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 <dl class="user"><dt><b>About:</b></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="user"><dt><b>Input:</b></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="user"><dt><b>Usage:</b></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="user"><dt><b>Examples:</b></dt><dd><ol type="1">
 <li>Construct matrix A according to structure: <div class="fragment"><pre class="fragment">sql&gt; SELECT * FROM data;
  row_num | row_val
 ---------+---------
        1 | {2,1}
        2 | {1,4}
 (2 rows)
 </pre></div></li>
 <li>Call conjugate gradient function: <div class="fragment"><pre class="fragment">sql&gt; SELECT <a class="code" href="conjugate__gradient_8sql__in.html#ab94e8a12cc9c2d0dac35168721ec8585" title="Compute conjugate gradient.">conjugate_gradient</a>(<span class="stringliteral">&#39;data&#39;</span>,<span class="stringliteral">&#39;row_val&#39;</span>,<span class="stringliteral">&#39;row_num&#39;</span>,<span class="stringliteral">&#39;{2,1}&#39;</span>,1E-6,1);
 INFO:  COMPUTE RESIDUAL ERROR 14.5655661859659
 INFO:  ERROR 0.144934004246004
 INFO:  ERROR 3.12963615962926e-31
 INFO:  TEST FINAL ERROR 2.90029642185163e-29
     <a class="code" href="conjugate__gradient_8sql__in.html#ab94e8a12cc9c2d0dac35168721ec8585" title="Compute conjugate gradient.">conjugate_gradient</a>
 ---------------------------
  {1,-1.31838984174237e-15}
 (1 row)
 </pre></div></li>
 </ol>
 </dd></dl>
 <dl class="user"><dt><b>Literature:</b></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="see"><dt><b>See also:</b></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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	<dl class="user"><dt><b>About:</b></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="user"><dt><b>Input:</b></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="user"><dt><b>Usage:</b></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="user"><dt><b>Examples:</b></dt><dd><ol type="1">
	<li>Construct matrix A according to structure: <div class="fragment"><pre class="fragment">sql> SELECT * FROM data;
	row_num \| row_val
	---------+---------
	1 \| {2,1}
	2 \| {1,4}
	(2 rows)
	</pre></div></li>
	<li>Call conjugate gradient function: <div class="fragment"><pre class="fragment">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);
	INFO: COMPUTE RESIDUAL ERROR 14.5655661859659
	INFO: ERROR 0.144934004246004
	INFO: ERROR 3.12963615962926e-31
	INFO: TEST FINAL ERROR 2.90029642185163e-29
	<a class="code" href="conjugate__gradient_8sql__in.html#ab94e8a12cc9c2d0dac35168721ec8585" title="Compute conjugate gradient.">conjugate_gradient</a>
	---------------------------
	{1,-1.31838984174237e-15}
	(1 row)
	</pre></div></li>
	</ol>
	</dd></dl>
	<dl class="user"><dt><b>Literature:</b></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="see"><dt><b>See also:</b></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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