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| <span id="projectnumber">1.14</span> |
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| <div id="projectbrief">User Documentation for Apache MADlib</div> |
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| <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"> |
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| 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">Matrix Factorization methods including Singular Value Decomposition and Low-rank Matrix Factorization. <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> |
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