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| <div class="title">Conjugate Gradient<div class="ingroups"><a class="el" href="group__grp__early__stage.html">Early Stage Development</a></div></div> </div> |
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| <div class="toc"><b>Contents</b> <ul> |
| <li> |
| <a href="#syntax">Function Syntax</a> </li> |
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| <a href="#examples">Examples</a> </li> |
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| </div><dl class="section warning"><dt>Warning</dt><dd><em> This MADlib method is still in early stage development. Interface and implementation are subject to change. </em></dd></dl> |
| <p>This function uses the iterative conjugate gradient method [1] to find a solution to the function: </p><p class="formulaDsp"> |
| \[ \boldsymbol Ax = \boldsymbol b \] |
| </p> |
| <p> where \( \boldsymbol A \) is a symmetric, positive definite matrix and \(x\) and \( \boldsymbol b \) are vectors.</p> |
| <p><a class="anchor" id="syntax"></a></p><dl class="section user"><dt>Function Syntax</dt><dd>Conjugate gradient returns x as an array. It has the following syntax.</dd></dl> |
| <pre class="syntax"> |
| conjugate_gradient( table_name, |
| name_of_row_values_col, |
| name_of_row_number_col, |
| aray_of_b_values, |
| desired_precision |
| ) |
| </pre><p>Matrix \( \boldsymbol A \) is assumed to be stored in a table where each row consists of at least two columns: array containing values of a given row, row number: </p><pre>{TABLE|VIEW} <em>matrix_A</em> ( |
| <em>row_number</em> FLOAT, |
| <em>row_values</em> FLOAT[], |
| )</pre><p> The number of elements in each row should be the same.</p> |
| <p>\( \boldsymbol b \) is passed as a FLOAT[] to the function.</p> |
| <p><a class="anchor" id="examples"></a></p><dl class="section user"><dt>Examples</dt><dd><ol type="1"> |
| <li>Construct matrix A according to structure. <pre class="example"> |
| SELECT * FROM data; |
| </pre> Result: <pre class="result"> |
| row_num | row_val |
|  --------+--------- |
| 1 | {2,1} |
| 2 | {1,4} |
| (2 rows) |
| </pre></li> |
| <li>Call the conjugate gradient function. <pre class="example"> |
| SELECT conjugate_gradient( 'data', |
| 'row_val', |
| 'row_num', |
| '{2,1}', |
| 1E-6,1 |
| ); |
| </pre> <pre class="result"> |
| INFO: COMPUTE RESIDUAL ERROR 14.5655661859659 |
| INFO: ERROR 0.144934004246004 |
| INFO: ERROR 3.12963615962926e-31 |
| INFO: TEST FINAL ERROR 2.90029642185163e-29 |
| conjugate_gradient |
|  -------------------------- |
| {1,-1.31838984174237e-15} |
| (1 row) |
| </pre></li> |
| </ol> |
| </dd></dl> |
| <p><a class="anchor" id="literature"></a></p><dl class="section user"><dt>Literature</dt><dd>[1] "Conjugate gradient method" Wikipedia - <a href="http://en.wikipedia.org/wiki/Conjugate_gradient_method">http://en.wikipedia.org/wiki/Conjugate_gradient_method</a></dd></dl> |
| <p><a class="anchor" id="related"></a></p><dl class="section user"><dt>Related Topics</dt><dd>File <a class="el" href="conjugate__gradient_8sql__in.html" title="SQL function computing Conjugate Gradient. ">conjugate_gradient.sql_in</a> documenting the SQL function. </dd></dl> |
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