/* -----------------------------------------------------------------------------
 * PCA Install Check.
 * -------------------------------------------------------------------------- */


--Test data (Identical to SVD). See the SVD module for details
--on how the data was generated
DROP TABLE IF EXISTS mat;
CREATE TABLE mat (
    row_id integer,
    row_vec double precision[]
);

COPY mat (row_id, row_vec) FROM stdin delimiter '|';
1|{396,840,353,446,318,886,15,584,159,383}
2|{691,58,899,163,159,533,604,582,269,390}
3|{293,742,298,75,404,857,941,662,846,2}
4|{462,532,787,265,982,306,600,608,212,885}
5|{304,151,337,387,643,753,603,531,459,652}
6|{327,946,368,943,7,516,272,24,591,204}
7|{877,59,260,302,891,498,710,286,864,675}
8|{458,959,774,376,228,354,300,669,718,565}
9|{824,390,818,844,180,943,424,520,65,913}
10|{882,761,398,688,761,405,125,484,222,873}
11|{528,1,860,18,814,242,314,965,935,809}
12|{492,220,576,289,321,261,173,1,44,241}
13|{415,701,221,503,67,393,479,218,219,916}
14|{350,192,211,633,53,783,30,444,176,932}
15|{909,472,871,695,930,455,398,893,693,838}
16|{739,651,678,577,273,935,661,47,373,618}
\.

-- DENSE PCA: Make sure all possible default calls for dense PCA work
-----------------------------------------------------------------------------
drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
select pca_train('mat', 'result_table_214712398172490837', 'row_id', 10);
select * from result_table_214712398172490837;

drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
select pca_train('mat', 'result_table_214712398172490837', 'row_id', 10, NULL);
select * from result_table_214712398172490837;

drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
select pca_train('mat', 'result_table_214712398172490837', 'row_id', 10, NULL, 0);
select * from result_table_214712398172490837;

drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
select pca_train('mat', 'result_table_214712398172490837', 'row_id', 10,
NULL, 0, FALSE);
select * from result_table_214712398172490837;

drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
select pca_train('mat', 'result_table_214712398172490837', 'row_id', 10,
NULL, 0, FALSE, NULL);
select * from result_table_214712398172490837;

drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
drop table if exists result_table_214712398172490838;
select pca_train('mat', 'result_table_214712398172490837', 'row_id', 10,
NULL, 0, FALSE, 'result_table_214712398172490838');
select * from result_table_214712398172490837;
select * from result_table_214712398172490838;

drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
drop table if exists result_table_214712398172490838;
select pca_train('mat', 'result_table_214712398172490837', 'row_id', 5,
NULL, 5, FALSE, 'result_table_214712398172490838');
select * from result_table_214712398172490837;
select * from result_table_214712398172490838;

drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
select pca_train('mat', 'result_table_214712398172490837', 'row_id', 0.8);
select * from result_table_214712398172490837;

drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
select pca_train('mat', 'result_table_214712398172490837', 'row_id', 0.8, NULL);
select * from result_table_214712398172490837;

drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
select pca_train('mat', 'result_table_214712398172490837', 'row_id', 0.8, NULL, 0);
select * from result_table_214712398172490837;

drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
select pca_train('mat', 'result_table_214712398172490837', 'row_id', 0.8,
NULL, 0, FALSE);
select * from result_table_214712398172490837;

drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
select pca_train('mat', 'result_table_214712398172490837', 'row_id', 0.8,
NULL, 0, FALSE, NULL);
select * from result_table_214712398172490837;

drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
drop table if exists result_table_214712398172490838;
select pca_train('mat', 'result_table_214712398172490837', 'row_id', 0.8,
NULL, 0, FALSE, 'result_table_214712398172490838');
select * from result_table_214712398172490837;
select * from result_table_214712398172490838;

drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
drop table if exists result_table_214712398172490838;
select pca_train('mat', 'result_table_214712398172490837', 'row_id', 0.8,
NULL, 5, FALSE, 'result_table_214712398172490838');
select * from result_table_214712398172490837;
select * from result_table_214712398172490838;

-- Test dense data with grouping
DROP TABLE IF EXISTS mat;
CREATE TABLE mat (
    id integer,
    row_vec double precision[],
    grp integer
);

COPY mat (id, row_vec, grp) FROM stdin delimiter '|';
1|{396,840,353,446,318,886,15,584,159,383}|1
2|{691,58,899,163,159,533,604,582,269,390}|1
3|{293,742,298,75,404,857,941,662,846,2}|1
4|{462,532,787,265,982,306,600,608,212,885}|1
5|{304,151,337,387,643,753,603,531,459,652}|1
6|{327,946,368,943,7,516,272,24,591,204}|1
7|{877,59,260,302,891,498,710,286,864,675}|1
8|{458,959,774,376,228,354,300,669,718,565}|2
9|{824,390,818,844,180,943,424,520,65,913}|2
10|{882,761,398,688,761,405,125,484,222,873}|2
11|{528,1,860,18,814,242,314,965,935,809}|2
12|{492,220,576,289,321,261,173,1,44,241}|2
13|{415,701,221,503,67,393,479,218,219,916}|2
14|{350,192,211,633,53,783,30,444,176,932}|2
15|{909,472,871,695,930,455,398,893,693,838}|2
16|{739,651,678,577,273,935,661,47,373,618}|2
\.

-- Learn individaul PCA models based on grouping column (grp)
drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
drop table if exists result_table_214712398172490838;
select pca_train('mat', 'result_table_214712398172490837', 'id', 0.8,
'grp', 5, FALSE, 'result_table_214712398172490838');
select * from result_table_214712398172490837;
select * from result_table_214712398172490838;

-- Matrix in the column format
DROP TABLE IF EXISTS cmat;
CREATE TABLE cmat (
    id  integer,
    val0    float8,
    val1    float8,
    val2    float8,
    val3    float8,
    val4    float8,
    val5    float8,
    val6    float8,
    val7    float8,
    val8    float8,
    val9    float8,
    grp     integer
);

COPY cmat (id, val0, val1, val2, val3, val4, val5, val6, val7, val8, val9, grp) FROM stdin delimiter '|';
1|396|840|353|446|318|886|15|584|159|383|1
2|691|58|899|163|159|533|604|582|269|390|1
3|293|742|298|75|404|857|941|662|846|2|1
4|462|532|787|265|982|306|600|608|212|885|1
5|304|151|337|387|643|753|603|531|459|652|1
6|327|946|368|943|7|516|272|24|591|204|1
7|877|59|260|302|891|498|710|286|864|675|2
8|458|959|774|376|228|354|300|669|718|565|2
9|824|390|818|844|180|943|424|520|65|913|2
10|882|761|398|688|761|405|125|484|222|873|2
11|528|1|860|18|814|242|314|965|935|809|2
12|492|220|576|289|321|261|173|1|44|241|2
13|415|701|221|503|67|393|479|218|219|916|2
14|350|192|211|633|53|783|30|444|176|932|2
15|909|472|871|695|930|455|398|893|693|838|2
16|739|651|678|577|273|935|661|47|373|618|2
\.
-- Learn individaul PCA models based on grouping column (grp)
drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
drop table if exists result_table_214712398172490838;
select pca_train('mat', 'result_table_214712398172490837', 'id', 0.8,
'grp', 5, FALSE, 'result_table_214712398172490838');
select * from result_table_214712398172490837;
select * from result_table_214712398172490838;

-- SPARSE PCA: Make sure all possible default calls for sparse PCA work
-----------------------------------------------------------------------------

DROP TABLE IF EXISTS sparse_mat;
CREATE TABLE sparse_mat (
    row_id integer,
    col_id integer,
    val_id integer
);
COPY sparse_mat (row_id, col_id, val_id) FROM stdin delimiter '|';
1|2|4
1|5|6
3|8|4
5|4|2
6|6|12
8|1|2
8|7|2
9|3|4
9|8|2
\.

--Note that the sparse PCA (and SVD) interfaces require that the matrix dimension
-- information NOT be included in the sparse matrix encoding.

drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
select pca_sparse_train('sparse_mat', 'result_table_214712398172490837',
'row_id', 'col_id', 'val_id', 10, 10, 10);
select * from result_table_214712398172490837;


drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
select pca_sparse_train('sparse_mat', 'result_table_214712398172490837',
'row_id', 'col_id', 'val_id', 10, 10, 10, NULL);
select * from result_table_214712398172490837;


drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
select pca_sparse_train('sparse_mat', 'result_table_214712398172490837',
'row_id', 'col_id', 'val_id', 10, 10, 10, NULL, 0);
select * from result_table_214712398172490837;


drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
select pca_sparse_train('sparse_mat', 'result_table_214712398172490837',
'row_id', 'col_id', 'val_id', 10, 10, 10, NULL, 0, FALSE);
select * from result_table_214712398172490837;


drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
select pca_sparse_train('sparse_mat', 'result_table_214712398172490837',
'row_id', 'col_id', 'val_id', 10, 10, 10, NULL, 0, FALSE, NULL);
select * from result_table_214712398172490837;


drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
drop table if exists result_table_214712398172490838;
select pca_sparse_train('sparse_mat', 'result_table_214712398172490837',
'row_id', 'col_id', 'val_id', 10, 10, 10, NULL, 0, FALSE, 'result_table_214712398172490838');
select * from result_table_214712398172490837;
select * from result_table_214712398172490838;


drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
select pca_sparse_train('sparse_mat', 'result_table_214712398172490837',
'row_id', 'col_id', 'val_id', 10, 10, 0.8);
select * from result_table_214712398172490837;

drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
select pca_sparse_train('sparse_mat', 'result_table_214712398172490837',
'row_id', 'col_id', 'val_id', 10, 10, 0.8, NULL);
select * from result_table_214712398172490837;


drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
select pca_sparse_train('sparse_mat', 'result_table_214712398172490837',
'row_id', 'col_id', 'val_id', 10, 10, 0.8, NULL, 0);
select * from result_table_214712398172490837;


drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
select pca_sparse_train('sparse_mat', 'result_table_214712398172490837',
'row_id', 'col_id', 'val_id', 10, 10, 0.8, NULL, 0, FALSE);
select * from result_table_214712398172490837;


drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
select pca_sparse_train('sparse_mat', 'result_table_214712398172490837',
'row_id', 'col_id', 'val_id', 10, 10, 0.8, NULL, 0, FALSE, NULL);
select * from result_table_214712398172490837;


drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
drop table if exists result_table_214712398172490838;
select pca_sparse_train('sparse_mat', 'result_table_214712398172490837',
'row_id', 'col_id', 'val_id', 10, 10, 0.8, NULL, 0, FALSE, 'result_table_214712398172490838');
select * from result_table_214712398172490837;
select * from result_table_214712398172490838;

-------------------------------------------------------------------------
-- test a different column name
alter table sparse_mat rename column row_id to rownr;
alter table sparse_mat rename column col_id to colnr;
alter table sparse_mat rename column val_id to vals;

drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
select pca_sparse_train('sparse_mat', 'result_table_214712398172490837',
'rownr', 'colnr', 'vals', 10, 10, 10);
select * from result_table_214712398172490837;

-- Sparse input data with grouping column
DROP TABLE IF EXISTS sparse_mat_grp;
CREATE TABLE sparse_mat_grp (
    id integer,
    col_id integer,
    val_id integer,
    grp    integer
);
COPY sparse_mat_grp (id, col_id, val_id, grp) FROM stdin delimiter '|';
1|2|4|1
1|5|6|1
3|8|4|1
5|4|2|1
1|2|4|2
1|5|6|2
3|8|4|2
5|4|2|2
\.
-- Learn individaul PCA models based on grouping column (grp)
drop table if exists result_table_214712398172490837;
drop table if exists result_table_214712398172490837_mean;
drop table if exists result_table_214712398172490838;
select pca_sparse_train('sparse_mat_grp', 'result_table_214712398172490837',
'id', 'col_id', 'val_id', 10, 10, 0.8, 'grp', 0, FALSE, 'result_table_214712398172490838');
select * from result_table_214712398172490837;
select * from result_table_214712398172490838;

-------------------------------------------------------------------------
drop table if exists mat;
-- Check the second input matrix format produces the same results as the first format
CREATE TABLE mat (
    row_id integer,
    col1 double precision,
    col2 double precision,
    col3 double precision
);

COPY mat (row_id, col1, col2, col3) FROM stdin delimiter '|';
1|4|7|5
2|1|2|5
3|7|4|4
4|9|2|4
5|8|5|7
6|0|5|5
\.

DROP TABLE IF EXISTS mat2;
CREATE TABLE mat2 (
    row_id integer,
    row_vec double precision[]
);

COPY mat2 (row_id, row_vec) FROM stdin delimiter '|';
1|{4,7,5}
2|{1,2,5}
3|{7,4,4}
4|{9,2,4}
5|{8,5,7}
6|{0,5,5}
\.

drop table if exists table_a;
drop table if exists table_a_mean;
select pca_train('mat', 'table_a', 'row_id', 3);
select * from table_a;

drop table if exists table_b;
drop table if exists table_b_mean;
select pca_train('mat2', 'table_b', 'row_id', 3);
select * from table_b;

--Check that the two formats generate the same result
--We take the square of each element to get around sign differences
SELECT assert(
    relative_error(table_a.std_dev, table_b.std_dev) < 1e-2
    AND
    relative_error(
        array_mult(table_a.principal_components, table_a.principal_components),
        array_mult(table_b.principal_components, table_b.principal_components)
    ) < 1e-2
    , 'PCA: The two input formats didn''t generate identical results!')
FROM table_a, table_b WHERE table_a.row_id = table_b.row_id;


-- Test grouping with text column ---------------------------------------------
-- MADLIB-1215 --
-------------------------------------------------------------------------------
DROP TABLE IF EXISTS mat_group_text;
CREATE TABLE mat_group_text (
id integer,
row_vec double precision[],
matrix_id_text text
);
INSERT INTO mat_group_text VALUES
(1, '{1,2,3}', '1'),
(2, '{2,1,2}', '1'),
(3, '{3,2,1}', '1'),
(4, '{1,2,3,4,5}', '2'),
(5, '{2,5,2,4,1}', '2'),
(6, '{5,4,3,2,1}', '2');

DROP TABLE IF EXISTS result_table_group_text, result_table_group_text_mean;
SELECT pca_train(
    'mat_group_text',           -- Source table
    'result_table_group_text',  -- Output table
    'id',                       -- Row id of source table
    0.8,                        -- Proportion of variance
    'matrix_id_text');          -- Grouping column