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 <p>SQL functions for logistic regression.
 <a href="#details">More...</a></p>

 <p><a href="logistic_8sql__in_source.html">Go to the source code of this file.</a></p>
 <table class="memberdecls">
 <tr><td colspan="2"><h2><a name="func-members"></a>
 Functions</h2></td></tr>
 <tr><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="logistic_8sql__in.html#a32880a39de2e36b6c6be72691a6a4a40">logregr_train</a> (varchar tbl_source, varchar tbl_output, varchar dep_col, varchar ind_col, varchar grouping_col, integer max_iter, varchar optimizer, float8 tolerance, boolean verbose)</td></tr>
 <tr><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute logistic-regression coefficients and diagnostic statistics.  <a href="#a32880a39de2e36b6c6be72691a6a4a40"></a><br/></td></tr>
 <tr><td class="memItemLeft" align="right" valign="top">float8&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="logistic_8sql__in.html#a4ded9be5c8b111dbb3109efaad83d69e">logistic</a> (float8 x)</td></tr>
 <tr><td class="mdescLeft">&#160;</td><td class="mdescRight">Evaluate the usual logistic function in an under-/overflow-safe way.  <a href="#a4ded9be5c8b111dbb3109efaad83d69e"></a><br/></td></tr>
 </table>
 <hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
 <div class="textblock"><dl class="date"><dt><b>Date:</b></dt><dd>January 2011</dd></dl>
 <dl class="see"><dt><b>See also:</b></dt><dd>For a brief introduction to <a class="el" href="logistic_8sql__in.html#a4ded9be5c8b111dbb3109efaad83d69e" title="Evaluate the usual logistic function in an under-/overflow-safe way.">logistic</a> regression, see the module description <a class="el" href="group__grp__logreg.html">Logistic Regression</a>. </dd></dl>

 <p>Definition in file <a class="el" href="logistic_8sql__in_source.html">logistic.sql_in</a>.</p>
 </div><hr/><h2>Function Documentation</h2>
 <a class="anchor" id="a4ded9be5c8b111dbb3109efaad83d69e"></a><!-- doxytag: member="logistic.sql_in::logistic" ref="a4ded9be5c8b111dbb3109efaad83d69e" args="(float8 x)" -->
 <div class="memitem">
 <div class="memproto">
       <table class="memname">
         <tr>
           <td class="memname">float8 logistic </td>
           <td>(</td>
           <td class="paramtype">float8&#160;</td>
           <td class="paramname"><em>x</em></td><td>)</td>
           <td></td>
         </tr>
       </table>
 </div>
 <div class="memdoc">
 <dl><dt><b>Parameters:</b></dt><dd>
   <table class="params">
     <tr><td class="paramname">x</td><td></td></tr>
   </table>
   </dd>
 </dl>
 <dl class="return"><dt><b>Returns:</b></dt><dd>\( \frac{1}{1 + \exp(-x)} \)</dd></dl>
 <p>Evaluating this expression directly can lead to under- or overflows. This function performs the evaluation in a safe manner, making use of the following observations:</p>
 <p>In order for the outcome of \( \exp(x) \) to be within the range of the minimum positive double-precision number (i.e., \( 2^{-1074} \)) and the maximum positive double-precision number (i.e., \( (1 + (1 - 2^{52})) * 2^{1023}) \), \( x \) has to be within the natural logarithm of these numbers, so roughly in between -744 and 709. However, \( 1 + \exp(x) \) will just evaluate to 1 if \( \exp(x) \) is less than the machine epsilon (i.e., \( 2^{-52} \)) or, equivalently, if \( x \) is less than the natural logarithm of that; i.e., in any case if \( x \) is less than -37. Note that taking the reciprocal of the largest double-precision number will not cause an underflow. Hence, no further checks are necessary. </p>

 <p>Definition at line <a class="el" href="logistic_8sql__in_source.html#l00598">598</a> of file <a class="el" href="logistic_8sql__in_source.html">logistic.sql_in</a>.</p>

 </div>
 </div>
 <a class="anchor" id="a32880a39de2e36b6c6be72691a6a4a40"></a><!-- doxytag: member="logistic.sql_in::logregr_train" ref="a32880a39de2e36b6c6be72691a6a4a40" args="(varchar tbl_source, varchar tbl_output, varchar dep_col, varchar ind_col, varchar grouping_col, integer max_iter, varchar optimizer, float8 tolerance, boolean verbose)" -->
 <div class="memitem">
 <div class="memproto">
       <table class="memname">
         <tr>
           <td class="memname">void logregr_train </td>
           <td>(</td>
           <td class="paramtype">varchar&#160;</td>
           <td class="paramname"><em>tbl_source</em>, </td>
         </tr>
         <tr>
           <td class="paramkey"></td>
           <td></td>
           <td class="paramtype">varchar&#160;</td>
           <td class="paramname"><em>tbl_output</em>, </td>
         </tr>
         <tr>
           <td class="paramkey"></td>
           <td></td>
           <td class="paramtype">varchar&#160;</td>
           <td class="paramname"><em>dep_col</em>, </td>
         </tr>
         <tr>
           <td class="paramkey"></td>
           <td></td>
           <td class="paramtype">varchar&#160;</td>
           <td class="paramname"><em>ind_col</em>, </td>
         </tr>
         <tr>
           <td class="paramkey"></td>
           <td></td>
           <td class="paramtype">varchar&#160;</td>
           <td class="paramname"><em>grouping_col</em>, </td>
         </tr>
         <tr>
           <td class="paramkey"></td>
           <td></td>
           <td class="paramtype">integer&#160;</td>
           <td class="paramname"><em>max_iter</em>, </td>
         </tr>
         <tr>
           <td class="paramkey"></td>
           <td></td>
           <td class="paramtype">varchar&#160;</td>
           <td class="paramname"><em>optimizer</em>, </td>
         </tr>
         <tr>
           <td class="paramkey"></td>
           <td></td>
           <td class="paramtype">float8&#160;</td>
           <td class="paramname"><em>tolerance</em>, </td>
         </tr>
         <tr>
           <td class="paramkey"></td>
           <td></td>
           <td class="paramtype">boolean&#160;</td>
           <td class="paramname"><em>verbose</em>&#160;</td>
         </tr>
         <tr>
           <td></td>
           <td>)</td>
           <td></td><td></td>
         </tr>
       </table>
 </div>
 <div class="memdoc">
 <p>To include an intercept in the model, set one coordinate in the <code>independentVariables</code> array to 1.</p>
 <dl><dt><b>Parameters:</b></dt><dd>
   <table class="params">
     <tr><td class="paramname">tbl_source</td><td>Name of the source relation containing the training data </td></tr>
     <tr><td class="paramname">tbl_output</td><td>Name of the output relation to store the model results Columns of the output relation are as follows:<ul>
 <li><code>coef FLOAT8[]</code> - Array of coefficients, \( \boldsymbol c \)</li>
 <li><code>log_likelihood FLOAT8</code> - Log-likelihood \( l(\boldsymbol c) \)</li>
 <li><code>std_err FLOAT8[]</code> - Array of standard errors, \( \mathit{se}(c_1), \dots, \mathit{se}(c_k) \)</li>
 <li><code>z_stats FLOAT8[]</code> - Array of Wald z-statistics, \( \boldsymbol z \)</li>
 <li><code>p_values FLOAT8[]</code> - Array of Wald p-values, \( \boldsymbol p \)</li>
 <li><code>odds_ratios FLOAT8[]</code>: Array of odds ratios, \( \mathit{odds}(c_1), \dots, \mathit{odds}(c_k) \)</li>
 <li><code>condition_no FLOAT8</code> - The condition number of matrix \( X^T A X \) during the iteration immediately <em>preceding</em> convergence (i.e., \( A \) is computed using the coefficients of the previous iteration) </li>
 </ul>
 </td></tr>
     <tr><td class="paramname">dep_col</td><td>Name of the dependent column (of type BOOLEAN) </td></tr>
     <tr><td class="paramname">ind_col</td><td>Name of the independent column (of type DOUBLE PRECISION[]) </td></tr>
     <tr><td class="paramname">grouping_col</td><td>Comma delimited list of column names to group-by </td></tr>
     <tr><td class="paramname">max_iter</td><td>The maximum number of iterations </td></tr>
     <tr><td class="paramname">optimizer</td><td>The optimizer to use (either <code>'irls'</code>/<code>'newton'</code> for iteratively reweighted least squares or <code>'cg'</code> for conjugent gradient) </td></tr>
     <tr><td class="paramname">tolerance</td><td>The difference between log-likelihood values in successive iterations that should indicate convergence. This value should be non-negative and a zero value here disables the convergence criterion, and execution will only stop after <code>maxNumIterations</code> iterations. </td></tr>
     <tr><td class="paramname">verbose</td><td>If true, any error or warning message will be printed to the console (irrespective of the 'client_min_messages' set by server). If false, no error/warning message is printed to console.</td></tr>
   </table>
   </dd>
 </dl>
 <dl class="user"><dt><b>Usage:</b></dt><dd><ul>
 <li>Get vector of coefficients \( \boldsymbol c \) and all diagnostic statistics:<br/>
  <pre>SELECT logregr_train('<em>sourceName</em>', '<em>outName</em>'
            '<em>dependentVariable</em>', '<em>independentVariables</em>');
           SELECT * from outName;
     </pre></li>
 <li>Get vector of coefficients \( \boldsymbol c \):<br/>
  <pre>SELECT coef from outName;</pre></li>
 <li>Get a subset of the output columns, e.g., only the array of coefficients \( \boldsymbol c \), the log-likelihood of determination \( l(\boldsymbol c) \), and the array of p-values \( \boldsymbol p \): <pre>SELECT coef, log_likelihood, p_values FROM outName;</pre></li>
 </ul>
 </dd></dl>
 <dl class="note"><dt><b>Note:</b></dt><dd>This function starts an iterative algorithm. It is not an aggregate function. Source, output, and column names have to be passed as strings (due to limitations of the SQL syntax). </dd></dl>

 <p>Definition at line <a class="el" href="logistic_8sql__in_source.html#l00495">495</a> of file <a class="el" href="logistic_8sql__in_source.html">logistic.sql_in</a>.</p>

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	<p>SQL functions for logistic regression.
	<a href="#details">More...</a></p>

	<p><a href="logistic_8sql__in_source.html">Go to the source code of this file.</a></p>
	<table class="memberdecls">
	<tr><td colspan="2"><h2><a name="func-members"></a>
	Functions</h2></td></tr>
	<tr><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="logistic_8sql__in.html#a32880a39de2e36b6c6be72691a6a4a40">logregr_train</a> (varchar tbl_source, varchar tbl_output, varchar dep_col, varchar ind_col, varchar grouping_col, integer max_iter, varchar optimizer, float8 tolerance, boolean verbose)</td></tr>
	<tr><td class="mdescLeft"> </td><td class="mdescRight">Compute logistic-regression coefficients and diagnostic statistics. <a href="#a32880a39de2e36b6c6be72691a6a4a40"></a><br/></td></tr>
	<tr><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="logistic_8sql__in.html#a4ded9be5c8b111dbb3109efaad83d69e">logistic</a> (float8 x)</td></tr>
	<tr><td class="mdescLeft"> </td><td class="mdescRight">Evaluate the usual logistic function in an under-/overflow-safe way. <a href="#a4ded9be5c8b111dbb3109efaad83d69e"></a><br/></td></tr>
	</table>
	<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
	<div class="textblock"><dl class="date"><dt><b>Date:</b></dt><dd>January 2011</dd></dl>
	<dl class="see"><dt><b>See also:</b></dt><dd>For a brief introduction to <a class="el" href="logistic_8sql__in.html#a4ded9be5c8b111dbb3109efaad83d69e" title="Evaluate the usual logistic function in an under-/overflow-safe way.">logistic</a> regression, see the module description <a class="el" href="group__grp__logreg.html">Logistic Regression</a>. </dd></dl>

	<p>Definition in file <a class="el" href="logistic_8sql__in_source.html">logistic.sql_in</a>.</p>
	</div><hr/><h2>Function Documentation</h2>
	<a class="anchor" id="a4ded9be5c8b111dbb3109efaad83d69e"></a><!-- doxytag: member="logistic.sql_in::logistic" ref="a4ded9be5c8b111dbb3109efaad83d69e" args="(float8 x)" -->
	<div class="memitem">
	<div class="memproto">
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	<td class="memname">float8 logistic </td>
	<td>(</td>
	<td class="paramtype">float8 </td>
	<td class="paramname"><em>x</em></td><td>)</td>
	<td></td>
	</tr>
	</table>
	</div>
	<div class="memdoc">
	<dl><dt><b>Parameters:</b></dt><dd>
	<table class="params">
	<tr><td class="paramname">x</td><td></td></tr>
	</table>
	</dd>
	</dl>
	<dl class="return"><dt><b>Returns:</b></dt><dd>\( \frac{1}{1 + \exp(-x)} \)</dd></dl>
	<p>Evaluating this expression directly can lead to under- or overflows. This function performs the evaluation in a safe manner, making use of the following observations:</p>
	<p>In order for the outcome of \( \exp(x) \) to be within the range of the minimum positive double-precision number (i.e., \( 2^{-1074} \)) and the maximum positive double-precision number (i.e., \( (1 + (1 - 2^{52})) * 2^{1023}) \), \( x \) has to be within the natural logarithm of these numbers, so roughly in between -744 and 709. However, \( 1 + \exp(x) \) will just evaluate to 1 if \( \exp(x) \) is less than the machine epsilon (i.e., \( 2^{-52} \)) or, equivalently, if \( x \) is less than the natural logarithm of that; i.e., in any case if \( x \) is less than -37. Note that taking the reciprocal of the largest double-precision number will not cause an underflow. Hence, no further checks are necessary. </p>

	<p>Definition at line <a class="el" href="logistic_8sql__in_source.html#l00598">598</a> of file <a class="el" href="logistic_8sql__in_source.html">logistic.sql_in</a>.</p>

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	<a class="anchor" id="a32880a39de2e36b6c6be72691a6a4a40"></a><!-- doxytag: member="logistic.sql_in::logregr_train" ref="a32880a39de2e36b6c6be72691a6a4a40" args="(varchar tbl_source, varchar tbl_output, varchar dep_col, varchar ind_col, varchar grouping_col, integer max_iter, varchar optimizer, float8 tolerance, boolean verbose)" -->
	<div class="memitem">
	<div class="memproto">
	<table class="memname">
	<tr>
	<td class="memname">void logregr_train </td>
	<td>(</td>
	<td class="paramtype">varchar </td>
	<td class="paramname"><em>tbl_source</em>, </td>
	</tr>
	<tr>
	<td class="paramkey"></td>
	<td></td>
	<td class="paramtype">varchar </td>
	<td class="paramname"><em>tbl_output</em>, </td>
	</tr>
	<tr>
	<td class="paramkey"></td>
	<td></td>
	<td class="paramtype">varchar </td>
	<td class="paramname"><em>dep_col</em>, </td>
	</tr>
	<tr>
	<td class="paramkey"></td>
	<td></td>
	<td class="paramtype">varchar </td>
	<td class="paramname"><em>ind_col</em>, </td>
	</tr>
	<tr>
	<td class="paramkey"></td>
	<td></td>
	<td class="paramtype">varchar </td>
	<td class="paramname"><em>grouping_col</em>, </td>
	</tr>
	<tr>
	<td class="paramkey"></td>
	<td></td>
	<td class="paramtype">integer </td>
	<td class="paramname"><em>max_iter</em>, </td>
	</tr>
	<tr>
	<td class="paramkey"></td>
	<td></td>
	<td class="paramtype">varchar </td>
	<td class="paramname"><em>optimizer</em>, </td>
	</tr>
	<tr>
	<td class="paramkey"></td>
	<td></td>
	<td class="paramtype">float8 </td>
	<td class="paramname"><em>tolerance</em>, </td>
	</tr>
	<tr>
	<td class="paramkey"></td>
	<td></td>
	<td class="paramtype">boolean </td>
	<td class="paramname"><em>verbose</em> </td>
	</tr>
	<tr>
	<td></td>
	<td>)</td>
	<td></td><td></td>
	</tr>
	</table>
	</div>
	<div class="memdoc">
	<p>To include an intercept in the model, set one coordinate in the <code>independentVariables</code> array to 1.</p>
	<dl><dt><b>Parameters:</b></dt><dd>
	<table class="params">
	<tr><td class="paramname">tbl_source</td><td>Name of the source relation containing the training data </td></tr>
	<tr><td class="paramname">tbl_output</td><td>Name of the output relation to store the model results Columns of the output relation are as follows:<ul>
	<li><code>coef FLOAT8[]</code> - Array of coefficients, \( \boldsymbol c \)</li>
	<li><code>log_likelihood FLOAT8</code> - Log-likelihood \( l(\boldsymbol c) \)</li>
	<li><code>std_err FLOAT8[]</code> - Array of standard errors, \( \mathit{se}(c_1), \dots, \mathit{se}(c_k) \)</li>
	<li><code>z_stats FLOAT8[]</code> - Array of Wald z-statistics, \( \boldsymbol z \)</li>
	<li><code>p_values FLOAT8[]</code> - Array of Wald p-values, \( \boldsymbol p \)</li>
	<li><code>odds_ratios FLOAT8[]</code>: Array of odds ratios, \( \mathit{odds}(c_1), \dots, \mathit{odds}(c_k) \)</li>
	<li><code>condition_no FLOAT8</code> - The condition number of matrix \( X^T A X \) during the iteration immediately <em>preceding</em> convergence (i.e., \( A \) is computed using the coefficients of the previous iteration) </li>
	</ul>
	</td></tr>
	<tr><td class="paramname">dep_col</td><td>Name of the dependent column (of type BOOLEAN) </td></tr>
	<tr><td class="paramname">ind_col</td><td>Name of the independent column (of type DOUBLE PRECISION[]) </td></tr>
	<tr><td class="paramname">grouping_col</td><td>Comma delimited list of column names to group-by </td></tr>
	<tr><td class="paramname">max_iter</td><td>The maximum number of iterations </td></tr>
	<tr><td class="paramname">optimizer</td><td>The optimizer to use (either <code>'irls'</code>/<code>'newton'</code> for iteratively reweighted least squares or <code>'cg'</code> for conjugent gradient) </td></tr>
	<tr><td class="paramname">tolerance</td><td>The difference between log-likelihood values in successive iterations that should indicate convergence. This value should be non-negative and a zero value here disables the convergence criterion, and execution will only stop after <code>maxNumIterations</code> iterations. </td></tr>
	<tr><td class="paramname">verbose</td><td>If true, any error or warning message will be printed to the console (irrespective of the 'client_min_messages' set by server). If false, no error/warning message is printed to console.</td></tr>
	</table>
	</dd>
	</dl>
	<dl class="user"><dt><b>Usage:</b></dt><dd><ul>
	<li>Get vector of coefficients \( \boldsymbol c \) and all diagnostic statistics:<br/>
	<pre>SELECT logregr_train('<em>sourceName</em>', '<em>outName</em>'
	'<em>dependentVariable</em>', '<em>independentVariables</em>');
	SELECT * from outName;
	</pre></li>
	<li>Get vector of coefficients \( \boldsymbol c \):<br/>
	<pre>SELECT coef from outName;</pre></li>
	<li>Get a subset of the output columns, e.g., only the array of coefficients \( \boldsymbol c \), the log-likelihood of determination \( l(\boldsymbol c) \), and the array of p-values \( \boldsymbol p \): <pre>SELECT coef, log_likelihood, p_values FROM outName;</pre></li>
	</ul>
	</dd></dl>
	<dl class="note"><dt><b>Note:</b></dt><dd>This function starts an iterative algorithm. It is not an aggregate function. Source, output, and column names have to be passed as strings (due to limitations of the SQL syntax). </dd></dl>

	<p>Definition at line <a class="el" href="logistic_8sql__in_source.html#l00495">495</a> of file <a class="el" href="logistic_8sql__in_source.html">logistic.sql_in</a>.</p>

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