/**
@mainpage
Apache MADlib (incubating) is an open-source library for scalable
in-database analytics. It provides data-parallel implementations of
mathematical, statistical and machine learning methods for structured
and unstructured data.

The MADlib mission: to foster widespread development of scalable analytic
skills, by harnessing efforts from commercial practice, academic research,
and open-source development.

Useful links:
<ul>
<li><a href="http://madlib.incubator.apache.org">MADlib web site</a></li>
<li><a href="https://cwiki.apache.org/confluence/display/MADLIB">MADlib wiki</a></li>
<li><a href="https://issues.apache.org/jira/browse/MADLIB/">JIRAs for reporting bugs and reviewing backlog</a></li>
<li><a href="https://mail-archives.apache.org/mod_mbox/incubator-madlib-user/">User mailing list</a></li>
<li><a href="https://mail-archives.apache.org/mod_mbox/incubator-madlib-dev/">Dev mailing list</a></li>
<li>User documentation for earlier releases:
    <a href="../v1.9.1/index.html">v1.9.1</a>,
    <a href="../v1.9/index.html">v1.9</a>,
    <a href="../v1.8/index.html">v1.8</a>,
    <a href="../v1.7.1/index.html">v1.7.1</a>,
    <a href="../v1.7/index.html">v1.7</a>,
    <a href="../v1.6/index.html">v1.6</a>,
    <a href="../v1.5/index.html">v1.5</a>,
    <a href="../v1.4/index.html">v1.4</a>,
    <a href="../v1.3/index.html">v1.3</a>,
    <a href="../v1.2/index.html">v1.2</a>
</li>
</ul>

Please refer to the <a href="https://github.com/apache/incubator-madlib/blob/master/ReadMe.txt">Read-Me</a> file for information
about incorporated third-party material. License information regarding MADlib
and included third-party libraries can be found inside the
<a href="https://github.com/apache/incubator-madlib/blob/master/LICENSE">License</a> directory.

@defgroup grp_datatrans Data Types and Transformations
@{Data types and transformation operations @}
    @defgroup grp_arraysmatrix Arrays and Matrices
    @ingroup grp_datatrans
    @brief Mathematical operations for arrays and matrices
    @details
These modules provide basic mathematical operations to be run on array and matrices.

For a distributed system, a matrix cannot simply be represented as a 2D array of numbers in memory.
<b>We provide two forms of distributed representation of a matrix</b>:

- Dense: The matrix is represented as a distributed collection of 1-D arrays.
        An example 3x10 matrix would be the below table:
<pre>
 row_id |         row_vec
--------+-------------------------
   1    | {9,6,5,8,5,6,6,3,10,8}
   2    | {8,2,2,6,6,10,2,1,9,9}
   3    | {3,9,9,9,8,6,3,9,5,6}
</pre>
- Sparse: The matrix is represented using the row and column indices for each
non-zero entry of the matrix. Example:
<pre>
 row_id | col_id | value
--------+--------+-------
      1 |      1 |     9
      1 |      5 |     6
      1 |      6 |     6
      2 |      1 |     8
      3 |      1 |     3
      3 |      2 |     9
      4 |      7 |     0
(6 rows)
</pre>
&nbsp;
All matrix operations work with either form of representation.

In many cases, a matrix function can be <b>decomposed to vector operations
applied independently on each row of a matrix (or corresponding rows of two
matrices)</b>. We have also provided access to these internal vector operations
(\ref grp_array) for greater flexibility. Matrix operations like
<em>matrix_add</em> use the corresponding vector operation (<em>array_add</em>)
and also include additional validation and formating. Other functions like
<em>matrix_mult</em> are complex and use a combination of such vector operations
and other SQL operations.

<b>It's important to note</b> that these array functions are only available for the
dense format representation of the matrix. In general, the scope of a single
array function invocation is limited to only an array (1-dimensional or
2-dimensional) that fits in memory. When such function is executed on a table of
arrays, the function is called multiple times - once for each  array (or pair of
arrays). On contrary, scope of a single matrix function invocation  is the
complete matrix stored as a distributed table.
    @{
        @defgroup grp_array Array Operations
        @defgroup grp_matrix Matrix Operations

        @defgroup grp_matrix_factorization Matrix Factorization
        @brief Matrix Factorization methods including Singular Value Decomposition and Low-rank Matrix Factorization
        @{
            @defgroup grp_lmf Low-rank Matrix Factorization
            @defgroup grp_svd Singular Value Decomposition
        @}

        @defgroup grp_linalg Norms and Distance functions
        @defgroup grp_svec Sparse Vectors
    @}

        @defgroup grp_pca Dimensionality Reduction
        @ingroup grp_datatrans
        @brief A collection of methods for dimensionality reduction.
        @details A collection of methods for dimensionality reduction.
        @{
            @defgroup grp_pca_train Principal Component Analysis
            @defgroup grp_pca_project Principal Component Projection
        @}

        @defgroup grp_encode_categorical Encoding Categorical Variables
        @ingroup grp_datatrans

        @defgroup grp_pivot Pivot
        @ingroup grp_datatrans

        @defgroup grp_stemmer Stemming
        @ingroup grp_datatrans
@defgroup grp_graph Graph
@{Contains graph algorithms. @}
    @defgroup grp_sssp Single Source Shortest Path
    @ingroup grp_graph

@defgroup grp_mdl Model Evaluation
@{Contains functions for evaluating accuracy and validation of predictive methods. @}
    @defgroup grp_validation Cross Validation
    @ingroup grp_mdl
    @defgroup grp_pred Prediction Metrics
    @ingroup grp_mdl

@defgroup grp_stats Statistics
@{Contains statistics modules @}
    @defgroup grp_desc_stats Descriptive Statistics
    @ingroup grp_stats
    @{A collection of methods to compute descriptive statistics of the dataset @}

        @defgroup grp_correlation Pearson's Correlation
        @ingroup grp_desc_stats

        @defgroup grp_summary Summary
        @ingroup grp_desc_stats

    @defgroup grp_inf_stats Inferential Statistics
    @ingroup grp_stats
    @{A collection of methods to compute inferential statistics on a dataset.@}
        @defgroup grp_stats_tests Hypothesis Tests
        @ingroup grp_inf_stats

    @defgroup grp_prob Probability Functions
    @ingroup grp_stats

@defgroup grp_super Supervised Learning
@{Contains methods which perform supervised learning tasks @}
    @defgroup grp_crf Conditional Random Field
    @ingroup grp_super

    @defgroup grp_regml Regression Models
    @ingroup grp_super
    A collection of methods for modeling conditional expectation of a response variable.
    @{
        @defgroup grp_clustered_errors Clustered Variance
        @defgroup grp_cox_prop_hazards Cox-Proportional Hazards Regression
        @defgroup grp_elasticnet Elastic Net Regularization
        @defgroup grp_glm Generalized Linear Models
        @defgroup grp_linreg Linear Regression
        @defgroup grp_logreg Logistic Regression
        @defgroup grp_marginal Marginal Effects
        @defgroup grp_multinom Multinomial Regression
        @defgroup grp_ordinal Ordinal Regression
        @defgroup grp_robust Robust Variance
    @}

    @defgroup grp_svm Support Vector Machines
    @ingroup grp_super

    @defgroup grp_tree Tree Methods
    @ingroup grp_super
    @{A collection of recursive partitioning (tree) methods.  @}
        @defgroup grp_decision_tree Decision Tree
        @ingroup grp_tree

        @defgroup grp_random_forest Random Forest
        @ingroup grp_tree

@defgroup grp_tsa Time Series Analysis
@{A collection of methods to analyze time series data. @}
    @defgroup grp_arima ARIMA
    @ingroup grp_tsa

@defgroup grp_unsupervised Unsupervised Learning
@{A collection of methods for unsupervised learning tasks @}
    @defgroup grp_association_rules Association Rules
    @ingroup grp_unsupervised
    @{A collection of methods used to uncover interesting patterns in transactional datasets. @}
        @defgroup grp_assoc_rules Apriori Algorithm
        @ingroup grp_association_rules
    @defgroup grp_clustering Clustering
    @ingroup grp_unsupervised
    @{A collection of methods for clustering data@}
        @defgroup grp_kmeans k-Means Clustering
        @ingroup grp_clustering
    @defgroup grp_topic_modelling Topic Modelling
    @ingroup grp_unsupervised
    @{A collection of methods to uncover abstract topics in a document corpus @}
        @defgroup grp_lda Latent Dirichlet Allocation
        @ingroup grp_topic_modelling


@defgroup grp_utility_functions Utility Functions
    @defgroup @grp_utilities Developer Database Functions
    @ingroup grp_utility_functions

    @defgroup grp_linear_solver Linear Solvers
    @ingroup grp_utility_functions
    @{A collection of methods that implement solutions for systems of consistent linear equations. @}

        @defgroup grp_dense_linear_solver Dense Linear Systems
        @ingroup grp_linear_solver

        @defgroup grp_sparse_linear_solver Sparse Linear Systems
        @ingroup grp_linear_solver

    @defgroup grp_path Path
    @ingroup grp_utility_functions

    @defgroup grp_pmml PMML Export
    @ingroup grp_utility_functions

    @defgroup grp_sessionize Sessionize
    @ingroup grp_utility_functions

    @defgroup grp_text_analysis Text Analysis
    @ingroup grp_utility_functions
    @{A collection of methods to find patterns in textual data. @}
        @defgroup grp_text_utilities Term Frequency
        @ingroup grp_text_analysis

@defgroup grp_early_stage Early Stage Development
@brief A collection of implementations which are in early stage of development.
There may be some issues that will be addressed in a future version.
Interface and implementation are subject to change.
@{
     @defgroup grp_sketches Cardinality Estimators
     @{
        @defgroup grp_countmin CountMin (Cormode-Muthukrishnan)
        @defgroup grp_fmsketch FM (Flajolet-Martin)
        @defgroup grp_mfvsketch MFV (Most Frequent Values)
     @}

    @defgroup grp_cg Conjugate Gradient
    @defgroup grp_bayes Naive Bayes Classification
    @defgroup grp_sample Random Sampling

    @defgroup grp_nene Nearest Neighbors
    @{A collection of methods to create nearest neigbor based models.

        @defgroup grp_knn k-Nearest Neighbors
    @}
@}

@defgroup grp_deprecated Deprecated Modules
@brief A collection of deprecated modules. These functions will be removed in the
next major version (2.0).
@{
    @defgroup grp_indicator Create Indicator Variables
    @defgroup grp_mlogreg Multinomial Logistic Regression
@}

*/