dt.sql_in

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/* ----------------------------------------------------------------------- *//**
 *
 * @file dt.sql_in
 *
 * @brief the common functions written in PL/PGSQL shared by C4.5 and RF
 * @date April 5, 2012
 *
 *//* ----------------------------------------------------------------------- */

m4_include(`SQLCommon.m4')

/* Own macro definitions */
m4_ifelse(
    m4_eval(
        m4_ifdef(`__GREENPLUM__', 1, 0) &&
        __DBMS_VERSION_MAJOR__ * 100 + __DBMS_VERSION_MINOR__ < 401
    ), 1,
    `m4_define(`__GREENPLUM_PRE_4_1__')'
)
m4_ifelse(
    m4_eval(
        m4_ifdef(`__POSTGRESQL__', 1, 0) &&
        __DBMS_VERSION_MAJOR__ < 9
    ), 1,
    `m4_define(`__POSTGRESQL_PRE_9_0__')'
)

m4_ifelse(
    m4_eval(
        m4_ifdef(`__GREENPLUM__', 1, 0) &&
        __DBMS_VERSION_MAJOR__ * 10000 +
            __DBMS_VERSION_MINOR__ * 100 +
            __DBMS_VERSION_PATCH__ >= 40201
    ), 1,
    `m4_define(`__GREENPLUM_GE_4_2_1__')'
)

/*
 * This is a global table to store information for various tree training.
 *
 *   classifier_name             The name of the classifier, e.g, 'C4.5' or 'RF'.
 *   result_table_oid            The OID of the result table.
 *   training_table_oid          The OID of the training table.
 *   training_metatable_oid      The OID of the metadata table.
 *   training_encoded_table_oid  The OID of the encoded table.
 *   validation_table_oid        The OID of the validation table.
 *   how2handle_missing_value    The approach name to handle missing value.
 *   split_criterion             The name of the split criterion for this training.
 *   sampling_percentage         The sampling percentage for training each tree.
 *   num_feature_chosen          The number of features will be chosen to find best split.
 *   num_trees                   The number of trees will be grow in training.
 *
 */
DROP TABLE IF EXISTS MADLIB_SCHEMA.training_info;
CREATE TABLE MADLIB_SCHEMA.training_info
    (
    classifier_name             TEXT NOT NULL,
    result_table_oid            OID NOT NULL,
    training_table_oid          OID,
    training_metatable_oid      OID,
    training_encoded_table_oid  OID,
    validation_table_oid        OID,
    how2handle_missing_value    TEXT,
    split_criterion             TEXT,
    sampling_percentage         FLOAT,
    num_feature_chosen          INT,
    num_trees                   INT,
    PRIMARY KEY (result_table_oid)
    ) m4_ifdef(`__GREENPLUM__', `DISTRIBUTED BY (result_table_oid)');
GRANT SELECT, INSERT, UPDATE, DELETE ON MADLIB_SCHEMA.training_info TO PUBLIC;


/*
 * @brief Remove the trained tree from training info table. 
 *
 * @param tree_table    The full name of the tree table.
 *
 */      
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__delete_traininginfo
    (
    tree_table TEXT 
    ) 
RETURNS void AS $$
BEGIN
    DELETE FROM MADLIB_SCHEMA.training_info 
    WHERE result_table_oid = tree_table::regclass;
end
$$ LANGUAGE PLPGSQL;


/*
 * @brief Insert the trained tree into training info table. 
 *
 * @param classifier_table_name         The name of the classifier.
 * @param result_table_name             The full name of the training result table.
 * @param training_table_name           The full name of the training table.
 * @param training_metatable_name       The full name of metatable.
 * @param training_encoded_table_name   The full name of the encoded table. 
 * @param validation_table_name         The full name of the validation table.
 * @param how2handle_missing_value      The name of the routine to process unknown 
 *                                      values.
 * @param split_criterion               The name of split criterion.
 * @param sampling_percentage           The percentage of bootstrap samples size in 
 *                                      training dataset.
 * @param num_features_chosen           The number of features to split on each tree
 *                                      node. 
 * @param num_trees                     The number of trees after completed the 
 *                                      training process.
 * 
 */ 
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__insert_into_traininginfo
    (
    classifier_table_name       TEXT,
    result_table_name           TEXT,
    training_table_name         TEXT,
    training_metatable_name     TEXT,
    training_encoded_table_name TEXT,
    validation_table_name       TEXT,
    how2handle_missing_value    TEXT,
    split_criterion             TEXT,
    sampling_percentage         FLOAT,
    num_features_chosen         INT,
    num_trees                   INT
    )
RETURNS void AS $$
BEGIN
    INSERT INTO MADLIB_SCHEMA.training_info VALUES
        (
            classifier_table_name,
            result_table_name::regclass,
            training_table_name::regclass,
            training_metatable_name::regclass,
            training_encoded_table_name::regclass,
            validation_table_name::regclass,
            how2handle_missing_value,
            split_criterion,
            sampling_percentage,
            num_features_chosen,
            num_trees
        );
END
$$ LANGUAGE PLPGSQL;


/*
 * @brief Get the name of the encoded table.  
 *
 * @param tree_table    The full name of the tree table.
 *
 * @return The full name of the encoded table.
 *
 */  
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__get_encode_table_name
    (
    tree_table TEXT 
    ) 
RETURNS TEXT AS $$
DECLARE
    encoded_table_name TEXT := '';
BEGIN
    SELECT MADLIB_SCHEMA.__regclass_to_text(training_encoded_table_oid) 
    FROM MADLIB_SCHEMA.training_info
    WHERE result_table_oid = tree_table::regclass 
    INTO encoded_table_name;
    
    RETURN encoded_table_name;
END
$$ LANGUAGE PLPGSQL STABLE;


/*
 * @brief Test if the given table is a valid encoded one. 
 *        A valid encoded table has the following characteristic:
 *            + Its OID is in the column "training_encoded_table_oid"
 *              of training_info table.
 *            + It has 5 columns, whose names are id, fid, fval,
 *              is_cont and class.
 *            + The types of the 5 columns are BIGINT, INT, FLOAT8
 *              BOOL and INT.
 *
 * @param enc_tbl_name    The full name of the encoded table.
 *
 * @return Ture if the given table is a valid encoded one.
 *         False if it's an invalid encoded table.
 *
 */  
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__is_valid_enc_table
    (
    enc_tbl_name TEXT 
    ) 
RETURNS BOOL AS $$
DECLARE
    num_enc_table  INT;
    num_cols       INT;
    ret            BOOL := 'f'::BOOL;
BEGIN
    -- test if the table is in the training_info table
    SELECT count(*) 
    FROM MADLIB_SCHEMA.training_info
    WHERE MADLIB_SCHEMA.__regclass_to_text(training_encoded_table_oid) = 
            enc_tbl_name
    INTO num_enc_table;
    
    -- test if the name and the type of a column are valid or not
    SELECT count(*) 
    FROM pg_attribute 
    WHERE attrelid= enc_tbl_name::regclass::oid AND
          attnum > 0 AND 
          not attisdropped AND
          attname in ('id', 'fid', 'fval', 'is_cont', 'class') AND
          atttypid in ('int8'::regtype, 'int'::regtype, 'float8'::regtype, 
                       'bool'::regtype, 'int'::regtype)
    INTO num_cols;

    IF ((num_enc_table > 0) AND (num_cols = 5)) THEN
        ret = 't'::BOOL;        
    END IF;
    
    RETURN ret;
END
$$ LANGUAGE PLPGSQL;


/*
 * @brief Get the meta table name by the tree table name. 
 *
 * @param tree_table    The full name of the tree table.
 * 
 * @return The full name of the metatable.
 *
 */      
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__get_metatable_name
    (
    tree_table TEXT 
    ) 
RETURNS TEXT AS $$
DECLARE
    metatable_name TEXT := '';
BEGIN

    PERFORM MADLIB_SCHEMA.__assert_table
            (
                tree_table::TEXT,
                't'::BOOL
            );     
    
    PERFORM MADLIB_SCHEMA.__assert_table
            (
                'MADLIB_SCHEMA.training_info'::TEXT,
                't'::BOOL
            ); 
            
    SELECT MADLIB_SCHEMA.__regclass_to_text(training_metatable_oid) 
    FROM MADLIB_SCHEMA.training_info 
    WHERE result_table_oid = tree_table::regclass 
    INTO metatable_name;
    
    RETURN metatable_name;
END
$$ LANGUAGE PLPGSQL;


/*
 * @brief Get the unknown values processing routine id. 
 *
 * @param tree_table    The full name of the tree table.
 *
 * @return The encoded missing value processing routine id.
 *
 */     
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__get_routine_id
    (
    tree_table TEXT 
    ) 
RETURNS INT AS $$
DECLARE
    name TEXT;
BEGIN
    name = MADLIB_SCHEMA.__get_routine_name(tree_table);
        
    IF (name = 'ignore') THEN
        RETURN 1;
    ELSIF (name = 'explicit') THEN
        RETURN 2;
    ELSE
        RAISE EXCEPTION '__get_routine_id: %', name; 
    END IF;
    
END
$$ LANGUAGE PLPGSQL;


/*
 * @brief Get the unknown values processing routine name. 
 *        The valid routine name is 'ignore' or 'explicit'.
 *
 * @param tree_table    The full name of the tree table.
 *
 * @return The encoded missing value processing routine name.
 *
 */     
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__get_routine_name
    (
    tree_table TEXT 
    ) 
RETURNS TEXT AS $$
DECLARE
    curstmt    TEXT;
    name       TEXT;
BEGIN
    PERFORM MADLIB_SCHEMA.__assert_table
        (
            'MADLIB_SCHEMA.training_info',
            't'
        );

    curstmt = MADLIB_SCHEMA.__format
        (
            'SELECT how2handle_missing_value 
             FROM   MADLIB_SCHEMA.training_info 
             WHERE  result_table_oid = ''%''::regclass',
            tree_table
        );
    EXECUTE curstmt INTO name;

    RETURN name;
END
$$ LANGUAGE PLPGSQL;


/*
 * @brief Get the name of the tree table from the encoded table name. 
 *
 * @param enc_table_name  The encoded table name.  
 *
 * @return The full name of the tree table.
 *
 */   
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__get_tree_table_name
    (
    enc_table_name TEXT 
    ) 
RETURNS TEXT AS $$
DECLARE
    curstmt    TEXT;
    name       TEXT;
BEGIN
    curstmt = MADLIB_SCHEMA.__format
        (
            'SELECT MADLIB_SCHEMA.__regclass_to_text(result_table_oid::regclass) 
             FROM MADLIB_SCHEMA.training_info
             WHERE training_encoded_table_oid = ''%''::regclass
             LIMIT 1',
            enc_table_name
        );
    EXECUTE curstmt INTO name;

    RETURN name;
END
$$ LANGUAGE PLPGSQL;


CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__best_scv_sfunc
    (
    result      FLOAT8[],    -- intermediate result
    scv         FLOAT8[],
    fid         INT,
    split_value FLOAT8
    ) 
RETURNS FLOAT8[]  
AS 'MODULE_PATHNAME', 'dt_best_scv_sfunc'
LANGUAGE C STRICT IMMUTABLE;


CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__best_scv_prefunc
    (
    sfunc1_result     FLOAT8[],
    sfunc2_result     FLOAT8[]
    ) 
RETURNS FLOAT8[]
AS 'MODULE_PATHNAME', 'dt_best_scv_prefunc'
LANGUAGE C STRICT IMMUTABLE;


DROP AGGREGATE IF EXISTS MADLIB_SCHEMA.__best_scv_aggr
    (
    FLOAT8[],       -- scv
    INT,            -- fid
    FLOAT8          -- split_value    
    ) CASCADE;
CREATE
AGGREGATE MADLIB_SCHEMA.__best_scv_aggr
    (
    FLOAT8[],       -- scv
    INT,            -- fid
    FLOAT8          -- split_value
    ) 
(
  SFUNC=MADLIB_SCHEMA.__best_scv_sfunc,
  m4_ifdef(`__GREENPLUM__', `prefunc=MADLIB_SCHEMA.__best_scv_prefunc,')
  STYPE=FLOAT8[],
  initcond = '{0, 0, 0, 0, 0, 0, 0}'
);


/*
 * @brief The step function is defined to process each record in the ACS set. 
 *        The records have this format: 
 *        {fid, fval, is_cont, split_value, le, total, tid, nid}
 *
 * @param result            The array used to keep the best attribute's info.
 * @param sc_code           The code of the split criterion.
 * @param is_cont           True  - The feature is continuous. 
 *                          False - The feature is discrete.
 * @param num_class         The total number of classes.
 * @param le_array          The le component of the ACS record. le_array[i] is the 
 *                          number of samples whose class code equals to i and 
 *                          whose fval is less-than or equal to the fval component 
 *                          of the ACS record being processed.
 * @param total_array       The total component of the ACS record. total_array[i] is
 *                          the number of samples whose class code equals to i.
 * @param true_total        The real total number of samples currently assigned to 
 *                          the node identified by (tid, nid). If there are missing
 *                          values in fval, the sum of all elements in total_array
 *                          will be less than true_total.
 *
 * @return A 9-element array. Please refer to the definition of SCV_STATE_ARRAY_INDEX
 *         in dt.c for the detailed information of this array.
 *
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__scv_aggr_sfunc
    (
    result          FLOAT8[],
    sc_code         INT,
    is_cont         BOOLEAN,
    num_class       INT,
    le_array        FLOAT8[],
    total_array     FLOAT8[],
    true_total      BIGINT
    )
RETURNS FLOAT8[]
AS 'MODULE_PATHNAME', 'dt_scv_aggr_sfunc'
LANGUAGE C IMMUTABLE;


/*
 * @brief The pre-function for the aggregation of splitting criteria values. It  
 *        takes the state array produced by two sfunc and combine them together.
 *
 * @param sfunc1_result     The array from sfunc1.
 * @param sfunc2_result     The array from sfunc2.
 *
 * @return A 9-element array. Please refer to the definition of SCV_STATE_ARRAY_INDEX
 *         in dt.c for the detailed information of this array.
 *
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__scv_aggr_prefunc
    (
    sfunc1_result     FLOAT8[],
    sfunc2_result     FLOAT8[]
    ) 
RETURNS FLOAT8[]
AS 'MODULE_PATHNAME', 'dt_scv_aggr_prefunc'
LANGUAGE C STRICT IMMUTABLE;


/*
 * @brief The final function for the aggregation of splitting criteria values.
 *        It takes the state array produced by the sfunc and produces a
 *        5-element array.
 *
 * @param internal_result   The 9-element array produced by dt_scv_aggr_prefunc
 *
 * @return A 5-element array. Please refer to the definition of SCV_FINAL_ARRAY_INDEX
 *         in dt.c for the detailed information of this array.
 *
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__scv_aggr_ffunc
    (
    internal_result     FLOAT8[]
    ) 
RETURNS FLOAT8[]
AS 'MODULE_PATHNAME', 'dt_scv_aggr_ffunc'
LANGUAGE C STRICT IMMUTABLE;


DROP AGGREGATE IF EXISTS MADLIB_SCHEMA.__scv_aggr
    (
    INT,        -- sc
    BOOLEAN,    -- is_cont
    INT,        -- total number of classes
    FLOAT8[],   -- le array
    FLOAT8[],   -- total count array
    BIGINT      -- the total number of samples
    ) CASCADE;
CREATE
AGGREGATE MADLIB_SCHEMA.__scv_aggr
    (
    INT,        -- sc
    BOOLEAN,    -- is_cont
    INT,        -- total number of classes
    FLOAT8[],   -- le array
    FLOAT8[],   -- total count array
    BIGINT      -- the total number of samples
    ) 
(
  SFUNC=MADLIB_SCHEMA.__scv_aggr_sfunc,
  m4_ifdef(`__GREENPLUM__', `prefunc=MADLIB_SCHEMA.__scv_aggr_prefunc,')
  FINALFUNC=MADLIB_SCHEMA.__scv_aggr_ffunc,
  STYPE=FLOAT8[],
  initcond = '{0, 0, 0, 0, 0, 0, 0, 0, 0}'
  -- 1   sc: 1 infogain, 2 gainratio, 3 gini
  -- 2   is_cont
  -- 3   scv_class_info
  -- 4   scv_attr_info
  -- 5   scv_class_attr_info
  -- 6   scv_count
  -- 7   scv_total
  -- 8   max_class_id
  -- 9   max_class_count
);


/*
 * @brief Retrieve the specified number of unique features for a node.
 *        Discrete features used by ancestor nodes will be excluded.
 *        If the number of remaining features is less or equal than the
 *        requested number of features, then all the remaining features
 *        will be returned. Otherwise, we will sample the requested 
 *        number of features from the remaining features.
 *
 * @param num_req_features  The number of requested features.
 * @param num_features      The total number of features.
 * @param nid               The ID of the node for which the
 *                          features are sampled.
 * @param dp_fids           The IDs of the discrete features
 *                          used by the ancestors.
 *
 * @return An array containing all the IDs of chosen features.
 *
 */
CREATE OR REPLACE FUNCTION 
MADLIB_SCHEMA.__dt_get_node_split_fids(INT4, INT4, INT4, INT4[])
RETURNS INT[]
AS 'MODULE_PATHNAME', 'dt_get_node_split_fids'
LANGUAGE C VOLATILE;


/*
 * @brief Retrieve the selected features for a node. We will create a table, named 
 *        sf_association, to store the association between selected feature IDs and
 *        node IDs.
 *
 * @param nid_table_name    The full name of the table which contains all the 
 *                          node IDs.
 * @param result_table_name The full name of the table which contains the parent
 *                          discrete features for each node.
 * @param num_chosen_fids   The number of feature IDs will be chosen for a node.
 * @param total_num_fids    The total number of feature IDs, total_num_fids 
 *                          >= num_chosen_fids.
 *                          If num_chosen_fids < total_num_fids, then we will 
 *                          randomly select num_chosen_fids features from all
 *                          the features. Otherwise, we will return all the  
 *                          features exception they belong to the parent discrete
 *                          features for a node.
 * @param verbosity         > 0 means this function runs in verbose mode.
 *                    
 * @return An constant string for the association table name.
 *
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__get_features_of_nodes
    (
    nid_table_name        TEXT,
    result_table_name     TEXT,
    num_chosen_fids       INT,
    total_num_fids        INT,
    verbosity             INT
    )
RETURNS TEXT AS $$
DECLARE
    curstmt     TEXT;
BEGIN
    -- The sf_association table records which features are used
    -- for finding the best split for a node.
    -- It has two columns:
    --      nid -- The id of a node.
    --      fid -- The id of a feature.
    EXECUTE 'TRUNCATE sf_assoc';
    
    curstmt = MADLIB_SCHEMA.__format
                (
                    'INSERT INTO sf_assoc(nid, fid) 
                     SELECT 
                       nid, 
                       unnest(MADLIB_SCHEMA.__dt_get_node_split_fids(%, %,
                                nid,dp_ids)) as fid
                     FROM (SELECT nid, dp_ids 
                           FROM % s1, % s2 
                           WHERE s1.nid = s2.id
                           GROUP BY nid, dp_ids) t',
                    ARRAY[
                        num_chosen_fids::TEXT,
                        total_num_fids::TEXT,
                        nid_table_name,
                        result_table_name
                        ]
                );
     
     IF (verbosity > 0) THEN
        RAISE INFO 'build sample feature association stmt: %', curstmt;
     END IF;
     
     EXECUTE curstmt;
     
     -- we return an constant string for the association table name
     return 'sf_assoc';
     
END
$$ LANGUAGE PLPGSQL;


/*
 * This UDT is used to keep the times of generating acc.
 *
 * calc_pre_time   The time of pre-processing.
 * calc_acc_time   The time of calculating acc.
 *
 */
DROP TYPE IF EXISTS MADLIB_SCHEMA.__gen_acc_time;
CREATE TYPE MADLIB_SCHEMA.__gen_acc_time AS 
(   
    calc_pre_time       INTERVAL,
    calc_acc_time       INTERVAL
);


/*
 * @brief Generate the ACC for current leaf nodes.
 *
 * @param encoded_table_name    The full name of the encoded table for the  
 *                              training table.
 * @param metatable_name        The full name of the metatable contains the  
 *                              relevant information of the input table.
 * @param result_table_name     The full name of the training result table.
 * @param num_featrue_try       The number of features will be chosen per node. 
 * @param num_classes           Total number of classes in training set.
 * @param verbosity             > 0 means this function runs in verbose mode. 
 *                    
 * @return The time information for generating ACC.
 *
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__gen_acc
    (
    encoded_table_name      TEXT,
    metatable_name          TEXT,
    result_table_name       TEXT,
    tr_table_name           TEXT,
    sf_table_name           TEXT,
    num_featrue_try         INT,
    num_classes             INT,
    sampling_needed         BOOLEAN,
    verbosity               INT
    )
RETURNS MADLIB_SCHEMA.__gen_acc_time AS $$
DECLARE
    curstmt             TEXT := '';
    num_fids            INT  := 1;
    begin_calc_acc      TIMESTAMP;
    begin_calc_pre      TIMESTAMP;
    ret                 MADLIB_SCHEMA.__gen_acc_time;
    select_stmt         TEXT;
BEGIN
    begin_calc_pre = clock_timestamp();

    -- get the number of features
    curstmt = MADLIB_SCHEMA.__format
                (
                'SELECT COUNT(id) 
                FROM % 
                WHERE column_type = ''f''',
                metatable_name
                );
    EXECUTE curstmt INTO num_fids;

    -- preprocessing time
    ret.calc_pre_time = clock_timestamp() - begin_calc_pre;
    begin_calc_acc    = clock_timestamp();
        
    IF (sampling_needed) THEN
        PERFORM MADLIB_SCHEMA.__get_features_of_nodes
            (
                tr_table_name,
                result_table_name,
                num_featrue_try,
                num_fids,
                verbosity
            );
        
        select_stmt =  MADLIB_SCHEMA.__format
             (
                'SELECT tr.tid, tr.nid, ed.fid, ed.fval, ed.is_cont, 
                        ed.class, sum(weight) as count
                 FROM % ed, % tr, % sf
                 WHERE tr.nid = sf.nid AND ed.fid = sf.fid AND ed.id = tr.id
                 GROUP BY   tr.tid, tr.nid, ed.fid, ed.fval, 
                            ed.is_cont, ed.class',
               ARRAY[
                   encoded_table_name,
                   tr_table_name,
                   sf_table_name
               ]
            );
    ELSE
        select_stmt =  MADLIB_SCHEMA.__format
             (
                'SELECT tr.tid, tr.nid, ed.fid, ed.fval, ed.is_cont, 
                        ed.class, sum(weight) as count
                 FROM % ed, % tr
                 WHERE ed.id = tr.id
                 GROUP BY   tr.tid, tr.nid, ed.fid, ed.fval, 
                            ed.is_cont, ed.class',
               ARRAY[
                   encoded_table_name,
                   tr_table_name
               ]
            );        
    END IF;
    DROP TABLE IF EXISTS training_instance_aux;
    curstmt = MADLIB_SCHEMA.__format
        (
            'CREATE TEMP TABLE training_instance_aux AS
             SELECT tid, nid, fid, fval, is_cont, 
                    MADLIB_SCHEMA.__dt_acc_count_aggr
                        (%,count::BIGINT,class::INT) AS count
             FROM 
             (
                 %           
             ) l
             GROUP BY tid,nid,fid, fval,is_cont 
             m4_ifdef(`__GREENPLUM__', `DISTRIBUTED BY (fid, fval)')',
            ARRAY[
                num_classes::TEXT,
                select_stmt
            ]
        );

    IF ( verbosity>0 ) THEN
        RAISE INFO '%', curstmt;
    END IF;
    
    EXECUTE curstmt;
    ret.calc_acc_time = clock_timestamp() - begin_calc_acc;
    
    RETURN ret;
END
$$ LANGUAGE PLPGSQL;


DROP TYPE IF EXISTS MADLIB_SCHEMA.__rep_type CASCADE;
CREATE TYPE MADLIB_SCHEMA.__rep_type AS
    (
    numOfOrgClasses BIGINT[]
    );


/*
 * @brief The step function for aggregating the class counts while doing Reduce 
 *        Error Pruning (REP).
 *
 * @param class_count_array     The array used to store the accumulated information.
 *                              [0]: the total number of mis-classified samples.
 *                              [i]: the number of samples belonging to the ith class.
 * @param classified_class      The predicted class based on our trained DT model.
 * @param original_class        The real class value provided in the validation set.
 * @param max_num_of_classes    The total number of distinct class values. 
 *                    
 * @return An updated class count array.
 *
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__rep_aggr_class_count_sfunc
    (
    class_count_array       BIGINT[],        
    classified_class        INT,
    original_class          INT,
    max_num_of_classes      INT
    ) 
RETURNS BIGINT[]
AS 'MODULE_PATHNAME', 'dt_rep_aggr_class_count_sfunc'
LANGUAGE C IMMUTABLE;


/*
 * @brief Add the corresponding elements of the input arrays 
 *        to create a new one.
 *
 * @param 1 arg     The array 1.
 * @param 2 arg     The array 2.
 *                    
 * @return The new array.
 *
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__bigint_array_add
    (
    BIGINT[],
    BIGINT[]
    ) 
RETURNS BIGINT[]
AS 'MODULE_PATHNAME', 'bigint_array_add'
LANGUAGE C IMMUTABLE;


/*
 * @brief The final function for aggregating the class counts for REP. 
 *        It takes the class count array produced by the sfunc and produces a 
 *        two-element array. The first element is the ID of the class that has 
 *        the maximum number of samples represented by the root node of the subtree
 *        being processed. The second element is the number of reduced  
 *        misclassified samples if the leave nodes of the subtree are pruned.
 *
 * @param class_count_data     The array containing all the information for the 
 *                             calculation of Reduced-Error pruning. 
 *                    
 * @return A two element array.
 *
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__rep_aggr_class_count_ffunc
    (
    class_count_array       BIGINT[]        
    ) 
RETURNS BIGINT[]
AS 'MODULE_PATHNAME', 'dt_rep_aggr_class_count_ffunc'
LANGUAGE C STRICT IMMUTABLE;


DROP AGGREGATE IF EXISTS MADLIB_SCHEMA.__rep_aggr_class_count
    (
    INT,
    INT,
    INT
    );
CREATE AGGREGATE MADLIB_SCHEMA.__rep_aggr_class_count
    (
    INT,
    INT,
    INT
    ) 
(
  SFUNC=MADLIB_SCHEMA.__rep_aggr_class_count_sfunc,
  m4_ifdef(`__GREENPLUM__', `prefunc=MADLIB_SCHEMA.__bigint_array_add,')
  FINALFUNC=MADLIB_SCHEMA.__rep_aggr_class_count_ffunc,
  STYPE=BIGINT[]
);


/*
 * @brief The step function of the aggregate __array_indexed_agg.
 *
 * @param state         The step state array of the aggregate function.
 * @param elem          The element to be filled into the state array.
 * @param elem_cnt      The number of elements.
 * @param elem_idx      the subscript of "elem" in the state array.
 * 
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__array_indexed_agg_sfunc
    (
    state       float8[], 
    elem        float8, 
    elem_cnt    int8, 
    elem_idx    int8
    )
RETURNS float8[]
AS 'MODULE_PATHNAME', 'dt_array_indexed_agg_sfunc' 
LANGUAGE C IMMUTABLE;


/*
 * @brief The Pre-function of the aggregate __array_indexed_agg.
 * 
 * @param arg0  The first state array.
 * @param arg1  The second state array.
 *  
 * @return The combined state.  
 *
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__array_indexed_agg_prefunc
    (
    float8[], 
    float8[]
    )
RETURNS float8[]
AS 'MODULE_PATHNAME', 'dt_array_indexed_agg_prefunc' 
LANGUAGE C STRICT IMMUTABLE;


/*
 * @brief The final function of __array_indexed_agg.
 * 
 * @param state  The state array.
 * 
 * @return The aggregate result.
 *
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__array_indexed_agg_ffunc
    (
    float8[]
    )
RETURNS float8[]
AS 'MODULE_PATHNAME', 'dt_array_indexed_agg_ffunc' 
LANGUAGE C IMMUTABLE;


/*
 * @brief The aggregate is the same with array_agg, which will accumulate
 *        The elements in each group to an array, except that we allow users 
 *        provide the subscript for each element. This aggregate will be 
 *        invoked as HashAggregate, while array_agg will be called as 
 *        GroupAggregate. Therefore, our implementation have better performance
 *        than the array_agg.
 * 
 * @param elem     The element to be fed into the returned array of this aggregate.
 * @param elem_cnt The number of elements.
 * @param elem_idx The subscript of the element.
 *
 * @return The aggregated array.
 *
 */
CREATE AGGREGATE MADLIB_SCHEMA.__array_indexed_agg(float8, int8, int8) (
    SFUNC = MADLIB_SCHEMA.__array_indexed_agg_sfunc,
    m4_ifdef( `__GREENPLUM__',`PREFUNC   = MADLIB_SCHEMA.__array_indexed_agg_prefunc,')
    FINALFUNC = MADLIB_SCHEMA.__array_indexed_agg_ffunc, 
    STYPE = float8[]
);


CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__dt_acc_count_sfunc
    (
    count_array         BIGINT[],
    num_of_class        INT,
    count               BIGINT,
    class               INT
    ) 
RETURNS BIGINT[]  
AS 'MODULE_PATHNAME', 'dt_acc_count_sfunc'
LANGUAGE C VOLATILE;


CREATE AGGREGATE MADLIB_SCHEMA.__dt_acc_count_aggr
    (
    INT,
    BIGINT,
    INT
    ) 
(
  SFUNC=MADLIB_SCHEMA.__dt_acc_count_sfunc,
  m4_ifdef(`__GREENPLUM__', `prefunc=MADLIB_SCHEMA.__bigint_array_add,')
  STYPE=BIGINT[]
);


/*
 * @brief The aggregate is created for the PostgreSQL, which doesn't support the
 *        function sum over an array.
 * 
 * @param elem     The element to be fed into the returned array of this aggregate.
 *
 * @return The array with the sum of all the input array in a group.
 *
 */
CREATE
AGGREGATE MADLIB_SCHEMA.__bigint_array_sum
    (
    BIGINT[]
    ) 
(
  SFUNC=MADLIB_SCHEMA.__bigint_array_add,
  m4_ifdef(`__GREENPLUM__', `prefunc=MADLIB_SCHEMA.__bigint_array_add,')
  STYPE=BIGINT[]
);


/*
 * @brief This function find the best split and return the information.
 *
 * @param table_name          The name of the table containing the training
 *                            set.
 * @param confidence_level    This parameter is used by the 'Error-Based Pruning'.
 *                            Please refer to the paper for detailed definition.
 *                            The paper's name is 'Error-Based Pruning of Decision  
 *                            Trees Grown on Very Large Data Sets Can Work!'.
 * @param feature_table_name  Is is the name of one internal table, which contains
 *                            meta data for each feature.
 * @param split_criterion     It defines the split criterion to be used.
 *                            (1- information gain. 2- gain ratio. 3- gini).
 * @param continue_grow       It specifies whether we should still grow the tree
 *                            on the selected branch.
 * @param output_table        It specifies the table used to store the chosen splits.
 * @param h2hmv_routine_id    Specifies how to handle missing values. 
 *                            1 ignore, 2 explicit.
 *                    
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__find_best_split
    (
    table_name              TEXT, 
    confidence_level        FLOAT,
    feature_table_name      TEXT, 
    split_criterion         INT, 
    continue_grow           INT,
    output_table            TEXT,
    h2hmv_routine_id        INT,
    num_classes             INT
    ) 
RETURNS VOID AS $$
DECLARE
    total_size         INT;
    curstmt            TEXT := '';
    begin_func_exec    TIMESTAMP;
    select_stmt        TEXT;
BEGIN    
    begin_func_exec = clock_timestamp();
    
    IF (h2hmv_routine_id=1) THEN
        -- For ignore, we need the true size of nodes to handle the missing values.
        select_stmt =  
           'SELECT t1.tid, t1.nid, t1.fid, t1.total, t2.node_size::BIGINT 
            FROM
            (
                SELECT tid, nid, fid, 
                m4_ifdef(`__GREENPLUM__', `sum(count)', `MADLIB_SCHEMA.__bigint_array_sum(count)') as total
                FROM training_instance_aux
                GROUP BY tid, nid, fid
            ) t1 INNER JOIN node_size_aux t2 
            ON t1.tid=t2.tid AND t1.nid=t2.nid';
    ELSE
        -- For explicit, the calculated node size from the aggregation is correct.
        -- We can set NULL, which denotes we can safely use the counted value.
        select_stmt =  
           'SELECT tid, nid, fid, 
            m4_ifdef(`__GREENPLUM__', `sum(count)', `MADLIB_SCHEMA.__bigint_array_sum(count)') as total, 
            NULL::BIGINT AS node_size
            FROM training_instance_aux
            GROUP BY tid, nid, fid';
    END IF;

    /*
     * This table is used to store information for the calculated best split 
     *
     * tid                  The ID of the tree.
     * node_id              The ID of one node in the specified tree.
     * feature              The ID of the selected feature.
     * probability          The predicted probability of our chosen class.
     * max_class            The ID of the class chosen by the algorithm.
     * max_scv              The maximum split criterion value.
     * live                 1- For the chosen split, we should split further.
     *                      0- For the chosen split, we shouldn't split further.
     * ebp_coeff            total error for error-based pruning.
     * is_cont              whether the selected feature is continuous.
     * split_value          If the selected feature is continuous, it specifies
     *                      the split value. Otherwise, it is of no use.
     * distinct_features    The number of distinct values for the selected feature.
     * node_size            The size of this tree node. 
     *
     */
    EXECUTE 'DROP TABLE IF EXISTS '||output_table;
    EXECUTE 'CREATE TEMP TABLE '||output_table||' 
    (
        tid                 INT,
        node_id             INT,
        feature             INT,
        probability         FLOAT,
        max_class           INTEGER,
        max_scv             FLOAT,
        live                INT,
        ebp_coeff           FLOAT,
        is_cont             BOOLEAN,
        split_value         FLOAT,
        distinct_features   INT,
        node_size           INT
    ) m4_ifdef(`__GREENPLUM__', `DISTRIBUTED BY (node_id)');';
     

    EXECUTE 'DROP TABLE IF EXISTS tmp_best_table';

    SELECT MADLIB_SCHEMA.__format
        (
        'INSERT INTO %
         SELECT tid, nid, best_scv[6], best_scv[4], best_scv[3], best_scv[1],
                CASE WHEN (best_scv[1] < 1e-9   OR 
                           best_scv[4] > 1-1e-9 OR % <= 0 ) THEN
                        0
                ELSE
                        1
                END AS live,
                MADLIB_SCHEMA.__ebp_calc_errors
                    (best_scv[5], best_scv[4], %) AS ebp_coeff,
                o2.is_cont, 
                CASE WHEN( o2.is_cont ) THEN
                    best_scv[7]
                ELSE
                    NULL
                END AS split_value,
                o2.num_dist_value, best_scv[5]
        FROM
        (
            SELECT s1.tid, s1.nid,  
                MADLIB_SCHEMA.__best_scv_aggr(scv, s1.fid, 
                    coalesce(s1.split_value,0)) as best_scv
            FROM (
                SELECT t1.tid, t1.nid, t1.fid, split_value,
                        MADLIB_SCHEMA.__scv_aggr
                            (%, is_cont, %, le, total, t2.node_size) AS scv
                FROM 
                    (
                        SELECT tid, nid, fid, fval, is_cont, 
                        CASE WHEN (is_cont) THEN
                           fval 
                        ELSE
                            NULL::FLOAT8
                        END AS split_value,
                        CASE WHEN (is_cont) THEN
                                m4_ifdef(`__GREENPLUM__', `sum(count)', `MADLIB_SCHEMA.__bigint_array_sum(count)') OVER 
                                    (PARTITION BY tid, nid, fid ORDER BY fval
                                     ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW)
                        ELSE
                                count
                        END AS le
                        FROM training_instance_aux
                    ) t1,
                    (
                        %
                    ) t2
                WHERE t1.tid = t2.tid AND t1.nid = t2.nid AND t1.fid = t2.fid
                GROUP BY t1.tid, t1.nid, t1.fid, split_value
            ) s1
            GROUP BY s1.tid, s1.nid
        ) o1 INNER JOIN % o2 ON o1.best_scv[6]::INT=o2.id',
            ARRAY[
                output_table,
                continue_grow::TEXT,
                confidence_level::TEXT, 
                split_criterion::TEXT,
                num_classes::TEXT,
                select_stmt,
                feature_table_name
            ]
        ) INTO curstmt;

    EXECUTE curstmt;
        
    RETURN;
END
$$ LANGUAGE PLPGSQL;


/*
 * @brief For training one decision tree, we need some internal tables
 *        to store intermediate results. This function creates those
 *        tables. Moreover, this function also creates the tree table
 *        specified by user.
 *
 * @param result_tree_table_name  The name of the tree specified by user. 
 *                    
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__create_tree_tables
    (
    result_tree_table_name TEXT
    ) 
RETURNS void AS $$ 
BEGIN
    --  The table of node_size_aux records the size of each node. It is used
    --  for missing value handling.
    DROP TABLE IF EXISTS node_size_aux CASCADE;
    CREATE TEMP TABLE node_size_aux
    (
        tid             INT,
        nid             INT,
        node_size       INT
    )m4_ifdef(`__GREENPLUM__', `DISTRIBUTED BY (tid,nid)');
    
    -- The table below stores the decision tree information just constructed.
    -- Columns:
    --      id:             The ID of the node represented by this row. Tree 
    --                      node IDs are unique across all trees. The IDs of 
    --                      all children of a node is made to be continuous.
    --      tree_location:  An array containing the encoded values of all the 
    --                      features on the path from the root node to the 
    --                      current node. For the root node, the location 
    --                      value is {0}.
    --      feature:        The ID of the best split feature chosen for the 
    --                      node represented by this row.
    --      probability:    If forced to make a call for a dominant class 
    --                      at a given point this would be the confidence of the 
    --                      call (this is only an estimated value).
    --      ebp_coeff:      The total errors used by error based pruning (ebp) 
    --                      based on the specified confidence level. RF does
    --                      not do EBP therefore for RF nodes, this column always 
    --                      contains 1.    
    --      max_class:      If forced to make a call for a dominant class 
    --                      at a given point this is the selected class.
    --      scv:            The splitting criteria value (scv) computed at this node.
    --      live:           Specifies whether the node should be further split 
    --                      or not. A positive value indicates further split of
    --                      the node represented by this row is needed.
    --      num_of_samples: The number of samples at this node.
    --      parent_id:      Id of the parent branch.
    --      lmc_nid:        Leftmost child (lmc) node id of the node represented
    --                      by the current row.
    --      lmc_fval:       The feature value which leads to the lmc node.    
    --                      An example of getting all the child nodes' ids 
    --                      and condition values
    --                      1. Get the right most node id
    --                      SELECT DISTINCT ON(parent_id) id FROM tree_table 
    --                      WHERE parent_id = $pid ORDER BY parent_id, id desc
    --                      INTO max_child_nid;
    --                      2. Get child nodes' ids and condition values by a 
    --                         while loop
    --                      node_count = 1;
    --                      WHILE (lmc_nid IS NOT NULL) AND 
    --                          (0 < node_count AND lmc_nid <= max_child_nid) LOOP
    --                          ...
    --                          lmc_nid  = lmc_nid  + 1;
    --                          lmc_fval = lmc_fval + 1; 
    --                          SELECT COUNT(id) FROM tree_table 
    --                          WHERE id = $lmc_nid AND parent_id = $pid 
    --                          INTO node_count;        
    --                      END LOOP;
    --      is_cont:        It specifies whether the selected feature is a 
    --                      continuous feature.
    --      split_value:    For continuous feature, it specifies the split value.
    --                      Otherwise, it is of no meaning and fixed to 0.  
    --      tid:            The id of a tree that this node belongs to.
    --      dp_ids:         An array containing the IDs of the non-continuous 
    --                      features chosen by all ancestors nodes (starting 
    --                      from the root) for splitting.
    --
    -- The table below stores the final decision tree information.
    -- It is an the table specified by users. 
    -- Please refer the table above for detailed column definition.
    EXECUTE 'DROP TABLE IF EXISTS '||result_tree_table_name||' CASCADE;';
    EXECUTE 'CREATE TABLE '||result_tree_table_name||'
    (
        id              INT,
        tree_location   INT[],
        feature         INT,
        probability     FLOAT,
        ebp_coeff       FLOAT,
        max_class       INTEGER,
        scv             FLOAT,
        live            INT,
        num_of_samples  INT,
        parent_id       INT,
        lmc_nid         INT,
        lmc_fval        INT,
        is_cont         BOOLEAN,
        split_value     FLOAT,
        tid             INT,
        dp_ids          INT[]
    ) m4_ifdef(`__GREENPLUM__', `DISTRIBUTED BY (tid,id)');';
 
    -- The following table stored the auxiliary information for updating the 
    -- association table, so that the updating operation only need to  
    -- join the encoded table with association table once
    EXECUTE 'DROP TABLE IF EXISTS assoc_aux CASCADE';
    CREATE TEMP TABLE assoc_aux
    (
        nid         INT, 
        fid         INT, 
        lmc_id      INT, 
        svalue      FLOAT, 
        is_cont     BOOL
    ) m4_ifdef(`__GREENPLUM__', `DISTRIBUTED BY (nid)'); 

    EXECUTE 'DROP TABLE IF EXISTS tr_assoc_ping CASCADE';
    EXECUTE 'DROP TABLE IF EXISTS tr_assoc_pong CASCADE';
    EXECUTE 'DROP TABLE IF EXISTS sf_assoc CASCADE';
 
m4_changequote(`>>>', `<<<')
m4_ifdef(>>>__GREENPLUM_GE_4_2_1__<<<, >>>
    CREATE TEMP TABLE tr_assoc_ping
    (
        id      BIGINT ENCODING (compresstype=RLE_TYPE),
        nid     INT    ENCODING (compresstype=RLE_TYPE),
        tid     INT    ENCODING (compresstype=RLE_TYPE),
        weight  INT    ENCODING (compresstype=RLE_TYPE) 
    )
    WITH(appendonly=true, orientation=column)
    DISTRIBUTED BY(id);

    CREATE TEMP TABLE tr_assoc_pong
    (
        id      BIGINT ENCODING (compresstype=RLE_TYPE),
        nid     INT    ENCODING (compresstype=RLE_TYPE),
        tid     INT    ENCODING (compresstype=RLE_TYPE),
        weight  INT    ENCODING (compresstype=RLE_TYPE)
    )
    WITH(appendonly=true, orientation=column)
    DISTRIBUTED BY(id);

    CREATE TEMP TABLE sf_assoc
    (
        nid     INT    ENCODING (compresstype=RLE_TYPE),
        fid     INT    ENCODING (compresstype=RLE_TYPE)
    )
    WITH(appendonly=true, orientation=column)
    DISTRIBUTED BY(fid);
<<<, >>>
    CREATE TEMP TABLE tr_assoc_ping
    (
        id      BIGINT,
        nid     INT,
        tid     INT,
        weight  INT
    )m4_ifdef(`__GREENPLUM__', `DISTRIBUTED BY (id)');
    CREATE TEMP TABLE tr_assoc_pong
    (
        id      BIGINT,
        nid     INT,
        tid     INT,
        weight  INT
    )m4_ifdef(`__GREENPLUM__', `DISTRIBUTED BY (id)');
    CREATE TEMP TABLE sf_assoc
    (
        nid     INT,
        fid     INT
    )m4_ifdef(`__GREENPLUM__', `DISTRIBUTED BY (fid)');    
<<<)
m4_changequote(>>>`<<<, >>>'<<<)    
END 
$$ LANGUAGE PLPGSQL;


/*
 * @brief Prune the trained tree with "Reduced Error Pruning" algorithm.
 *
 * @param tree_table_name   The name of the table containing the tree. 
 * @param validation_table  The name of the table containing validation set. 
 * @param max_num_classes   The count of different classes. 
 *                    
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__rep_prune_tree
    (
    tree_table_name     TEXT, 
    validation_table    TEXT, 
    max_num_classes     INT
    ) 
RETURNS void AS $$
DECLARE
    num_parent_ids          INTEGER;
    cf_table_name           TEXT;
    encoded_table_name      TEXT;
    metatable_name          TEXT;
    curstmt                 TEXT;
    id_col_name             TEXT;
    class_col_name          TEXT;
    classify_result         TEXT;
    temp_text               TEXT;
    n                       INT;
    table_names             TEXT[];
BEGIN
    metatable_name  = MADLIB_SCHEMA.__get_metatable_name(tree_table_name);
    id_col_name     = MADLIB_SCHEMA.__get_id_column_name(metatable_name);
    class_col_name  = MADLIB_SCHEMA.__get_class_column_name(metatable_name);
    
    -- the value of class column in validation table must in the KV table
    SELECT MADLIB_SCHEMA.__format
        (
        'SELECT COUNT(*) 
         FROM %
         WHERE MADLIB_SCHEMA.__to_char(%) NOT IN
            (SELECT fval FROM % WHERE fval IS NOT NULL)',
        ARRAY[
            validation_table,
            class_col_name,
            MADLIB_SCHEMA.__get_classtable_name(metatable_name)
        ]
        )
    INTO curstmt;
    
    EXECUTE curstmt INTO n;
    
    PERFORM MADLIB_SCHEMA.__assert
            (
                n = 0,
                'the value of class column in validation table must in 
                 training table'
            ); 
                                
    table_names = MADLIB_SCHEMA.__treemodel_classify_internal
                  (
                    validation_table, 
                    tree_table_name, 
                    0
                  );
   
    encoded_table_name = table_names[1];
    classify_result    = table_names[2];
    cf_table_name      = classify_result;

    -- after encoding in classification, class_col_name is fixed to class
    class_col_name  = 'class';
    
m4_changequote(`>>>', `<<<')
m4_ifdef(>>>__GREENPLUM_PRE_4_1__<<<, >>>
    EXECUTE 'DROP TABLE IF EXISTS tree_rep_pong CASCADE';
    EXECUTE 'CREATE TEMP TABLE tree_rep_pong AS SELECT * FROM ' || 
             classify_result || 
             ' LIMIT 0 m4_ifdef(`__GREENPLUM__', `DISTRIBUTED BY (id)')';
<<<)
m4_changequote(>>>`<<<, >>>'<<<)
    
    LOOP
        DROP TABLE IF EXISTS selected_parent_ids_rep;
        CREATE TEMP TABLE selected_parent_ids_rep
        (
            parent_id BIGINT,
            max_class  INT
        ) m4_ifdef(`__GREENPLUM__', `DISTRIBUTED BY (parent_id)');
       
        SELECT MADLIB_SCHEMA.__format
            (
                'INSERT INTO selected_parent_ids_rep 
                SELECT parent_id, t.g[1] as max_class 
                FROM 
                (
                    SELECT parent_id, 
                           MADLIB_SCHEMA.__rep_aggr_class_count
                               (
                               c.class, 
                               s.%, 
                               % 
                               ) AS g 
                    FROM % c, % s 
                    WHERE c.id=s.% 
                    GROUP BY parent_id
                ) t 
                WHERE t.g[2] >= 0 AND 
                      t.parent_id IN 
                      (
                          Select parent_id FROM % 
                          WHERE parent_id NOT IN
                              (
                                  Select parent_id  
                                  FROM % 
                                  WHERE lmc_nid IS NOT NULL
                              ) and id <> 1
                      );',
                  ARRAY[
                      class_col_name,
                      MADLIB_SCHEMA.__to_char(max_num_classes),
                      classify_result,
                      encoded_table_name,
                      id_col_name,
                      tree_table_name,
                      tree_table_name
                  ]
              )
              INTO curstmt;
            
        EXECUTE curstmt;
                        
        EXECUTE 'SELECT parent_id FROM selected_parent_ids_rep limit 1;' 
            INTO num_parent_ids;
        IF (num_parent_ids IS NULL)  THEN
            EXIT;
        END IF;

m4_changequote(`>>>', `<<<')
m4_ifdef(`__GREENPLUM_PRE_4_1__', >>>
        -- for some databases, update operation can't distribute data across segments
        -- we use two tables to update the data
        IF (classify_result = 'tree_rep_pong') THEN
            temp_text = cf_table_name;
        ELSE
            temp_text =  'tree_rep_pong';
        END IF;
        
        EXECUTE 'TRUNCATE ' ||  temp_text;
        SELECT MADLIB_SCHEMA.__format
            (
            'INSERT INTO %(id, class, parent_id, leaf_id)
             SELECT m.id,  t.max_class, t.parent_id, t.id
             FROM % m, % t
             WHERE t.id IN (SELECT parent_id FROM selected_parent_ids_rep) AND
             m.parent_id = t.id',
            ARRAY[
                temp_text,
                classify_result,
                tree_table_name
            ]
            )
        INTO curstmt;
        
        EXECUTE curstmt;
        
        classify_result = temp_text;
<<<, >>>
        SELECT MADLIB_SCHEMA.__format
            (
                'UPDATE % m set class = t.max_class, 
                 parent_id = t.parent_id,leaf_id = t.id  
                 FROM % t
                 WHERE t.id IN (SELECT parent_id FROM selected_parent_ids_rep) AND
                 m.parent_id=t.id',
                classify_result,
                tree_table_name
            )
        INTO curstmt;
        EXECUTE curstmt;        
<<<)
m4_changequote(>>>`<<<, >>>'<<<)
            
        SELECT MADLIB_SCHEMA.__format
            (
                'DELETE FROM % WHERE parent_id IN 
                 (SELECT parent_id FROM selected_parent_ids_rep)',
                tree_table_name
            )
            INTO curstmt;
        
        EXECUTE curstmt;

        SELECT MADLIB_SCHEMA.__format
            (
                'UPDATE % t1 SET lmc_nid = NULL, 
                 lmc_fval = NULL, max_class = t2.max_class 
                 FROM selected_parent_ids_rep t2
                 WHERE t1.id = t2.parent_id;',
                tree_table_name
            )
            INTO curstmt;
        
        EXECUTE curstmt;
        
    END LOOP;
    
    EXECUTE 'DROP TABLE IF EXISTS ' || encoded_table_name || ' CASCADE;';
END
$$ LANGUAGE PLPGSQL;


/*
 * @brief Calculates the total errors used by Error Based Pruning (EBP).
 *
 * @param total             The number of total samples represented by the node 
 *                          being processed. 
 * @param prob              The probability to mis-classify samples represented by the 
 *                          child nodes if they are pruned with EBP. 
 * @param confidence_level  A certainty factor to calculate the confidence limits
 *                          for the probability of error using the binomial theorem. 
 *  
 * @return The computed total error.
 *
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__ebp_calc_errors
    (
    total               FLOAT8,
    prob                FLOAT8,
    confidence_level    FLOAT8
    ) RETURNS FLOAT8 
AS 'MODULE_PATHNAME', 'dt_ebp_calc_errors'
LANGUAGE C STRICT IMMUTABLE;


/*
 * @brief Prune the trained tree with "Error-based Pruning" algorithm.
 *
 * @param tree_table_name  The name of the table containing the tree. 
 *  
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__ebp_prune_tree
    (
    tree_table_name TEXT
    ) 
RETURNS void AS $$
DECLARE
    num_parent_ids INTEGER;
    curstmt TEXT;
BEGIN
    LOOP
        DROP TABLE IF EXISTS selected_parent_ids_ebp;
        CREATE TEMP TABLE selected_parent_ids_ebp(parent_id BIGINT) 
            m4_ifdef(`__GREENPLUM__', `DISTRIBUTED BY(parent_id)');
        
        SELECT MADLIB_SCHEMA.__format
            (
                'INSERT INTO selected_parent_ids_ebp 
                SELECT s.parent_id as parent_id 
                FROM  
                (
                    Select parent_id, sum(ebp_coeff) as ebp_coeff 
                    FROM 
                    (
                        Select parent_id, ebp_coeff 
                        FROM % 
                        WHERE parent_id NOT IN 
                            (
                            Select parent_id  FROM % WHERE lmc_nid IS NOT NULL
                            )  and id <> 1
                    ) m 
                    GROUP BY m.parent_id
                 ) s 
                 LEFT JOIN  % p 
                    ON p.id = s.parent_id 
                 WHERE  p.ebp_coeff < s.ebp_coeff;',
                 tree_table_name,
                 tree_table_name,
                 tree_table_name
            )
            INTO curstmt;
         
        EXECUTE curstmt;
                 
        EXECUTE 'SELECT parent_id FROM selected_parent_ids_ebp LIMIT 1;' 
                 INTO num_parent_ids;

        IF (num_parent_ids IS NULL)  THEN
            EXIT;
        END IF;
        
        SELECT MADLIB_SCHEMA.__format
            (
                'DELETE FROM % 
                WHERE parent_id IN 
                    (SELECT parent_id FROM selected_parent_ids_ebp)',
                tree_table_name
            )
            INTO curstmt;
            
        EXECUTE curstmt;
        
        SELECT MADLIB_SCHEMA.__format
            (
                'UPDATE %  
                SET lmc_nid = NULL, lmc_fval = NULL 
                WHERE id IN 
                    (SELECT parent_id FROM selected_parent_ids_ebp)',
                tree_table_name
            )
            INTO curstmt;
            
        EXECUTE curstmt;
        
    END LOOP;
END
$$ LANGUAGE PLPGSQL;


/*
 * @brief Generate the final trained tree.
 *
 * @param result_tree_table_name  The name of the table containing the tree.
 *  
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__generate_final_tree
    (
    result_tree_table_name TEXT
    ) 
RETURNS void AS $$
DECLARE
    tree_size           INTEGER;
    curstmt             TEXT;
    num_redundant_nodes INTEGER;
BEGIN

    EXECUTE ' DELETE FROM ' || result_tree_table_name || 
            ' WHERE COALESCE(num_of_samples,0) = 0';
    
    -- for each node, find the left most child node id and the feature value,
    -- and update the node's lmc_nid and lmc_fval column     
    SELECT MADLIB_SCHEMA.__format
            (
                'UPDATE % k
                 SET lmc_nid = g.lmc_nid, lmc_fval = g.lmc_fval
                 FROM  
                    (
                    SELECT parent_id,
                           min(id) as lmc_nid,
                           min(tree_location[array_upper(tree_location,1)]) 
                           as lmc_fval
                    FROM %
                    GROUP BY parent_id
                    ) g
                WHERE k.id = g.parent_id',
                ARRAY[
                    result_tree_table_name,
                    result_tree_table_name
                    ]
            )
    INTO curstmt;   
    EXECUTE curstmt;

    /*
     *  For a certain node, if all of its children are leaf nodes and have the 
     *  same class label, we can safely remove its children. After removal, we
     *  should apply the same operation to the new leaf nodes until no nodes 
     *  meet this criterion.
     */
    LOOP
        EXECUTE 'DROP TABLE IF EXISTS trim_tree_aux_table CASCADE';
        -- Find nodes whose children should be removed.
        curstmt = MADLIB_SCHEMA.__format
            (
            'CREATE TEMP TABLE trim_tree_aux_table AS
            SELECT parent_id FROM
            (
                SELECT parent_id, count(distinct max_class) as class_count 
                FROM %
                WHERE parent_id IN
                    (
                    SELECT parent_id FROM % 
                    WHERE parent_id NOT IN
                        (
                            SELECT parent_id  
                            FROM % 
                            WHERE lmc_nid IS NOT NULL
                        ) and parent_id <> 0
                    )  
                GROUP BY parent_id
            ) l
            where l.class_count=1
            m4_ifdef(`__GREENPLUM__', `DISTRIBUTED BY (parent_id)')',
            ARRAY[
                result_tree_table_name,
                result_tree_table_name,
                result_tree_table_name
                ]
            );
        EXECUTE curstmt;

        EXECUTE 'SELECT count(*) FROM trim_tree_aux_table' 
            INTO num_redundant_nodes;

        IF (num_redundant_nodes <= 0) THEN
            EXIT;
        END IF;
 
        -- Delete the found redundant nodes.
        curstmt = MADLIB_SCHEMA.__format
            (
            '
            DELETE FROM % t
            WHERE t.parent_id IN
            (SELECT parent_id FROM trim_tree_aux_table)',
            ARRAY[
                result_tree_table_name
                ]
            );
        EXECUTE curstmt;

        -- Set the nodes, whose children are removed, to be leaf nodes.
        curstmt =  MADLIB_SCHEMA.__format
                (
                'UPDATE % k
                 SET lmc_nid = NULL, lmc_fval = NULL
                 FROM  
                    (
                    SELECT parent_id FROM trim_tree_aux_table
                    ) g
                 WHERE k.id = g.parent_id',
                ARRAY[
                    result_tree_table_name
                    ]
                );
        EXECUTE curstmt;
    END LOOP;
END
$$ LANGUAGE PLPGSQL;


/*
 * The UDT for the training result.
 *
 *      num_of_samples           It means how many records there exists in the 
 *                               training set.   
 *      features_per_node        The number of features chosen for each tree.
 *      num_tree_nodes           The number of tree nodes.
 *      max_tree_depth           The max tree depth.
 *      calc_acc_time            Total time of calculating acc.
 *      calc_pre_time            Time of preprocessing when calculating acc.
 *      update_time              Total time of updating operation after found
 *                               the best time. 
 *      update_best              Time of updating the best splits' information.
 *      update_child             Time of generating the child nodes.
 *      update_nid               Time of updating the assigned node IDs.
 *      scv_acs_time             Time of calculating the best splits.     
 *      prune_time               Time of tree pruning.
 *
 */
DROP TYPE IF EXISTS MADLIB_SCHEMA.__train_result;
CREATE TYPE MADLIB_SCHEMA.__train_result AS 
(   
    num_of_samples           BIGINT,   
    features_per_node        INT,
    num_tree_nodes           INT,
    max_tree_depth           INT,
    calc_acc_time            INTERVAL,
    calc_pre_time            INTERVAL,
    update_time              INTERVAL,
    update_best              INTERVAL,
    update_child             INTERVAL,
    update_nid               INTERVAL,
    scv_acs_time             INTERVAL,
    prune_time               INTERVAL
);


/*
 * @brief The function samples a set of integer values between low and high.
 *
 * @param num_of_samples  The number of records to be sampled.
 * @param low             The low limit of sampled values.
 * @param high            The high limit of sampled values.
 *
 * @return A set of integer values sampled randomly between [low, high].
 *
 */
DROP FUNCTION IF EXISTS MADLIB_SCHEMA.__sample_within_range
    (
    BIGINT,
    BIGINT,
    BIGINT
    )CASCADE;
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__sample_within_range
    (
    num_of_samples      BIGINT,
    low                 BIGINT,
    high                BIGINT
    ) 
RETURNS SETOF BIGINT  
AS 'MODULE_PATHNAME', 'dt_sample_within_range'
LANGUAGE C STRICT VOLATILE;


/*
 * @brief The function samples with replacement from source table and store
 *        the results to target table.
 * 
 *        In this function, we firstly calculate how many samples should be
 *        generated in each segment. Then, we let those segments sample with
 *        replacement between the maximum ID and minimum ID of the source table 
 *        in parallel and assign samples to different trees. 
 *
 *        If there are gaps in the ID column of the source table, we sample
 *        extra records in proportion to the number of gaps. At last, we remove
 *        these invalid samples with an inner join operation with the source
 *        table. Since we target big data, this strategy works quite well.
 *
 * @param num_of_tree     The number of trees to be trained.
 * @param size_per_tree   The number of records to be sampled for each tree.
 * @param src_table       The name of the table to be sampled from.
 * @param target_table    The name of the table used to store the results.
 *
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__sample_with_replacement
    ( 
    num_of_tree     INT,
    size_per_tree   BIGINT, 
    src_table       TEXT,
    target_table    TEXT
    ) 
RETURNS VOID AS $$
DECLARE
    segment_num     INT;
    sample_per_seg  BIGINT;
    sample_ratio    FLOAT8;
    record_num      FLOAT8;
    min_id          BIGINT;
    max_id          BIGINT;
    range           FLOAT8;
    stmt            TEXT;
BEGIN

m4_changequote(`>>>', `<<<')
m4_ifdef(>>>__GREENPLUM__<<<, >>>
    -- get the segment number
    SELECT COUNT(distinct content) FROM gp_segment_configuration 
        WHERE content<>-1 INTO segment_num;
<<<, >>>
    -- fix the segment number to 1 for PG
    segment_num = 1;
<<<)
m4_changequote(>>>`<<<, >>>'<<<)


    DROP TABLE IF EXISTS auxiliary_segment_table;
    CREATE TEMP TABLE auxiliary_segment_table
    (
        segment_id  INT   
    ) m4_ifdef(`__GREENPLUM__', `DISTRIBUTED BY(segment_id)');

    -- Insert segment_num of records distributed by segment id
    EXECUTE 'INSERT INTO auxiliary_segment_table 
        SELECT generate_series(1,'||segment_num||');';

    EXECUTE 'SELECT max(id),min(id), count(id) as record_num 
        FROM '||src_table||';' INTO max_id,min_id,record_num;
    range=max_id-min_id+1;

    -- compute the sample ratio
    sample_ratio= range/record_num;

    -- compute how many records should be sampled by each segment
    sample_per_seg=((sample_ratio*num_of_tree*size_per_tree)/segment_num)::BIGINT;
    
    -- add the weight field

    IF (range > record_num) THEN
        -- remove those invalid samples with join operation
        stmt = MADLIB_SCHEMA.__format
            (
            'INSERT INTO %(id, tid, nid, weight)
              SELECT record_id, 
                     tid AS tid, 
                     tid AS nid, 
                     count(*) AS weight
              FROM
                (
                    SELECT  MADLIB_SCHEMA.__sample_within_range(%, %, %) AS record_id,
                            MADLIB_SCHEMA.__sample_within_range(%, 1, %) AS tid   
                    FROM auxiliary_segment_table
                ) t, 
                % k
              WHERE t.record_id=k.id
              GROUP BY record_id, tid, nid',
            ARRAY[
                target_table,
                sample_per_seg::TEXT,
                min_id::TEXT,
                max_id::TEXT,
                sample_per_seg::TEXT,
                num_of_tree::TEXT,
                src_table
            ]
            );
    ELSE
        stmt = MADLIB_SCHEMA.__format
            (
            'INSERT INTO %(id, tid, nid, weight)
              SELECT record_id, 
                     tid AS tid, 
                     tid AS nid, 
                     count(*) AS weight
              FROM
                (
                    SELECT  MADLIB_SCHEMA.__sample_within_range(%, %, %) AS record_id,
                            MADLIB_SCHEMA.__sample_within_range(%, 1, %) AS tid   
                    FROM auxiliary_segment_table
                ) t 
              GROUP BY record_id, tid, nid',
            ARRAY[
                target_table,
                sample_per_seg::TEXT,
                min_id::TEXT,
                max_id::TEXT,
                sample_per_seg::TEXT,
                num_of_tree::TEXT
            ]
            );
    END IF;

    EXECUTE stmt;
END
$$ LANGUAGE PLPGSQL VOLATILE;


/*
 * @brief This function trains a decision tree or random forest.
 *
 * @param split_criterion             This parameter specifies which split criterion 
 *                                    should be used for tree construction and 
 *                                    pruning. The valid values are infogain, 
 *                                    gainratio, and gini.
 * @param num_trees                   Total number of trees to be trained. 
 * @param features_per_node           Total number of features used to compute split 
 *                                    gain for each node. 
 * @param training_table_name         The name of the table/view with the source data. 
 * @param training_table_meta         The name of the table with the meta data. 
 * @param result_tree_table_name      The name of the table where the resulting 
 *                                    DT/RF will be stored. 
 * @param validation_table_name       The validation table used for pruning tree.  
 * @param id_col_name                 The name of the column containing id of each point.  
 * @param class_col_name              The name of the column containing correct class 
 *                                    of each point.  
 * @param confidence_level            A statistical confidence interval of the 
 *                                    resubstitution error.  
 * @param max_tree_depth              Maximum decision tree depth.  
 * @param node_prune_threshold        Specifies the minimum number of samples required 
 *                                    in a child node.  
 * @param node_split_threshold        Specifies the minimum number of samples required 
 *                                    in a node in order for a further split   
 *                                    to be possible.  
 * @param sampling_needed             Whether enabling the sampling functionality.  
 * @param h2hmv_routine_id            Specifies how to handle missing values. 
 *                                    1 ignore, 2 explicit.
 * @param verbosity                   > 0 means this function runs in verbose mode. 
 *  
 * @return The record including training related information.
 *         Details please refer to the UDT: MADLIB_SCHEMA.__train_result.
 *
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__train_tree
    (
    split_criterion         TEXT,
    num_trees               INT,
    features_per_node       INT,
    training_table_name     TEXT, 
    training_table_meta     TEXT,
    result_tree_table_name  TEXT,
    validation_table_name   TEXT,
    id_col_name             TEXT, 
    class_col_name          TEXT, 
    confidence_level        FLOAT, 
    max_tree_depth          INT,
    sampling_percentage     FLOAT,
    node_prune_threshold    FLOAT,
    node_split_threshold    FLOAT,
    sampling_needed         BOOLEAN,
    h2hmv_routine_id        INT,
    verbosity               INT
    ) 
RETURNS MADLIB_SCHEMA.__train_result AS $$
DECLARE
    num_live_nodes              INT;
    max_nid                     INT;
    location                    INT[];
    temp_location               INT[];
    num_classes                 INT;
    answer                      record;
    location_size               INT;
    begin_func_exec             TIMESTAMP;
    begin_find_best             TIMESTAMP;
    scv_acs_time                INTERVAL;
    begin_data_transfer         TIMESTAMP;
    begin_update_best           TIMESTAMP;
    begin_update_child          TIMESTAMP;
    begin_update_nid            TIMESTAMP;
    calc_update_best            INTERVAL;
    calc_update_child           INTERVAL;
    calc_update_nid             INTERVAL;
    ins_upd_time                INTERVAL;
    begin_olap_acs              TIMESTAMP;
    calc_acc_time               INTERVAL;
    calc_pre_time               INTERVAL;
    calc_olap_time              INTERVAL;
    begin_bld_assoc             TIMESTAMP;
    bld_assoc_time              INTERVAL;    
    begin_prune                 TIMESTAMP;
    prune_time                  INTERVAL;
    total_size                  FLOAT;
    sc_code                     INT := 1;
    curstmt                     TEXT := '';
    grow_tree                   INT := max_tree_depth;
    ret                         MADLIB_SCHEMA.__train_result;
    curr_level                  INT := 1;
    dp_ids                      INT[];
    dp_ids_text                 TEXT;
    instance_time               MADLIB_SCHEMA.__gen_acc_time;
    tr_table_index              INT := 1;
    tr_tables                   TEXT[] := '{tr_assoc_ping, tr_assoc_pong}';
    cur_tr_table                TEXT := 'tr_assoc_ping';
    need_analyze                BOOL := 't'::BOOL;
    attr_count                  INT;
BEGIN  
    -- record the time costed in different steps when training
    begin_func_exec     = clock_timestamp();
    scv_acs_time        = begin_func_exec - begin_func_exec;
    calc_olap_time      = scv_acs_time;
    calc_acc_time       = scv_acs_time;
    calc_pre_time       = scv_acs_time;
    ins_upd_time        = scv_acs_time;
    calc_update_best    = scv_acs_time;
    calc_update_child   = scv_acs_time;
    calc_update_nid     = scv_acs_time;
    bld_assoc_time      = scv_acs_time;
    prune_time          = scv_acs_time;
   
    IF(split_criterion = 'infogain') THEN
        sc_code = 1;
    ELSIF (split_criterion = 'gainratio') THEN
        sc_code = 2;
    ELSIF (split_criterion = 'gini') THEN
        sc_code = 3;
    ELSE
        RAISE EXCEPTION '%', 'Invalid split criterion!';
    END IF;

    num_classes = MADLIB_SCHEMA.__num_of_class(training_table_meta); 
    
    IF(verbosity > 0) THEN
        RAISE INFO 'NUMBER OF CLASSES IN THE TRAINING SET %', num_classes;
    END IF;
    
    IF(num_classes < 2) THEN
        RAISE EXCEPTION 'the number of classes must be greater than 2';
    END IF;

    curstmt = MADLIB_SCHEMA.__format
        (
            'SELECT
                count(*)
             FROM %
             WHERE column_type=''f''',
            training_table_meta
        );
    EXECUTE curstmt INTO attr_count;

    -- generate the horizontal table for updating assinged node IDs
    PERFORM MADLIB_SCHEMA.__gen_horizontal_encoded_table
        (
            'tmp_dt_hori_table',
            training_table_name,
            attr_count,
            verbosity
        );

    EXECUTE 'SELECT count(*) FROM tmp_dt_hori_table' INTO total_size;
    
    IF(verbosity > 0) THEN
        RAISE INFO 'INPUT TABLE SIZE: %', total_size;
    END IF;

    begin_bld_assoc = clock_timestamp();
    cur_tr_table = tr_tables[tr_table_index];

    -- The table of tr_assoc holds the information of which records are 
    -- used during training for each tree.
    -- It has four columns.
    --     id     --   The id of one record.
    --     tid    --   The id of a tree.
    --     nid    --   The id of a node in a tree.
    --     weight --   The times a record is assigned to a node.
    IF (sampling_needed) THEN
        PERFORM MADLIB_SCHEMA.__sample_with_replacement
            (
            num_trees,
            round(sampling_percentage * total_size)::BIGINT,
            'tmp_dt_hori_table',
            cur_tr_table
            );
    ELSE
        curstmt = MADLIB_SCHEMA.__format
             (
                'INSERT INTO % 
                 SELECT id, 1 as tid, 1 as nid, 1 as weight 
                 FROM %',
                 ARRAY[
                    cur_tr_table,
                    'tmp_dt_hori_table'
                ]
             );
        EXECUTE curstmt;    
    END IF;
   
    -- analyze ping
    EXECUTE 'ANALYZE ' || cur_tr_table;
    bld_assoc_time = clock_timestamp() - begin_bld_assoc;

    -- generate the root node for all trees.
    -- the generated numbers are the same for the two generate_series
    SELECT MADLIB_SCHEMA.__format
        (
            'INSERT INTO % 
                (id, tree_location, feature, probability, max_class,scv, 
                 live, num_of_samples, parent_id, tid) 
            SELECT generate_series(1, %), ARRAY[0], 0, 1, 1, 1, 1, 0, 0, 
                   generate_series(1, %)',
            ARRAY[
                result_tree_table_name,
                num_trees::TEXT,
                num_trees::TEXT
            ]
        ) INTO curstmt;
    
    EXECUTE curstmt;
    
    max_nid         = num_trees;
    location_size   = 0;


    LOOP
        EXECUTE 'SELECT COUNT(id) FROM ' || result_tree_table_name || 
            ' WHERE live > 0 AND array_upper(tree_location,1)='||
            curr_level||';' INTO num_live_nodes;
        
        IF (num_live_nodes < 1) THEN
            IF(verbosity > 0) THEN
                RAISE INFO 'EXIT: %', 'no live nodes to split';
            END IF;
            
            EXIT;
        END IF;

        IF (verbosity > 0) THEN
            RAISE INFO 'Running on level:%', curr_level;
        END IF;
        
        begin_olap_acs = clock_timestamp();
        
        instance_time = MADLIB_SCHEMA.__gen_acc
            (
            training_table_name,
            training_table_meta,
            result_tree_table_name,
            cur_tr_table,
            'sf_assoc',
            features_per_node,
            num_classes,
            sampling_needed,
            verbosity
            );

        IF (h2hmv_routine_id=1) THEN
            -- For ignore, we need the true size of nodes to handle the
            -- missing values.
            TRUNCATE node_size_aux;
         
            curstmt = MADLIB_SCHEMA.__format
                (
                    'INSERT INTO node_size_aux 
                     SELECT tr.tid, tr.nid, sum(weight) as count
                     FROM % tr
                     GROUP BY tr.tid, tr.nid',
                    cur_tr_table
                );

            EXECUTE curstmt;
        END IF;

        calc_pre_time  = calc_pre_time + instance_time.calc_pre_time;
        calc_acc_time  = calc_acc_time + instance_time.calc_acc_time;
        calc_olap_time = calc_olap_time + (clock_timestamp() - begin_olap_acs);

        curr_level = curr_level + 1;
        
        begin_find_best = clock_timestamp();

        PERFORM MADLIB_SCHEMA.__find_best_split
               (
               'training_instance',
               confidence_level,
               training_table_meta,
               sc_code,
               grow_tree,
               'find_best_answer_table',
               h2hmv_routine_id,
               num_classes
               );
        IF (verbosity > 0) THEN
            RAISE INFO 'find best time at this level:%', 
                clock_timestamp() - begin_find_best;
        END IF;
        grow_tree = grow_tree - 1;
        
        scv_acs_time        = scv_acs_time + 
                              (clock_timestamp() - begin_find_best);
        begin_data_transfer = clock_timestamp();
        begin_update_best   = clock_timestamp();
        
        -- We get the calculation result for current level. 
        -- Update the nodes of previous level firstly.
        SELECT MADLIB_SCHEMA.__format
            (
                'UPDATE % t 
                 SET feature        = c.feature,
                     probability    = c.probability,
                     max_class      = c.max_class,
                     scv            = c.max_scv,
                     ebp_coeff      = c.ebp_coeff,
                     num_of_samples = c.node_size,
                     live           = 0,
                     is_cont        = c.is_cont,
                     split_value    = c.split_value 
                 FROM find_best_answer_table c
                 WHERE t.id=c.node_id AND t.tid=c.tid',
                 ARRAY[
                    result_tree_table_name::TEXT
                 ]
             ) INTO curstmt;
            
        EXECUTE curstmt;
        
        calc_update_best    = calc_update_best + 
                              (clock_timestamp() - begin_update_best);
        begin_update_child  = clock_timestamp();

        curstmt=
            MADLIB_SCHEMA.__format(
                   'INSERT INTO %(id, tree_location, feature, probability, 
                        max_class, scv, live, parent_id, tid, dp_ids)
                        SELECT %+row, array_append(tree_location, fval),
                            0, 1, 1, 1, %, ans.node_id, ans.tid, 
                            CASE when(NOT ans.is_cont) then
                                array_append( dp_ids, ans.feature)
                            ELSE
                                dp_ids
                            END
                        FROM % tree,
                        (
                            SELECT  *, 
                                    row_number() 
                                    OVER (ORDER BY l.tid, l.node_id, l.fval) AS row
                            FROM
                            (
                                SELECT  *,  
                                        CASE WHEN (is_cont) THEN
                                            generate_series(1,2)
                                        ELSE
                                            generate_series(1, distinct_features)
                                        END AS fval 
                                FROM
                                find_best_answer_table
                                WHERE live>0 AND coalesce(feature, 0) <> 0 
                                      AND node_size >= % AND node_size >= %
                            ) l
                        ) ans
                        WHERE tree.id=ans.node_id and tree.tid=ans.tid;',
                        ARRAY[
                            result_tree_table_name,
                            (max_nid)::TEXT,
                            curr_level::TEXT,
                            result_tree_table_name,
                            (total_size * node_prune_threshold)::TEXT,
                            (total_size * node_split_threshold)::TEXT                            
                        ]
                        );
        IF(verbosity > 0) THEN
            RAISE INFO 'Generate Child Nodes:%', curstmt;
        END IF;

        EXECUTE curstmt;
        
        EXECUTE 'SELECT max(id) FROM '||result_tree_table_name INTO max_nid;

        IF(verbosity > 0) THEN
            RAISE INFO 'Max nid:%, level:%', max_nid, curr_level;
        END IF;

        -- insert the leftmost child node id and relevant info
        -- to the assoc_aux table, so that we will make use of this 
        -- info to  update the assigned nid the samples belong to
        -- the current node whose id is answer.node_id.
        SELECT MADLIB_SCHEMA.__format
            (
                'INSERT INTO assoc_aux
                 (nid, fid, lmc_id, svalue, is_cont)
                    SELECT t.id, t.feature, min(l.id), 
                            t.split_value, t.is_cont
                    FROM
                        (SELECT id, parent_id 
                        FROM % 
                        WHERE array_upper(tree_location,1)=%) l,
                        % t
                    WHERE l.parent_id=t.id
                    GROUP BY t.id, t.feature, t.split_value, t.is_cont;',
                ARRAY[
                    result_tree_table_name,
                    curr_level::TEXT,
                    result_tree_table_name
                ]
            ) INTO curstmt;

        IF(verbosity > 0) THEN
            RAISE INFO 'Update lmc_child Info:%', curstmt;
        END IF;

        EXECUTE curstmt;

        -- delete the unused nodes on the previous level
        -- delete those nodes with a size less than node_prune_threshold
        -- node_prune_threshold will not apply to root node, 
        -- the level is 1 (curr_level - 1 = 1);
        IF (curr_level > 2) THEN
            curstmt = MADLIB_SCHEMA.__format
                        (
                            'DELETE FROM % t 
                             WHERE t.num_of_samples < % OR live = %;',
                            ARRAY[
                                result_tree_table_name::TEXT,
                                (total_size * node_prune_threshold)::TEXT,
                                (curr_level - 1)::TEXT
                            ]
                        );
            EXECUTE curstmt;
        END IF;
        
        calc_update_child   = calc_update_child + (clock_timestamp() - begin_update_child);
        begin_update_nid    = clock_timestamp();
        
        -- update the assigned node id for each sample on the current level
        tr_table_index = (tr_table_index % 2) + 1;        
        curstmt = MADLIB_SCHEMA.__format
            (
                'INSERT INTO % (id, nid, tid, weight)
                 SELECT 
                    tr.id,
                    au.lmc_id - 1 +
                    CASE WHEN (au.is_cont) THEN
                            CASE WHEN (svalue < vt.fvals[au.fid]) THEN
                                2
                            ELSE
                                1
                            END
                    ELSE
                        vt.fvals[au.fid]::INT
                    END AS nid,
                    tid, weight
                  FROM % tr, % vt, assoc_aux au
                  WHERE tr.nid = au.nid AND vt.id = tr.id AND vt.fvals[au.fid] IS NOT NULL',
                ARRAY[
                    tr_tables[tr_table_index],
                    cur_tr_table,
                    'tmp_dt_hori_table'
                ]
            );        
        IF (verbosity > 0) THEN
            RAISE INFO '%', curstmt;
        END IF;

        EXECUTE curstmt;  
        EXECUTE 'TRUNCATE ' || cur_tr_table;    
        cur_tr_table = tr_tables[tr_table_index];

        IF (need_analyze) THEN
            -- analyze pong table
            EXECUTE 'ANALYZE ' || cur_tr_table;
            need_analyze = 'f'::BOOL;
        END IF;

        EXECUTE 'TRUNCATE assoc_aux';
        
        calc_update_nid = calc_update_nid + (clock_timestamp() - begin_update_nid);
        
        ins_upd_time = ins_upd_time + 
            (clock_timestamp() - begin_data_transfer);             
        IF(verbosity > 0) THEN
            RAISE INFO 'computation time in this level:%',
                (clock_timestamp() - begin_find_best);
        END IF;
        
    END LOOP;
    
    PERFORM MADLIB_SCHEMA.__generate_final_tree(result_tree_table_name);
    
    begin_prune = clock_timestamp();
    IF (confidence_level < 100.0) THEN
       PERFORM MADLIB_SCHEMA.__ebp_prune_tree(result_tree_table_name);
    END IF;
    
    IF (validation_table_name IS NOT NULL) THEN
       PERFORM MADLIB_SCHEMA.__rep_prune_tree
                  (
                  result_tree_table_name, 
                  validation_table_name , 
                  num_classes
                  );
    END IF;
    prune_time = clock_timestamp() - begin_prune;
    
    IF(verbosity > 0) THEN
        RAISE INFO 'time of sampling with replacement: %', bld_assoc_time;
        RAISE INFO 'time of finding best and calculating ACS: %', scv_acs_time;
        RAISE INFO 'time of calculating ACC: %', calc_acc_time;
        RAISE INFO 'time of Insert/update operation: %', ins_upd_time;
        RAISE INFO 'time of pruning: %', prune_time;
        RAISE INFO 'time of training: %', clock_timestamp() - begin_func_exec;        
    END IF;
    
    SELECT MADLIB_SCHEMA.__format
        (
            'SELECT COUNT(id), max(array_upper(tree_location, 1))
             FROM %',
             ARRAY[
                result_tree_table_name
             ]
        ) INTO curstmt;
        
    EXECUTE curstmt INTO ret.num_tree_nodes, ret.max_tree_depth;
    
    ret.features_per_node   = features_per_node;            
    ret.num_of_samples        = total_size;
    ret.calc_acc_time       = calc_acc_time;
    ret.calc_pre_time       = calc_pre_time;
    ret.update_time         = ins_upd_time;
    ret.update_best         = calc_update_best;
    ret.update_child        = calc_update_child;
    ret.update_nid          = calc_update_nid;
    ret.scv_acs_time        = scv_acs_time;   
    ret.prune_time          = prune_time;
    
    RETURN ret;
END
$$ LANGUAGE PLPGSQL;


/*
 * @brief This is an internal function for displaying one tree node in human  
 *        readable format. It is the step function of aggregation named 
 *        __display_tree_aggr.
 *
 * @param state     This variable is used to store the accumulated tree 
 *                  display information.
 * @param depth     The depth of this node. 
 * @param is_cont   Whether the feature used to split is continuous. 
 * @param feat_name The name of the feature used to split.
 * @param curr_val  The value of the splitting feature for this node.
 * @param split_value    For continuous feature, it specifies the split value. 
 *                  Otherwise, it is of no meaning.
 * @param max_prob  For those elements in this node, the probability that
 *                  an element belongs to the max_class.
 * @param max_class The class ID with the largest number of elements 
 *                  for those elements in this node.
 * @param num_of_samples Total count of samples in this node. 
 *
 * @return It returns the text containing the information of human  
 *         readable information for trees.
 *
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__display_node_sfunc
    (
    state           TEXT,
    depth           INT,
    is_cont         BOOLEAN,
    feat_name       TEXT,
    curr_val        TEXT,
    split_value     FLOAT8,
    max_prob        FLOAT8,
    max_class       TEXT,
    num_of_samples  INT
    ) 
RETURNS TEXT AS $$ 
DECLARE
    ret                     TEXT := '';
    index                   INT;
BEGIN
    -- We add indentation based on the depth.
    FOR index IN 0..depth LOOP
        ret = ret || '    ';
    END LOOP;
    
    IF (depth > 0) THEN
        ret = ret ||coalesce(feat_name,'null')||': ';
        -- For continuous features, there are two splits.
        -- We will mark curr_val to 1 for '<='. Otherwise, 
        -- we will mark curr_val to 2.
        IF (is_cont) THEN
            IF (curr_val::INT = 1) THEN
                ret = ret || ' <= ';
            ELSE
                ret = ret || ' > ';
            END IF;
            ret = ret||coalesce(split_value,0)||' ';
        ELSE
            ret = ret||' = '||coalesce(curr_val,'null')||' ';
        END IF;
    ELSE
        ret = ret||'Root Node ';
    END IF;

    ret = ret                               || 
          ' : class('                       ||  
          coalesce(max_class,null)          || 
          ')   num_elements('               || 
          coalesce(num_of_samples,0)        || 
          ')  predict_prob('                ||
          coalesce(max_prob,0)              ||
          ')';

    ret = ret || E'\n';

    -- If there exists information, append the information
    -- for this node.
    IF (state IS NOT NULL) THEN
        ret = state || ret;
    END IF;
    
    RETURN ret;
END 
$$ LANGUAGE PLPGSQL;


DROP AGGREGATE IF EXISTS MADLIB_SCHEMA.__display_tree_aggr
    (
    INT,        -- depth
    BOOLEAN,    -- is_cont
    TEXT,       -- feature name
    TEXT,       -- curr_val
    FLOAT8,     -- split value
    FLOAT8,     -- max_probability
    TEXT,       -- max_class
    INT         -- num_of_samples
    ) CASCADE;
CREATE 
m4_ifdef(`__GREENPLUM__', m4_ifdef(`__HAS_ORDERED_AGGREGATES__', `ORDERED'))
AGGREGATE MADLIB_SCHEMA.__display_tree_aggr
    (
    INT,        -- depth
    BOOLEAN,    -- is_cont
    TEXT,       -- feature name
    TEXT,       -- curr_val
    FLOAT8,     -- split value
    FLOAT8,     -- max_probability
    TEXT,       -- max_class
    INT         -- num_of_samples
    ) 
(
  SFUNC=MADLIB_SCHEMA.__display_node_sfunc,
  STYPE=TEXT
);


/*
 * @brief Display the trained model with human readable format. This function
 *        leverages ordered aggregate to display the tree with only one scan of
 *        the tree_table.
 *
 * @param tree_table  The full name of the tree table. 
 * @param tree_id     The array contains the IDs of the trees to be displayed.
 * @param max_depth   The max depth to be displayed. If it is set to null,
 *                    this function will show all levels. 
 *
 * @return The text representing the tree with human readable format.
 *
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__treemodel_display_with_ordered_aggr
    (
    tree_table  TEXT,
    tree_id     INT[],    
    max_depth   INT
    ) 
RETURNS SETOF TEXT AS $$
DECLARE
    metatable_name  TEXT := null;
    curr_stmt       TEXT := null;
    feature_name    TEXT := null;
    table_name      TEXT := null;
    result          TEXT := '';
    result_rec      RECORD;
BEGIN
    PERFORM MADLIB_SCHEMA.__assert_table
            (
                tree_table,
                't'
            );   
            
    metatable_name = MADLIB_SCHEMA.__get_metatable_name( tree_table );
 
    -- This table is used for tree display.
    -- It is filled with the original information before
    -- encoding to facilitate the display procedure.
    DROP TABLE IF EXISTS auxiliary_tree_display;
    CREATE TEMP TABLE auxiliary_tree_display
    (
        tid                     INT,
        id                      INT,
        tree_location           INT[],
        probability             FLOAT8, 
        max_class               TEXT,
        num_of_samples          INT,
        parent_id               INT,
        curr_value              TEXT,
        parent_feature_id       INT,
        is_parent_feature_cont  BOOLEAN,
        parent_split_value      FLOAT8,
        parent_feature_name     TEXT
    ) m4_ifdef(`__GREENPLUM__', `DISTRIBUTED BY (id)');
    
    -- We made a self join for the tree table. For each node, we get the 
    -- feature information at its parent node so as to display this node. 
    SELECT MADLIB_SCHEMA.__format(
        'INSERT INTO auxiliary_tree_display SELECT m.*, 
        n.column_name as parent_feature_name
        FROM 
        (SELECT * FROM
            (SELECT t1.tid,t1.id, t1.tree_location,
            t1.probability,t1.max_class::TEXT,
            t1.num_of_samples,t1.parent_id, 
            t1.tree_location[array_upper(t1.tree_location,1)]::TEXT 
                as curr_value, 
            t2.feature as parent_feature_id, 
            t2.is_cont as is_parent_feature_cont, 
            t2.split_value as parent_split_value 
            FROM % t1 LEFT JOIN % t2 ON 
            (t1.parent_id = t2.id AND 
            (coalesce(t1.tid,0)=coalesce(t2.tid,0)) ) ) l
            WHERE l.tid in ( % ) ) m 
         LEFT JOIN % n 
            on m.parent_feature_id = n.id;',
        ARRAY[
            tree_table,
            tree_table,
            array_to_string(tree_id,','),
            metatable_name
        ]
        )
    INTO curr_stmt;   
    EXECUTE curr_stmt;

    -- Get the metatable storing the encoding information of class.
    SELECT MADLIB_SCHEMA.__format
        (
            'SELECT 
                column_name,
                MADLIB_SCHEMA.__regclass_to_text(table_oid) as table_name
             FROM  %
             WHERE column_type=''c'' LIMIT 1',
            ARRAY[
                metatable_name
            ]
        ) INTO curr_stmt;
    
    EXECUTE curr_stmt INTO result_rec;
            
    table_name = result_rec.table_name;
    
    IF (table_name IS NOT NULL) THEN
        -- Convert back for the class column.
        SELECT MADLIB_SCHEMA.__format(
            'UPDATE auxiliary_tree_display n 
             SET max_class = MADLIB_SCHEMA.__to_char(m.fval) 
             FROM % m 
             WHERE m.code = n.max_class::INT
            ',
            ARRAY[
                table_name
            ]
            )
        INTO curr_stmt;  
        EXECUTE curr_stmt;
    END IF;

    -- Get the metatables storing the encoding information for discrete features.
    SELECT MADLIB_SCHEMA.__format
        (
            'SELECT 
        id,
                column_name,
                MADLIB_SCHEMA.__regclass_to_text(table_oid) as table_name 
             FROM % 
             WHERE NOT is_cont AND column_type=''f'';',
            ARRAY[
                metatable_name
            ]
        )
    INTO curr_stmt;  
    
    -- Convert back for discrete features.
    FOR result_rec IN EXECUTE (curr_stmt) LOOP
        SELECT MADLIB_SCHEMA.__format(
            'UPDATE auxiliary_tree_display n 
             SET curr_value = MADLIB_SCHEMA.__to_char(m.fval) 
             FROM % m 
             WHERE m.code::INT = n.curr_value::INT AND
           m.fid = %              AND 
                   n.parent_feature_name = %
            ',
            ARRAY[
                result_rec.table_name,
        result_rec.id::TEXT,
                quote_literal(result_rec.column_name)
            ]
            )
        INTO curr_stmt;  
        EXECUTE curr_stmt;   
    END LOOP;

    -- Now we already get all the information. Invoke the
    -- aggregation to show the tree.
    -- If we order by tree_location, we can get the sequence 
    -- of depth first traversal.
    curr_stmt = 'SELECT tid,MADLIB_SCHEMA.__display_tree_aggr(
                array_upper(tree_location,1)-1,
                is_parent_feature_cont,
                parent_feature_name,
                curr_value,
                parent_split_value,
                probability,
                max_class,
                num_of_samples 
                order by tree_location) AS disp_str
         FROM auxiliary_tree_display';

    IF (max_depth IS NOT NULL) THEN
        curr_stmt = curr_stmt                                   ||
                    ' WHERE array_upper(tree_location,1) - 1 <='  ||
                    max_depth;
    END IF;
    
    curr_stmt = curr_stmt||' GROUP BY tid ORDER BY tid;';
    
    FOR result_rec IN EXECUTE curr_stmt LOOP
        SELECT MADLIB_SCHEMA.__format(
            E'\nTree %\n%',
            ARRAY[
                result_rec.tid::TEXT,
                result_rec.disp_str
            ]
            )
        INTO result;  
        RETURN NEXT result;
        --RETURN NEXT E'\nTree '||result_rec.tid||E'\n'||result_rec.disp_str;
    END LOOP;
    RETURN;
END $$ LANGUAGE PLPGSQL;


/*
 * @brief This is an internal function for displaying the tree in human readable
 *        format. It uses the depth-first strategy to traverse a tree and print 
 *        values. This function is used on databases, e.g. PG 8.4, that do not 
 *        support ordered aggregate.
 *
 * @param tree_table      The full name of the tree table. 
 * @param id              The ID of current node. This node and all of its  
 *                        children are displayed.
 * @param feature_id      The ID of a feature, which is used to split in the 
 *                        parent of current node.
 * @param depth           The depth of current node.
 * @param is_cont         It specifies whether the feature denoted by 'feature_id'
 *                        is continuous or not.
 * @param split_value     For continuous feature, it specifies the split value. 
 *                        Otherwise, it is of no meaning.
 * @param metatable_name  For tabular format, this table contains the meta data
 *                        to encode the input table.
 * @param max_depth       The max depth to be displayed. If it is set to null,
 *                        this function will show all levels. 
 * @param tree_id         The ID of the tree to be displayed.
 *
 * @return The text representing the tree with human readable format.
 *
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__display_tree_no_ordered_aggr
    (
    tree_table      TEXT, 
    id              INT, 
    feature_id      INT, 
    depth           INT, 
    is_cont         BOOLEAN, 
    split_value     FLOAT,
    metatable_name  TEXT,
    max_depth       INT,
    tree_id         INT
    ) 
RETURNS TEXT AS $$ 
DECLARE
    ret                     TEXT := '';
    tree_location           INT[];
    feature                 INT;
    max_class               INT;
    num_of_samples          INT;
    is_cont                 BOOLEAN;
    temp_split_value        FLOAT;
    index                   INT;
    curr_value              INT;
    probability             FLOAT;
    curstmt                 TEXT;
    child_nid               INT;
BEGIN
    IF (id IS NULL OR id <= 0) THEN
        RETURN ret;
    END IF;

    SELECT MADLIB_SCHEMA.__format
            (
                'SELECT tree_location, feature, is_cont, 
                        split_value, max_class,num_of_samples,probability
                 FROM %
                 WHERE id = % AND tid=%',
                 ARRAY[
                    tree_table,
                    MADLIB_SCHEMA.__to_char(id),
                    MADLIB_SCHEMA.__to_char(tree_id)
                 ]
             )
    INTO curstmt;
    
    EXECUTE curstmt INTO tree_location, feature, is_cont, 
                         temp_split_value, max_class, num_of_samples, probability;  

    curr_value = tree_location[array_upper(tree_location,1)];

    FOR index IN 0..depth LOOP
        ret = ret || '    ';
    END LOOP;
    
    IF (id >tree_id) THEN
        ret = ret ||MADLIB_SCHEMA.__get_feature_name(feature_id,metatable_name)||': ';

        IF (is_cont) THEN
            IF (curr_value = 1) THEN
                ret = ret || ' <= ';
            ELSE
                ret = ret || ' > ';
            END IF;
            ret = ret || split_value;
        ELSE
            ret = ret   || 
                  ' = ' || 
                  MADLIB_SCHEMA.__get_feature_value
                    (
                    feature_id, 
                    curr_value, 
                    metatable_name
                    );
        END IF;
    ELSE
        ret = ret||'Root Node ';
    END IF;

    ret = ret                                                       || 
          ' : class('                                               ||  
          MADLIB_SCHEMA.__get_class_value(max_class,metatable_name)  || 
          ')   num_elements('                                       || 
          num_of_samples                                                 || 
          ')  predict_prob('                                        ||
          probability                                               ||
          ')';

    ret = ret || E'\n';
    
    IF (max_depth IS NOT NULL AND 
        depth >= max_depth) THEN
        RETURN ret;
    END IF;
    
    curstmt = MADLIB_SCHEMA.__format
                (
                    'SELECT id
                     FROM %
                     WHERE parent_id = % AND tid=%
                     ORDER BY id',
                    ARRAY[
                        tree_table,
                        MADLIB_SCHEMA.__to_char(id),
                        MADLIB_SCHEMA.__to_char(tree_id)
                        ]
                );

    FOR child_nid IN EXECUTE curstmt LOOP
        ret = ret || MADLIB_SCHEMA.__display_tree_no_ordered_aggr(
                        tree_table,
                        child_nid,
                        feature,
                        depth + 1,
                        is_cont,
                        temp_split_value,
                        metatable_name,
                        max_depth,
                        tree_id);   
    END LOOP;

    RETURN ret;
END $$ LANGUAGE PLPGSQL;


/*
 * @brief Display the trained model with human readable format. It use the 
 *        recursive algorithm, which is slower than the version with 
 *        ordered aggregate. We only use it when ordered aggregate is unavailable.
 *
 * @param tree_table  The full name of the tree table. 
 * @param tree_id     The array contains the IDs of the trees to be displayed.
 * @param max_depth   The max depth to be displayed. If it is set to null,
 *                    this function will show all levels. 
 *
 * @return The text representing the tree with human readable format.
 *
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__treemodel_display_no_ordered_aggr
    (
    tree_table  TEXT,
    tree_id     INT[],
    max_depth   INT
    ) 
RETURNS SETOF TEXT AS $$
DECLARE
    metatable_name  TEXT := null;
    curstmt         TEXT := '';
    index           INT;
    result          TEXT := '';
    root_id         INT;
BEGIN
    PERFORM MADLIB_SCHEMA.__assert_table
            (
                tree_table,
                't'
            );   
            
    metatable_name = MADLIB_SCHEMA.__get_metatable_name( tree_table );

    index= array_lower(tree_id,1);
    
    WHILE (index<=array_upper(tree_id,1) ) LOOP
        EXECUTE 'SELECT id FROM '||tree_table||
            ' WHERE parent_id=0 and tid='||tree_id[index]||';' INTO root_id;  

        RETURN NEXT E'\nTree '||tree_id[index]||E'\n'||
            MADLIB_SCHEMA.__display_tree_no_ordered_aggr(tree_table, root_id, 0, 0, 'f', 
            0, metatable_name,max_depth,tree_id[index]);
        index=index+1;
    END LOOP;
    RETURN;
END $$ LANGUAGE PLPGSQL;


/*
 * @brief Multiple trees may classify the same record to different classes. 
 *        This function gets the results voted by multiple trees.
 *
 * @param src_table    The full name of the table containing original data.
 * @param dst_table    The full name of the table to store the voted results. 
 *
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__treemodel_get_vote_result
    (
    src_table   TEXT, 
    dst_table   TEXT
    )
RETURNS VOID AS $$
DECLARE
    curstmt TEXT;
BEGIN
    EXECUTE 'DROP TABLE IF EXISTS '||dst_table;
    EXECUTE 'CREATE TEMP TABLE '||dst_table||E'
    (
        id          BIGINT,
        class       INT,
        prob        FLOAT8
    )m4_ifdef(`__GREENPLUM__', `DISTRIBUTED BY (id)');';

    SELECT MADLIB_SCHEMA.__format(
        'INSERT INTO %
        SELECT id, max_array[3], max_array[2] FROM 
            (SELECT id, max(array[count,prob,class]) AS max_array FROM
                (SELECT id, class, COUNT(*) AS count, AVG(prob) as prob FROM
                    % GROUP BY id,class) t1 GROUP BY id) t2',
        ARRAY[
            dst_table,
            src_table
        ]
        ) 
    INTO curstmt;
    EXECUTE curstmt;
    RETURN;
END
$$ LANGUAGE PLPGSQL;


/*
 * @brief An internal classification function. It classifies with all trees at 
 *        the same time. For medium/small data sets, tests shows that it is more
 *        efficient than the serial classification function. 
 *
 * @param classification_table_name  The full name of the table containing the 
 *                                   classification set.
 * @param tree_table_name            The full name of the tree table.
 * @param verbosity                  > 0 means this function runs in verbose mode. 
 *
 * @return An array containing the encoded table name and classification result 
 *         table name (We encode the source table during the classification).
 *
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__treemodel_classify_internal
    (
    classification_table_name   TEXT, 
    tree_table_name             TEXT, 
    verbosity                   INT
    ) 
RETURNS TEXT[] AS $$
DECLARE
    table_pick              INT    := 1;
    remains_to_classify     INT;
    size_finished           INT;
    time_stamp              TIMESTAMP;
    metatable_name          TEXT   := '';
    id_col_name             TEXT   := 'id';
    curr_level              INT    := 1;
    max_level               INT    := 0;
    h2hmv_routine_id        INT    := 0;
    curstmt                 TEXT   := '';
    result_table_name       TEXT   := 'dt_classify_internal_rt';
    encoded_table_name      TEXT   := 'dt_classify_internal_edt';
    table_names             TEXT[] := '{classified_instance_ping,classified_instance_pong}';
    tree_id                 INT;
BEGIN
    time_stamp = clock_timestamp();

    PERFORM MADLIB_SCHEMA.__assert
            (
                (classification_table_name IS NOT NULL) AND
                (
                 MADLIB_SCHEMA.__table_exists
                    (
                        classification_table_name
                    )
                ),
                'the specified classification table' || 
                coalesce('<' || classification_table_name || 
                '> does not exists', ' is NULL')
            );   

    PERFORM MADLIB_SCHEMA.__assert
            (
                (tree_table_name IS NOT NULL) AND
                (
                 MADLIB_SCHEMA.__table_exists
                    (
                        tree_table_name
                    )
                ),
                'the specified tree table' || 
                coalesce('<' || tree_table_name || '> does not exists', ' is NULL')
            ); 
                  
    PERFORM MADLIB_SCHEMA.__assert
            (
                verbosity IS NOT NULL,                
                'verbosity must be non-null'
            );    

    EXECUTE 'DROP TABLE IF EXISTS ' || encoded_table_name || ' CASCADE';
                                 
    SELECT MADLIB_SCHEMA.__get_metatable_name(tree_table_name) INTO metatable_name;

    SELECT MADLIB_SCHEMA.__get_routine_id(tree_table_name) INTO h2hmv_routine_id;
    
    PERFORM MADLIB_SCHEMA.__encode_table
        (
            classification_table_name, 
            encoded_table_name, 
            metatable_name, 
            h2hmv_routine_id,
            verbosity
        );
        
    IF (verbosity > 0) THEN
        RAISE INFO 'tabular format. id_col_name: %', id_col_name;
    END IF;        
    
    /*
     *  The table of classified_instance_ping and classified_instance_pong are
     *  auxiliary tables used during the classification process.
     *  For each record, these tables tell us which node it belongs to. They also
     *  hold the information of class and probability.
     *  We use transfer data between these two tables rather than update a single
     *  table during the classification process. We find the operation of update
     *  is quite expensive.
     */
    DROP TABLE IF EXISTS classified_instance_ping;
    CREATE TEMP TABLE classified_instance_ping
    (
        tid         INT,
        id          BIGINT,
        jump        INT,
        class       INT,
        prob        FLOAT,
        parent_id   INT,
        leaf_id     INT
    ) m4_ifdef(`__GREENPLUM__', `DISTRIBUTED BY (id)');
    
    DROP TABLE IF EXISTS classified_instance_pong;
    CREATE TEMP TABLE classified_instance_pong
    (
        tid         INT,
        id          BIGINT,
        jump        INT,
        class       INT,
        prob        FLOAT,
        parent_id   INT,
        leaf_id     INT
    ) m4_ifdef(`__GREENPLUM__', `DISTRIBUTED BY (id)');


    EXECUTE 'DROP TABLE IF EXISTS ' || result_table_name || ' CASCADE';
    EXECUTE 'CREATE TEMP TABLE ' || result_table_name || E'
    (
        tid         INT,
        id          BIGINT,
        jump        INT,
        class       INT,
        prob        FLOAT,
        parent_id   INT,
        leaf_id     INT
    ) m4_ifdef(`__GREENPLUM__', `DISTRIBUTED BY (id)');';


    EXECUTE 'INSERT INTO classified_instance_ping (id, jump, class, prob,tid) 
        SELECT m.'||id_col_name||', t.id, 0, 0, t.tid 
        FROM ' || encoded_table_name || ' m CROSS JOIN 
        (SELECT DISTINCT tid,id FROM '||tree_table_name||' WHERE parent_id=0) t;';  

    
    EXECUTE 'SELECT max(array_upper(tree_location,1)) FROM '||tree_table_name||';'  
        INTO max_level;

    IF( max_level is NULL ) THEN
        RAISE EXCEPTION 'tree should not be empty';
    END IF;

    FOR curr_level IN 1..max_level LOOP
        IF (verbosity > 0) THEN  
            RAISE INFO 'new_depth: %', curr_level;
        END IF;
        
        table_pick = table_pick % 2 + 1; 
        
        EXECUTE 'TRUNCATE '|| table_names[table_pick] ||';';
        EXECUTE 'SELECT count(id) FROM '||result_table_name||';' INTO size_finished;
        
        IF (verbosity > 0) THEN  
            RAISE INFO 'size_finished %', size_finished;
        END IF;       
        
        EXECUTE 'SELECT count(*) FROM '|| table_names[(table_pick) % 2 + 1] ||';' 
            INTO remains_to_classify;
            
        IF (remains_to_classify = 0) THEN
            IF (verbosity > 0) THEN  
                RAISE INFO 'size_finished: % remains_to_classify: %', 
                    size_finished, remains_to_classify;
            END IF;  
                  
            EXIT;
        END IF;
        
        SELECT MADLIB_SCHEMA.__format(
            'INSERT INTO %
            SELECT pt.tid, pt.id, 
            CASE WHEN (is_cont) THEN 
                    CASE WHEN (gt.lmc_nid IS NULL) THEN
                        0
                    ELSE
                        gt.lmc_nid + 
                        float8lt(gt.split_value, fvals[gt.feature])::INT4 + 1 -
                        gt.lmc_fval
                    END
                ELSE 
                    CASE WHEN (gt.lmc_nid IS NULL) THEN
                        0
                    ELSE                    
                        gt.lmc_nid + fvals[gt.feature] - gt.lmc_fval
                    END
                END as newjump,
            gt.max_class, gt.probability, gt.parent_id, gt.id 
            FROM 
            (SELECT t1.tid, t1.id, t1.jump, fvals  
                FROM % t1 
                LEFT JOIN % t2 
                ON t1.id = t2.id)  AS pt, 
            (SELECT tid,lmc_nid, lmc_fval, max_class,feature, probability, 
                    parent_id, id, is_cont, split_value
                FROM % 
                WHERE array_upper(tree_location,1) = %) AS gt 
            WHERE pt.jump = gt.id AND pt.tid=gt.tid;',
            ARRAY[
                table_names[table_pick],
                table_names[(table_pick) % 2 + 1],
                encoded_table_name,
                tree_table_name,
                MADLIB_SCHEMA.__to_char(curr_level)
            ]
            )
        INTO curstmt;     
        EXECUTE curstmt;
        /*
         *  if the node (whose id is "jump") doesn't exist, 
         *  then insert them into result table 
         *  (be classified to max_class of its corrsponding node)
         */
        FOR tree_id IN EXECUTE 'SELECT DISTINCT tid FROM '||tree_table_name LOOP
            SELECT MADLIB_SCHEMA.__format(
                'INSERT INTO %(tid,id, jump, class, prob, parent_id, leaf_id) 
                SELECT tid,id, 0, class, prob, parent_id, leaf_id
                FROM %
                WHERE jump NOT IN (SELECT id FROM % WHERE tid=%) 
                AND tid=%',
                ARRAY[
                    result_table_name,
                    table_names[table_pick],
                    tree_table_name,
                    MADLIB_SCHEMA.__to_char(tree_id),
                    MADLIB_SCHEMA.__to_char(tree_id)
                ]
                ) 
            INTO curstmt;
            EXECUTE curstmt;
        
            -- delete from the being classified data table
            SELECT MADLIB_SCHEMA.__format(
                'DELETE FROM %
                WHERE jump NOT IN (SELECT id FROM % WHERE tid=%)
                AND tid=%',
                ARRAY[
                    table_names[table_pick],
                    tree_table_name,
                    MADLIB_SCHEMA.__to_char(tree_id),
                    MADLIB_SCHEMA.__to_char(tree_id)
                ]
                ) 
            INTO curstmt;
            EXECUTE curstmt;
        END LOOP;  
    END LOOP;

    EXECUTE 'INSERT INTO '||result_table_name||' SELECT * FROM '|| 
        table_names[table_pick] ||' WHERE jump = 0;';
    EXECUTE 'INSERT INTO '||result_table_name||' SELECT * FROM '|| 
        table_names[table_pick % 2 + 1] ||' WHERE jump = 0;';
    
    IF (verbosity > 0) THEN  
        RAISE INFO 'final classification time:%', clock_timestamp() - time_stamp;
    END IF;
    
    RETURN ARRAY[encoded_table_name, result_table_name];
END
$$ LANGUAGE PLPGSQL;


/*
 * @brief An internal classification function. It classifies with one tree 
 *        after another. For large data sets, tests shows that it is more
 *        efficient than the parallel classification function.   
 *
 * @param classification_table_name  The full name of the table containing the 
 *                                   classification set.
 * @param tree_table_name            The full name of the tree table.
 * @param verbosity                  > 0 means this function runs in verbose mode. 
 *
 * @return An array containing the encoded table name and classification result 
 *         table name (We encode the source table during the classification).
 *
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__treemodel_classify_internal_serial
    (
    classification_table_name   TEXT, 
    tree_table_name             TEXT, 
    verbosity                   INT
    ) 
RETURNS TEXT[] AS $$
DECLARE
    table_pick              INT    := 1;
    remains_to_classify     INT;
    size_finished           INT;
    time_stamp              TIMESTAMP;
    metatable_name          TEXT   := '';
    id_col_name             TEXT   := 'id';
    curr_level              INT    := 1;
    max_level               INT    := 0;
    h2hmv_routine_id        INT    := 0;
    curstmt                 TEXT   := '';
    result_table_name       TEXT   := 'dt_classify_internal_rt';
    encoded_table_name      TEXT   := 'dt_classify_internal_edt';
    table_names             TEXT[] := ARRAY[ 
                                        'classified_instance_ping',
                                        'classified_instance_pong'
                                        ];
    tree_id                 INT;
    root_id                 INT;
BEGIN
    time_stamp = clock_timestamp();

    PERFORM MADLIB_SCHEMA.__assert
            (
                (classification_table_name IS NOT NULL) AND
                (
                 MADLIB_SCHEMA.__table_exists
                    (
                        classification_table_name
                    )
                ),
                'the specified classification table' || 
                coalesce('<'                         || 
                classification_table_name            || 
                '> does not exists', ' is NULL')
            );   

    PERFORM MADLIB_SCHEMA.__assert
            (
                (tree_table_name IS NOT NULL) AND
                (
                 MADLIB_SCHEMA.__table_exists
                    (
                        tree_table_name
                    )
                ),
                'the specified tree table'  || 
                coalesce('<'                || 
                tree_table_name             || 
                '> does not exists', ' is NULL')
            ); 

                                    
    PERFORM MADLIB_SCHEMA.__assert
            (
                verbosity IS NOT NULL,                
                'verbosity must be non-null'
            );    
            
    EXECUTE 'DROP TABLE IF EXISTS ' || encoded_table_name || ' CASCADE';
                                 
    metatable_name   = MADLIB_SCHEMA.__get_metatable_name(tree_table_name);

    h2hmv_routine_id = MADLIB_SCHEMA.__get_routine_id(tree_table_name);
    
    PERFORM MADLIB_SCHEMA.__encode_table
        (
            classification_table_name, 
            encoded_table_name, 
            metatable_name, 
            h2hmv_routine_id,
            verbosity
        );
        
    IF (verbosity > 0) THEN
        RAISE INFO 'tabular format. id_col_name: %', id_col_name;
    END IF;        
    
    /*
     *  The table of classified_instance_ping and classified_instance_pong are
     *  auxiliary tables used during the classification process.
     *  For each record, these tables tell us which node it belongs to. They also
     *  hold the information of class and probability.
     *  We use transfer data between these two tables rather than update a single
     *  table during the classification process. We find the operation of update
     *  is quite expensive.
     */    
    DROP TABLE IF EXISTS classified_instance_ping;
    CREATE TEMP TABLE classified_instance_ping
    (
        id          BIGINT,
        jump        INT,
        class       INT,
        prob        FLOAT,
        parent_id   INT,
        leaf_id     INT
    ) m4_ifdef(`__GREENPLUM__', `DISTRIBUTED BY (id)');
    
    DROP TABLE IF EXISTS classified_instance_pong;
    CREATE TEMP TABLE classified_instance_pong
    (
        id          BIGINT,
        jump        INT,
        class       INT,
        prob        FLOAT,
        parent_id   INT,
        leaf_id     INT
    ) m4_ifdef(`__GREENPLUM__', `DISTRIBUTED BY (id)');

    
    EXECUTE 'DROP TABLE IF EXISTS '||result_table_name || ' CASCADE'; 
    EXECUTE 'CREATE TEMP TABLE ' || result_table_name || E'
    (
        tid         INT,
        id          BIGINT,
        jump        INT,
        class       INT,
        prob        FLOAT,
        parent_id   INT,
        leaf_id     INT
    ) m4_ifdef(`__GREENPLUM__', `DISTRIBUTED BY (id)');';
    
    FOR tree_id IN EXECUTE 'SELECT DISTINCT tid FROM '||tree_table_name LOOP
        EXECUTE 'SELECT max(array_upper(tree_location,1)) FROM '||
            tree_table_name||' WHERE tid='||tree_id||';'  INTO max_level;
        IF (verbosity > 0) THEN   
            RAISE INFO 'tree_id: %, max_level: %', tree_id,max_level;
        END IF;


        IF( max_level is NULL ) THEN
            RAISE EXCEPTION 'tree should not be empty';
        END IF;
    
        TRUNCATE classified_instance_ping;
        TRUNCATE classified_instance_pong;

        EXECUTE 'SELECT id FROM '||tree_table_name||
            ' WHERE parent_id=0 and tid='||tree_id||';' INTO root_id;
        EXECUTE 'INSERT INTO classified_instance_ping (id, jump, class, prob) 
                 SELECT '||id_col_name||', '||root_id||', 0, 0 FROM ' || 
                 encoded_table_name || ';';  
        table_pick= 1;
        FOR curr_level IN 1..max_level LOOP
            IF (verbosity > 0) THEN  
                RAISE INFO 'new_depth: %', curr_level;
            END IF;
            
            table_pick = table_pick % 2 + 1; 
            
            EXECUTE 'TRUNCATE '|| table_names[table_pick] ||';';
            EXECUTE 'SELECT count(id) FROM '||result_table_name||';' 
                     INTO size_finished;
            
            IF (verbosity > 0) THEN  
                RAISE INFO 'size_finished %', size_finished;
            END IF;       
            
            EXECUTE 'SELECT count(*) FROM '|| 
                     table_names[(table_pick) % 2 + 1] ||';' 
                     INTO remains_to_classify;
                
            IF (remains_to_classify = 0) THEN
                IF (verbosity > 0) THEN  
                    RAISE INFO 'size_finished: % remains_to_classify: %', 
                        size_finished, remains_to_classify;
                END IF;  
                      
                EXIT;
            END IF;

            SELECT MADLIB_SCHEMA.__format(
                'INSERT INTO %
                SELECT pt.id, 
                CASE WHEN (is_cont) THEN 
                        CASE WHEN (gt.lmc_nid IS NULL) THEN
                            0
                        ELSE
                            gt.lmc_nid + 
                            float8lt(gt.split_value, fvals[gt.feature])::INT4 
                            + 1 - gt.lmc_fval
                        END
                    ELSE 
                        CASE WHEN (gt.lmc_nid IS NULL) THEN
                            0
                        ELSE                    
                            gt.lmc_nid + fvals[gt.feature] - gt.lmc_fval
                        END
                    END as newjump,
                gt.max_class, gt.probability, gt.parent_id, gt.id 
                FROM 
                (
                    SELECT t1.id, t1.jump, fvals  
                    FROM % t1 
                    LEFT JOIN % t2 
                    ON t1.id = t2.id
                ) AS pt,
                (
                    SELECT  lmc_nid, lmc_fval, max_class, feature, probability, 
                            parent_id, id, is_cont, split_value
                    FROM % 
                    WHERE array_upper(tree_location,1) = % AND tid=%
                ) AS gt
                WHERE pt.jump = gt.id;',
                ARRAY[
                    table_names[table_pick],
                    table_names[(table_pick) % 2 + 1],
                    encoded_table_name,
                    tree_table_name,
                    MADLIB_SCHEMA.__to_char(curr_level),
                    MADLIB_SCHEMA.__to_char(tree_id)
                ]
                )
            INTO curstmt;     
            EXECUTE curstmt;
    
            /*
             *  if the node (whose id is "jump") doesn't exist, 
             *  then insert them into result table 
             *  (be classified to max_class of its corrsponding node)
             */
            SELECT MADLIB_SCHEMA.__format(
                'INSERT INTO %(tid,id, jump, class, prob, parent_id, leaf_id) 
                 SELECT '||tree_id||',id, 0, class, prob, parent_id, leaf_id
                 FROM %
                 WHERE jump NOT IN (SELECT id FROM % WHERE tid=%)',
                ARRAY[
                    result_table_name,
                    table_names[table_pick],
                    tree_table_name,
                    MADLIB_SCHEMA.__to_char(tree_id)
                    ]
                ) 
            INTO curstmt;
            EXECUTE curstmt;
            
            -- delete from the being classified data table
            SELECT MADLIB_SCHEMA.__format(
                'DELETE FROM %
                 WHERE jump NOT IN (SELECT id FROM % WHERE tid=%)',
                ARRAY[
                    table_names[table_pick],
                    tree_table_name,
                    MADLIB_SCHEMA.__to_char(tree_id)
                    ]
                ) 
            INTO curstmt;
            EXECUTE curstmt;
        END LOOP;

        EXECUTE 'INSERT INTO '||result_table_name||' SELECT '||tree_id||',* FROM '|| 
            table_names[table_pick] ||' WHERE jump = 0;';
        EXECUTE 'INSERT INTO '||result_table_name||' SELECT '||tree_id||',* FROM '|| 
            table_names[table_pick % 2 + 1] ||' WHERE jump = 0;';
    END LOOP;

    IF (verbosity > 0) THEN  
        RAISE INFO 'final classification time:%', clock_timestamp() - time_stamp;
    END IF;
    
    RETURN ARRAY[encoded_table_name, result_table_name];
END
$$ LANGUAGE PLPGSQL;


/*
 * @brief This function check the accuracy of the trained tree model.
 * 
 * @param tree_table_name     The name of the tree containing the model.
 * @param scoring_table_name  The full name of the table/view with the 
 *                            data to be scored.
 * @param verbosity           > 0 means this function runs in verbose mode.
 *
 * @return The estimated accuracy information.
 *
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__treemodel_score
    (
    tree_table_name             TEXT, 
    scoring_table_name          TEXT, 
    verbosity                   INT
    ) 
RETURNS FLOAT AS $$
DECLARE
    result_table_name           TEXT;
    result_table_name_final TEXT;
    id_col_name             TEXT  := 'id';
    class_col_name          TEXT  := 'class';
    curstmt                 TEXT  := '';
    num_of_row              FLOAT := 0.0;
    mis_of_row              FLOAT := 0.0;
    encoded_table_name      TEXT  := '';
    table_names                 TEXT[];
BEGIN

    IF (verbosity > 0) THEN
        -- get rid of the messages whose severity level is lower than 'WARNING'
        SET client_min_messages = WARNING;
    END IF;
    
    PERFORM MADLIB_SCHEMA.__assert
            (
                (tree_table_name IS NOT NULL) AND
                (
                 MADLIB_SCHEMA.__table_exists
                    (
                        tree_table_name
                    )
                ),
                'the specified tree table' || coalesce('<' || tree_table_name 
                || '> does not exist', ' is NULL')
            ); 

    PERFORM MADLIB_SCHEMA.__assert
            (
                (scoring_table_name IS NOT NULL) AND
                (
                 MADLIB_SCHEMA.__table_exists
                    (
                        scoring_table_name
                    )
                ),
                'the specified scoring table'      || 
                coalesce('<' || scoring_table_name || 
                '> does not exist', ' is NULL')
            ); 

    PERFORM MADLIB_SCHEMA.__assert
        (
            MADLIB_SCHEMA.__column_exists
                (
                    scoring_table_name,
                    MADLIB_SCHEMA.__get_class_column_name
                        (
                        MADLIB_SCHEMA.__get_metatable_name(tree_table_name)
                        )
                ),
            'the specified scoring table<' || scoring_table_name || 
            '> does not have class column'
        );
            
    table_names = MADLIB_SCHEMA.__treemodel_classify_internal
                    (
                        scoring_table_name, 
                        tree_table_name, 
                        verbosity
                    ); 
    encoded_table_name      = table_names[1];
    result_table_name       = table_names[2];
    result_table_name_final = result_table_name||'_final';
    
    PERFORM MADLIB_SCHEMA.__treemodel_get_vote_result
        (
        result_table_name, 
        result_table_name_final
        );

    SELECT MADLIB_SCHEMA.__format
        (
        'SELECT count(id) FROM %;',
        result_table_name_final
        ) 
    INTO curstmt;
    
    EXECUTE curstmt INTO num_of_row;

    SELECT MADLIB_SCHEMA.__format
        (
        'SELECT count(t2.id) 
     FROM % t1, % t2 
         WHERE t1.% = t2.id AND t1.% <> t2.class',
        ARRAY[
            encoded_table_name,
            result_table_name_final,
            id_col_name,
            class_col_name
        ]
        ) 
    INTO curstmt;
     
    EXECUTE curstmt INTO mis_of_row;
     
    EXECUTE 'DROP TABLE IF EXISTS ' || encoded_table_name || ';';
    EXECUTE 'DROP TABLE IF EXISTS ' || result_table_name || ';';
    EXECUTE 'DROP TABLE IF EXISTS ' || result_table_name_final || ';';    
    RETURN (num_of_row - mis_of_row) / num_of_row;
END;
$$ LANGUAGE PLPGSQL;


/*
 * @brief Cleanup the trained model table and any relevant tables.
 *
 * @param model_table_name The name of the table containing
 *                         the model's information.
 *
 * @return The status of that cleanup operation.
 *
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__treemodel_clean
    ( 
    model_table_name TEXT
    ) 
RETURNS BOOLEAN AS $$
DECLARE
    metatable_name TEXT;
    ref_count      INT;
BEGIN
    -- get rid of the messages whose severity level is lower than 'WARNING'
    SET client_min_messages = WARNING;
        
    PERFORM MADLIB_SCHEMA.__assert
            (
                (model_table_name IS NOT NULL) AND
                (
                 MADLIB_SCHEMA.__table_exists
                    (
                        model_table_name
                    )
                ),
                'the specified tree table'      || 
                coalesce('<'                    || 
                model_table_name                || 
                '> does not exists', ' is NULL')
            ); 
                                    
    IF (MADLIB_SCHEMA.__table_exists('MADLIB_SCHEMA.training_info')) THEN
        metatable_name = MADLIB_SCHEMA.__get_metatable_name(model_table_name);
        IF( metatable_name IS NOT NULL) THEN
            SELECT count(*) 
            FROM MADLIB_SCHEMA.training_info
            WHERE training_metatable_oid = metatable_name::regclass
            INTO ref_count; 
            
            -- if the metatable is not referenced by other training procedure.
            IF (ref_count = 1) THEN
                PERFORM MADLIB_SCHEMA.__drop_metatable(metatable_name);
                EXECUTE 'DROP TABLE IF EXISTS ' || 
                     MADLIB_SCHEMA.__get_encode_table_name(model_table_name) || ';';
            END IF;
        END IF;
        
        -- remove the record first, and then drop the table
        PERFORM MADLIB_SCHEMA.__delete_traininginfo(model_table_name);
        EXECUTE 'DROP TABLE IF EXISTS ' || model_table_name;
        
    ELSE
        EXECUTE 'DROP TABLE IF EXISTS ' || model_table_name;
    END IF;
    
    RETURN 't';    
END
$$ LANGUAGE PLPGSQL;

/*
 * @brief Validate the common parameters for C4.5 and RF API.
 *
 * @param split_criterion           The name of the split criterion that should be used 
 *                                  for tree construction. The valid values are
 *                                  ‘infogain’, ‘gainratio’, and ‘gini’. It can't be NULL.
 * @param training_table_name       The name of the table/view with the source data.
 * @param result_table_name         The name of the table where the resulting DT 
 *                                  will be kept.
 * @param continuous_feature_names  A comma-separated list of the names of features whose values 
 *                                  are continuous. The default is null, which means there are 
 *                                  no continuous features in the training table.
 * @param feature_col_names         A comma-separated list of the names of table columns, each of
 *                                  which defines a feature. The default value is null, which means 
 *                                  all the columns in the training table, except columns named 
 *                                   ‘id’ and ‘class’, will be used as features.
 * @param id_col_name               The name of the column containing an ID for each record.
 * @param class_col_name            The name of the column containing the labeled class. 
 * @param how2handle_missing_value  The way to handle missing value. The valid value 
 *                                  is 'explicit' or 'ignore'.
 * @param max_tree_depth            Specifies the maximum number of levels in the result DT 
 *                                  to avoid overgrown DTs. 
 * @param node_prune_threshold      The minimum percentage of the number of records required in a
 *                                  child node. It can't be NULL. The range of it is in [0.0, 1.0].
 *                                  This threshold only applies to the non-root nodes. Therefore,
 *                                  if its value is 1, then the trained tree only has one node (the root node);
 *                                  if its value is 0, then no nodes will be pruned by this parameter.
 * @param node_split_threshold      The minimum percentage of the number of records required in a
 *                                  node in order for a further split to be possible.
 *                                  It can't be NULL. The range of it is in [0.0, 1.0].
 *                                  If it's value is 1, then the trained tree only has two levels, since
 *                                  only the root node can grow; if its value is 0, then trees can grow
 *                                  extensively.
 * @param verbosity                 > 0 means this function runs in verbose mode.   
 * @param error_msg                 The reported error message when result_table_name is invalid.
 *
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__check_dt_common_params
    (
    split_criterion             TEXT,
    training_table_name         TEXT, 
    result_table_name           TEXT,
    continuous_feature_names    TEXT, 
    feature_col_names           TEXT, 
    id_col_name                 TEXT, 
    class_col_name              TEXT, 
    how2handle_missing_value    TEXT,
    max_tree_depth              INT,
    node_prune_threshold        FLOAT,
    node_split_threshold        FLOAT, 
    verbosity                   INT,
    error_msg                   TEXT
    ) 
RETURNS void AS $$
DECLARE
    num_of_element  BIGINT;
BEGIN
    PERFORM MADLIB_SCHEMA.__assert
        (
            (split_criterion IS NOT NULL)   AND
            (
             split_criterion = 'infogain'   OR 
             split_criterion = 'gainratio'  OR 
             split_criterion = 'gini'
            ),
            'split_criterion must be infogain, gainratio or gini'
        );

    PERFORM MADLIB_SCHEMA.__assert
        (
            how2handle_missing_value = 'ignore' OR 
            how2handle_missing_value = 'explicit',
            'how2handle_missing_value must be ignore or explicit!'
        );    

    PERFORM MADLIB_SCHEMA.__assert
        (
            max_tree_depth IS NOT NULL    AND
            max_tree_depth > 0,
            'max_tree_depth value must be greater than 0'
        );

    PERFORM MADLIB_SCHEMA.__assert
        (
            node_prune_threshold IS NOT NULL    AND
            float8ge(node_prune_threshold, 0)   AND
            float8le(node_prune_threshold, 1),
            'node_prune_threshold value must be in range from 0 to 1'
        );

    PERFORM MADLIB_SCHEMA.__assert
        (
            node_split_threshold IS NOT NULL   AND                
            float8ge(node_split_threshold, 0)  AND
            float8le(node_split_threshold, 1),                
            'node_split_threshold value must be in range from 0 to 1'
        );
            
    PERFORM MADLIB_SCHEMA.__assert
        (
            verbosity IS NOT NULL,                
            'verbosity must be non-null'
        );
                        
    PERFORM MADLIB_SCHEMA.__assert
        (
            id_col_name IS NOT NULL AND
            class_col_name IS NOT NULL AND
            length(btrim(id_col_name, ' ')) > 0 AND
            length(btrim(class_col_name, ' ')) > 0,
            'invalid id column name or class column name'
        );

    PERFORM MADLIB_SCHEMA.__assert
        (
            training_table_name IS NOT NULL AND
            MADLIB_SCHEMA.__table_exists
                (
                    training_table_name
                ),
            'the specified training table' || 
            coalesce('<'                   || 
            training_table_name            || 
            '> does not exist', ' is NULL')
        );

    EXECUTE 'SELECT count(*) FROM
                (SELECT * FROM '||training_table_name||' LIMIT 1) l' 
        INTO num_of_element;

    PERFORM MADLIB_SCHEMA.__assert
            (
                num_of_element > 0,
                'the specified training table <'||training_table_name||
                '> should not be empty'
            );

    
    PERFORM MADLIB_SCHEMA.__assert
            (
                result_table_name IS NOT NULL,
                'the specified result ' || error_msg ||  ' table name is NULL'
            );
    
    PERFORM MADLIB_SCHEMA.__assert
            (
                NOT MADLIB_SCHEMA.__table_exists
                    (
                        result_table_name 
                    )
                ,
                'the specified result ' || error_msg || ' table<' || 
                result_table_name || 
                '> exists' 
            );
END
$$ LANGUAGE PLPGSQL STABLE;


/*
 * @brief Get the name of the encoded table and the name of
 *        its meta table.
 * @param result_table_name   The name of the table where the 
 *                            resulting DT will be kept 
 * @param error_msg           The reported error message when the
 *                            length of result schema name plus
 *                            the length of result table name is
 *                            larger than 58.
 * 
 * @return A text array that contains two elements. The firest element
 *        is the encoded table name and the second is the meta table name.
 *                            
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__gen_enc_meta_names
    (
    result_table_name     TEXT,
    error_msg             TEXT
    ) 
RETURNS TEXT[] AS $$
DECLARE
    result_schema_name    TEXT;
    table_names           TEXT[];
BEGIN
    result_schema_name = MADLIB_SCHEMA.__get_schema_name(result_table_name);
            
    -- the maximum length of an identifier 63
    -- encoding table name convension:  <schema name>_<table name>_ed
    -- data info table name convension: <schema name>_<table name>_di
    -- the KV table name convension:    <schema name>_<table name>_<####>
    -- therefore, the maximum length of '<schema name>_<table name>' is 58
    PERFORM MADLIB_SCHEMA.__assert
        (
            length(
                result_schema_name      || 
                '_'                   || 
                result_table_name) <= 58,
            'the maximum length of ''' || error_msg || ''' is 58'
        );

    -- the encoded table and meta table will be under the specified schema
    table_names[1]  = result_schema_name                      || 
                    '.'                                   || 
                    replace(result_table_name, '.', '_')    || 
                    '_ed';
    table_names[2] = result_schema_name                      || 
                    '.'                                   || 
                    replace(result_table_name, '.', '_')    || 
                    '_di';        
    RETURN table_names;
END
$$ LANGUAGE PLPGSQL STABLE;


/*
 * @brief Validate if the provided columns are in the training table or not.
 *
 * @param training_table_name       The name of the table/view with the source data.
 * @param continuous_feature_names  A text array that contains all the continuous 
 *                                  features' names. 
 * @param feature_col_names         A text array that contains all the features' names.
 * @param id_col_name               The name of the column containing an ID for each record.
 * @param class_col_name            The name of the column containing the labeled class. 
 * @param features_per_node         The number of features to be considered when finding 
 *                                  a best split.
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__check_training_table
    (
    training_table_name         TEXT,
    continuous_feature_names    TEXT[], 
    feature_col_names           TEXT[], 
    id_col_name                 TEXT, 
    class_col_name              TEXT,
    features_per_node           INT
    ) 
RETURNS VOID AS $$
DECLARE
    num_attrs                 INT;
BEGIN
    PERFORM MADLIB_SCHEMA.__assert
        (
            MADLIB_SCHEMA.__column_exists
                (
                    training_table_name,
                    lower(btrim(id_col_name, ' '))
                ),
            'the specified training table<' || 
            training_table_name             || 
            '> does not have column '''     || 
            id_col_name                     || 
            ''''
        );

    PERFORM MADLIB_SCHEMA.__assert
        (
            MADLIB_SCHEMA.__column_exists
                (
                    training_table_name,
                    lower(btrim(class_col_name, ' '))
                ),
            'the specified training table<'     || 
            training_table_name                 || 
            '> does not have column '''         || 
            class_col_name                      || 
            ''''
        );

    IF (feature_col_names IS NULL) THEN
        -- 2 means the id and class column
        num_attrs = MADLIB_SCHEMA.__num_of_columns(training_table_name) - 2;
        
        PERFORM MADLIB_SCHEMA.__assert
            (
                (features_per_node IS NULL AND num_attrs > 0)  OR
                (features_per_node IS NOT NULL AND num_attrs >= features_per_node),
                'the value of features_per_node must be less than or equal to the total number ' ||
                'of features of the training table'
           );        
        PERFORM MADLIB_SCHEMA.__assert
            (
                MADLIB_SCHEMA.__columns_in_table(continuous_feature_names, training_table_name),
                'each feature in continuous_feature_names must be a column of the training table'
            );
    ELSE
        num_attrs = array_upper(feature_col_names, 1);
        PERFORM MADLIB_SCHEMA.__assert
            (
                (features_per_node IS NULL AND num_attrs > 0) OR
                (features_per_node IS NOT NULL AND num_attrs >= features_per_node),
                'the value of features_per_node must be less than or equal to the total number ' ||
                'of features of the training table'
           );    
        PERFORM MADLIB_SCHEMA.__assert
            (
                MADLIB_SCHEMA.__columns_in_table(feature_col_names, training_table_name),
                'each feature in feature_col_names must be a column of the training table'
            );

        PERFORM MADLIB_SCHEMA.__assert
            (
                coalesce(continuous_feature_names, '{}'::TEXT[]) <@ feature_col_names,
                'each feature in continuous_feature_names must be in the feature_col_names'
            );
    END IF;
END
$$ LANGUAGE PLPGSQL STABLE;


/* @ brief If the training table is a valid encoded table, then we use it directly.
 *         If the training table is not encoded, then we invoke the encoding procedure
 *         to transform the training table. 
 *         With the encoded table, we call the tree grow engine to generate the final tree.
 *
 * @param dt_algo_name                The name of the algorithom. Currently, it's
 *                                    'C4.5' or 'RF'
 * @param split_criterion             This parameter specifies which split criterion 
 *                                    should be used for tree construction and 
 *                                    pruning. The valid values are infogain, 
 *                                    gainratio, and gini.
 * @param num_trees                   Total number of trees to be trained. 
 * @param features_per_node           Total number of features used to compute split 
 *                                    gain for each node. 
 * @param training_table_name         The name of the table/view with the source data. 
 * @param validation_table_name       The name of the validation table. 
 * @param tree_table_name             The name of the table where the resulting 
 *                                    DT/RF will be stored. 
 * @param continuous_feature_names    A comma-separated list of the names of features whose values 
 *                                    are continuous. The default is null, which means there are 
 *                                    no continuous features in the training table.
 * @param feature_col_names           A comma-separated list of the names of table columns, each of
 *                                    which defines a feature. The default value is null, which means 
 *                                    all the columns in the training table, except columns named 
 *                                   ‘id’ and ‘class’, will be used as features.
 * @param id_col_name                 The name of the column containing id of each point.  
 * @param class_col_name              The name of the column containing correct class 
 *                                    of each point.  
 * @param confidence_level            A statistical confidence interval of the 
 *                                    resubstitution error.  
 * @param how2handle_missing_value    The way to handle missing value. The valid value 
 *                                    is 'explicit' or 'ignore'.
 * @param max_tree_depth              Maximum decision tree depth.  
 * @param sampling_percentage         The percentage of records sampled to train a tree.
 *                                    If it's NULL, 0.632 bootstrap will be used
 * @param sampling_needed             Whether enabling the sampling functionality.  
 * @param node_prune_threshold        Specifies the minimum number of samples required 
 *                                    in a child node.  
 * @param node_split_threshold        Specifies the minimum number of samples required 
 *                                    in a node in order for a further split   
 *                                    to be possible.  
 * @param error_msg                   The reported error message when the result table
 *                                    name is invalid.
 * @param verbosity                   > 0 means this function runs in verbose mode. 
 *
 * @return An instance of __train_result.
 *
 */
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__encode_and_train
    (
    dt_algo_name                TEXT,
    split_criterion             TEXT,
    num_trees                   INT,
    features_per_node           INT,
    training_table_name         TEXT,
    validation_table_name       TEXT,
    tree_table_name             TEXT,
    continuous_feature_names    TEXT,
    feature_col_names           TEXT, 
    id_col_name                 TEXT, 
    class_col_name              TEXT, 
    confidence_level            FLOAT8,    
    how2handle_missing_value    TEXT,
    max_tree_depth              INT,
    sampling_percentage         FLOAT8,
    sampling_needed             BOOL,
    node_prune_threshold        FLOAT8,
    node_split_threshold        FLOAT8, 
    error_msg                   TEXT,
    verbosity                   INT
    ) 
RETURNS RECORD AS $$
DECLARE
    table_names             TEXT[]; -- 1: encoded table; 2: meta table
    h2hmv_routine_id        INT := 1;  
    h2hmv_routine_name      TEXT;
    n_fids                  INT;
    curstmt                 TEXT;
    enc_tree_name           TEXT;
    cont_feature_col_names  TEXT[];
    feature_name_array      TEXT[];
    train_rs                MADLIB_SCHEMA.__train_result;
BEGIN
    cont_feature_col_names  = MADLIB_SCHEMA.__csvstr_to_array(continuous_feature_names);
    feature_name_array      = MADLIB_SCHEMA.__csvstr_to_array(feature_col_names);
    
    -- if the training table is an valid encoded table, then we retrieve
    -- the relevant information from training_info table directly.
    IF (MADLIB_SCHEMA.__is_valid_enc_table(training_table_name)) THEN
        enc_tree_name       = MADLIB_SCHEMA.__get_tree_table_name 
                                    (training_table_name);
        table_names[1]      = training_table_name;        
        table_names[2]      = MADLIB_SCHEMA.__get_metatable_name(enc_tree_name);
        h2hmv_routine_name  = MADLIB_SCHEMA.__get_routine_name(enc_tree_name);
        IF (h2hmv_routine_name = 'ignore') THEN
            h2hmv_routine_id = 1;
        ELSE
            h2hmv_routine_id = 2;
        END IF;
        
        -- validate the metatable
        PERFORM MADLIB_SCHEMA.__validate_metatable(table_names[2]);  

        n_fids = MADLIB_SCHEMA.__num_of_feature(table_names[2]);
        PERFORM MADLIB_SCHEMA.__assert
            (
                features_per_node IS NULL OR
                n_fids >= features_per_node,
                'the value of features_per_node must be less than or equal to the total number ' ||
                'of features of the training table'
           );  
        -- create tree table and auxiliary tables
        -- so that we can get the schema name of the table  
        PERFORM MADLIB_SCHEMA.__create_tree_tables(tree_table_name);
    ELSE
        -- the provided columns must be in the training table
        PERFORM MADLIB_SCHEMA.__check_training_table
            (
                training_table_name,
                cont_feature_col_names, 
                feature_name_array, 
                id_col_name, 
                class_col_name,
                features_per_node
            ); 

        h2hmv_routine_name = btrim(how2handle_missing_value, ' ');        
        IF (h2hmv_routine_name = 'ignore') THEN
            h2hmv_routine_id = 1;
        ELSE
            h2hmv_routine_id = 2;
        END IF;
        
        -- create tree table and auxiliary tables
        -- so that we can get the schema name of the table  
        PERFORM MADLIB_SCHEMA.__create_tree_tables(tree_table_name);

        -- encode the training table
        table_names = MADLIB_SCHEMA.__gen_enc_meta_names(tree_table_name, error_msg); 
        PERFORM MADLIB_SCHEMA.__encode_table
            (
                training_table_name,
                lower(id_col_name),
                feature_name_array,
                lower(class_col_name),
                cont_feature_col_names,
                table_names[1],
                table_names[2],
                h2hmv_routine_id,
                verbosity
            );
        n_fids = MADLIB_SCHEMA.__num_of_feature(table_names[2]);
    END IF;
    
    IF (sampling_needed) THEN
        IF (features_per_node IS NULL) THEN
            n_fids = round(sqrt(n_fids) - 0.5)::INT + 1;
        ELSE
            n_fids = features_per_node;
        END IF;
    END IF;

    IF (verbosity > 0) THEN
        RAISE INFO 'features_per_node: %', n_fids;
    END IF;
    
    -- insert data to the training_info table
    PERFORM MADLIB_SCHEMA.__insert_into_traininginfo
        (
            dt_algo_name,
            tree_table_name,
            training_table_name,
            table_names[2],
            table_names[1],
            validation_table_name,
            h2hmv_routine_name,
            split_criterion,
            sampling_percentage,
            n_fids,
            num_trees
        );
    
    -- call the tree grow engine
    train_rs = MADLIB_SCHEMA.__train_tree
        (
            split_criterion,
            num_trees,
            n_fids ,
            table_names[1],
            table_names[2],
            tree_table_name,
            validation_table_name, 
            'id', 
            'class', 
            confidence_level,              
            max_tree_depth, 
            sampling_percentage,
            node_prune_threshold,
            node_split_threshold,
            sampling_needed,
            h2hmv_routine_id,
            verbosity
        );

    RETURN train_rs;
END
$$ LANGUAGE PLPGSQL STABLE;