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+<div class="title">Generalized Linear Models<div class="ingroups"><a class="el" href="group__grp__super.html">Supervised Learning</a> » <a class="el" href="group__grp__regml.html">Regression Models</a></div></div> </div>
+</div><!--header-->
+<div class="contents">
+<div class="toc"><b>Contents</b><ul>
+<li class="level1">
+<a href="#train">Training Function</a> </li>
+<li class="level1">
+<a href="#predict">Prediction Function</a> </li>
+<li class="level1">
+<a href="#examples">Examples</a> </li>
+<li class="level1">
+<a href="#related">Related Topics</a> </li>
+</ul>
+</div><p>Generalized linear models extends ordinary linear regression by allowing the response variable to follow a more general set of distributions (rather than simply Gaussian distributions), and for a general family of functions of the response variable (the link function) to vary linearly with the predicted values (rather than assuming that the response itself must vary linearly).</p>
+<p>For example, data of counts would typically be modeled with a Poisson distribution and a log link, while binary outcomes would typically be modeled with a Bernoulli distribution (or binomial distribution, depending on exactly how the problem is phrased) and a log-odds (or logit) link function.</p>
+<p>Currently, the implemented distribution families are </p><center> <table class="doxtable">
+<tr>
+<th>Distribution Family </th><th>Link Functions </th></tr>
+<tr>
+<td>Binomial </td><td>logit, probit </td></tr>
+<tr>
+<td>Gamma </td><td>inverse, identity, log </td></tr>
+<tr>
+<td>Gaussian </td><td>identity, inverse, log </td></tr>
+<tr>
+<td>Inverse Gaussian </td><td>inverse of square, inverse, identity, log </td></tr>
+<tr>
+<td>Poisson </td><td>log, identity, square-root<br />
+ </td></tr>
+</table>
+</center><p><a class="anchor" id="train"></a></p><dl class="section user"><dt>Training Function</dt><dd>GLM training function has the following format: <pre class="syntax">
+glm(source_table,
+ model_table,
+ dependent_varname,
+ independent_varname,
+ family_params,
+ grouping_col,
+ optim_params,
+ verbose
+ )
+</pre> <b>Arguments</b> <dl class="arglist">
+<dt>source_table </dt>
+<dd><p class="startdd">TEXT. The name of the table containing the training data.</p>
+<p class="enddd"></p>
+</dd>
+<dt>model_table </dt>
+<dd><p class="startdd">TEXT. Name of the generated table containing the model.</p>
+<p>The model table produced by glm contains the following columns:</p>
+<table class="output">
+<tr>
+<th><...> </th><td><p class="starttd">Text. Grouping columns, if provided in input. This could be multiple columns depending on the <code>grouping_col</code> input. </p>
+<p class="endtd"></p>
+</td></tr>
+<tr>
+<th>coef </th><td><p class="starttd">FLOAT8. Vector of the coefficients in linear predictor. </p>
+<p class="endtd"></p>
+</td></tr>
+<tr>
+<th>log_likelihood </th><td><p class="starttd">FLOAT8. The log-likelihood \( l(\boldsymbol \beta) \). We use the maximum likelihood estimate of dispersion parameter to calculate the log-likelihood while R and Python use deviance estimate and Pearson estimate respectively. </p>
+<p class="endtd"></p>
+</td></tr>
+<tr>
+<th>std_err </th><td><p class="starttd">FLOAT8[]. Vector of the standard error of the coefficients. </p>
+<p class="endtd"></p>
+</td></tr>
+<tr>
+<th>z_stats or t_stats </th><td><p class="starttd">FLOAT8[]. Vector of the z-statistics (in Poisson distribtuion and Binomial distribution) or the t-statistics (in all other distributions) of the coefficients. </p>
+<p class="endtd"></p>
+</td></tr>
+<tr>
+<th>p_values </th><td><p class="starttd">FLOAT8[]. Vector of the p-values of the coefficients. </p>
+<p class="endtd"></p>
+</td></tr>
+<tr>
+<th>dispersion </th><td><p class="starttd">FLOAT8. The dispersion value (Pearson estimate). When family=poisson or family=binomial, the dispersion is always 1. </p>
+<p class="endtd"></p>
+</td></tr>
+<tr>
+<th>num_rows_processed </th><td><p class="starttd">BIGINT. Numbers of rows processed. </p>
+<p class="endtd"></p>
+</td></tr>
+<tr>
+<th>num_rows_skipped </th><td><p class="starttd">BIGINT. Numbers of rows skipped due to missing values or failures. </p>
+<p class="endtd"></p>
+</td></tr>
+<tr>
+<th>num_iterations </th><td>INTEGER. The number of iterations actually completed. This would be different from the <code>nIterations</code> argument if a <code>tolerance</code> parameter is provided and the algorithm converges before all iterations are completed. </td></tr>
+</table>
+<p>A summary table named <model_table>_summary is also created at the same time, which has the following columns: </p><table class="output">
+<tr>
+<th>method </th><td><p class="starttd">'glm' </p>
+<p class="endtd"></p>
+</td></tr>
+<tr>
+<th>source_table </th><td><p class="starttd">The data source table name. </p>
+<p class="endtd"></p>
+</td></tr>
+<tr>
+<th>model_table </th><td><p class="starttd">The model table name. </p>
+<p class="endtd"></p>
+</td></tr>
+<tr>
+<th>dependent_varname </th><td><p class="starttd">The dependent variable. </p>
+<p class="endtd"></p>
+</td></tr>
+<tr>
+<th>independent_varname </th><td><p class="starttd">The independent variables </p>
+<p class="endtd"></p>
+</td></tr>
+<tr>
+<th>family_params </th><td><p class="starttd">A string that contains family parameters, and has the form of 'family=..., link=...' </p>
+<p class="endtd"></p>
+</td></tr>
+<tr>
+<th>grouping_col </th><td><p class="starttd">Name of grouping columns. </p>
+<p class="endtd"></p>
+</td></tr>
+<tr>
+<th>optimizer_params </th><td><p class="starttd">A string that contains optimizer parameters, and has the form of 'optimizer=..., max_iter=..., tolerance=...' </p>
+<p class="endtd"></p>
+</td></tr>
+<tr>
+<th>num_all_groups </th><td><p class="starttd">Number of groups in glm training. </p>
+<p class="endtd"></p>
+</td></tr>
+<tr>
+<th>num_failed_groups </th><td><p class="starttd">Number of failed groups in glm training. </p>
+<p class="endtd"></p>
+</td></tr>
+<tr>
+<th>total_rows_processed </th><td><p class="starttd">BIGINT. Total numbers of rows processed in all groups. </p>
+<p class="endtd"></p>
+</td></tr>
+<tr>
+<th>total_rows_skipped </th><td><p class="starttd">BIGINT. Total numbers of rows skipped in all groups due to missing values or failures. </p>
+<p class="endtd"></p>
+</td></tr>
+</table>
+<p class="enddd"></p>
+</dd>
+<dt>dependent_varname </dt>
+<dd><p class="startdd">TEXT. Name of the dependent variable column.</p>
+<p class="enddd"></p>
+</dd>
+<dt>independent_varname </dt>
+<dd><p class="startdd">TEXT. Expression list to evaluate for the independent variables. An intercept variable is not assumed. It is common to provide an explicit intercept term by including a single constant <code>1</code> term in the independent variable list.</p>
+<p class="enddd"></p>
+</dd>
+<dt>family_params (optional) </dt>
+<dd><p class="startdd">TEXT, Parameters for distribution family. Currently, we support</p>
+<p>(1) family=poisson and link=[log or identity or sqrt].</p>
+<p>(2) family=gaussian and link=[identity or log or inverse]. And when family=gaussian and link=identity, the GLM model is exactly the same as the linear regression.</p>
+<p>(3) family=gamma and link=[inverse or identity or log].</p>
+<p>(4) family=inverse_gaussian and link=[sqr_inverse or log or identity or inverse].</p>
+<p>(5) family=binomial and link=[probit or logit]. </p>
+<p class="enddd"></p>
+</dd>
+<dt>grouping_col (optional) </dt>
+<dd><p class="startdd">TEXT, default: NULL. An expression list used to group the input dataset into discrete groups, running one regression per group. Similar to the SQL "GROUP BY" clause. When this value is NULL, no grouping is used and a single model is generated.</p>
+<p class="enddd"></p>
+</dd>
+<dt>optim_params (optional) </dt>
+<dd><p class="startdd">TEXT, default: 'max_iter=100,optimizer=irls,tolerance=1e-6'. Parameters for optimizer. Currently, we support tolerance=[tolerance for relative error between log-likelihoods], max_iter=[maximum iterations to run], optimizer=irls.</p>
+<p class="enddd"></p>
+</dd>
+<dt>verbose (optional) </dt>
+<dd>BOOLEAN, default: FALSE. Provides verbose output of the results of training. </dd>
+</dl>
+</dd></dl>
+<dl class="section note"><dt>Note</dt><dd>For p-values, we just return the computation result directly. Other statistical packages, like 'R', produce the same result, but on printing the result to screen, another format function is used and any p-value that is smaller than the machine epsilon (the smallest positive floating-point number 'x' such that '1 + x != 1') will be printed on screen as "< xxx" (xxx is the value of the machine epsilon). Although the results may look different, they are in fact the same. </dd></dl>
+<p><a class="anchor" id="predict"></a></p><dl class="section user"><dt>Prediction Function</dt><dd>The prediction function is provided to estimate the conditional mean given a new predictor. It has the following syntax: <pre class="syntax">
+glm_predict(coef,
+ col_ind_var
+ link)
+</pre></dd></dl>
+<p><b>Arguments</b> </p><dl class="arglist">
+<dt>coef </dt>
+<dd><p class="startdd">DOUBLE PRECISION[]. Model coefficients obtained from <a class="el" href="glm_8sql__in.html#a3f8eb219013e05675626acb8cf4612cc">glm()</a>.</p>
+<p class="enddd"></p>
+</dd>
+<dt>col_ind_var </dt>
+<dd><p class="startdd">New predictor, as a DOUBLE array. This should be the same length as the array obtained by evaluation of the 'independent_varname' argument in <a class="el" href="glm_8sql__in.html#a3f8eb219013e05675626acb8cf4612cc">glm()</a>.</p>
+<p class="enddd"></p>
+</dd>
+<dt>link </dt>
+<dd>link function, as a string. This should match the link function the user inputted in <a class="el" href="glm_8sql__in.html#a3f8eb219013e05675626acb8cf4612cc">glm()</a>. </dd>
+</dl>
+<p><a class="anchor" id="examples"></a></p><dl class="section user"><dt>Examples</dt><dd><ol type="1">
+<li>Create the training data table. <pre class="example">
+CREATE TABLE warpbreaks(
+ id serial,
+ breaks integer,
+ wool char(1),
+ tension char(1)
+);
+INSERT INTO warpbreaks(breaks, wool, tension) VALUES
+(26, 'A', 'L'),
+(30, 'A', 'L'),
+(54, 'A', 'L'),
+(25, 'A', 'L'),
+(70, 'A', 'L'),
+(52, 'A', 'L'),
+(51, 'A', 'L'),
+(26, 'A', 'L'),
+(67, 'A', 'L'),
+(18, 'A', 'M'),
+(21, 'A', 'M'),
+(29, 'A', 'M'),
+(17, 'A', 'M'),
+(12, 'A', 'M'),
+(18, 'A', 'M'),
+(35, 'A', 'M'),
+(30, 'A', 'M'),
+(36, 'A', 'M'),
+(36, 'A', 'H'),
+(21, 'A', 'H'),
+(24, 'A', 'H'),
+(18, 'A', 'H'),
+(10, 'A', 'H'),
+(43, 'A', 'H'),
+(28, 'A', 'H'),
+(15, 'A', 'H'),
+(26, 'A', 'H'),
+(27, 'B', 'L'),
+(14, 'B', 'L'),
+(29, 'B', 'L'),
+(19, 'B', 'L'),
+(29, 'B', 'L'),
+(31, 'B', 'L'),
+(41, 'B', 'L'),
+(20, 'B', 'L'),
+(44, 'B', 'L'),
+(42, 'B', 'M'),
+(26, 'B', 'M'),
+(19, 'B', 'M'),
+(16, 'B', 'M'),
+(39, 'B', 'M'),
+(28, 'B', 'M'),
+(21, 'B', 'M'),
+(39, 'B', 'M'),
+(29, 'B', 'M'),
+(20, 'B', 'H'),
+(21, 'B', 'H'),
+(24, 'B', 'H'),
+(17, 'B', 'H'),
+(13, 'B', 'H'),
+(15, 'B', 'H'),
+(15, 'B', 'H'),
+(16, 'B', 'H'),
+(28, 'B', 'H');
+SELECT create_indicator_variables('warpbreaks', 'warpbreaks_dummy', 'wool,tension');
+</pre></li>
+<li>Train a GLM model. <pre class="example">
+SELECT glm('warpbreaks_dummy',
+ 'glm_model',
+ 'breaks',
+ 'ARRAY[1.0,"wool_B","tension_M", "tension_H"]',
+ 'family=poisson, link=log');
+</pre></li>
+<li>View the regression results. <pre class="example">
+-- Set extended display on for easier reading of output
+\x on
+SELECT * FROM glm_model;
+</pre> Result: <pre class="result">
+coef | {3.69196314494079,-0.205988442638621,-0.321320431600611,-0.51848849651156}
+log_likelihood | -242.527983208979
+std_err | {0.04541079434248,0.0515712427835191,0.0602659166951256,0.0639595193956924}
+z_stats | {81.3014438174473,-3.99425011926316,-5.3317106786264,-8.10651020224019}
+p_values | {0,6.48993254938271e-05,9.72918600322907e-08,5.20943463005751e-16}
+num_rows_processed | 54
+num_rows_skipped | 0
+iteration | 5
+</pre> Alternatively, unnest the arrays in the results for easier reading of output: <pre class="example">
+\x off
+SELECT unnest(coef) as coefficient,
+ unnest(std_err) as standard_error,
+ unnest(z_stats) as z_stat,
+ unnest(p_values) as pvalue
+FROM glm_model;
+</pre></li>
+<li>Predicting dependent variable using GLM model. (This example uses the original data table to perform the prediction. Typically a different test dataset with the same features as the original training dataset would be used for prediction.) <pre class="example">
+\x off
+-- Display predicted mean value on the original dataset
+SELECT
+ w.id,
+ madlib.glm_predict(
+ coef,
+ ARRAY[1, "wool_B", "tension_M", "tension_H"]::float8[],
+ 'log') AS mu
+FROM warpbreaks_dummy w, glm_model m
+ORDER BY w.id;
+</pre> <pre class="example">
+-- Display predicted counts (which are predicted mean values rounded to the nearest integral value) on the original dataset
+SELECT
+ w.id,
+ madlib.glm_predict_poisson(
+ coef,
+ ARRAY[1, "wool_B", "tension_M", "tension_H"]::float8[],
+ 'log') AS poisson_count
+FROM warpbreaks_dummy w, glm_model m
+ORDER BY w.id;
+</pre></li>
+</ol>
+</dd></dl>
+<p><b>Example for Gaussian family:</b></p>
+<ol type="1">
+<li>Create a testing data table <pre class="example">
+CREATE TABLE abalone (
+ id integer,
+ sex text,
+ length double precision,
+ diameter double precision,
+ height double precision,
+ whole double precision,
+ shucked double precision,
+ viscera double precision,
+ shell double precision,
+ rings integer
+);
+INSERT INTO abalone VALUES
+(3151, 'F', 0.655000000000000027, 0.505000000000000004, 0.165000000000000008, 1.36699999999999999, 0.583500000000000019, 0.351499999999999979, 0.396000000000000019, 10),
+(2026, 'F', 0.550000000000000044, 0.469999999999999973, 0.149999999999999994, 0.920499999999999985, 0.381000000000000005, 0.243499999999999994, 0.267500000000000016, 10),
+(3751, 'I', 0.434999999999999998, 0.375, 0.110000000000000001, 0.41549999999999998, 0.170000000000000012, 0.0759999999999999981, 0.14499999999999999, 8),
+(720, 'I', 0.149999999999999994, 0.100000000000000006, 0.0250000000000000014, 0.0149999999999999994, 0.00449999999999999966, 0.00400000000000000008, 0.0050000000000000001, 2),
+(1635, 'F', 0.574999999999999956, 0.469999999999999973, 0.154999999999999999, 1.1160000000000001, 0.509000000000000008, 0.237999999999999989, 0.340000000000000024, 10),
+(2648, 'I', 0.5, 0.390000000000000013, 0.125, 0.582999999999999963, 0.293999999999999984, 0.132000000000000006, 0.160500000000000004, 8),
+(1796, 'F', 0.57999999999999996, 0.429999999999999993, 0.170000000000000012, 1.47999999999999998, 0.65349999999999997, 0.32400000000000001, 0.41549999999999998, 10),
+(209, 'F', 0.525000000000000022, 0.41499999999999998, 0.170000000000000012, 0.832500000000000018, 0.275500000000000023, 0.168500000000000011, 0.309999999999999998, 13),
+(1451, 'I', 0.455000000000000016, 0.33500000000000002, 0.135000000000000009, 0.501000000000000001, 0.274000000000000021, 0.0995000000000000051, 0.106499999999999997, 7),
+(1108, 'I', 0.510000000000000009, 0.380000000000000004, 0.115000000000000005, 0.515499999999999958, 0.214999999999999997, 0.113500000000000004, 0.166000000000000009, 8),
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+</pre></li>
+<li>Train a model with family=gaussian and link=identity <pre class="example">
+SELECT madlib.glm(
+ 'abalone',
+ 'abalone_out',
+ 'rings',
+ 'ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]',
+ 'family=gaussian, link=identity');
+</pre></li>
+</ol>
+<p><b>Example for Gamma family:</b> (reuse the dataset in Gaussian case)</p>
+<ol type="1">
+<li>Reuse the test data set in Gaussian</li>
+<li>Train a model with family=gamma and link=inverse <pre class="example">
+SELECT madlib.glm(
+ 'abalone',
+ 'abalone_out',
+ 'rings',
+ 'ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]',
+ 'family=gamma, link=inverse');
+</pre></li>
+</ol>
+<p><b>Example for Inverse Gaussian family:</b> (reuse the dataset in Gaussian case)</p>
+<ol type="1">
+<li>Reuse the test data set in Gaussian</li>
+<li>Train a model with family=inverse_gaussian and link=sqr_inverse <pre class="example">
+SELECT madlib.glm(
+ 'abalone',
+ 'abalone_out',
+ 'rings',
+ 'ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]',
+ 'family=inverse_gaussian, link=sqr_inverse');
+</pre></li>
+</ol>
+<p><b>Example for Binomial family:</b> (reuse the dataset in Gaussian case)</p>
+<ol type="1">
+<li>Reuse the test data set in Gaussian</li>
+<li>Train a model with family=binomial and link=probit <pre class="example">
+SELECT madlib.glm(
+ 'abalone',
+ 'abalone_out',
+ 'rings < 10',
+ 'ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]',
+ 'family=binomial, link=probit');
+</pre></li>
+<li>Predict output probabilities <pre class="example">
+SELECT madlib.glm_predict(
+ coef,
+ ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]::float8[],
+ 'probit')
+FROM abalone_out, abalone;
+</pre></li>
+<li>Predict output categories <pre class="example">
+SELECT madlib.glm_predict(
+SELECT madlib.glm_predict_binomial(
+ coef,
+ ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]::float8[],
+ 'probit')
+FROM abalone_out, abalone;
+</pre></li>
+</ol>
+<p><a class="anchor" id="notes"></a></p><dl class="section user"><dt>Notes</dt><dd>All table names can be optionally schema qualified (current_schemas() would be searched if a schema name is not provided) and all table and column names should follow case-sensitivity and quoting rules per the database. (For instance, 'mytable' and 'MyTable' both resolve to the same entity, i.e. 'mytable'. If mixed-case or multi-byte characters are desired for entity names then the string should be double-quoted; in this case the input would be '"MyTable"').</dd></dl>
+<p>Currently implementation uses Newton's method and, according to performance tests, when number of features are over 1000, this GLM function could be running slowly.</p>
+<p>Functions in <a class="el" href="group__grp__linreg.html">Linear Regression</a> is prefered to GLM with family=gaussian,link=identity, as the former require only a single pass over the training data. In addition, if user expects to use robust variance, clustered variance, or marginal effects on top of the trained model, functions in <a class="el" href="group__grp__linreg.html">Linear Regression</a> and <a class="el" href="group__grp__logreg.html">Logistic Regression</a> should be used.</p>
+<p><a class="anchor" id="related"></a></p><dl class="section user"><dt>Related Topics</dt><dd></dd></dl>
+<p>File <a class="el" href="glm_8sql__in.html" title="SQL functions for GLM (Poisson) ">glm.sql_in</a> documenting the training function</p>
+<p><a class="el" href="group__grp__linreg.html">Linear Regression</a></p>
+<p><a class="el" href="group__grp__logreg.html">Logistic Regression</a></p>
+<p><a class="el" href="group__grp__mlogreg.html">Multinomial Logistic Regression</a></p>
+<p><a class="el" href="group__grp__robust.html">Robust Variance</a></p>
+<p><a class="el" href="group__grp__clustered__errors.html">Clustered Variance</a></p>
+<p><a class="el" href="group__grp__validation.html">Cross Validation</a></p>
+<p><a class="el" href="group__grp__marginal.html">Marginal Effects</a></p>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+ <ul>
+ <li class="footer">Generated on Mon Oct 15 2018 11:24:30 for MADlib by
+ <a href="http://www.doxygen.org/index.html">
+ <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.14 </li>
+ </ul>
+</div>
+</body>
+</html>
http://git-wip-us.apache.org/repos/asf/madlib-site/blob/af0e5f14/docs/v1.15.1/group__grp__graph.html
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+<title>MADlib: Graph</title>
+<link href="tabs.css" rel="stylesheet" type="text/css"/>
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+<link href="doxygen.css" rel="stylesheet" type="text/css" />
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+<table cellspacing="0" cellpadding="0">
+ <tbody>
+ <tr style="height: 56px;">
+ <td id="projectlogo"><a href="http://madlib.apache.org"><img alt="Logo" src="madlib.png" height="50" style="padding-left:0.5em;" border="0"/ ></a></td>
+ <td style="padding-left: 0.5em;">
+ <div id="projectname">
+ <span id="projectnumber">1.15.1</span>
+ </div>
+ <div id="projectbrief">User Documentation for Apache MADlib</div>
+ </td>
+ <td> <div id="MSearchBox" class="MSearchBoxInactive">
+ <span class="left">
+ <img id="MSearchSelect" src="search/mag_sel.png"
+ onmouseover="return searchBox.OnSearchSelectShow()"
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+ alt=""/>
+ <input type="text" id="MSearchField" value="Search" accesskey="S"
+ onfocus="searchBox.OnSearchFieldFocus(true)"
+ onblur="searchBox.OnSearchFieldFocus(false)"
+ onkeyup="searchBox.OnSearchFieldChange(event)"/>
+ </span><span class="right">
+ <a id="MSearchClose" href="javascript:searchBox.CloseResultsWindow()"><img id="MSearchCloseImg" border="0" src="search/close.png" alt=""/></a>
+ </span>
+ </div>
+</td>
+ </tr>
+ </tbody>
+</table>
+</div>
+<!-- end header part -->
+<!-- Generated by Doxygen 1.8.14 -->
+<script type="text/javascript">
+/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&dn=gpl-2.0.txt GPL-v2 */
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+/* @license-end */
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+</div><!-- top -->
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+ class="ui-resizable-handle">
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+/* @license-end */
+</script>
+<div id="doc-content">
+<!-- window showing the filter options -->
+<div id="MSearchSelectWindow"
+ onmouseover="return searchBox.OnSearchSelectShow()"
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+
+<!-- iframe showing the search results (closed by default) -->
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+<iframe src="javascript:void(0)" frameborder="0"
+ name="MSearchResults" id="MSearchResults">
+</iframe>
+</div>
+
+<div class="header">
+ <div class="summary">
+<a href="#groups">Modules</a> </div>
+ <div class="headertitle">
+<div class="title">Graph</div> </div>
+</div><!--header-->
+<div class="contents">
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<p>Graph algorithms and measures associated with graphs. </p>
+<table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="groups"></a>
+Modules</h2></td></tr>
+<tr class="memitem:group__grp__apsp"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__grp__apsp.html">All Pairs Shortest Path</a></td></tr>
+<tr class="memdesc:group__grp__apsp"><td class="mdescLeft"> </td><td class="mdescRight">Finds the shortest paths between every vertex pair in a given graph. <br /></td></tr>
+<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:group__grp__bfs"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__grp__bfs.html">Breadth-First Search</a></td></tr>
+<tr class="memdesc:group__grp__bfs"><td class="mdescLeft"> </td><td class="mdescRight">Finds the nodes reachable from a given source vertex using a breadth-first approach. <br /></td></tr>
+<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:group__grp__hits"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__grp__hits.html">HITS</a></td></tr>
+<tr class="memdesc:group__grp__hits"><td class="mdescLeft"> </td><td class="mdescRight">Find the HITS scores(authority and hub) of all vertices in a directed graph. <br /></td></tr>
+<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:group__grp__graph__measures"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__grp__graph__measures.html">Measures</a></td></tr>
+<tr class="memdesc:group__grp__graph__measures"><td class="mdescLeft"> </td><td class="mdescRight">A collection of metrics computed on a graph. <br /></td></tr>
+<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:group__grp__pagerank"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__grp__pagerank.html">PageRank</a></td></tr>
+<tr class="memdesc:group__grp__pagerank"><td class="mdescLeft"> </td><td class="mdescRight">Find the PageRank of all vertices in a directed graph. <br /></td></tr>
+<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:group__grp__sssp"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__grp__sssp.html">Single Source Shortest Path</a></td></tr>
+<tr class="memdesc:group__grp__sssp"><td class="mdescLeft"> </td><td class="mdescRight">Finds the shortest path from a single source vertex to every other vertex in a given graph. <br /></td></tr>
+<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:group__grp__wcc"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__grp__wcc.html">Weakly Connected Components</a></td></tr>
+<tr class="memdesc:group__grp__wcc"><td class="mdescLeft"> </td><td class="mdescRight">Find all weakly connected components of a graph. <br /></td></tr>
+<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
+</table>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+ <ul>
+ <li class="footer">Generated on Mon Oct 15 2018 11:24:30 for MADlib by
+ <a href="http://www.doxygen.org/index.html">
+ <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.14 </li>
+ </ul>
+</div>
+</body>
+</html>
http://git-wip-us.apache.org/repos/asf/madlib-site/blob/af0e5f14/docs/v1.15.1/group__grp__graph.js
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+ [ "Breadth-First Search", "group__grp__bfs.html", null ],
+ [ "HITS", "group__grp__hits.html", null ],
+ [ "Measures", "group__grp__graph__measures.html", "group__grp__graph__measures" ],
+ [ "PageRank", "group__grp__pagerank.html", null ],
+ [ "Single Source Shortest Path", "group__grp__sssp.html", null ],
+ [ "Weakly Connected Components", "group__grp__wcc.html", null ]
+];
\ No newline at end of file
http://git-wip-us.apache.org/repos/asf/madlib-site/blob/af0e5f14/docs/v1.15.1/group__grp__graph__avg__path__length.html
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+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
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+<title>MADlib: Average Path Length</title>
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+ <div id="projectbrief">User Documentation for Apache MADlib</div>
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+ name="MSearchResults" id="MSearchResults">
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+
+<div class="header">
+ <div class="headertitle">
+<div class="title">Average Path Length<div class="ingroups"><a class="el" href="group__grp__graph.html">Graph</a> » <a class="el" href="group__grp__graph__measures.html">Measures</a></div></div> </div>
+</div><!--header-->
+<div class="contents">
+<div class="toc"><b>Contents</b> <ul>
+<li>
+<a href="#avg_path_length">Average Path Length</a> </li>
+<li>
+<a href="#examples">Examples</a> </li>
+</ul>
+</div><p>This function computes the average of the shortest paths between each pair of vertices. Average path length is based on "reachable target vertices", so it ignores infinite-length paths between vertices that are not connected.</p>
+<dl class="section note"><dt>Note</dt><dd>This function assumes a valid output from a prior APSP run - both the APSP table and the associated output summary table. APSP is a computationally expensive algorithm because it finds the shortest path between all nodes in the graph. The worst case run-time for this implementation is O(V^2 * E) where V is the number of vertices and E is the number of edges. In practice, run-time will be generally be much less than this, depending on the graph.</dd></dl>
+<p><a class="anchor" id="avg_path_length"></a></p><dl class="section user"><dt>Average Path Length</dt><dd><pre class="syntax">
+graph_avg_path_length( apsp_table,
+ output_table
+ )
+</pre></dd></dl>
+<p><b>Arguments</b> </p><dl class="arglist">
+<dt>apsp_table </dt>
+<dd><p class="startdd">TEXT. Name of the output table generated by a prior run of all pairs shortest path (APSP). </p>
+<p class="enddd"></p>
+</dd>
+<dt>out_table </dt>
+<dd>TEXT. Name of the table to store the average path length. It contains a row for every group, and the average path value. </dd>
+</dl>
+<p><a class="anchor" id="examples"></a></p><dl class="section user"><dt>Examples</dt><dd></dd></dl>
+<ol type="1">
+<li>Create vertex and edge tables to represent the graph: <pre class="syntax">
+DROP TABLE IF EXISTS vertex, edge;
+CREATE TABLE vertex(
+ id INTEGER,
+ name TEXT
+ );
+CREATE TABLE edge(
+ src_id INTEGER,
+ dest_id INTEGER,
+ edge_weight FLOAT8
+ );
+INSERT INTO vertex VALUES
+(0, 'A'),
+(1, 'B'),
+(2, 'C'),
+(3, 'D'),
+(4, 'E'),
+(5, 'F'),
+(6, 'G'),
+(7, 'H');
+INSERT INTO edge VALUES
+(0, 1, 1.0),
+(0, 2, 1.0),
+(0, 4, 10.0),
+(1, 2, 2.0),
+(1, 3, 10.0),
+(2, 3, 1.0),
+(2, 5, 1.0),
+(2, 6, 3.0),
+(3, 0, 1.0),
+(4, 0, -2.0),
+(5, 6, 1.0),
+(6, 7, 1.0);
+</pre></li>
+<li>Calculate the all-pair shortest paths: <pre class="syntax">
+DROP TABLE IF EXISTS out_apsp, out_apsp_summary;
+SELECT madlib.graph_apsp('vertex', -- Vertex table
+ 'id', -- Vertix id column (NULL means use default naming)
+ 'edge', -- Edge table
+ 'src=src_id, dest=dest_id, weight=edge_weight',
+ -- Edge arguments (NULL means use default naming)
+ 'out_apsp'); -- Output table of shortest paths
+</pre></li>
+<li>Compute the average path length measure: <pre class="syntax">
+DROP TABLE IF EXISTS out_avg_path_length;
+SELECT madlib.graph_avg_path_length('out_apsp', 'out_avg_path_length');
+SELECT * FROM out_avg_path_length;
+</pre> <pre class="result">
+ avg_path_length
+------------------
+ 2.01785714285714
+(1 row)
+</pre></li>
+<li>Create a graph with 2 groups and find APSP for each group: <pre class="syntax">
+DROP TABLE IF EXISTS edge_gr;
+CREATE TABLE edge_gr AS
+(
+ SELECT *, 0 AS grp FROM edge
+ UNION
+ SELECT *, 1 AS grp FROM edge WHERE src_id < 6 AND dest_id < 6
+);
+INSERT INTO edge_gr VALUES
+(4,5,-20,1);
+</pre></li>
+<li>Find APSP for all groups: <pre class="syntax">
+DROP TABLE IF EXISTS out_gr, out_gr_summary;
+SELECT madlib.graph_apsp(
+ 'vertex', -- Vertex table
+ NULL, -- Vertex id column (NULL means use default naming)
+ 'edge_gr', -- Edge table
+ 'src=src_id, dest=dest_id, weight=edge_weight',
+ 'out_gr', -- Output table of shortest paths
+ 'grp' -- Grouping columns
+);
+</pre></li>
+<li>Find the average path length in every group <pre class="syntax">
+DROP TABLE IF EXISTS out_gr_path;
+SELECT madlib.graph_avg_path_length('out_gr', 'out_gr_path');
+SELECT * FROM out_gr_path ORDER BY grp;
+</pre> <pre class="result">
+ grp | avg_path_length
+----—+-----------------—
+ 0 | 2.01785714285714
+ 1 | 0.466666666666667
+(2 rows)
+</pre> </li>
+</ol>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
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+ <li class="footer">Generated on Mon Oct 15 2018 11:24:30 for MADlib by
+ <a href="http://www.doxygen.org/index.html">
+ <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.14 </li>
+ </ul>
+</div>
+</body>
+</html>
http://git-wip-us.apache.org/repos/asf/madlib-site/blob/af0e5f14/docs/v1.15.1/group__grp__graph__closeness.html
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diff --git a/docs/v1.15.1/group__grp__graph__closeness.html b/docs/v1.15.1/group__grp__graph__closeness.html
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@@ -0,0 +1,281 @@
+<!-- HTML header for doxygen 1.8.4-->
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
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+<title>MADlib: Closeness</title>
+<link href="tabs.css" rel="stylesheet" type="text/css"/>
+<script type="text/javascript" src="jquery.js"></script>
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+ <td style="padding-left: 0.5em;">
+ <div id="projectname">
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+ </div>
+ <div id="projectbrief">User Documentation for Apache MADlib</div>
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+</table>
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+<!-- end header part -->
+<!-- Generated by Doxygen 1.8.14 -->
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+<div id="MSearchSelectWindow"
+ onmouseover="return searchBox.OnSearchSelectShow()"
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+ name="MSearchResults" id="MSearchResults">
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+
+<div class="header">
+ <div class="headertitle">
+<div class="title">Closeness<div class="ingroups"><a class="el" href="group__grp__graph.html">Graph</a> » <a class="el" href="group__grp__graph__measures.html">Measures</a></div></div> </div>
+</div><!--header-->
+<div class="contents">
+<div class="toc"><b>Contents</b> <ul>
+<li>
+<a href="#closeness">Closeness</a> </li>
+<li>
+<a href="#examples">Examples</a> </li>
+</ul>
+</div><p>The Closeness function returns various closeness centrality measures and the k-degree for given subset of vertices. The closeness measures are the inverse of the sum, the inverse of the average, and the sum of inverses of the shortest distances to all reachable target vertices (excluding the source vertex).</p>
+<dl class="section note"><dt>Note</dt><dd>The closeness measures require a valid output from a prior APSP run - both the APSP table and the associated output summary table. APSP is a computationally expensive algorithm because it finds the shortest path between all nodes in the graph. The worst case run-time for this implementation is O(V^2 E) where V is the number of vertices and E is the number of edges. In practice, run-time will be generally be much less than this, depending on the graph.</dd></dl>
+<p><a class="anchor" id="closeness"></a></p><dl class="section user"><dt>Closeness</dt><dd><pre class="syntax">
+graph_closeness( apsp_table,
+ output_table,
+ vertex_filter_expr
+ )
+</pre></dd></dl>
+<p><b>Arguments</b> </p><dl class="arglist">
+<dt>apsp_table </dt>
+<dd><p class="startdd">TEXT. Name of the output table generated by a prior run of all pairs shortest path (APSP). </p>
+<p class="enddd"></p>
+</dd>
+<dt>out_table </dt>
+<dd><p class="startdd">TEXT. Name of the table to store the closeness measures. It contains a row for every vertex of every group and have the following columns (in addition to the grouping columns):</p><ul>
+<li>inverse_sum_dist: Inverse of the sum of shortest distances to all reachable vertices.</li>
+<li>inverse_average_dist: Inverse of the average of shortest distances to all reachable vertices.</li>
+<li>sum_inverse_dist: Sum of the inverse of shortest distances to all reachable vertices.</li>
+<li>k_degree: Total number of reachable vertices. </li>
+</ul>
+<p class="enddd"></p>
+</dd>
+<dt>vertex_filter_expr (optional) </dt>
+<dd><p class="startdd">TEXT, default = NULL. Valid PostgreSQL expression that describes the vertices to generate closeness measures for. If this parameter is not specified, closeness measures are generated for all vertices in the apsp table. You can think of this input parameter as being like a WHERE clause.</p>
+<p>Some example inputs:</p><ul>
+<li>If you want a short list of vertices, say 1, 2 and 3: <pre>vertex_id IN (1, 2, 3)</pre></li>
+<li>If you want a range of vertices between 1000 and 2000: <pre>vertix_id BETWEEN 1000 AND 2000</pre></li>
+<li>If you want a set of vertices from a separate table satisfying to a condition <pre>EXISTS (SELECT vertex_id FROM vertices_of_interest
+ WHERE vertex_id > 5000 AND condition = 'xyz')
+</pre></li>
+</ul>
+<p class="enddd"></p>
+</dd>
+</dl>
+<p><a class="anchor" id="examples"></a></p><dl class="section user"><dt>Examples</dt><dd></dd></dl>
+<ol type="1">
+<li>Create vertex and edge tables to represent the graph: <pre class="syntax">
+DROP TABLE IF EXISTS vertex, edge;
+CREATE TABLE vertex(
+ id INTEGER,
+ name TEXT
+ );
+CREATE TABLE edge(
+ src_id INTEGER,
+ dest_id INTEGER,
+ edge_weight FLOAT8
+ );
+INSERT INTO vertex VALUES
+(0, 'A'),
+(1, 'B'),
+(2, 'C'),
+(3, 'D'),
+(4, 'E'),
+(5, 'F'),
+(6, 'G'),
+(7, 'H');
+INSERT INTO edge VALUES
+(0, 1, 1.0),
+(0, 2, 1.0),
+(0, 4, 10.0),
+(1, 2, 2.0),
+(1, 3, 10.0),
+(2, 3, 1.0),
+(2, 5, 1.0),
+(2, 6, 3.0),
+(3, 0, 1.0),
+(4, 0, -2.0),
+(5, 6, 1.0),
+(6, 7, 1.0);
+</pre></li>
+<li>Calculate the all-pair shortest paths: <pre class="syntax">
+DROP TABLE IF EXISTS out_apsp, out_apsp_summary;
+SELECT madlib.graph_apsp('vertex', -- Vertex table
+ 'id', -- Vertix id column (NULL means use default naming)
+ 'edge', -- Edge table
+ 'src=src_id, dest=dest_id, weight=edge_weight',
+ -- Edge arguments (NULL means use default naming)
+ 'out_apsp'); -- Output table of shortest paths
+</pre></li>
+<li>Compute the closeness measure for all nodes: <pre class="syntax">
+DROP TABLE IF EXISTS out_closeness;
+SELECT madlib.graph_closeness('out_apsp', 'out_closeness');
+SELECT * FROM out_closeness;
+</pre> <pre class="result">
+ src_id | inverse_sum_dist | inverse_avg_dist | sum_inverse_dist | k_degree
+--------+--------------------+-------------------+------------------+----------
+ 1 | 0.0285714285714286 | 0.2 | 1.93809523809524 | 7
+ 3 | 0.0357142857142857 | 0.25 | 2.87424242424242 | 7
+ 4 | -1 | -7 | -1 | 7
+ 0 | 0.0434782608695652 | 0.304347826086957 | 3.68333333333333 | 7
+ 6 | 1 | 1 | 1 | 1
+ 2 | 0.0416666666666667 | 0.291666666666667 | 3.75 | 7
+ 5 | 0.333333333333333 | 0.666666666666667 | 1.5 | 2
+ 7 | [NULL] | [NULL] | 0 | 0
+(8 rows)
+</pre></li>
+<li>Create a graph with 2 groups and find APSP for each group: <pre class="syntax">
+DROP TABLE IF EXISTS edge_gr;
+CREATE TABLE edge_gr AS
+(
+ SELECT *, 0 AS grp FROM edge
+ UNION
+ SELECT *, 1 AS grp FROM edge WHERE src_id < 6 AND dest_id < 6
+);
+INSERT INTO edge_gr VALUES
+(4,5,-20,1);
+</pre></li>
+<li>Find APSP for all groups: <pre class="syntax">
+DROP TABLE IF EXISTS out_gr, out_gr_summary;
+SELECT madlib.graph_apsp(
+ 'vertex', -- Vertex table
+ NULL, -- Vertex id column (NULL means use default naming)
+ 'edge_gr', -- Edge table
+ 'src=src_id, dest=dest_id, weight=edge_weight',
+ 'out_gr', -- Output table of shortest paths
+ 'grp' -- Grouping columns
+);
+</pre></li>
+<li>Compute closeness measure for vertex 0 to vertex 5 in every group <pre class="syntax">
+DROP TABLE IF EXISTS out_gr_path;
+SELECT madlib.graph_closeness('out_gr', 'out_gr_closeness', 'src_id >= 0 and src_id <=5');
+SELECT * FROM out_gr_closeness ORDER BY grp;
+</pre> <pre class="result">
+ grp | src_id | inverse_sum_dist | inverse_avg_dist | sum_inverse_dist | k_degree
+----—+-------—+--------------------—+-------------------—+------------------—+---------—
+ 0 | 0 | 0.0434782608695652 | 0.304347826086957 | 3.68333333333333 | 7
+ 0 | 5 | 0.333333333333333 | 0.666666666666667 | 1.5 | 2
+ 0 | 4 | -1 | -7 | -1 | 7
+ 0 | 3 | 0.0357142857142857 | 0.25 | 2.87424242424242 | 7
+ 0 | 1 | 0.0285714285714286 | 0.2 | 1.93809523809524 | 7
+ 0 | 2 | 0.0416666666666667 | 0.291666666666667 | 3.75 | 7
+ 1 | 3 | 0.142857142857143 | 0.714285714285714 | 1.97979797979798 | 5
+ 1 | 5 | [NULL] | [NULL] | 0 | 0
+ 1 | 0 | 0.25 | 1.25 | 2.5 | 5
+ 1 | 1 | 0.0588235294117647 | 0.294117647058824 | 0.988095238095238 | 5
+ 1 | 2 | 0.1 | 0.5 | 1.79166666666667 | 5
+ 1 | 4 | -0.0416666666666667 | -0.208333333333333 | -2.55 | 5
+(12 rows)
+</pre> </li>
+</ol>
+</div><!-- contents -->
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+ <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.14 </li>
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http://git-wip-us.apache.org/repos/asf/madlib-site/blob/af0e5f14/docs/v1.15.1/group__grp__graph__diameter.html
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+<div class="title">Graph Diameter<div class="ingroups"><a class="el" href="group__grp__graph.html">Graph</a> » <a class="el" href="group__grp__graph__measures.html">Measures</a></div></div> </div>
+</div><!--header-->
+<div class="contents">
+<div class="toc"><b>Contents</b> <ul>
+<li>
+<a href="#diameter">Diameter</a> </li>
+<li>
+<a href="#examples">Examples</a> </li>
+</ul>
+</div><p>Diameter is defined as the longest of all shortest paths in a graph.</p>
+<dl class="section note"><dt>Note</dt><dd>This function assumes a valid output from a prior APSP run - both the APSP table and the associated output summary table. APSP is a computationally expensive algorithm because it finds the shortest path between all nodes in the graph. The worst case run-time for this implementation is O(V^2 * E) where V is the number of vertices and E is the number of edges. In practice, run-time will be generally be much less than this, depending on the graph.</dd></dl>
+<p><a class="anchor" id="diameter"></a></p><dl class="section user"><dt>Diameter</dt><dd><pre class="syntax">
+graph_diameter( apsp_table,
+ output_table
+ )
+</pre></dd></dl>
+<p><b>Arguments</b> </p><dl class="arglist">
+<dt>apsp_table </dt>
+<dd><p class="startdd">TEXT. Name of the output table generated by a prior run of all pairs shortest path (APSP). </p>
+<p class="enddd"></p>
+</dd>
+<dt>out_table </dt>
+<dd><p class="startdd">TEXT. Name of the table to store the diameter. It contains a row for every group, the diameter value and the two vertices that are the farthest apart. </p>
+<p class="enddd"></p>
+</dd>
+</dl>
+<p><a class="anchor" id="examples"></a></p><dl class="section user"><dt>Examples</dt><dd></dd></dl>
+<ol type="1">
+<li>Create vertex and edge tables to represent the graph: <pre class="syntax">
+DROP TABLE IF EXISTS vertex, edge;
+CREATE TABLE vertex(
+ id INTEGER,
+ name TEXT
+ );
+CREATE TABLE edge(
+ src_id INTEGER,
+ dest_id INTEGER,
+ edge_weight FLOAT8
+ );
+INSERT INTO vertex VALUES
+(0, 'A'),
+(1, 'B'),
+(2, 'C'),
+(3, 'D'),
+(4, 'E'),
+(5, 'F'),
+(6, 'G'),
+(7, 'H');
+INSERT INTO edge VALUES
+(0, 1, 1.0),
+(0, 2, 1.0),
+(0, 4, 10.0),
+(1, 2, 2.0),
+(1, 3, 10.0),
+(2, 3, 1.0),
+(2, 5, 1.0),
+(2, 6, 3.0),
+(3, 0, 1.0),
+(4, 0, -2.0),
+(5, 6, 1.0),
+(6, 7, 1.0);
+</pre></li>
+<li>Calculate the all-pair shortest paths: <pre class="syntax">
+DROP TABLE IF EXISTS out_apsp, out_apsp_summary;
+SELECT madlib.graph_apsp('vertex', -- Vertex table
+ 'id', -- Vertix id column (NULL means use default naming)
+ 'edge', -- Edge table
+ 'src=src_id, dest=dest_id, weight=edge_weight',
+ -- Edge arguments (NULL means use default naming)
+ 'out_apsp'); -- Output table of shortest paths
+</pre></li>
+<li>Compute the diameter measure for the graph: <pre class="syntax">
+DROP TABLE IF EXISTS out_diameter;
+SELECT madlib.graph_diameter('out_apsp', 'out_diameter');
+SELECT * FROM out_diameter;
+</pre> <pre class="result">
+diameter | diameter_end_vertices
+---------+-----------------------
+ 14 | {{1,4}}
+(1 row)
+</pre></li>
+<li>Create a graph with 2 groups and find APSP for each group: <pre class="syntax">
+DROP TABLE IF EXISTS edge_gr;
+CREATE TABLE edge_gr AS
+(
+ SELECT *, 0 AS grp FROM edge
+ UNION
+ SELECT *, 1 AS grp FROM edge WHERE src_id < 6 AND dest_id < 6
+);
+INSERT INTO edge_gr VALUES
+(4,5,-20,1);
+</pre></li>
+<li>Find APSP for all groups: <pre class="syntax">
+DROP TABLE IF EXISTS out_gr, out_gr_summary;
+SELECT madlib.graph_apsp(
+ 'vertex', -- Vertex table
+ NULL, -- Vertex id column (NULL means use default naming)
+ 'edge_gr', -- Edge table
+ 'src=src_id, dest=dest_id, weight=edge_weight',
+ 'out_gr', -- Output table of shortest paths
+ 'grp' -- Grouping columns
+);
+</pre></li>
+<li>Find the diameter of graph in every group <pre class="syntax">
+DROP TABLE IF EXISTS out_gr_path;
+SELECT madlib.graph_diameter('out_gr', 'out_gr_diameter');
+SELECT * FROM out_gr_diameter ORDER BY grp;
+</pre> <pre class="result">
+grp | diameter | diameter_end_vertices
+---—+---------—+----------------------—
+ 0 | 14 | {{1,4}}
+ 1 | 14 | {{1,4}}
+(2 rows)
+</pre> </li>
+</ol>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+ <ul>
+ <li class="footer">Generated on Mon Oct 15 2018 11:24:30 for MADlib by
+ <a href="http://www.doxygen.org/index.html">
+ <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.14 </li>
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