a>00192 <span class="stringliteral">);</span> |
| <a name="l00193"></a>00193 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00194"></a>00194 <span class="comment">/**</span> |
| <a name="l00195"></a>00195 <span class="comment"> * @brief Given matrix \f$ M \f$ and vector \f$ \vec x \f$ compute the columns</span> |
| <a name="l00196"></a>00196 <span class="comment"> * of \f$ M \f$ that are closest to \f$ \vec x \f$</span> |
| <a name="l00197"></a>00197 <span class="comment"> *</span> |
| <a name="l00198"></a>00198 <span class="comment"> * This function does essentially the same as \ref closest_column(), except that</span> |
| <a name="l00199"></a>00199 <span class="comment"> * it allows to specify the number of closest columns to return. The return</span> |
| <a name="l00200"></a>00200 <span class="comment"> * value is a composite value:</span> |
| <a name="l00201"></a>00201 <span class="comment"> * - <tt>columns_ids INTEGER[]</tt> - The 0-based indices of the \c num columns</span> |
| <a name="l00202"></a>00202 <span class="comment"> * of \f$ M \f$ that are closest to \f$ x \f$. In case of ties, the first</span> |
| <a name="l00203"></a>00203 <span class="comment"> * such indices are returned.</span> |
| <a name="l00204"></a>00204 <span class="comment"> * - <tt>distances DOUBLE PRECISION[]</tt> - The distances between the columns</span> |
| <a name="l00205"></a>00205 <span class="comment"> * of \f$ M \f$ with indices in \c columns_ids and \f$ x \f$. That is,</span> |
| <a name="l00206"></a>00206 <span class="comment"> * <tt>distances[i]</tt> contains</span> |
| <a name="l00207"></a>00207 <span class="comment"> * \f$ \operatorname{dist}(\vec{m_j}, \vec x) \f$, where \f$ j = \f$</span> |
| <a name="l00208"></a>00208 <span class="comment"> * <tt>columns_ids[i]</tt>.</span> |
| <a name="l00209"></a>00209 <span class="comment"> */</span> |
| <a name="l00210"></a>00210 CREATE FUNCTION MADLIB_SCHEMA.closest_columns( |
| <a name="l00211"></a>00211 M DOUBLE PRECISION[][], |
| <a name="l00212"></a>00212 x DOUBLE PRECISION[], |
| <a name="l00213"></a>00213 num INTEGER, |
| <a name="l00214"></a>00214 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> |
| <a name="l00215"></a>00215 <span class="stringliteral">) RETURNS MADLIB_SCHEMA.closest_columns_result</span> |
| <a name="l00216"></a>00216 <span class="stringliteral">IMMUTABLE</span> |
| <a name="l00217"></a>00217 <span class="stringliteral">STRICT</span> |
| <a name="l00218"></a>00218 <span class="stringliteral">LANGUAGE C</span> |
| <a name="l00219"></a>00219 <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">';</span> |
| <a name="l00220"></a>00220 <span class="stringliteral"></span> |
| <a name="l00221"></a>00221 <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.closest_columns(</span> |
| <a name="l00222"></a>00222 <span class="stringliteral"> M DOUBLE PRECISION[][],</span> |
| <a name="l00223"></a>00223 <span class="stringliteral"> x DOUBLE PRECISION[],</span> |
| <a name="l00224"></a>00224 <span class="stringliteral"> num INTEGER</span> |
| <a name="l00225"></a>00225 <span class="stringliteral">) RETURNS MADLIB_SCHEMA.closest_columns_result</span> |
| <a name="l00226"></a>00226 <span class="stringliteral">IMMUTABLE</span> |
| <a name="l00227"></a>00227 <span class="stringliteral">STRICT</span> |
| <a name="l00228"></a>00228 <span class="stringliteral">LANGUAGE sql</span> |
| <a name="l00229"></a>00229 <span class="stringliteral">AS $$</span> |
| <a name="l00230"></a>00230 <span class="stringliteral"> SELECT MADLIB_SCHEMA.closest_columns($1, $2, $3,</span> |
| <a name="l00231"></a>00231 <span class="stringliteral"> '</span>MADLIB_SCHEMA.squared_dist_norm2<span class="stringliteral">')</span> |
| <a name="l00232"></a><a class="code" href="linalg_8sql__in.html#ad3e16fc5435474b96b182ba20905461e">00232</a> <span class="stringliteral">$$;</span> |
| <a name="l00233"></a>00233 <span class="stringliteral"></span> |
| <a name="l00234"></a>00234 <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.avg_vector_transition(</span> |
| <a name="l00235"></a>00235 <span class="stringliteral"> state DOUBLE PRECISION[],</span> |
| <a name="l00236"></a>00236 <span class="stringliteral"> x DOUBLE PRECISION[]</span> |
| <a name="l00237"></a>00237 <span class="stringliteral">) RETURNS DOUBLE PRECISION[]</span> |
| <a name="l00238"></a>00238 <span class="stringliteral">LANGUAGE c</span> |
| <a name="l00239"></a>00239 <span class="stringliteral">IMMUTABLE</span> |
| <a name="l00240"></a>00240 <span class="stringliteral">CALLED ON NULL INPUT</span> |
| <a name="l00241"></a>00241 <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">';</span> |
| <a name="l00242"></a>00242 <span class="stringliteral"></span> |
| <a name="l00243"></a>00243 <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.avg_vector_merge(</span> |
| <a name="l00244"></a>00244 <span class="stringliteral"> state_left DOUBLE PRECISION[],</span> |
| <a name="l00245"></a>00245 <span class="stringliteral"> state_right DOUBLE PRECISION[]</span> |
| <a name="l00246"></a>00246 <span class="stringliteral">) RETURNS DOUBLE PRECISION[]</span> |
| <a name="l00247"></a>00247 <span class="stringliteral">LANGUAGE c</span> |
| <a name="l00248"></a>00248 <span class="stringliteral">IMMUTABLE</span> |
| <a name="l00249"></a>00249 <span class="stringliteral">STRICT</span> |
| <a name="l00250"></a>00250 <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">';</span> |
| <a name="l00251"></a>00251 <span class="stringliteral"></span> |
| <a name="l00252"></a>00252 <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.avg_vector_final(</span> |
| <a name="l00253"></a>00253 <span class="stringliteral"> state DOUBLE PRECISION[]</span> |
| <a name="l00254"></a>00254 <span class="stringliteral">) RETURNS DOUBLE PRECISION[]</span> |
| <a name="l00255"></a>00255 <span class="stringliteral">LANGUAGE c</span> |
| <a name="l00256"></a>00256 <span class="stringliteral">IMMUTABLE</span> |
| <a name="l00257"></a>00257 <span class="stringliteral">STRICT</span> |
| <a name="l00258"></a>00258 <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">';</span> |
| <a name="l00259"></a>00259 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00260"></a>00260 <span class="comment">/**</span> |
| <a name="l00261"></a>00261 <span class="comment"> * @brief Compute the average of vectors</span> |
| <a name="l00262"></a>00262 <span class="comment"> *</span> |
| <a name="l00263"></a>00263 <span class="comment"> * Given vectors \f$ x_1, \dots, x_n \f$, compute the average</span> |
| <a name="l00264"></a>00264 <span class="comment"> * \f$ \frac 1n \sum_{i=1}^n x_i \f$.</span> |
| <a name="l00265"></a>00265 <span class="comment"> *</span> |
| <a name="l00266"></a>00266 <span class="comment"> * @param x Point \f$ x_i \f$</span> |
| <a name="l00267"></a>00267 <span class="comment"> * @returns Average \f$ \frac 1n \sum_{i=1}^n x_i \f$</span> |
| <a name="l00268"></a>00268 <span class="comment"> */</span> |
| <a name="l00269"></a>00269 CREATE AGGREGATE MADLIB_SCHEMA.avg( |
| <a name="l00270"></a>00270 /*+ x */ DOUBLE PRECISION[] |
| <a name="l00271"></a>00271 ) ( |
| <a name="l00272"></a>00272 STYPE=DOUBLE PRECISION[], |
| <a name="l00273"></a>00273 SFUNC=MADLIB_SCHEMA.avg_vector_transition, |
| <a name="l00274"></a>00274 m4_ifdef(`__GREENPLUM__', `PREFUNC=MADLIB_SCHEMA.avg_vector_merge,<span class="stringliteral">')</span> |
| <a name="l00275"></a>00275 <span class="stringliteral"> FINALFUNC=MADLIB_SCHEMA.avg_vector_final,</span> |
| <a name="l00276"></a>00276 <span class="stringliteral"> INITCOND='</span>{0,0,0}<span class="stringliteral">'</span> |
| <a name="l00277"></a>00277 <span class="stringliteral">);</span> |
| <a name="l00278"></a>00278 <span class="stringliteral"></span> |
| <a name="l00279"></a>00279 <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.normalized_avg_vector_transition(</span> |
| <a name="l00280"></a>00280 <span class="stringliteral"> state DOUBLE PRECISION[],</span> |
| <a name="l00281"></a>00281 <span class="stringliteral"> x DOUBLE PRECISION[]</span> |
| <a name="l00282"></a>00282 <span class="stringliteral">) RETURNS DOUBLE PRECISION[]</span> |
| <a name="l00283"></a>00283 <span class="stringliteral">LANGUAGE c</span> |
| <a name="l00284"></a>00284 <span class="stringliteral">IMMUTABLE</span> |
| <a name="l00285"></a>00285 <span class="stringliteral">CALLED ON NULL INPUT</span> |
| <a name="l00286"></a>00286 <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">';</span> |
| <a name="l00287"></a>00287 <span class="stringliteral"></span> |
| <a name="l00288"></a>00288 <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.normalized_avg_vector_final(</span> |
| <a name="l00289"></a>00289 <span class="stringliteral"> state DOUBLE PRECISION[]</span> |
| <a name="l00290"></a>00290 <span class="stringliteral">) RETURNS DOUBLE PRECISION[]</span> |
| <a name="l00291"></a><a class="code" href="linalg_8sql__in.html#a1aa37f73fb1cd8d7d106aa518dd8c0b4">00291</a> <span class="stringliteral">LANGUAGE c</span> |
| <a name="l00292"></a>00292 <span class="stringliteral">IMMUTABLE</span> |
| <a name="l00293"></a>00293 <span class="stringliteral">STRICT</span> |
| <a name="l00294"></a>00294 <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">';</span> |
| <a name="l00295"></a>00295 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00296"></a>00296 <span class="comment">/**</span> |
| <a name="l00297"></a>00297 <span class="comment"> * @brief Compute the normalized average of vectors</span> |
| <a name="l00298"></a>00298 <span class="comment"> *</span> |
| <a name="l00299"></a>00299 <span class="comment"> * Given vectors \f$ x_1, \dots, x_n \f$, define</span> |
| <a name="l00300"></a>00300 <span class="comment"> * \f$ \widetilde{x} := \frac 1n \sum_{i=1}^n \frac{x_i}{\| x_i \|} \f$, and</span> |
| <a name="l00301"></a>00301 <span class="comment"> * compute the normalized average</span> |
| <a name="l00302"></a>00302 <span class="comment"> * \f$ \frac{\widetilde{x}}{\| \widetilde{x} \|} \f$.</span> |
| <a name="l00303"></a>00303 <span class="comment"> *</span> |
| <a name="l00304"></a>00304 <span class="comment"> * @param x Point \f$ x_i \f$</span> |
| <a name="l00305"></a>00305 <span class="comment"> * @returns Normalized average \f$ \frac{\widetilde{x}}{\| \widetilde{x} \|} \f$</span> |
| <a name="l00306"></a>00306 <span class="comment"> */</span> |
| <a name="l00307"></a>00307 CREATE AGGREGATE MADLIB_SCHEMA.normalized_avg( |
| <a name="l00308"></a>00308 /*+ x */ DOUBLE PRECISION[] |
| <a name="l00309"></a>00309 ) ( |
| <a name="l00310"></a>00310 STYPE=DOUBLE PRECISION[], |
| <a name="l00311"></a>00311 SFUNC=MADLIB_SCHEMA.normalized_avg_vector_transition, |
| <a name="l00312"></a>00312 m4_ifdef(`__GREENPLUM__', `PREFUNC=MADLIB_SCHEMA.avg_vector_merge,<span class="stringliteral">')</span> |
| <a name="l00313"></a>00313 <span class="stringliteral"> FINALFUNC=MADLIB_SCHEMA.normalized_avg_vector_final,</span> |
| <a name="l00314"></a>00314 <span class="stringliteral"> INITCOND='</span>{0,0,0}<span class="stringliteral">'</span> |
| <a name="l00315"></a>00315 <span class="stringliteral">);</span> |
| <a name="l00316"></a>00316 <span class="stringliteral"></span> |
| <a name="l00317"></a>00317 <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.matrix_agg_transition(</span> |
| <a name="l00318"></a>00318 <span class="stringliteral"> state DOUBLE PRECISION[],</span> |
| <a name="l00319"></a>00319 <span class="stringliteral"> x DOUBLE PRECISION[]</span> |
| <a name="l00320"></a>00320 <span class="stringliteral">) RETURNS DOUBLE PRECISION[]</span> |
| <a name="l00321"></a>00321 <span class="stringliteral">LANGUAGE c</span> |
| <a name="l00322"></a>00322 <span class="stringliteral">IMMUTABLE</span> |
| <a name="l00323"></a>00323 <span class="stringliteral">STRICT</span> |
| <a name="l00324"></a>00324 <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">';</span> |
| <a name="l00325"></a>00325 <span class="stringliteral"></span> |
| <a name="l00326"></a>00326 <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.matrix_agg_final(</span> |
| <a name="l00327"></a>00327 <span class="stringliteral"> state DOUBLE PRECISION[]</span> |
| <a name="l00328"></a>00328 <span class="stringliteral">) RETURNS DOUBLE PRECISION[]</span> |
| <a name="l00329"></a><a class="code" href="linalg_8sql__in.html#a0b04663ca206f03e66aed5ea2b4cc461">00329</a> <span class="stringliteral">LANGUAGE c</span> |
| <a name="l00330"></a>00330 <span class="stringliteral">IMMUTABLE</span> |
| <a name="l00331"></a>00331 <span class="stringliteral">STRICT</span> |
| <a name="l00332"></a>00332 <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">';</span> |
| <a name="l00333"></a>00333 <span class="stringliteral"></span><span class="comment"></span> |
| <a name="l00334"></a>00334 <span class="comment">/**</span> |
| <a name="l00335"></a>00335 <span class="comment"> * @brief Combine vectors to a matrix</span> |
| <a name="l00336"></a>00336 <span class="comment"> *</span> |
| <a name="l00337"></a>00337 <span class="comment"> * Given vectors \f$ \vec x_1, \dots, \vec x_n \in \mathbb R^m \f$,</span> |
| <a name="l00338"></a>00338 <span class="comment"> * return matrix \f$ ( \vec x_1 \dots \vec x_n ) \in \mathbb R^{m \times n}\f$.</span> |
| <a name="l00339"></a>00339 <span class="comment"> *</span> |
| <a name="l00340"></a>00340 <span class="comment"> * @param x Vector \f$ x_i \f$</span> |
| <a name="l00341"></a>00341 <span class="comment"> * @returns Matrix with columns \f$ x_1, \dots, x_n \f$</span> |
| <a name="l00342"></a>00342 <span class="comment"> */</span> |
| <a name="l00343"></a>00343 CREATE |
| <a name="l00344"></a>00344 m4_ifdef(`__GREENPLUM__', m4_ifdef(`__HAS_ORDERED_AGGREGATES__<span class="stringliteral">', `ORDERED'</span>)) |
| <a name="l00345"></a>00345 AGGREGATE MADLIB_SCHEMA.matrix_agg( |
| <a name="l00346"></a>00346 <span class="comment">/*+ x */</span> DOUBLE PRECISION[] |
| <a name="l00347"></a>00347 ) ( |
| <a name="l00348"></a>00348 STYPE=DOUBLE PRECISION[], |
| <a name="l00349"></a>00349 SFUNC=MADLIB_SCHEMA.matrix_agg_transition, |
| <a name="l00350"></a>00350 FINALFUNC=MADLIB_SCHEMA.matrix_agg_final, |
| <a name="l00351"></a>00351 INITCOND=<span class="stringliteral">'{0,0,0}'</span> |
| <a name="l00352"></a>00352 ); |
| <a name="l00353"></a>00353 <span class="comment"></span> |
| <a name="l00354"></a>00354 <span class="comment">/**</span> |
| <a name="l00355"></a>00355 <span class="comment"> * @brief Return the column of a matrix</span> |
| <a name="l00356"></a>00356 <span class="comment"> *</span> |
| <a name="l00357"></a>00357 <span class="comment"> * @param matrix Two-dimensional matrix</span> |
| <a name="l00358"></a>00358 <span class="comment"> * @param col Column of the matrix to return (0-based index)</span> |
| <a name="l00359"></a>00359 <span class="comment"> */</span> |
| <a name="l00360"></a>00360 CREATE FUNCTION MADLIB_SCHEMA.matrix_column( |
| <a name="l00361"></a>00361 matrix DOUBLE PRECISION[][], |
| <a name="l00362"></a>00362 col INTEGER |
| <a name="l00363"></a>00363 ) RETURNS DOUBLE PRECISION[] |
| <a name="l00364"></a>00364 LANGUAGE c |
| <a name="l00365"></a><a class="code" href="linalg_8sql__in.html#a9c439706f35d6cac89f151d553a5f111">00365</a> IMMUTABLE |
| <a name="l00366"></a>00366 STRICT |
| <a name="l00367"></a>00367 AS <span class="stringliteral">'MODULE_PATHNAME'</span>; |
| </pre></div></div> |
| </div> |
| <div id="nav-path" class="navpath"> |
| <ul> |
| <li class="navelem"><a class="el" href="linalg_8sql__in.html">linalg.sql_in</a> </li> |
| <!-- window showing the filter options --> |
| <div id="MSearchSelectWindow" |
| onmouseover="return searchBox.OnSearchSelectShow()" |
| onmouseout="return searchBox.OnSearchSelectHide()" |
| onkeydown="return searchBox.OnSearchSelectKey(event)"> |
| <a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(0)"><span class="SelectionMark"> </span>All</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(1)"><span class="SelectionMark"> </span>Files</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(2)"><span class="SelectionMark"> </span>Functions</a></div> |
| |
| <!-- iframe showing the search results (closed by default) --> |
| <div id="MSearchResultsWindow"> |
| <iframe src="javascript:void(0)" frameborder="0" |
| name="MSearchResults" id="MSearchResults"> |
| </iframe> |
| </div> |
| |
| |
| <li class="footer">Generated on Tue Apr 2 2013 14:57:03 for MADlib by |
| <a href="http://www.doxygen.org/index.html"> |
| <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.7.5.1 </li> |
| </ul> |
| </div> |
| |
| |
| </body> |
| </html> |
