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<title>MADlib: Conjugate Gradient</title>
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<div class="header">
  <div class="headertitle">
<div class="title">Conjugate Gradient<div class="ingroups"><a class="el" href="group__grp__early__stage.html">Early Stage Development</a></div></div>  </div>
</div><!--header-->
<div class="contents">
<div class="toc"><b>Contents</b> <ul>
<li>
<a href="#syntax">Function Syntax</a> </li>
<li>
<a href="#examples">Examples</a> </li>
<li>
<a href="#related">Related Topics</a> </li>
</ul>
</div><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>
<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
&#160;--------+---------
       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
&#160;--------------------------
 {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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