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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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| <dl class="section warning"><dt>Warning</dt><dd><em> This MADlib method is still in early stage development. There may be some issues that will be addressed in a future version. Interface and implementation is subject to change. </em></dd></dl> |
| <dl class="section user"><dt>About:</dt><dd>This function uses the iterative conjugate gradient method [1] to find a solution to the function: <p class="formulaDsp"> |
| \[ \boldsymbol Ax = \boldsymbol b \] |
| </p> |
| where \( \boldsymbol A \) is a symmetric, positive definite matrix and \(x\) and \( \boldsymbol b \) are vectors.</dd></dl> |
| <dl class="section user"><dt>Input:</dt><dd>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: <pre>{TABLE|VIEW} <em>matrix_A</em> ( |
| <em>row_number</em> FLOAT, |
| <em>row_values</em> FLOAT[], |
| )</pre> The number of elements in each row should be the same.</dd></dl> |
| <p>\( \boldsymbol b \) is passed as a FLOAT[] to the function.</p> |
| <dl class="section user"><dt>Usage:</dt><dd>Conjugate gradient can be called as follows: <pre>SELECT <a class="el" href="conjugate__gradient_8sql__in.html#ab94e8a12cc9c2d0dac35168721ec8585">conjugate_gradient</a>('<em>table_name</em>', |
| '<em>name_of_row_values_col</em>', '<em>name_of_row_number_col</em>', '<em>aray_of_b_values</em>', |
| '<em>desired_precision</em>');</pre> Function returns x as an array.</dd></dl> |
| <dl class="section user"><dt>Examples:</dt><dd><ol type="1"> |
| <li>Construct matrix A according to structure: <div class="fragment"><div class="line">sql> SELECT * FROM data;</div> |
| <div class="line"> row_num | row_val </div> |
| <div class="line">---------+---------</div> |
| <div class="line"> 1 | {2,1}</div> |
| <div class="line"> 2 | {1,4}</div> |
| <div class="line">(2 rows)</div> |
| </div><!-- fragment --></li> |
| <li>Call conjugate gradient function: <div class="fragment"><div class="line">sql> SELECT <a class="code" href="conjugate__gradient_8sql__in.html#ab94e8a12cc9c2d0dac35168721ec8585" title="Compute conjugate gradient. ">conjugate_gradient</a>(<span class="stringliteral">'data'</span>,<span class="stringliteral">'row_val'</span>,<span class="stringliteral">'row_num'</span>,<span class="stringliteral">'{2,1}'</span>,1E-6,1);</div> |
| <div class="line">INFO: COMPUTE RESIDUAL ERROR 14.5655661859659</div> |
| <div class="line">INFO: ERROR 0.144934004246004</div> |
| <div class="line">INFO: ERROR 3.12963615962926e-31</div> |
| <div class="line">INFO: TEST FINAL ERROR 2.90029642185163e-29</div> |
| <div class="line"> <a class="code" href="conjugate__gradient_8sql__in.html#ab94e8a12cc9c2d0dac35168721ec8585" title="Compute conjugate gradient. ">conjugate_gradient</a> </div> |
| <div class="line">---------------------------</div> |
| <div class="line"> {1,-1.31838984174237e-15}</div> |
| <div class="line">(1 row)</div> |
| </div><!-- fragment --></li> |
| </ol> |
| </dd></dl> |
| <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> |
| <dl class="section see"><dt>See Also</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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