| <!-- HTML header for doxygen 1.8.4--> |
| <!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"/> |
| <meta http-equiv="X-UA-Compatible" content="IE=9"/> |
| <meta name="generator" content="Doxygen 1.8.13"/> |
| <meta name="keywords" content="madlib,postgres,greenplum,machine learning,data mining,deep learning,ensemble methods,data science,market basket analysis,affinity analysis,pca,lda,regression,elastic net,huber white,proportional hazards,k-means,latent dirichlet allocation,bayes,support vector machines,svm"/> |
| <title>MADlib: Arrays and Matrices</title> |
| <link href="tabs.css" rel="stylesheet" type="text/css"/> |
| <script type="text/javascript" src="jquery.js"></script> |
| <script type="text/javascript" src="dynsections.js"></script> |
| <link href="navtree.css" rel="stylesheet" type="text/css"/> |
| <script type="text/javascript" src="resize.js"></script> |
| <script type="text/javascript" src="navtreedata.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/searchdata.js"></script> |
| <script type="text/javascript" src="search/search.js"></script> |
| <script type="text/javascript"> |
| $(document).ready(function() { init_search(); }); |
| </script> |
| <script type="text/x-mathjax-config"> |
| MathJax.Hub.Config({ |
| extensions: ["tex2jax.js", "TeX/AMSmath.js", "TeX/AMSsymbols.js"], |
| jax: ["input/TeX","output/HTML-CSS"], |
| }); |
| </script><script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js"></script> |
| <!-- hack in the navigation tree --> |
| <script type="text/javascript" src="eigen_navtree_hacks.js"></script> |
| <link href="doxygen.css" rel="stylesheet" type="text/css" /> |
| <link href="madlib_extra.css" rel="stylesheet" type="text/css"/> |
| <!-- google analytics --> |
| <script> |
| (function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){ |
| (i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o), |
| m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m) |
| })(window,document,'script','//www.google-analytics.com/analytics.js','ga'); |
| ga('create', 'UA-45382226-1', 'madlib.apache.org'); |
| ga('send', 'pageview'); |
| </script> |
| </head> |
| <body> |
| <div id="top"><!-- do not remove this div, it is closed by doxygen! --> |
| <div id="titlearea"> |
| <table cellspacing="0" cellpadding="0"> |
| <tbody> |
| <tr style="height: 56px;"> |
| <td id="projectlogo"><a href="http://madlib.apache.org"><img alt="Logo" src="madlib.png" height="50" style="padding-left:0.5em;" border="0"/ ></a></td> |
| <td style="padding-left: 0.5em;"> |
| <div id="projectname"> |
| <span id="projectnumber">1.21.0</span> |
| </div> |
| <div id="projectbrief">User Documentation for Apache MADlib</div> |
| </td> |
| <td> <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> |
| </td> |
| </tr> |
| </tbody> |
| </table> |
| </div> |
| <!-- end header part --> |
| <!-- Generated by Doxygen 1.8.13 --> |
| <script type="text/javascript"> |
| var searchBox = new SearchBox("searchBox", "search",false,'Search'); |
| </script> |
| </div><!-- top --> |
| <div id="side-nav" class="ui-resizable side-nav-resizable"> |
| <div id="nav-tree"> |
| <div id="nav-tree-contents"> |
| <div id="nav-sync" class="sync"></div> |
| </div> |
| </div> |
| <div id="splitbar" style="-moz-user-select:none;" |
| class="ui-resizable-handle"> |
| </div> |
| </div> |
| <script type="text/javascript"> |
| $(document).ready(function(){initNavTree('group__grp__arraysmatrix.html','');}); |
| </script> |
| <div id="doc-content"> |
| <!-- window showing the filter options --> |
| <div id="MSearchSelectWindow" |
| onmouseover="return searchBox.OnSearchSelectShow()" |
| onmouseout="return searchBox.OnSearchSelectHide()" |
| onkeydown="return searchBox.OnSearchSelectKey(event)"> |
| </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> |
| |
| <div class="header"> |
| <div class="summary"> |
| <a href="#groups">Modules</a> </div> |
| <div class="headertitle"> |
| <div class="title">Arrays and Matrices<div class="ingroups"><a class="el" href="group__grp__datatrans.html">Data Types and Transformations</a></div></div> </div> |
| </div><!--header--> |
| <div class="contents"> |
| <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2> |
| <p>These modules provide basic mathematical operations to be run on array and matrices.</p> |
| <p>For a distributed system, a matrix cannot simply be represented as a 2D array of numbers in memory. <b>We provide two forms of distributed representation of a matrix</b>:</p> |
| <ul> |
| <li>Dense: The matrix is represented as a distributed collection of 1-D arrays. An example 3x10 matrix would be the below table: <pre> |
| row_id | row_vec |
| --------+------------------------- |
| 1 | {9,6,5,8,5,6,6,3,10,8} |
| 2 | {8,2,2,6,6,10,2,1,9,9} |
| 3 | {3,9,9,9,8,6,3,9,5,6} |
| </pre></li> |
| <li>Sparse: The matrix is represented using the row and column indices for each non-zero entry of the matrix. Example: <pre> |
| row_id | col_id | value |
| --------+--------+------- |
| 1 | 1 | 9 |
| 1 | 5 | 6 |
| 1 | 6 | 6 |
| 2 | 1 | 8 |
| 3 | 1 | 3 |
| 3 | 2 | 9 |
| 4 | 7 | 0 |
| (6 rows) |
| </pre>   All matrix operations work with either form of representation.</li> |
| </ul> |
| <p>In many cases, a matrix function can be <b>decomposed to vector operations applied independently on each row of a matrix (or corresponding rows of two matrices)</b>. We have also provided access to these internal vector operations (<a class="el" href="group__grp__array.html">Array Operations</a>) for greater flexibility. Matrix operations like <em>matrix_add</em> use the corresponding vector operation (<em>array_add</em>) and also include additional validation and formating. Other functions like <em>matrix_mult</em> are complex and use a combination of such vector operations and other SQL operations.</p> |
| <p><b>It's important to note</b> that these array functions are only available for the dense format representation of the matrix. In general, the scope of a single array function invocation is limited to only an array (1-dimensional or 2-dimensional) that fits in memory. When such function is executed on a table of arrays, the function is called multiple times - once for each array (or pair of arrays). On contrary, scope of a single matrix function invocation is the complete matrix stored as a distributed table. </p> |
| <table class="memberdecls"> |
| <tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="groups"></a> |
| Modules</h2></td></tr> |
| <tr class="memitem:group__grp__array"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__grp__array.html">Array Operations</a></td></tr> |
| <tr class="memdesc:group__grp__array"><td class="mdescLeft"> </td><td class="mdescRight">Provides fast array operations supporting other MADlib modules. <br /></td></tr> |
| <tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:group__grp__matrix"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__grp__matrix.html">Matrix Operations</a></td></tr> |
| <tr class="memdesc:group__grp__matrix"><td class="mdescLeft"> </td><td class="mdescRight">Provides fast matrix operations supporting other MADlib modules. <br /></td></tr> |
| <tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:group__grp__matrix__factorization"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__grp__matrix__factorization.html">Matrix Factorization</a></td></tr> |
| <tr class="memdesc:group__grp__matrix__factorization"><td class="mdescLeft"> </td><td class="mdescRight">Linear algebra methods that factorize a matrix into a product of matrices. <br /></td></tr> |
| <tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:group__grp__linalg"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__grp__linalg.html">Norms and Distance Functions</a></td></tr> |
| <tr class="memdesc:group__grp__linalg"><td class="mdescLeft"> </td><td class="mdescRight">Provides utility functions for basic linear algebra operations. <br /></td></tr> |
| <tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:group__grp__svec"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__grp__svec.html">Sparse Vectors</a></td></tr> |
| <tr class="memdesc:group__grp__svec"><td class="mdescLeft"> </td><td class="mdescRight">Implements a sparse vector data type that provides compressed storage of vectors that may have many duplicate elements. <br /></td></tr> |
| <tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr> |
| </table> |
| </div><!-- contents --> |
| </div><!-- doc-content --> |
| <!-- start footer part --> |
| <div id="nav-path" class="navpath"><!-- id is needed for treeview function! --> |
| <ul> |
| <li class="footer">Generated on Thu Feb 23 2023 19:26:36 for MADlib by |
| <a href="http://www.doxygen.org/index.html"> |
| <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.13 </li> |
| </ul> |
| </div> |
| </body> |
| </html> |
