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Posted to commits@madlib.apache.org by es...@apache.org on 2017/08/29 19:09:46 UTC
[15/51] [partial] incubator-madlib-site git commit: Update website
for 1.21 release.
http://git-wip-us.apache.org/repos/asf/incubator-madlib-site/blob/4ddf1756/docs/v1.12/group__grp__tree.html
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diff --git a/docs/v1.12/group__grp__tree.html b/docs/v1.12/group__grp__tree.html
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http://git-wip-us.apache.org/repos/asf/incubator-madlib-site/blob/4ddf1756/docs/v1.12/group__grp__unsupervised.html
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+ <li class="footer">Generated on Tue Aug 29 2017 09:14:35 for MADlib by
+ <a href="http://www.doxygen.org/index.html">
+ <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.13 </li>
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+<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
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+<title>MADlib: Developer Database Functions</title>
+<link href="tabs.css" rel="stylesheet" type="text/css"/>
+<script type="text/javascript" src="jquery.js"></script>
+<script type="text/javascript" src="dynsections.js"></script>
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+ <td style="padding-left: 0.5em;">
+ <div id="projectname">
+ <span id="projectnumber">1.12</span>
+ </div>
+ <div id="projectbrief">User Documentation for MADlib</div>
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+</div><!--header-->
+<div class="contents">
+<div class="toc"><b>Contents</b> <ul>
+<li>
+<a href="#utilities">Utility Functions</a> </li>
+<li>
+<a href="#rel;ated">Related Topics</a> </li>
+</ul>
+</div><p>The utility module consists of useful utility functions to assist data scientists in using the product. Several of these functions can be used while implementing new algorithms.</p>
+<p><a class="anchor" id="utilities"></a></p><dl class="section user"><dt>Utility Functions</dt><dd></dd></dl>
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+<tr>
+<th><a class="el" href="utilities_8sql__in.html#a9ce7ffa76acc8a0638e9bc48be99f36a" title="Return MADlib build information. ">version()</a> </th><td><p class="starttd">Return MADlib build information. </p>
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+<th><a class="el" href="utilities_8sql__in.html#ab194d6a1222672c314ea39b78aad8fd0" title="Create volatile noop function. ">noop()</a> </th><td><p class="starttd">Create volatile noop function. </p>
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+<th><a class="el" href="utilities_8sql__in.html#aab5ea2cd6201e38e24ca62b0fb91fb7a" title="Drop all tables matching pattern 'madlib_temp' in a given schema. ">cleanup_madlib_temp_tables()</a> </th><td><p class="starttd">Drop all tables matching pattern 'madlib_temp' in a given schema. </p>
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+</td></tr>
+</table>
+<p>Note: If the function <a class="el" href="utilities_8sql__in.html#aab5ea2cd6201e38e24ca62b0fb91fb7a" title="Drop all tables matching pattern 'madlib_temp' in a given schema. ">cleanup_madlib_temp_tables()</a> gives an Out-of-memory error, then the number of tables to be dropped is too high to execute in one transaction. In such a case, please follow the instructions provided with the error to execute the command in multiple transactions.</p>
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+<p>File <a class="el" href="utilities_8sql__in.html" title="SQL functions for carrying out routine tasks. ">utilities.sql_in</a> documenting the SQL functions. </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 Tue Aug 29 2017 09:14:35 for MADlib by
+ <a href="http://www.doxygen.org/index.html">
+ <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.13 </li>
+ </ul>
+</div>
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http://git-wip-us.apache.org/repos/asf/incubator-madlib-site/blob/4ddf1756/docs/v1.12/group__grp__utility__functions.html
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+</div><!-- contents -->
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+<!-- start footer part -->
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+ <ul>
+ <li class="footer">Generated on Tue Aug 29 2017 09:14:35 for MADlib by
+ <a href="http://www.doxygen.org/index.html">
+ <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.13 </li>
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new file mode 100644
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+ <div class="headertitle">
+<div class="title">Cross Validation<div class="ingroups"><a class="el" href="group__grp__mdl.html">Model Selection</a></div></div> </div>
+</div><!--header-->
+<div class="contents">
+<div class="toc"><b>Contents</b> <ul>
+<li>
+<a href="#cvfunction">Cross-Validation Function</a> </li>
+<li>
+<a href="#examples">Examples</a> </li>
+<li>
+<a href="#notes">Notes</a> </li>
+<li>
+<a href="#background">Technical Background</a> </li>
+<li>
+<a href="#related">Related Topics</a> </li>
+</ul>
+</div><p>Estimates the fit of a predictive model given a data set and specifications for the training, prediction, and error estimation functions.</p>
+<p>Cross validation, sometimes called rotation estimation, is a technique for assessing how the results of a statistical analysis will generalize to an independent data set. It is mainly used in settings where the goal is prediction, and you want to estimate how accurately a predictive model will perform in practice.</p>
+<p>The cross-validation function provided by this module is very flexible and can work with algorithms you want to cross validate, including algorithms you write yourself. Among the inputs to the cross-validation function are specifications of the modelling, prediction, and error metric functions. These three-part specifications include the name of the function, an array of arguments to pass to the function, and an array of the data types of the arguments. This makes it possible to use functions from other MADlib modules or user-defined functions that you supply.</p>
+<ul>
+<li>The modelling (training) function takes in a given data set with independent and dependent variables and produces a model, which is stored in an output table.</li>
+<li>The prediction function takes in the model generated by the modelling function and a different data set with independent variables, and produces a prediction of the dependent variables based on the model, which is stored in an output table. The prediction function should take a unique ID column name in the data table as one of the inputs, so that the prediction result can be compared with the validation values. Note: Prediction function in some MADlib modules do not save results into an output table. These prediction functions are not suitable for cross-validation.</li>
+<li>The error metric function compares the prediction results with the known values of the dependent variables in the data set that was fed into the prediction function. It computes the error metric using the specified error metric function, storing the results in a table.</li>
+</ul>
+<p>Other inputs include the output table name, k value for the k-fold cross validation, and how many folds to try. For example, you can choose to run a simple validation instead of a full cross validation.</p>
+<p><a class="anchor" id="cvfunction"></a></p><dl class="section user"><dt>Cross-Validation Function</dt><dd></dd></dl>
+<pre class="syntax">
+cross_validation_general( modelling_func,
+ modelling_params,
+ modelling_params_type,
+ param_explored,
+ explore_values,
+ predict_func,
+ predict_params,
+ predict_params_type,
+ metric_func,
+ metric_params,
+ metric_params_type,
+ data_tbl,
+ data_id,
+ id_is_random,
+ validation_result,
+ data_cols,
+ fold_num
+ )</pre><p> <b>Arguments</b> </p><dl class="arglist">
+<dt>modelling_func </dt>
+<dd>VARCHAR. The name of the function that trains the model. </dd>
+<dt>modelling_params </dt>
+<dd>VARCHAR[]. An array of parameters to supply to the modelling function. </dd>
+<dt>modelling_params_type </dt>
+<dd>VARCHAR[]. An array of data type names for each of the parameters supplied to the modelling function. </dd>
+<dt>param_explored </dt>
+<dd>VARCHAR. The name of the parameter that will be checked to find the optimum value. The name must appear in the <em>modelling_params</em> array. </dd>
+<dt>explore_values </dt>
+<dd>VARCHAR. The name of the parameter whose values are to be studied. </dd>
+<dt>predict_func </dt>
+<dd>VARCHAR. The name of the prediction function. </dd>
+<dt>predict_params </dt>
+<dd>VARCHAR[]. An array of parameters to supply to the prediction function. </dd>
+<dt>predict_params_type </dt>
+<dd>VARCHAR[]. An array of data type names for each of the parameters supplied to the prediction function. </dd>
+<dt>metric_func </dt>
+<dd>VARCHAR. The name of the function for measuring errors. </dd>
+<dt>metric_params </dt>
+<dd>VARCHAR[]. An array of parameters to supply to the error metric function. </dd>
+<dt>metric_params_type </dt>
+<dd>VARCHAR[]. An array of data type names for each of the parameters supplied to the metric function. </dd>
+<dt>data_tbl </dt>
+<dd>VARCHAR. The name of the data table that will be split into training and validation parts. </dd>
+<dt>data_id </dt>
+<dd><p class="startdd">VARCHAR. The name of the column containing a unique ID associated with each row, or NULL if the table has no such column.</p>
+<p class="enddd">Ideally, the data set has a unique ID for each row, so that it is easier to partition the data set into the training part and the validation part. Set the <em>id_is_random</em> argument to inform the cross-validation function whether the ID value is randomly assigned to each row. If it is not randomly assigned, the cross-validation function generates a random ID for each row. </p>
+</dd>
+<dt>id_is_random </dt>
+<dd>BOOLEAN. TRUE if the provided ID is randomly assigned to each row. </dd>
+<dt>validation_result </dt>
+<dd>VARCHAR. The name of the table to store the output of the cross-validation function. The output table has the following columns: <table class="output">
+<tr>
+<th>param_explored </th><td>The name of the parameter checked to find the optimum value. This is the same name specified in the <em>param_explored</em> argument of the <em><a class="el" href="cross__validation_8sql__in.html#a2a7791b05f51e8748ab7b6ccf328a7e2">cross_validation_general()</a></em> function. </td></tr>
+<tr>
+<th>average error </th><td>The average of the errors computed by the error metric function. </td></tr>
+<tr>
+<th>standard deviation of error </th><td>The standard deviation of the errors. </td></tr>
+</table>
+</dd>
+<dt>data_cols </dt>
+<dd><p class="startdd">A comma-separated list of names of data columns to use in the calculation. When its value is NULL, the function will automatically figure out all the column names of the data table. This is only used if the <em>data_id</em> argument is NULL, otherwise it is ignored.</p>
+<p>If the data set has no unique ID for each row, the cross-validation function copies the data set to a temporary table with a randomly assigned ID column. Setting this argument to the list of independent and dependent variables that are to be used in the calculation minimizes the copying workload by only copying the required data.</p>
+<p class="enddd">The new temporary table is dropped after the computation has finished. </p>
+</dd>
+<dt><em>fold_num</em> </dt>
+<dd>INTEGER, default: 10. Value of k. How many folds validation? Each validation uses 1/fold_num fraction of the data for validation. </dd>
+</dl>
+<p>The parameter arrays for the modelling, prediction and metric functions can include the following special keywords:</p>
+<ul>
+<li><em>%data%</em> – The argument position for training/validation data</li>
+<li><em>%model%</em> – The argument position for the output/input of modelling/prediction function</li>
+<li><em>%id%</em> – The argument position of the unique ID column (user-provided or generated by the cross-validation function, as described above)</li>
+<li><em>%prediction%</em> – The argument position for the output/input of prediction/metric function</li>
+<li><em>%error%</em> – The argument position for the output of the metric function</li>
+</ul>
+<p><b>Note</b>: If the argument <em>explore_values</em> is NULL or has zero length, then the cross-validation function will only run a data folding.</p>
+<p><a class="anchor" id="examples"></a></p><dl class="section user"><dt>Examples</dt><dd></dd></dl>
+<p>This example uses cross validation with an elastic net regression to find the best value of the regularization parameter.</p>
+<ol type="1">
+<li>Populate the table <code>cvtest</code> with 101 dimensional independent variables <code>val</code>, and dependent variable <code>dep</code>.</li>
+<li>Run the general cross-validation function. <pre class="example">
+SELECT madlib.cross_validation_general
+ ( 'madlib.elastic_net_train',
+ '{%data%, %model%, dep, indep, gaussian, 1, lambda, TRUE, NULL, fista,
+ "{eta = 2, max_stepsize = 2, use_active_set = t}",
+ NULL, 2000, 1e-6}'::varchar[],
+ '{varchar, varchar, varchar, varchar, varchar, double precision,
+ double precision, boolean, varchar, varchar, varchar, varchar,
+ integer, double precision}'::varchar[],
+ 'lambda',
+ '{0.02, 0.04, 0.06, 0.08, 0.10, 0.12, 0.14, 0.16, 0.18, 0.20,
+ 0.22, 0.24, 0.26, 0.28, 0.30, 0.32, 0.34, 0.36}'::varchar[],
+ 'madlib.elastic_net_predict',
+ '{%model%, %data%, %id%, %prediction%}'::varchar[],
+ '{text, text, text, text}'::varchar[],
+ 'madlib.mse_error',
+ '{%prediction%, %data%, %id%, dep, %error%}'::varchar[],
+ '{varchar, varchar, varchar, varchar, varchar}'::varchar[],
+ 'cvtest',
+ NULL::varchar,
+ FALSE,
+ 'valid_rst_tbl',
+ '{indep, dep}'::varchar[],
+ 10
+);
+</pre></li>
+</ol>
+<p><a class="anchor" id="notes"></a></p><dl class="section user"><dt>Notes</dt><dd></dd></dl>
+<p><em>max_locks_per_transaction</em>, which usually is set to the default value of 64, limits the number of tables that can be dropped inside a single transaction (the cross-validation function). Thus, the number of different values of <em>param_explored</em> (or the length of the <em>explored_values</em> array) cannot be too large. For 10-fold cross validation, the limit of <code>length(<em>explored_values</em>)</code> is around 40. If the limit is exceeded, you may get an "out of shared memory" error because <em>max_locks_per_transaction</em> is exceeded.</p>
+<p>One way to overcome this limitation is to run the cross-validation function multiple times, with each run covering a different region of values of the parameter.</p>
+<p>In the future, MADlib may implement cross-validation functions for each individual applicable module, where it is possible to optimize the calculation to avoid dropping tables and prevent exceeding the <em>max_locks_per_transaction</em> limitation. Since module-specific cross-validation functions depend upon the implementation details of the modules to perform the optimization, they will not be as flexible as the generalized cross-validation function provided here.</p>
+<p><a class="anchor" id="background"></a></p><dl class="section user"><dt>Technical Background</dt><dd></dd></dl>
+<p>One round of cross validation involves partitioning a sample of data into complementary subsets, performing the analysis on one subset (called the training set), and validating the analysis on the other subset (called the validation set or testing set). To reduce variability, multiple rounds of cross validation are performed using different partitions, and the validation results are averaged over the rounds.</p>
+<p>In k-fold cross validation, the original sample is randomly partitioned into k equal sized subsamples. Of the k subsamples, a single subsample is retained as the validation data for testing the model, and the remaining k−1 subsamples are used as training data. The cross-validation process is repeated k times (the folds), with each of the k subsamples used exactly once as the validation data. The k results from the folds can be averaged (or otherwise combined) to produce a single estimation. The advantage of this method over repeated random sub-sampling is that all observations are used for both training and validation, and each observation is used for validation exactly once. 10-fold cross validation is commonly used, but in general k remains an unfixed parameter.</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="cross__validation_8sql__in.html" title="SQL functions for cross validation. ">cross_validation.sql_in</a> documenting the SQL functions. </p>
+</div><!-- contents -->
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http://git-wip-us.apache.org/repos/asf/incubator-madlib-site/blob/4ddf1756/docs/v1.12/group__grp__wcc.html
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+ </div>
+ <div id="projectbrief">User Documentation for MADlib</div>
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+<div class="title">Weakly Connected Components<div class="ingroups"><a class="el" href="group__grp__graph.html">Graph</a></div></div> </div>
+</div><!--header-->
+<div class="contents">
+<div class="toc"><b>Contents</b> <ul>
+<li>
+<a href="#wcc">Weakly Connected Components</a> </li>
+<li>
+<a href="#rlcc">Retrieve Largest Connected Component</a> </li>
+<li>
+<a href="#hist">Build Histogram</a> </li>
+<li>
+<a href="#samecpt">Check Vertices in Same Connected Component</a> </li>
+<li>
+<a href="#reach">Retrieve Reachable Vertices</a> </li>
+<li>
+<a href="#count">Count Connected Components</a> </li>
+<li>
+<a href="#examples">Examples</a> </li>
+</ul>
+</div><p>Given a directed graph, a weakly connected component (WCC) is a subgraph of the original graph where all vertices are connected to each other by some path, ignoring the direction of edges. In case of an undirected graph, a weakly connected component is also a strongly connected component. This module also includes a number of helper functions that operate on the WCC output.</p>
+<p><a class="anchor" id="wcc"></a></p><dl class="section user"><dt>Weakly Connected Components</dt><dd><pre class="syntax">
+weakly_connected_components( vertex_table,
+ vertex_id,
+ edge_table,
+ edge_args,
+ out_table,
+ grouping_cols
+ )
+</pre></dd></dl>
+<p><b>Arguments</b> </p><dl class="arglist">
+<dt>vertex_table </dt>
+<dd><p class="startdd">TEXT. Name of the table containing the vertex data for the graph. Must contain the column specified in the 'vertex_id' parameter below.</p>
+<p class="enddd"></p>
+</dd>
+<dt>vertex_id </dt>
+<dd><p class="startdd">TEXT, default = 'id'. Name of the column in 'vertex_table' containing vertex ids. The vertex ids are of type INTEGER with no duplicates. They do not need to be contiguous.</p>
+<p class="enddd"></p>
+</dd>
+<dt>edge_table </dt>
+<dd><p class="startdd">TEXT. Name of the table containing the edge data. The edge table must contain columns for source vertex and destination vertex.</p>
+<p class="enddd"></p>
+</dd>
+<dt>edge_args </dt>
+<dd><p class="startdd">TEXT. A comma-delimited string containing multiple named arguments of the form "name=value". The following parameters are supported for this string argument:</p><ul>
+<li>src (INTEGER): Name of the column containing the source vertex ids in the edge table. Default column name is 'src'.</li>
+<li>dest (INTEGER): Name of the column containing the destination vertex ids in the edge table. Default column name is 'dest'.</li>
+</ul>
+<p class="enddd"></p>
+</dd>
+<dt>out_table </dt>
+<dd><p class="startdd">TEXT. Name of the table to store the component ID associated with each vertex. It will contain a row for every vertex from 'vertex_table' with the following columns:</p><ul>
+<li>vertex_id : The id of a vertex. Will use the input parameter 'vertex_id' for column naming.</li>
+<li>component_id : Component that the vertex belongs to. We use the convention where 'component_id' is the id of the first vertex in a particular group. It means that component ids are generally not contiguous.</li>
+<li>grouping_cols : Grouping column (if any) values associated with the vertex_id.</li>
+</ul>
+<p>A summary table named <out_table>_summary is also created. This is an internal table that keeps a record of some of the input parameters and is used by the weakly connected component helper functions. </p>
+<p class="enddd"></p>
+</dd>
+<dt>grouping_cols (optional) </dt>
+<dd>TEXT, default: NULL. A single column or a list of comma-separated columns that divides the input data into discrete groups, which are treated independently as separate graphs. When this value is NULL, no grouping is used and weakly connected components are generated for all data (single graph). <dl class="section note"><dt>Note</dt><dd>Expressions are not currently supported for 'grouping_cols'.</dd></dl>
+</dd>
+</dl>
+<p><a class="anchor" id="rlcc"></a></p><dl class="section user"><dt>Retrieve Largest Connected Component</dt><dd></dd></dl>
+<p>The largest connected component retrieval function finds the largest weakly connected component(s) in a graph. If weakly connected components was run with grouping, the largest connected components are computed for each group.</p>
+<pre class="syntax">
+graph_wcc_largest_cpt( wcc_table,
+ largest_cpt_table
+ )
+</pre><p><b>Arguments</b> </p><dl class="arglist">
+<dt>wcc_table </dt>
+<dd><p class="startdd">TEXT. Name of the table that contains the output of weakly connected components.</p>
+<p class="enddd"></p>
+</dd>
+<dt>largest_cpt_table </dt>
+<dd>TEXT. Name of the output table that contains the largest component's information. It contains one or more rows for every group and has the following columns:<ul>
+<li>grouping_cols: The grouping columns given in the creation of wcc_table. If there are no grouping columns, this column is not created.</li>
+<li>component_id: The ID of the largest component. Recall that we use the convention where 'component_id' is the id of the first vertex in a particular group. It means that component ids are generally not contiguous. If there are multiple components of the same size, a row is created for each component. If grouping_cols is specified, the largest component is computed for each group.</li>
+<li>num_vertices: Number of vertices in the largest component. </li>
+</ul>
+</dd>
+</dl>
+<p><a class="anchor" id="hist"></a></p><dl class="section user"><dt>Retrieve Histogram of Vertices Per Connected Component</dt><dd></dd></dl>
+<p>This function creates a histogram of the number of vertices per connected component.</p>
+<pre class="syntax">
+graph_wcc_histogram( wcc_table,
+ histogram_table
+ )
+</pre><p><b>Arguments</b> </p><dl class="arglist">
+<dt>wcc_table </dt>
+<dd><p class="startdd">TEXT. Name of the table that contains the output of weakly connected components.</p>
+<p class="enddd"></p>
+</dd>
+<dt>histogram_table </dt>
+<dd><p class="startdd">TEXT. Name of the output table that contains the number of vertices per component. A row is created for every comoponent in every group if grouping_cols was specified when running weakly connected components. The output table has the following columns:</p><ul>
+<li>grouping_cols: The grouping columns given during the creation of the wcc_table. If there are no grouping columns, this column is not created.</li>
+<li>component_id: The ID of the component.</li>
+<li>num_vertices: Number of vertices in the component specified by the component_id column.</li>
+</ul>
+<p class="enddd"></p>
+</dd>
+</dl>
+<p><a class="anchor" id="samecpt"></a></p><dl class="section user"><dt>Check if Two Vertices Belong to the Same Component</dt><dd></dd></dl>
+<p>This function determines if two vertices belong to the same component.</p>
+<pre class="syntax">
+graph_wcc_vertex_check( wcc_table,
+ vertex_pair,
+ pair_table
+ )
+</pre><p><b>Arguments</b> </p><dl class="arglist">
+<dt>wcc_table </dt>
+<dd><p class="startdd">TEXT. Name of the table that contains the output of weakly connected components.</p>
+<p class="enddd"></p>
+</dd>
+<dt>vertex_pair </dt>
+<dd><p class="startdd">TEXT. A pair of vertex IDs separated by a comma.</p>
+<p class="enddd"></p>
+</dd>
+<dt>pair_table </dt>
+<dd><p class="startdd">TEXT. Name of the output table that specifies if the two vertices in vertex_pair belong to the same component. If wcc_table was generated using grouping_cols, all the components in all groups are considered. The output table has the following columns:</p><ul>
+<li>component_id: Component ID that contains both the vertices in vertex_pair.</li>
+<li>grouping_cols: The grouping columns given in the creation of wcc_table. If there are no grouping columns, this column is not created.</li>
+</ul>
+<p class="enddd"></p>
+</dd>
+</dl>
+<p><a class="anchor" id="reach"></a></p><dl class="section user"><dt>Retrieve All Vertices Reachable from a Vertex</dt><dd></dd></dl>
+<p>This function finds all the vertices that can be reached from a given vertex via weakly connected paths.</p>
+<pre class="syntax">
+graph_wcc_reachable_vertices( wcc_table,
+ src,
+ reachable_vertices_table
+ )
+</pre><p><b>Arguments</b> </p><dl class="arglist">
+<dt>wcc_table </dt>
+<dd><p class="startdd">TEXT. Name of the table that contains the output of weakly connected components.</p>
+<p class="enddd"></p>
+</dd>
+<dt>src </dt>
+<dd><p class="startdd">TEXT. The vertex ID from which all reachable vertices have to be found.</p>
+<p class="enddd"></p>
+</dd>
+<dt>reachable_vertices_table </dt>
+<dd><p class="startdd">TEXT. Name of the output table that contains the list of vertices that are reachable from the src vertex. The output table has the following columns:</p><ul>
+<li>grouping_cols : The grouping columns given in the creation of wcc_table. If there are no grouping columns, this column is not created.</li>
+<li>component_id : The ID of the component that both the src and dest vertices belong to.</li>
+<li>dest : Vertex ID that is reachable from the src vertex. Reachability is computed with regard to a component.</li>
+</ul>
+<p class="enddd"></p>
+</dd>
+</dl>
+<p><a class="anchor" id="count"></a></p><dl class="section user"><dt>Count of Connected Components</dt><dd></dd></dl>
+<p>This function finds the total number of components in the input graph.</p>
+<pre class="syntax">
+graph_wcc_num_cpts( wcc_table,
+ count_table
+ )
+</pre><p><b>Arguments</b> </p><dl class="arglist">
+<dt>wcc_table </dt>
+<dd><p class="startdd">TEXT. Name of the table that contains the output of weakly connected components.</p>
+<p class="enddd"></p>
+</dd>
+<dt>count_table </dt>
+<dd><p class="startdd">TEXT. Name of the output table that contains the total number of components per group in the graph, if there are any grouping_cols in wcc_table. The output table has the following columns:</p><ul>
+<li>grouping_cols : The grouping columns given in the creation of wcc_table. If there are no grouping columns, this column is not created, and count is with regard to the entire graph.</li>
+<li>num_components : Count of weakly connected components in a graph, or the number of components within a group if grouping_cols is defined. </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
+);
+CREATE TABLE edge(
+ src INTEGER,
+ dest INTEGER,
+ user_id INTEGER
+);
+INSERT INTO vertex VALUES
+(0),
+(1),
+(2),
+(3),
+(4),
+(5),
+(6),
+(10),
+(11),
+(12),
+(13),
+(14),
+(15),
+(16);
+INSERT INTO edge VALUES
+(0, 1, 1),
+(0, 2, 1),
+(1, 2, 1),
+(1, 3, 1),
+(2, 3, 1),
+(2, 5, 1),
+(2, 6, 1),
+(3, 0, 1),
+(5, 6, 1),
+(6, 3, 1),
+(10, 11, 2),
+(10, 12, 2),
+(11, 12, 2),
+(11, 13, 2),
+(12, 13, 2),
+(13, 10, 2),
+(15, 16, 2),
+(15, 14, 2);
+</pre></li>
+<li>Find all the weakly connected components in the graph: <pre class="syntax">
+DROP TABLE IF EXISTS wcc_out, wcc_out_summary;
+SELECT madlib.weakly_connected_components(
+ 'vertex', -- Vertex table
+ 'id', -- Vertix id column
+ 'edge', -- Edge table
+ 'src=src, dest=dest', -- Comma delimted string of edge arguments
+ 'wcc_out'); -- Output table of weakly connected components
+SELECT * FROM wcc_out ORDER BY component_id, id;
+</pre> <pre class="result">
+ id | component_id
+----+--------------
+ 0 | 0
+ 1 | 0
+ 2 | 0
+ 3 | 0
+ 5 | 0
+ 6 | 0
+ 4 | 4
+ 10 | 10
+ 11 | 10
+ 12 | 10
+ 13 | 10
+ 14 | 14
+ 15 | 14
+ 16 | 14
+(14 rows)
+</pre></li>
+<li>Now get the weakly connected components associated with each 'user_id' using the grouping feature: <pre class="syntax">
+DROP TABLE IF EXISTS wcc_out, wcc_out_summary;
+SELECT madlib.weakly_connected_components(
+ 'vertex', -- Vertex table
+ 'id', -- Vertix id column
+ 'edge', -- Edge table
+ 'src=src, dest=dest', -- Comma delimted string of edge arguments
+ 'wcc_out', -- Output table of weakly connected components
+ 'user_id'); -- Grouping column name
+SELECT * FROM wcc_out ORDER BY user_id, component_id, id;
+</pre> <pre class="result">
+ id | component_id | user_id
+----+--------------+---------
+ 0 | 0 | 1
+ 1 | 0 | 1
+ 2 | 0 | 1
+ 3 | 0 | 1
+ 5 | 0 | 1
+ 6 | 0 | 1
+ 10 | 10 | 2
+ 11 | 10 | 2
+ 12 | 10 | 2
+ 13 | 10 | 2
+ 14 | 14 | 2
+ 15 | 14 | 2
+ 16 | 14 | 2
+(13 rows)
+</pre> Note that vertex 4 is not identified as a separate component above. This is because there is no entry in the edge table for vertex 4 indicating which group it belongs to (though you could do that if you wanted to).</li>
+<li>Retrieve the largest connected component: <pre class="syntax">
+DROP TABLE IF EXISTS largest_cpt_table;
+SELECT madlib.graph_wcc_largest_cpt(
+ 'wcc_out', -- WCC output table
+ 'largest_cpt_table'); -- output table containing largest component ID
+SELECT * FROM largest_cpt_table ORDER BY component_id;
+</pre> <pre class="result">
+ user_id | component_id | num_vertices
+---------+--------------+--------------
+ 1 | 0 | 6
+ 2 | 10 | 4
+(2 rows)
+</pre></li>
+<li>Retrieve histogram of the number of vertices per connected component: <pre class="syntax">
+DROP TABLE IF EXISTS histogram_table;
+SELECT madlib.graph_wcc_histogram(
+ 'wcc_out', -- WCC output table
+ 'histogram_table'); -- output table containing the histogram of vertices
+SELECT * FROM histogram_table ORDER BY component_id;
+</pre> <pre class="result">
+ user_id | component_id | num_vertices
+---------+--------------+--------------
+ 1 | 0 | 6
+ 2 | 10 | 4
+ 2 | 14 | 3
+(3 rows)
+</pre></li>
+<li>Check if two vertices belong to the same component: <pre class="syntax">
+DROP TABLE IF EXISTS vc_table;
+SELECT madlib.graph_wcc_vertex_check(
+ 'wcc_out', -- WCC output table
+ '14,15', -- Pair of vertex IDs
+ 'vc_table'); -- output table containing components that contain the two vertices
+SELECT * FROM vc_table ORDER BY component_id;
+</pre> <pre class="result">
+ user_id | component_id
+---------+--------------
+ 2 | 14
+(1 row)
+</pre></li>
+<li>Retrieve all vertices reachable from a vertex <pre class="syntax">
+DROP TABLE IF EXISTS reach_table;
+SELECT madlib.graph_wcc_reachable_vertices(
+ 'wcc_out', -- WCC output table
+ '0', -- source vertex
+ 'reach_table'); -- output table containing all vertices reachable from source vertex
+SELECT * FROM reach_table ORDER BY component_id, dest;
+</pre> <pre class="result">
+ user_id | component_id | dest
+---------+--------------+------
+ 1 | 0 | 1
+ 1 | 0 | 2
+ 1 | 0 | 3
+ 1 | 0 | 5
+ 1 | 0 | 6
+(5 rows)
+</pre></li>
+<li>Count of connected components: <pre class="syntax">
+DROP TABLE IF EXISTS count_table;
+SELECT madlib.graph_wcc_num_cpts(
+ 'wcc_out', -- WCC output table
+ 'count_table'); -- output table containing number of components per group
+SELECT * FROM count_table;
+</pre> <pre class="result">
+ user_id | num_components
+------—+-------------—
+ 1 | 1
+ 2 | 2
+(2 rows)
+</pre> </li>
+</ol>
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