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crankshaft/release/crankshaft--0.6.0--0.6.1.sql
Raul Marin 0d840b65f0 Release 0.6.1
2017-11-23 10:07:52 +01:00

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PL/PgSQL
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--DO NOT MODIFY THIS FILE, IT IS GENERATED AUTOMATICALLY FROM SOURCES
-- Complain if script is sourced in psql, rather than via CREATE EXTENSION
\echo Use "CREATE EXTENSION crankshaft" to load this file. \quit
-- Version number of the extension release
CREATE OR REPLACE FUNCTION cdb_crankshaft_version()
RETURNS text AS $$
SELECT '0.6.1'::text;
$$ language 'sql' IMMUTABLE STRICT PARALLEL SAFE;
-- Internal identifier of the installed extension instence
-- e.g. 'dev' for current development version
CREATE OR REPLACE FUNCTION _cdb_crankshaft_internal_version()
RETURNS text AS $$
SELECT installed_version FROM pg_available_extensions where name='crankshaft' and pg_available_extensions IS NOT NULL;
$$ language 'sql' STABLE STRICT PARALLEL SAFE;
-- Internal function.
-- Set the seeds of the RNGs (Random Number Generators)
-- used internally.
CREATE OR REPLACE FUNCTION
_cdb_random_seeds (seed_value INTEGER) RETURNS VOID
AS $$
from crankshaft import random_seeds
random_seeds.set_random_seeds(seed_value)
$$ LANGUAGE plpythonu VOLATILE PARALLEL UNSAFE;
CREATE OR REPLACE FUNCTION
CDB_PyAggS(current_state Numeric[], current_row Numeric[])
returns NUMERIC[] as $$
BEGIN
if array_upper(current_state,1) is null then
RAISE NOTICE 'setting state %',array_upper(current_row,1);
current_state[1] = array_upper(current_row,1);
end if;
return array_cat(current_state,current_row) ;
END
$$ LANGUAGE plpgsql IMMUTABLE PARALLEL SAFE;
-- Create aggregate if it did not exist
DO $$
BEGIN
IF NOT EXISTS (
SELECT *
FROM pg_catalog.pg_proc p
LEFT JOIN pg_catalog.pg_namespace n ON n.oid = p.pronamespace
WHERE n.nspname = 'cdb_crankshaft'
AND p.proname = 'cdb_pyagg'
AND p.proisagg)
THEN
CREATE AGGREGATE CDB_PyAgg(NUMERIC[]) (
SFUNC = CDB_PyAggS,
STYPE = Numeric[],
PARALLEL = SAFE,
INITCOND = "{}"
);
END IF;
END
$$ LANGUAGE plpgsql;
CREATE OR REPLACE FUNCTION
CDB_CreateAndPredictSegment(
target NUMERIC[],
features NUMERIC[],
target_features NUMERIC[],
target_ids NUMERIC[],
n_estimators INTEGER DEFAULT 1200,
max_depth INTEGER DEFAULT 3,
subsample DOUBLE PRECISION DEFAULT 0.5,
learning_rate DOUBLE PRECISION DEFAULT 0.01,
min_samples_leaf INTEGER DEFAULT 1)
RETURNS TABLE(cartodb_id NUMERIC, prediction NUMERIC, accuracy NUMERIC)
AS $$
import numpy as np
import plpy
from crankshaft.segmentation import create_and_predict_segment_agg
model_params = {'n_estimators': n_estimators,
'max_depth': max_depth,
'subsample': subsample,
'learning_rate': learning_rate,
'min_samples_leaf': min_samples_leaf}
def unpack2D(data):
dimension = data.pop(0)
a = np.array(data, dtype=float)
return a.reshape(len(a)/dimension, dimension)
return create_and_predict_segment_agg(np.array(target, dtype=float),
unpack2D(features),
unpack2D(target_features),
target_ids,
model_params)
$$ LANGUAGE plpythonu VOLATILE PARALLEL RESTRICTED;
CREATE OR REPLACE FUNCTION
CDB_CreateAndPredictSegment (
query TEXT,
variable_name TEXT,
target_table TEXT,
n_estimators INTEGER DEFAULT 1200,
max_depth INTEGER DEFAULT 3,
subsample DOUBLE PRECISION DEFAULT 0.5,
learning_rate DOUBLE PRECISION DEFAULT 0.01,
min_samples_leaf INTEGER DEFAULT 1)
RETURNS TABLE (cartodb_id TEXT, prediction NUMERIC, accuracy NUMERIC)
AS $$
from crankshaft.segmentation import create_and_predict_segment
model_params = {'n_estimators': n_estimators, 'max_depth':max_depth, 'subsample' : subsample, 'learning_rate': learning_rate, 'min_samples_leaf' : min_samples_leaf}
return create_and_predict_segment(query,variable_name,target_table, model_params)
$$ LANGUAGE plpythonu VOLATILE PARALLEL UNSAFE;
CREATE OR REPLACE FUNCTION CDB_Gravity(
IN target_query text,
IN weight_column text,
IN source_query text,
IN pop_column text,
IN target bigint,
IN radius integer,
IN minval numeric DEFAULT -10e307
)
RETURNS TABLE(
the_geom geometry,
source_id bigint,
target_id bigint,
dist numeric,
h numeric,
hpop numeric) AS $$
DECLARE
t_id bigint[];
t_geom geometry[];
t_weight numeric[];
s_id bigint[];
s_geom geometry[];
s_pop numeric[];
BEGIN
EXECUTE 'WITH foo as('+target_query+') SELECT array_agg(cartodb_id), array_agg(the_geom), array_agg(' || weight_column || ') FROM foo' INTO t_id, t_geom, t_weight;
EXECUTE 'WITH foo as('+source_query+') SELECT array_agg(cartodb_id), array_agg(the_geom), array_agg(' || pop_column || ') FROM foo' INTO s_id, s_geom, s_pop;
RETURN QUERY
SELECT g.* FROM t, s, CDB_Gravity(t_id, t_geom, t_weight, s_id, s_geom, s_pop, target, radius, minval) g;
END;
$$ language plpgsql VOLATILE PARALLEL UNSAFE;
CREATE OR REPLACE FUNCTION CDB_Gravity(
IN t_id bigint[],
IN t_geom geometry[],
IN t_weight numeric[],
IN s_id bigint[],
IN s_geom geometry[],
IN s_pop numeric[],
IN target bigint,
IN radius integer,
IN minval numeric DEFAULT -10e307
)
RETURNS TABLE(
the_geom geometry,
source_id bigint,
target_id bigint,
dist numeric,
h numeric,
hpop numeric) AS $$
DECLARE
t_type text;
s_type text;
t_center geometry[];
s_center geometry[];
BEGIN
t_type := GeometryType(t_geom[1]);
s_type := GeometryType(s_geom[1]);
IF t_type = 'POINT' THEN
t_center := t_geom;
ELSE
WITH tmp as (SELECT unnest(t_geom) as g) SELECT array_agg(ST_Centroid(g)) INTO t_center FROM tmp;
END IF;
IF s_type = 'POINT' THEN
s_center := s_geom;
ELSE
WITH tmp as (SELECT unnest(s_geom) as g) SELECT array_agg(ST_Centroid(g)) INTO s_center FROM tmp;
END IF;
RETURN QUERY
with target0 as(
SELECT unnest(t_center) as tc, unnest(t_weight) as tw, unnest(t_id) as td
),
source0 as(
SELECT unnest(s_center) as sc, unnest(s_id) as sd, unnest (s_geom) as sg, unnest(s_pop) as sp
),
prev0 as(
SELECT
source0.sg,
source0.sd as sourc_id,
coalesce(source0.sp,0) as sp,
target.td as targ_id,
coalesce(target.tw,0) as tw,
GREATEST(1.0,ST_Distance(geography(target.tc), geography(source0.sc)))::numeric as distance
FROM source0
CROSS JOIN LATERAL
(
SELECT
*
FROM target0
WHERE tw > minval
AND ST_DWithin(geography(source0.sc), geography(tc), radius)
) AS target
),
deno as(
SELECT
sourc_id,
sum(tw/distance) as h_deno
FROM
prev0
GROUP BY sourc_id
)
SELECT
p.sg as the_geom,
p.sourc_id as source_id,
p.targ_id as target_id,
case when p.distance > 1 then p.distance else 0.0 end as dist,
100*(p.tw/p.distance)/d.h_deno as h,
p.sp*(p.tw/p.distance)/d.h_deno as hpop
FROM
prev0 p,
deno d
WHERE
p.targ_id = target AND
p.sourc_id = d.sourc_id;
END;
$$ language plpgsql IMMUTABLE PARALLEL SAFE;
-- 0: nearest neighbor(s)
-- 1: barymetric
-- 2: IDW
-- 3: krigin ---> TO DO
CREATE OR REPLACE FUNCTION CDB_SpatialInterpolation(
IN query text,
IN point geometry,
IN method integer DEFAULT 1,
IN p1 numeric DEFAULT 0,
IN p2 numeric DEFAULT 0
)
RETURNS numeric AS
$$
DECLARE
gs geometry[];
vs numeric[];
output numeric;
BEGIN
EXECUTE 'WITH a AS('||query||') SELECT array_agg(the_geom), array_agg(attrib) FROM a' INTO gs, vs;
SELECT CDB_SpatialInterpolation(gs, vs, point, method, p1,p2) INTO output FROM a;
RETURN output;
END;
$$
language plpgsql VOLATILE PARALLEL UNSAFE;
CREATE OR REPLACE FUNCTION CDB_SpatialInterpolation(
IN geomin geometry[],
IN colin numeric[],
IN point geometry,
IN method integer DEFAULT 1,
IN p1 numeric DEFAULT 0,
IN p2 numeric DEFAULT 0
)
RETURNS numeric AS
$$
DECLARE
gs geometry[];
vs numeric[];
gs2 geometry[];
vs2 numeric[];
g geometry;
vertex geometry[];
sg numeric;
sa numeric;
sb numeric;
sc numeric;
va numeric;
vb numeric;
vc numeric;
output numeric;
BEGIN
-- output := -999.999;
-- nearest neighbors
-- p1: limit the number of neighbors, 0-> closest one
IF method = 0 THEN
IF p1 = 0 THEN
p1 := 1;
END IF;
WITH a as (SELECT unnest(geomin) as g, unnest(colin) as v),
b as (SELECT a.v as v FROM a ORDER BY point<->a.g LIMIT p1::integer)
SELECT avg(b.v) INTO output FROM b;
RETURN output;
-- barymetric
ELSIF method = 1 THEN
WITH a as (SELECT unnest(geomin) AS e),
b as (SELECT ST_DelaunayTriangles(ST_Collect(a.e),0.001, 0) AS t FROM a),
c as (SELECT (ST_Dump(t)).geom as v FROM b),
d as (SELECT v FROM c WHERE ST_Within(point, v))
SELECT v INTO g FROM d;
IF g is null THEN
-- out of the realm of the input data
RETURN -888.888;
END IF;
-- vertex of the selected cell
WITH a AS (SELECT (ST_DumpPoints(g)).geom AS v)
SELECT array_agg(v) INTO vertex FROM a;
-- retrieve the value of each vertex
WITH a AS(SELECT unnest(geomin) as geo, unnest(colin) as c)
SELECT c INTO va FROM a WHERE ST_Equals(geo, vertex[1]);
WITH a AS(SELECT unnest(geomin) as geo, unnest(colin) as c)
SELECT c INTO vb FROM a WHERE ST_Equals(geo, vertex[2]);
WITH a AS(SELECT unnest(geomin) as geo, unnest(colin) as c)
SELECT c INTO vc FROM a WHERE ST_Equals(geo, vertex[3]);
SELECT ST_area(g), ST_area(ST_MakePolygon(ST_MakeLine(ARRAY[point, vertex[2], vertex[3], point]))), ST_area(ST_MakePolygon(ST_MakeLine(ARRAY[point, vertex[1], vertex[3], point]))), ST_area(ST_MakePolygon(ST_MakeLine(ARRAY[point,vertex[1],vertex[2], point]))) INTO sg, sa, sb, sc;
output := (coalesce(sa,0) * coalesce(va,0) + coalesce(sb,0) * coalesce(vb,0) + coalesce(sc,0) * coalesce(vc,0)) / coalesce(sg);
RETURN output;
-- IDW
-- p1: limit the number of neighbors, 0->no limit
-- p2: order of distance decay, 0-> order 1
ELSIF method = 2 THEN
IF p2 = 0 THEN
p2 := 1;
END IF;
WITH a as (SELECT unnest(geomin) as g, unnest(colin) as v),
b as (SELECT a.g, a.v FROM a ORDER BY point<->a.g)
SELECT array_agg(b.g), array_agg(b.v) INTO gs, vs FROM b;
IF p1::integer>0 THEN
gs2:=gs;
vs2:=vs;
FOR i IN 1..p1
LOOP
gs2 := gs2 || gs[i];
vs2 := vs2 || vs[i];
END LOOP;
ELSE
gs2:=gs;
vs2:=vs;
END IF;
WITH a as (SELECT unnest(gs2) as g, unnest(vs2) as v),
b as (
SELECT
(1/ST_distance(point, a.g)^p2::integer) as k,
(a.v/ST_distance(point, a.g)^p2::integer) as f
FROM a
)
SELECT sum(b.f)/sum(b.k) INTO output FROM b;
RETURN output;
-- krigin
ELSIF method = 3 THEN
-- TO DO
END IF;
RETURN -777.777;
END;
$$
language plpgsql IMMUTABLE PARALLEL SAFE;
-- =============================================================================================
--
-- CDB_Voronoi
--
-- =============================================================================================
CREATE OR REPLACE FUNCTION CDB_voronoi(
IN geomin geometry[],
IN buffer numeric DEFAULT 0.5,
IN tolerance numeric DEFAULT 1e-9
)
RETURNS geometry AS $$
DECLARE
geomout geometry;
BEGIN
-- we need to make the geometry calculations in (pseudo)meters!!!
with a as (
SELECT unnest(geomin) as g1
),
b as(
SELECT st_transform(g1, 3857) g2 from a
)
SELECT array_agg(g2) INTO geomin from b;
WITH
convexhull_1 as (
SELECT
ST_ConvexHull(ST_Collect(geomin)) as g,
buffer * |/ (st_area(ST_ConvexHull(ST_Collect(geomin)))/PI()) as r
),
clipper as(
SELECT
st_buffer(ST_MinimumBoundingCircle(a.g), buffer*a.r) as g
FROM convexhull_1 a
),
env0 as (
SELECT
(st_dumppoints(st_expand(a.g, buffer*a.r))).geom as e
FROM convexhull_1 a
),
env as (
SELECT
array_agg(env0.e) as e
FROM env0
),
sample AS (
SELECT
ST_Collect(geomin || env.e) as geom
FROM env
),
convexhull as (
SELECT
ST_ConvexHull(ST_Collect(geomin)) as cg
),
tin as (
SELECT
ST_Dump(ST_DelaunayTriangles(geom, tolerance, 0)) as gd
FROM
sample
),
tin_polygons as (
SELECT
(gd).Path as id,
(gd).Geom as pg,
ST_Centroid(ST_MinimumBoundingCircle((gd).Geom, 180)) as ct
FROM tin
),
tin_lines as (
SELECT
id,
ST_ExteriorRing(pg) as lg
FROM tin_polygons
),
tin_nodes as (
SELECT
id,
ST_PointN(lg,1) p1,
ST_PointN(lg,2) p2,
ST_PointN(lg,3) p3
FROM tin_lines
),
tin_edges AS (
SELECT
p.id,
UNNEST(ARRAY[
ST_MakeLine(n.p1,n.p2) ,
ST_MakeLine(n.p2,n.p3) ,
ST_MakeLine(n.p3,n.p1)]) as Edge,
ST_Force2D(cdb_crankshaft._Find_Circle(n.p1,n.p2,n.p3)) as ct,
CASE WHEN st_distance(p.ct, ST_ExteriorRing(p.pg)) < tolerance THEN
TRUE
ELSE FALSE END AS ctx,
p.pg,
ST_within(p.ct, convexhull.cg) as ctin
FROM
tin_polygons p,
tin_nodes n,
convexhull
WHERE p.id = n.id
),
voro_nodes as (
SELECT
CASE WHEN x.ctx = TRUE THEN
ST_Centroid(x.edge)
ELSE
x.ct
END as xct,
CASE WHEN y.id is null THEN
CASE WHEN x.ctin = TRUE THEN
ST_SetSRID(ST_MakePoint(
ST_X(x.ct) + ((ST_X(ST_Centroid(x.edge)) - ST_X(x.ct)) * (1+buffer)),
ST_Y(x.ct) + ((ST_Y(ST_Centroid(x.edge)) - ST_Y(x.ct)) * (1+buffer))
), ST_SRID(x.ct))
END
ELSE
y.ct
END as yct
FROM
tin_edges x
LEFT OUTER JOIN
tin_edges y
ON x.id <> y.id AND ST_Equals(x.edge, y.edge)
),
voro_edges as(
SELECT
ST_LineMerge(ST_Collect(ST_MakeLine(xct, yct))) as v
FROM
voro_nodes
),
voro_cells as(
SELECT
ST_Polygonize(
ST_Node(
ST_LineMerge(
ST_Union(v, ST_ExteriorRing(
ST_Convexhull(v)
)
)
)
)
) as g
FROM
voro_edges
),
voro_set as(
SELECT
(st_dump(v.g)).geom as g
FROM voro_cells v
),
clipped_voro as(
SELECT
ST_intersection(c.g, v.g) as g
FROM
voro_set v,
clipper c
WHERE
ST_GeometryType(v.g) = 'ST_Polygon'
)
SELECT
st_collect(
ST_Transform(
ST_ConvexHull(g),
4326
)
)
INTO geomout
FROM
clipped_voro;
RETURN geomout;
END;
$$ language plpgsql IMMUTABLE PARALLEL SAFE;
/** ----------------------------------------------------------------------------------------
* @function : FindCircle
* @precis : Function that determines if three points form a circle. If so a table containing
* centre and radius is returned. If not, a null table is returned.
* @version : 1.0.1
* @param : p_pt1 : First point in curve
* @param : p_pt2 : Second point in curve
* @param : p_pt3 : Third point in curve
* @return : geometry : In which X,Y ordinates are the centre X, Y and the Z being the radius of found circle
* or NULL if three points do not form a circle.
* @history : Simon Greener - Feb 2012 - Original coding.
* Rafa de la Torre - Aug 2016 - Small fix for type checking
* Raul Marin - Sept 2017 - Remove unnecessary NULL checks and set function categories
* @copyright : Simon Greener @ 2012
* Licensed under a Creative Commons Attribution-Share Alike 2.5 Australia License. (http://creativecommons.org/licenses/by-sa/2.5/au/)
**/
CREATE OR REPLACE FUNCTION _Find_Circle(
IN p_pt1 geometry,
IN p_pt2 geometry,
IN p_pt3 geometry)
RETURNS geometry AS
$BODY$
DECLARE
v_Centre geometry;
v_radius NUMERIC;
v_CX NUMERIC;
v_CY NUMERIC;
v_dA NUMERIC;
v_dB NUMERIC;
v_dC NUMERIC;
v_dD NUMERIC;
v_dE NUMERIC;
v_dF NUMERIC;
v_dG NUMERIC;
BEGIN
IF ( ST_GeometryType(p_pt1) <> 'ST_Point' OR
ST_GeometryType(p_pt2) <> 'ST_Point' OR
ST_GeometryType(p_pt3) <> 'ST_Point' ) THEN
RAISE EXCEPTION 'All supplied geometries must be points.';
RETURN NULL;
END IF;
v_dA := ST_X(p_pt2) - ST_X(p_pt1);
v_dB := ST_Y(p_pt2) - ST_Y(p_pt1);
v_dC := ST_X(p_pt3) - ST_X(p_pt1);
v_dD := ST_Y(p_pt3) - ST_Y(p_pt1);
v_dE := v_dA * (ST_X(p_pt1) + ST_X(p_pt2)) + v_dB * (ST_Y(p_pt1) + ST_Y(p_pt2));
v_dF := v_dC * (ST_X(p_pt1) + ST_X(p_pt3)) + v_dD * (ST_Y(p_pt1) + ST_Y(p_pt3));
v_dG := 2.0 * (v_dA * (ST_Y(p_pt3) - ST_Y(p_pt2)) - v_dB * (ST_X(p_pt3) - ST_X(p_pt2)));
-- If v_dG is zero then the three points are collinear and no finite-radius
-- circle through them exists.
IF ( v_dG = 0 ) THEN
RETURN NULL;
ELSE
v_CX := (v_dD * v_dE - v_dB * v_dF) / v_dG;
v_CY := (v_dA * v_dF - v_dC * v_dE) / v_dG;
v_Radius := SQRT(POWER(ST_X(p_pt1) - v_CX,2) + POWER(ST_Y(p_pt1) - v_CY,2) );
END IF;
RETURN ST_SetSRID(ST_MakePoint(v_CX, v_CY, v_radius),ST_Srid(p_pt1));
END;
$BODY$
LANGUAGE plpgsql IMMUTABLE STRICT PARALLEL SAFE;
-- Moran's I Global Measure (public-facing)
CREATE OR REPLACE FUNCTION
CDB_AreasOfInterestGlobal(
subquery TEXT,
column_name TEXT,
w_type TEXT DEFAULT 'knn',
num_ngbrs INT DEFAULT 5,
permutations INT DEFAULT 99,
geom_col TEXT DEFAULT 'the_geom',
id_col TEXT DEFAULT 'cartodb_id')
RETURNS TABLE (moran NUMERIC, significance NUMERIC)
AS $$
from crankshaft.clustering import Moran
# TODO: use named parameters or a dictionary
moran = Moran()
return moran.global_stat(subquery, column_name, w_type,
num_ngbrs, permutations, geom_col, id_col)
$$ LANGUAGE plpythonu VOLATILE PARALLEL UNSAFE;
-- Moran's I Local (internal function)
CREATE OR REPLACE FUNCTION
_CDB_AreasOfInterestLocal(
subquery TEXT,
column_name TEXT,
w_type TEXT,
num_ngbrs INT,
permutations INT,
geom_col TEXT,
id_col TEXT)
RETURNS TABLE (moran NUMERIC, quads TEXT, significance NUMERIC, rowid INT, vals NUMERIC)
AS $$
from crankshaft.clustering import Moran
moran = Moran()
# TODO: use named parameters or a dictionary
return moran.local_stat(subquery, column_name, w_type,
num_ngbrs, permutations, geom_col, id_col)
$$ LANGUAGE plpythonu VOLATILE PARALLEL UNSAFE;
-- Moran's I Local (public-facing function)
CREATE OR REPLACE FUNCTION
CDB_AreasOfInterestLocal(
subquery TEXT,
column_name TEXT,
w_type TEXT DEFAULT 'knn',
num_ngbrs INT DEFAULT 5,
permutations INT DEFAULT 99,
geom_col TEXT DEFAULT 'the_geom',
id_col TEXT DEFAULT 'cartodb_id')
RETURNS TABLE (moran NUMERIC, quads TEXT, significance NUMERIC, rowid INT, vals NUMERIC)
AS $$
SELECT moran, quads, significance, rowid, vals
FROM cdb_crankshaft._CDB_AreasOfInterestLocal(subquery, column_name, w_type, num_ngbrs, permutations, geom_col, id_col);
$$ LANGUAGE SQL VOLATILE PARALLEL UNSAFE;
-- Moran's I only for HH and HL (public-facing function)
CREATE OR REPLACE FUNCTION
CDB_GetSpatialHotspots(
subquery TEXT,
column_name TEXT,
w_type TEXT DEFAULT 'knn',
num_ngbrs INT DEFAULT 5,
permutations INT DEFAULT 99,
geom_col TEXT DEFAULT 'the_geom',
id_col TEXT DEFAULT 'cartodb_id')
RETURNS TABLE (moran NUMERIC, quads TEXT, significance NUMERIC, rowid INT, vals NUMERIC)
AS $$
SELECT moran, quads, significance, rowid, vals
FROM cdb_crankshaft._CDB_AreasOfInterestLocal(subquery, column_name, w_type, num_ngbrs, permutations, geom_col, id_col)
WHERE quads IN ('HH', 'HL');
$$ LANGUAGE SQL VOLATILE PARALLEL UNSAFE;
-- Moran's I only for LL and LH (public-facing function)
CREATE OR REPLACE FUNCTION
CDB_GetSpatialColdspots(
subquery TEXT,
attr TEXT,
w_type TEXT DEFAULT 'knn',
num_ngbrs INT DEFAULT 5,
permutations INT DEFAULT 99,
geom_col TEXT DEFAULT 'the_geom',
id_col TEXT DEFAULT 'cartodb_id')
RETURNS TABLE (moran NUMERIC, quads TEXT, significance NUMERIC, rowid INT, vals NUMERIC)
AS $$
SELECT moran, quads, significance, rowid, vals
FROM cdb_crankshaft._CDB_AreasOfInterestLocal(subquery, attr, w_type, num_ngbrs, permutations, geom_col, id_col)
WHERE quads IN ('LL', 'LH');
$$ LANGUAGE SQL VOLATILE PARALLEL UNSAFE;
-- Moran's I only for LH and HL (public-facing function)
CREATE OR REPLACE FUNCTION
CDB_GetSpatialOutliers(
subquery TEXT,
attr TEXT,
w_type TEXT DEFAULT 'knn',
num_ngbrs INT DEFAULT 5,
permutations INT DEFAULT 99,
geom_col TEXT DEFAULT 'the_geom',
id_col TEXT DEFAULT 'cartodb_id')
RETURNS TABLE (moran NUMERIC, quads TEXT, significance NUMERIC, rowid INT, vals NUMERIC)
AS $$
SELECT moran, quads, significance, rowid, vals
FROM cdb_crankshaft._CDB_AreasOfInterestLocal(subquery, attr, w_type, num_ngbrs, permutations, geom_col, id_col)
WHERE quads IN ('HL', 'LH');
$$ LANGUAGE SQL VOLATILE PARALLEL UNSAFE;
-- Moran's I Global Rate (public-facing function)
CREATE OR REPLACE FUNCTION
CDB_AreasOfInterestGlobalRate(
subquery TEXT,
numerator TEXT,
denominator TEXT,
w_type TEXT DEFAULT 'knn',
num_ngbrs INT DEFAULT 5,
permutations INT DEFAULT 99,
geom_col TEXT DEFAULT 'the_geom',
id_col TEXT DEFAULT 'cartodb_id')
RETURNS TABLE (moran FLOAT, significance FLOAT)
AS $$
from crankshaft.clustering import Moran
moran = Moran()
# TODO: use named parameters or a dictionary
return moran.global_rate_stat(subquery, numerator, denominator, w_type,
num_ngbrs, permutations, geom_col, id_col)
$$ LANGUAGE plpythonu VOLATILE PARALLEL UNSAFE;
-- Moran's I Local Rate (internal function)
CREATE OR REPLACE FUNCTION
_CDB_AreasOfInterestLocalRate(
subquery TEXT,
numerator TEXT,
denominator TEXT,
w_type TEXT,
num_ngbrs INT,
permutations INT,
geom_col TEXT,
id_col TEXT)
RETURNS
TABLE(moran NUMERIC, quads TEXT, significance NUMERIC, rowid INT, vals NUMERIC)
AS $$
from crankshaft.clustering import Moran
moran = Moran()
# TODO: use named parameters or a dictionary
return moran.local_rate_stat(subquery, numerator, denominator, w_type, num_ngbrs, permutations, geom_col, id_col)
$$ LANGUAGE plpythonu VOLATILE PARALLEL UNSAFE;
-- Moran's I Local Rate (public-facing function)
CREATE OR REPLACE FUNCTION
CDB_AreasOfInterestLocalRate(
subquery TEXT,
numerator TEXT,
denominator TEXT,
w_type TEXT DEFAULT 'knn',
num_ngbrs INT DEFAULT 5,
permutations INT DEFAULT 99,
geom_col TEXT DEFAULT 'the_geom',
id_col TEXT DEFAULT 'cartodb_id')
RETURNS
TABLE(moran NUMERIC, quads TEXT, significance NUMERIC, rowid INT, vals NUMERIC)
AS $$
SELECT moran, quads, significance, rowid, vals
FROM cdb_crankshaft._CDB_AreasOfInterestLocalRate(subquery, numerator, denominator, w_type, num_ngbrs, permutations, geom_col, id_col);
$$ LANGUAGE SQL VOLATILE PARALLEL UNSAFE;
-- Moran's I Local Rate only for HH and HL (public-facing function)
CREATE OR REPLACE FUNCTION
CDB_GetSpatialHotspotsRate(
subquery TEXT,
numerator TEXT,
denominator TEXT,
w_type TEXT DEFAULT 'knn',
num_ngbrs INT DEFAULT 5,
permutations INT DEFAULT 99,
geom_col TEXT DEFAULT 'the_geom',
id_col TEXT DEFAULT 'cartodb_id')
RETURNS
TABLE(moran NUMERIC, quads TEXT, significance NUMERIC, rowid INT, vals NUMERIC)
AS $$
SELECT moran, quads, significance, rowid, vals
FROM cdb_crankshaft._CDB_AreasOfInterestLocalRate(subquery, numerator, denominator, w_type, num_ngbrs, permutations, geom_col, id_col)
WHERE quads IN ('HH', 'HL');
$$ LANGUAGE SQL VOLATILE PARALLEL UNSAFE;
-- Moran's I Local Rate only for LL and LH (public-facing function)
CREATE OR REPLACE FUNCTION
CDB_GetSpatialColdspotsRate(
subquery TEXT,
numerator TEXT,
denominator TEXT,
w_type TEXT DEFAULT 'knn',
num_ngbrs INT DEFAULT 5,
permutations INT DEFAULT 99,
geom_col TEXT DEFAULT 'the_geom',
id_col TEXT DEFAULT 'cartodb_id')
RETURNS
TABLE(moran NUMERIC, quads TEXT, significance NUMERIC, rowid INT, vals NUMERIC)
AS $$
SELECT moran, quads, significance, rowid, vals
FROM cdb_crankshaft._CDB_AreasOfInterestLocalRate(subquery, numerator, denominator, w_type, num_ngbrs, permutations, geom_col, id_col)
WHERE quads IN ('LL', 'LH');
$$ LANGUAGE SQL VOLATILE PARALLEL UNSAFE;
-- Moran's I Local Rate only for LH and HL (public-facing function)
CREATE OR REPLACE FUNCTION
CDB_GetSpatialOutliersRate(
subquery TEXT,
numerator TEXT,
denominator TEXT,
w_type TEXT DEFAULT 'knn',
num_ngbrs INT DEFAULT 5,
permutations INT DEFAULT 99,
geom_col TEXT DEFAULT 'the_geom',
id_col TEXT DEFAULT 'cartodb_id')
RETURNS
TABLE(moran NUMERIC, quads TEXT, significance NUMERIC, rowid INT, vals NUMERIC)
AS $$
SELECT moran, quads, significance, rowid, vals
FROM cdb_crankshaft._CDB_AreasOfInterestLocalRate(subquery, numerator, denominator, w_type, num_ngbrs, permutations, geom_col, id_col)
WHERE quads IN ('HL', 'LH');
$$ LANGUAGE SQL VOLATILE PARALLEL UNSAFE;
-- Spatial k-means clustering
CREATE OR REPLACE FUNCTION CDB_KMeans(query text, no_clusters integer, no_init integer default 20)
RETURNS table (cartodb_id integer, cluster_no integer) as $$
from crankshaft.clustering import Kmeans
kmeans = Kmeans()
return kmeans.spatial(query, no_clusters, no_init)
$$ LANGUAGE plpythonu VOLATILE PARALLEL UNSAFE;
CREATE OR REPLACE FUNCTION CDB_WeightedMeanS(state Numeric[],the_geom GEOMETRY(Point, 4326), weight NUMERIC)
RETURNS Numeric[] AS
$$
DECLARE
newX NUMERIC;
newY NUMERIC;
newW NUMERIC;
BEGIN
IF weight IS NULL OR the_geom IS NULL THEN
newX = state[1];
newY = state[2];
newW = state[3];
ELSE
newX = state[1] + ST_X(the_geom)*weight;
newY = state[2] + ST_Y(the_geom)*weight;
newW = state[3] + weight;
END IF;
RETURN Array[newX,newY,newW];
END
$$ LANGUAGE plpgsql IMMUTABLE PARALLEL SAFE;
CREATE OR REPLACE FUNCTION CDB_WeightedMeanF(state Numeric[])
RETURNS GEOMETRY AS
$$
BEGIN
IF state[3] = 0 THEN
RETURN ST_SetSRID(ST_MakePoint(state[1],state[2]), 4326);
ELSE
RETURN ST_SETSRID(ST_MakePoint(state[1]/state[3], state[2]/state[3]),4326);
END IF;
END
$$ LANGUAGE plpgsql IMMUTABLE PARALLEL SAFE;
-- Create aggregate if it did not exist
DO $$
BEGIN
IF NOT EXISTS (
SELECT *
FROM pg_catalog.pg_proc p
LEFT JOIN pg_catalog.pg_namespace n ON n.oid = p.pronamespace
WHERE n.nspname = 'cdb_crankshaft'
AND p.proname = 'cdb_weightedmean'
AND p.proisagg)
THEN
CREATE AGGREGATE CDB_WeightedMean(geometry(Point, 4326), NUMERIC) (
SFUNC = CDB_WeightedMeanS,
FINALFUNC = CDB_WeightedMeanF,
STYPE = Numeric[],
PARALLEL = SAFE,
INITCOND = "{0.0,0.0,0.0}"
);
END IF;
END
$$ LANGUAGE plpgsql;
-- Spatial Markov
-- input table format:
-- id | geom | date_1 | date_2 | date_3
-- 1 | Pt1 | 12.3 | 13.1 | 14.2
-- 2 | Pt2 | 11.0 | 13.2 | 12.5
-- ...
-- Sample Function call:
-- SELECT CDB_SpatialMarkov('SELECT * FROM real_estate',
-- Array['date_1', 'date_2', 'date_3'])
CREATE OR REPLACE FUNCTION
CDB_SpatialMarkovTrend (
subquery TEXT,
time_cols TEXT[],
num_classes INT DEFAULT 7,
w_type TEXT DEFAULT 'knn',
num_ngbrs INT DEFAULT 5,
permutations INT DEFAULT 99,
geom_col TEXT DEFAULT 'the_geom',
id_col TEXT DEFAULT 'cartodb_id')
RETURNS TABLE (trend NUMERIC, trend_up NUMERIC, trend_down NUMERIC, volatility NUMERIC, rowid INT)
AS $$
from crankshaft.space_time_dynamics import Markov
markov = Markov()
## TODO: use named parameters or a dictionary
return markov.spatial_trend(subquery, time_cols, num_classes, w_type, num_ngbrs, permutations, geom_col, id_col)
$$ LANGUAGE plpythonu VOLATILE PARALLEL UNSAFE;
-- input table format: identical to above but in a predictable format
-- Sample function call:
-- SELECT cdb_spatial_markov('SELECT * FROM real_estate',
-- 'date_1')
-- CREATE OR REPLACE FUNCTION
-- cdb_spatial_markov (
-- subquery TEXT,
-- time_col_min text,
-- time_col_max text,
-- date_format text, -- '_YYYY_MM_DD'
-- num_time_per_bin INT DEFAULT 1,
-- permutations INT DEFAULT 99,
-- geom_column TEXT DEFAULT 'the_geom',
-- id_col TEXT DEFAULT 'cartodb_id',
-- w_type TEXT DEFAULT 'knn',
-- num_ngbrs int DEFAULT 5)
-- RETURNS TABLE (moran FLOAT, quads TEXT, significance FLOAT, ids INT)
-- AS $$
-- plpy.execute('SELECT cdb_crankshaft._cdb_crankshaft_activate_py()')
-- from crankshaft.clustering import moran_local
-- # TODO: use named parameters or a dictionary
-- return spatial_markov(subquery, time_cols, permutations, geom_column, id_col, w_type, num_ngbrs)
-- $$ LANGUAGE plpythonu;
--
-- -- input table format:
-- -- id | geom | date | measurement
-- -- 1 | Pt1 | 12/3 | 13.2
-- -- 2 | Pt2 | 11/5 | 11.3
-- -- 3 | Pt1 | 11/13 | 12.9
-- -- 4 | Pt3 | 12/19 | 10.1
-- -- ...
--
-- CREATE OR REPLACE FUNCTION
-- cdb_spatial_markov (
-- subquery TEXT,
-- time_col text,
-- num_time_per_bin INT DEFAULT 1,
-- permutations INT DEFAULT 99,
-- geom_column TEXT DEFAULT 'the_geom',
-- id_col TEXT DEFAULT 'cartodb_id',
-- w_type TEXT DEFAULT 'knn',
-- num_ngbrs int DEFAULT 5)
-- RETURNS TABLE (moran FLOAT, quads TEXT, significance FLOAT, ids INT)
-- AS $$
-- plpy.execute('SELECT cdb_crankshaft._cdb_crankshaft_activate_py()')
-- from crankshaft.clustering import moran_local
-- # TODO: use named parameters or a dictionary
-- return spatial_markov(subquery, time_cols, permutations, geom_column, id_col, w_type, num_ngbrs)
-- $$ LANGUAGE plpythonu;
-- Based on:
-- https://github.com/mapbox/polylabel/blob/master/index.js
-- https://sites.google.com/site/polesofinaccessibility/
-- Requires: https://github.com/CartoDB/cartodb-postgresql
-- Based on:
-- https://github.com/mapbox/polylabel/blob/master/index.js
-- https://sites.google.com/site/polesofinaccessibility/
-- Requires: https://github.com/CartoDB/cartodb-postgresql
CREATE OR REPLACE FUNCTION CDB_PIA(
IN polygon geometry,
IN tolerance numeric DEFAULT 1.0
)
RETURNS geometry AS $$
DECLARE
env geometry[];
cells geometry[];
cell geometry;
best_c geometry;
best_d numeric;
test_d numeric;
test_mx numeric;
test_h numeric;
test_cells geometry[];
width numeric;
height numeric;
h numeric;
i integer;
n integer;
sqr numeric;
p geometry;
BEGIN
sqr := |/2;
polygon := ST_Transform(polygon, 3857);
-- grid #0 cell size
height := ST_YMax(polygon) - ST_YMin(polygon);
width := ST_XMax(polygon) - ST_XMin(polygon);
h := 0.5*LEAST(height, width);
-- grid #0
with c1 as(
SELECT cdb_crankshaft.CDB_RectangleGrid(polygon, h, h) as c
)
SELECT array_agg(c) INTO cells FROM c1;
-- 1st guess: centroid
best_d := cdb_crankshaft._Signed_Dist(polygon, ST_Centroid(Polygon));
-- looping the loop
n := array_length(cells,1);
i := 1;
LOOP
EXIT WHEN i > n;
cell := cells[i];
i := i+1;
-- cell side size, it's square
test_h := ST_XMax(cell) - ST_XMin(cell) ;
-- check distance
test_d := cdb_crankshaft._Signed_Dist(polygon, ST_Centroid(cell));
IF test_d > best_d THEN
best_d := test_d;
best_c := cells[i];
END IF;
-- longest distance within the cell
test_mx := test_d + (test_h/2 * sqr);
-- if the cell has no chance to contains the desired point, continue
CONTINUE WHEN test_mx - best_d <= tolerance;
-- resample the cell
with c1 as(
SELECT cdb_crankshaft.CDB_RectangleGrid(cell, test_h/2, test_h/2) as c
)
SELECT array_agg(c) INTO test_cells FROM c1;
-- concat the new cells to the former array
cells := cells || test_cells;
-- prepare next iteration
n := array_length(cells,1);
END LOOP;
RETURN ST_transform(ST_Centroid(best_c), 4326);
END;
$$ language plpgsql IMMUTABLE PARALLEL SAFE;
-- signed distance point to polygon with holes
-- negative is the point is out the polygon
CREATE OR REPLACE FUNCTION _Signed_Dist(
IN polygon geometry,
IN point geometry
)
RETURNS numeric AS $$
DECLARE
i integer;
within integer;
holes integer;
dist numeric;
BEGIN
dist := 1e999;
SELECT LEAST(dist, ST_distance(point, ST_ExteriorRing(polygon))::numeric) INTO dist;
SELECT CASE WHEN ST_Within(point,polygon) THEN 1 ELSE -1 END INTO within;
SELECT ST_NumInteriorRings(polygon) INTO holes;
IF holes > 0 THEN
FOR i IN 1..holes
LOOP
SELECT LEAST(dist, ST_distance(point, ST_InteriorRingN(polygon, i))::numeric) INTO dist;
END LOOP;
END IF;
dist := dist * within::numeric;
RETURN dist;
END;
$$ language plpgsql IMMUTABLE PARALLEL SAFE;
--
-- Iterative densification of a set of points using Delaunay triangulation
-- the new points have as assigned value the average value of the 3 vertex (centroid)
--
-- @param geomin - array of geometries (points)
--
-- @param colin - array of numeric values in that points
--
-- @param iterations - integer, number of iterations
--
--
-- Returns: TABLE(geomout geometry, colout numeric)
--
--
CREATE OR REPLACE FUNCTION CDB_Densify(
IN geomin geometry[],
IN colin numeric[],
IN iterations integer
)
RETURNS TABLE(geomout geometry, colout numeric) AS $$
DECLARE
geotemp geometry[];
coltemp numeric[];
i integer;
gs geometry[];
g geometry;
vertex geometry[];
va numeric;
vb numeric;
vc numeric;
center geometry;
centerval numeric;
tmp integer;
BEGIN
geotemp := geomin;
coltemp := colin;
FOR i IN 1..iterations
LOOP
-- generate TIN
WITH a as (SELECT unnest(geotemp) AS e),
b as (SELECT ST_DelaunayTriangles(ST_Collect(a.e),0.001, 0) AS t FROM a),
c as (SELECT (ST_Dump(t)).geom AS v FROM b)
SELECT array_agg(v) INTO gs FROM c;
-- loop cells
FOREACH g IN ARRAY gs
LOOP
-- append centroid
SELECT ST_Centroid(g) INTO center;
geotemp := array_append(geotemp, center);
-- retrieve the value of each vertex
WITH a AS (SELECT (ST_DumpPoints(g)).geom AS v)
SELECT array_agg(v) INTO vertex FROM a;
WITH a AS(SELECT unnest(geotemp) as geo, unnest(coltemp) as c)
SELECT c INTO va FROM a WHERE ST_Equals(geo, vertex[1]);
WITH a AS(SELECT unnest(geotemp) as geo, unnest(coltemp) as c)
SELECT c INTO vb FROM a WHERE ST_Equals(geo, vertex[2]);
WITH a AS(SELECT unnest(geotemp) as geo, unnest(coltemp) as c)
SELECT c INTO vc FROM a WHERE ST_Equals(geo, vertex[3]);
-- calc the value at the center
centerval := (va + vb + vc) / 3;
-- append the value
coltemp := array_append(coltemp, centerval);
END LOOP;
END LOOP;
RETURN QUERY SELECT unnest(geotemp ) as geomout, unnest(coltemp ) as colout;
END;
$$ language plpgsql IMMUTABLE PARALLEL SAFE;
CREATE OR REPLACE FUNCTION CDB_TINmap(
IN geomin geometry[],
IN colin numeric[],
IN iterations integer
)
RETURNS TABLE(geomout geometry, colout numeric) AS $$
DECLARE
p geometry[];
vals numeric[];
gs geometry[];
g geometry;
vertex geometry[];
centerval numeric;
va numeric;
vb numeric;
vc numeric;
coltemp numeric[];
BEGIN
SELECT array_agg(dens.geomout), array_agg(dens.colout) INTO p, vals FROM cdb_crankshaft.CDB_Densify(geomin, colin, iterations) dens;
WITH a as (SELECT unnest(p) AS e),
b as (SELECT ST_DelaunayTriangles(ST_Collect(a.e),0.001, 0) AS t FROM a),
c as (SELECT (ST_Dump(t)).geom AS v FROM b)
SELECT array_agg(v) INTO gs FROM c;
FOREACH g IN ARRAY gs
LOOP
-- retrieve the vertex of each triangle
WITH a AS (SELECT (ST_DumpPoints(g)).geom AS v)
SELECT array_agg(v) INTO vertex FROM a;
-- retrieve the value of each vertex
WITH a AS(SELECT unnest(p) as geo, unnest(vals) as c)
SELECT c INTO va FROM a WHERE ST_Equals(geo, vertex[1]);
WITH a AS(SELECT unnest(p) as geo, unnest(vals) as c)
SELECT c INTO vb FROM a WHERE ST_Equals(geo, vertex[2]);
WITH a AS(SELECT unnest(p) as geo, unnest(vals) as c)
SELECT c INTO vc FROM a WHERE ST_Equals(geo, vertex[3]);
-- calc the value at the center
centerval := (va + vb + vc) / 3;
-- append the value
coltemp := array_append(coltemp, centerval);
END LOOP;
RETURN QUERY SELECT unnest(gs) as geomout, unnest(coltemp ) as colout;
END;
$$ language plpgsql IMMUTABLE PARALLEL SAFE;
-- Getis-Ord's G
-- Hotspot/Coldspot Analysis tool
CREATE OR REPLACE FUNCTION
CDB_GetisOrdsG(
subquery TEXT,
column_name TEXT,
w_type TEXT DEFAULT 'knn',
num_ngbrs INT DEFAULT 5,
permutations INT DEFAULT 999,
geom_col TEXT DEFAULT 'the_geom',
id_col TEXT DEFAULT 'cartodb_id')
RETURNS TABLE (z_score NUMERIC, p_value NUMERIC, p_z_sim NUMERIC, rowid BIGINT)
AS $$
from crankshaft.clustering import Getis
getis = Getis()
return getis.getis_ord(subquery, column_name, w_type, num_ngbrs, permutations, geom_col, id_col)
$$ LANGUAGE plpythonu VOLATILE PARALLEL UNSAFE;
-- TODO: make a version that accepts the values as arrays
-- Find outliers using a static threshold
--
CREATE OR REPLACE FUNCTION CDB_StaticOutlier(column_value numeric, threshold numeric)
RETURNS boolean
AS $$
BEGIN
RETURN column_value > threshold;
END;
$$ LANGUAGE plpgsql IMMUTABLE PARALLEL SAFE ;
-- Find outliers by a percentage above the threshold
-- TODO: add symmetric option? `is_symmetric boolean DEFAULT false`
CREATE OR REPLACE FUNCTION CDB_PercentOutlier(column_values numeric[], outlier_fraction numeric, ids int[])
RETURNS TABLE(is_outlier boolean, rowid int)
AS $$
DECLARE
avg_val numeric;
out_vals boolean[];
BEGIN
SELECT avg(i) INTO avg_val
FROM unnest(column_values) As x(i);
IF avg_val = 0 THEN
RAISE EXCEPTION 'Mean value is zero. Try another outlier method.';
END IF;
SELECT array_agg(
outlier_fraction < i / avg_val) INTO out_vals
FROM unnest(column_values) As x(i);
RETURN QUERY
SELECT unnest(out_vals) As is_outlier,
unnest(ids) As rowid;
END;
$$ LANGUAGE plpgsql IMMUTABLE PARALLEL SAFE;
-- Find outliers above a given number of standard deviations from the mean
CREATE OR REPLACE FUNCTION CDB_StdDevOutlier(column_values numeric[], num_deviations numeric, ids int[], is_symmetric boolean DEFAULT true)
RETURNS TABLE(is_outlier boolean, rowid int)
AS $$
DECLARE
stddev_val numeric;
avg_val numeric;
out_vals boolean[];
BEGIN
SELECT stddev(i), avg(i) INTO stddev_val, avg_val
FROM unnest(column_values) As x(i);
IF stddev_val = 0 THEN
RAISE EXCEPTION 'Standard deviation of input data is zero';
END IF;
IF is_symmetric THEN
SELECT array_agg(
abs(i - avg_val) / stddev_val > num_deviations) INTO out_vals
FROM unnest(column_values) As x(i);
ELSE
SELECT array_agg(
(i - avg_val) / stddev_val > num_deviations) INTO out_vals
FROM unnest(column_values) As x(i);
END IF;
RETURN QUERY
SELECT unnest(out_vals) As is_outlier,
unnest(ids) As rowid;
END;
$$ LANGUAGE plpgsql IMMUTABLE PARALLEL SAFE;
CREATE OR REPLACE FUNCTION CDB_Contour(
IN geomin geometry[],
IN colin numeric[],
IN buffer numeric,
IN intmethod integer,
IN classmethod integer,
IN steps integer,
IN max_time integer DEFAULT 60000
)
RETURNS TABLE(
the_geom geometry,
bin integer,
min_value numeric,
max_value numeric,
avg_value numeric
) AS $$
DECLARE
cell_count integer;
tin geometry[];
resolution integer;
BEGIN
-- nasty trick to override issue #121
IF max_time = 0 THEN
max_time = -90;
END IF;
resolution := max_time;
max_time := -1 * resolution;
-- calc the optimal number of cells for the current dataset
SELECT
CASE intmethod
WHEN 0 THEN round(3.7745903782 * max_time - 9.4399210051 * array_length(geomin,1) - 1350.8778213073)
WHEN 1 THEN round(2.2855592156 * max_time - 87.285217133 * array_length(geomin,1) + 17255.7085601797)
WHEN 2 THEN round(0.9799471999 * max_time - 127.0334085369 * array_length(geomin,1) + 22707.9579721218)
ELSE 10000
END INTO cell_count;
-- we don't have iterative barycentric interpolation in CDB_interpolation,
-- and it's a costy function, so let's make a custom one here till
-- we update the code
-- tin := ARRAY[]::geometry[];
IF intmethod=1 THEN
WITH
a as (SELECT unnest(geomin) AS e),
b as (SELECT ST_DelaunayTriangles(ST_Collect(a.e),0.001, 0) AS t FROM a),
c as (SELECT (ST_Dump(t)).geom as v FROM b)
SELECT array_agg(v) INTO tin FROM c;
END IF;
-- Delaunay stuff performed just ONCE!!
-- magic
RETURN QUERY
WITH
convexhull as (
SELECT
ST_ConvexHull(ST_Collect(geomin)) as g,
buffer * |/ st_area(ST_ConvexHull(ST_Collect(geomin)))/PI() as r
),
envelope as (
SELECT
st_expand(a.g, a.r) as e
FROM convexhull a
),
envelope3857 as(
SELECT
ST_Transform(e, 3857) as geom
FROM envelope
),
resolution as(
SELECT
CASE WHEN resolution <= 0 THEN
round(|/ (
ST_area(geom) / abs(cell_count)
))
ELSE
resolution
END AS cell
FROM envelope3857
),
grid as(
SELECT
ST_Transform(cdb_crankshaft.CDB_RectangleGrid(e.geom, r.cell, r.cell), 4326) as geom
FROM envelope3857 e, resolution r
),
interp as(
SELECT
geom,
CASE
WHEN intmethod=1 THEN cdb_crankshaft._interp_in_tin(geomin, colin, tin, ST_Centroid(geom))
ELSE cdb_crankshaft.CDB_SpatialInterpolation(geomin, colin, ST_Centroid(geom), intmethod)
END as val
FROM grid
),
classes as(
SELECT CASE
WHEN classmethod = 0 THEN
cdb_crankshaft.CDB_EqualIntervalBins(array_agg(val), steps)
WHEN classmethod = 1 THEN
cdb_crankshaft.CDB_HeadsTailsBins(array_agg(val), steps)
WHEN classmethod = 2 THEN
cdb_crankshaft.CDB_JenksBins(array_agg(val), steps)
ELSE
cdb_crankshaft.CDB_QuantileBins(array_agg(val), steps)
END as b
FROM interp
where val is not null
),
classified as(
SELECT
i.*,
width_bucket(i.val, c.b) as bucket
FROM interp i left join classes c
ON 1=1
),
classified2 as(
SELECT
geom,
val,
CASE
WHEN bucket = steps THEN bucket - 1
ELSE bucket
END as b
FROM classified
),
final as(
SELECT
st_union(geom) as the_geom,
b as bin,
min(val) as min_value,
max(val) as max_value,
avg(val) as avg_value
FROM classified2
GROUP BY bin
)
SELECT
*
FROM final
where final.bin is not null
;
END;
$$ language plpgsql VOLATILE PARALLEL RESTRICTED;
-- =====================================================================
-- Interp in grid, so we can use barycentric with a precalculated tin (NNI)
-- =====================================================================
CREATE OR REPLACE FUNCTION _interp_in_tin(
IN geomin geometry[],
IN colin numeric[],
IN tin geometry[],
IN point geometry
)
RETURNS numeric AS
$$
DECLARE
g geometry;
vertex geometry[];
sg numeric;
sa numeric;
sb numeric;
sc numeric;
va numeric;
vb numeric;
vc numeric;
output numeric;
BEGIN
-- get the cell the point is within
WITH
a as (SELECT unnest(tin) as v),
b as (SELECT v FROM a WHERE ST_Within(point, v))
SELECT v INTO g FROM b;
-- if we're out of the data realm,
-- return null
IF g is null THEN
RETURN null;
END IF;
-- vertex of the selected cell
WITH a AS (
SELECT (ST_DumpPoints(g)).geom AS v
)
SELECT array_agg(v) INTO vertex FROM a;
-- retrieve the value of each vertex
WITH a AS(SELECT unnest(geomin) as geo, unnest(colin) as c)
SELECT c INTO va FROM a WHERE ST_Equals(geo, vertex[1]);
WITH a AS(SELECT unnest(geomin) as geo, unnest(colin) as c)
SELECT c INTO vb FROM a WHERE ST_Equals(geo, vertex[2]);
WITH a AS(SELECT unnest(geomin) as geo, unnest(colin) as c)
SELECT c INTO vc FROM a WHERE ST_Equals(geo, vertex[3]);
-- calc the areas
SELECT
ST_area(g),
ST_area(ST_MakePolygon(ST_MakeLine(ARRAY[point, vertex[2], vertex[3], point]))),
ST_area(ST_MakePolygon(ST_MakeLine(ARRAY[point, vertex[1], vertex[3], point]))),
ST_area(ST_MakePolygon(ST_MakeLine(ARRAY[point,vertex[1],vertex[2], point]))) INTO sg, sa, sb, sc;
output := (coalesce(sa,0) * coalesce(va,0) + coalesce(sb,0) * coalesce(vb,0) + coalesce(sc,0) * coalesce(vc,0)) / coalesce(sg,1);
RETURN output;
END;
$$
language plpgsql IMMUTABLE PARALLEL SAFE;
-- Function by Stuart Lynn for a simple interpolation of a value
-- from a polygon table over an arbitrary polygon
-- (weighted by the area proportion overlapped)
-- Aereal weighting is a very simple form of aereal interpolation.
--
-- Parameters:
-- * geom a Polygon geometry which defines the area where a value will be
-- estimated as the area-weighted sum of a given table/column
-- * target_table_name table name of the table that provides the values
-- * target_column column name of the column that provides the values
-- * schema_name optional parameter to defina the schema the target table
-- belongs to, which is necessary if its not in the search_path.
-- Note that target_table_name should never include the schema in it.
-- Return value:
-- Aereal-weighted interpolation of the column values over the geometry
CREATE OR REPLACE
FUNCTION cdb_overlap_sum(geom geometry, target_table_name text, target_column text, schema_name text DEFAULT NULL)
RETURNS numeric AS
$$
DECLARE
result numeric;
qualified_name text;
BEGIN
IF schema_name IS NULL THEN
qualified_name := Format('%I', target_table_name);
ELSE
qualified_name := Format('%I.%s', schema_name, target_table_name);
END IF;
EXECUTE Format('
SELECT sum(%I*ST_Area(St_Intersection($1, a.the_geom))/ST_Area(a.the_geom))
FROM %s AS a
WHERE $1 && a.the_geom
', target_column, qualified_name)
USING geom
INTO result;
RETURN result;
END;
$$ LANGUAGE plpgsql STABLE PARALLEL SAFE;
CREATE OR REPLACE FUNCTION
CDB_GWR(subquery text, dep_var text, ind_vars text[],
bw numeric default null, fixed boolean default False,
kernel text default 'bisquare', geom_col text default 'the_geom',
id_col text default 'cartodb_id')
RETURNS table(coeffs JSON, stand_errs JSON, t_vals JSON,
filtered_t_vals JSON, predicted numeric,
residuals numeric, r_squared numeric, bandwidth numeric,
rowid bigint)
AS $$
from crankshaft.regression import GWR
gwr = GWR()
return gwr.gwr(subquery, dep_var, ind_vars, bw, fixed, kernel, geom_col, id_col)
$$ LANGUAGE plpythonu VOLATILE PARALLEL UNSAFE;
CREATE OR REPLACE FUNCTION
CDB_GWR_Predict(subquery text, dep_var text, ind_vars text[],
bw numeric default null, fixed boolean default False,
kernel text default 'bisquare',
geom_col text default 'the_geom',
id_col text default 'cartodb_id')
RETURNS table(coeffs JSON, stand_errs JSON, t_vals JSON,
r_squared numeric, predicted numeric, rowid bigint)
AS $$
from crankshaft.regression import GWR
gwr = GWR()
return gwr.gwr_predict(subquery, dep_var, ind_vars, bw, fixed, kernel, geom_col, id_col)
$$ LANGUAGE plpythonu VOLATILE PARALLEL UNSAFE;
--
-- Creates N points randomly distributed arround the polygon
--
-- @param g - the geometry to be turned in to points
--
-- @param no_points - the number of points to generate
--
-- @params max_iter_per_point - the function generates points in the polygon's bounding box
-- and discards points which don't lie in the polygon. max_iter_per_point specifies how many
-- misses per point the funciton accepts before giving up.
--
-- Returns: Multipoint with the requested points
CREATE OR REPLACE FUNCTION cdb_dot_density(geom geometry , no_points Integer, max_iter_per_point Integer DEFAULT 1000)
RETURNS GEOMETRY AS $$
DECLARE
extent GEOMETRY;
test_point Geometry;
width NUMERIC;
height NUMERIC;
x0 NUMERIC;
y0 NUMERIC;
xp NUMERIC;
yp NUMERIC;
no_left INTEGER;
remaining_iterations INTEGER;
points GEOMETRY[];
bbox_line GEOMETRY;
intersection_line GEOMETRY;
BEGIN
extent := ST_Envelope(geom);
width := ST_XMax(extent) - ST_XMIN(extent);
height := ST_YMax(extent) - ST_YMIN(extent);
x0 := ST_XMin(extent);
y0 := ST_YMin(extent);
no_left := no_points;
LOOP
if(no_left=0) THEN
EXIT;
END IF;
yp = y0 + height*random();
bbox_line = ST_MakeLine(
ST_SetSRID(ST_MakePoint(yp, x0),4326),
ST_SetSRID(ST_MakePoint(yp, x0+width),4326)
);
intersection_line = ST_Intersection(bbox_line,geom);
test_point = ST_LineInterpolatePoint(st_makeline(st_linemerge(intersection_line)),random());
points := points || test_point;
no_left = no_left - 1 ;
END LOOP;
RETURN ST_Collect(points);
END;
$$
LANGUAGE plpgsql VOLATILE PARALLEL RESTRICTED;
-- Make sure by default there are no permissions for publicuser
-- NOTE: this happens at extension creation time, as part of an implicit transaction.
-- REVOKE ALL PRIVILEGES ON SCHEMA cdb_crankshaft FROM PUBLIC, publicuser CASCADE;
-- Grant permissions on the schema to publicuser (but just the schema)
GRANT USAGE ON SCHEMA cdb_crankshaft TO publicuser;
-- Revoke execute permissions on all functions in the schema by default
-- REVOKE EXECUTE ON ALL FUNCTIONS IN SCHEMA cdb_crankshaft FROM PUBLIC, publicuser;
--
-- Fill given extent with a rectangular coverage
--
-- @param ext Extent to fill. Only rectangles with center point falling
-- inside the extent (or at the lower or leftmost edge) will
-- be emitted. The returned hexagons will have the same SRID
-- as this extent.
--
-- @param width With of each rectangle
--
-- @param height Height of each rectangle
--
-- @param origin Optional origin to allow for exact tiling.
-- If omitted the origin will be 0,0.
-- The parameter is checked for having the same SRID
-- as the extent.
--
--
CREATE OR REPLACE FUNCTION CDB_RectangleGrid(ext GEOMETRY, width FLOAT8, height FLOAT8, origin GEOMETRY DEFAULT NULL)
RETURNS SETOF GEOMETRY
AS $$
DECLARE
h GEOMETRY; -- rectangle cell
hstep FLOAT8; -- horizontal step
vstep FLOAT8; -- vertical step
hw FLOAT8; -- half width
hh FLOAT8; -- half height
vstart FLOAT8;
hstart FLOAT8;
hend FLOAT8;
vend FLOAT8;
xoff FLOAT8;
yoff FLOAT8;
xgrd FLOAT8;
ygrd FLOAT8;
x FLOAT8;
y FLOAT8;
srid INTEGER;
BEGIN
srid := ST_SRID(ext);
xoff := 0;
yoff := 0;
IF origin IS NOT NULL THEN
IF ST_SRID(origin) != srid THEN
RAISE EXCEPTION 'SRID mismatch between extent (%) and origin (%)', srid, ST_SRID(origin);
END IF;
xoff := ST_X(origin);
yoff := ST_Y(origin);
END IF;
--RAISE DEBUG 'X offset: %', xoff;
--RAISE DEBUG 'Y offset: %', yoff;
hw := width/2.0;
hh := height/2.0;
xgrd := hw;
ygrd := hh;
--RAISE DEBUG 'X grid size: %', xgrd;
--RAISE DEBUG 'Y grid size: %', ygrd;
hstep := width;
vstep := height;
-- Tweak horizontal start on hstep grid from origin
hstart := xoff + ceil((ST_XMin(ext)-xoff)/hstep)*hstep;
--RAISE DEBUG 'hstart: %', hstart;
-- Tweak vertical start on vstep grid from origin
vstart := yoff + ceil((ST_Ymin(ext)-yoff)/vstep)*vstep;
--RAISE DEBUG 'vstart: %', vstart;
hend := ST_XMax(ext);
vend := ST_YMax(ext);
--RAISE DEBUG 'hend: %', hend;
--RAISE DEBUG 'vend: %', vend;
x := hstart;
WHILE x < hend LOOP -- over X
y := vstart;
h := ST_MakeEnvelope(x-hw, y-hh, x+hw, y+hh, srid);
WHILE y < vend LOOP -- over Y
RETURN NEXT h;
h := ST_Translate(h, 0, vstep);
y := yoff + round(((y + vstep)-yoff)/ygrd)*ygrd; -- round to grid
END LOOP;
x := xoff + round(((x + hstep)-xoff)/xgrd)*xgrd; -- round to grid
END LOOP;
RETURN;
END
$$ LANGUAGE 'plpgsql' IMMUTABLE PARALLEL SAFE;
--
-- Calculate the equal interval bins for a given column
--
-- @param in_array A numeric array of numbers to determine the best
-- to determine the bin boundary
--
-- @param breaks The number of bins you want to find.
--
--
-- Returns: upper edges of bins
--
--
CREATE OR REPLACE FUNCTION CDB_EqualIntervalBins ( in_array NUMERIC[], breaks INT ) RETURNS NUMERIC[] as $$
DECLARE
diff numeric;
min_val numeric;
max_val numeric;
tmp_val numeric;
i INT := 1;
reply numeric[];
BEGIN
SELECT min(e), max(e) INTO min_val, max_val FROM ( SELECT unnest(in_array) e ) x WHERE e IS NOT NULL;
diff = (max_val - min_val) / breaks::numeric;
LOOP
IF i < breaks THEN
tmp_val = min_val + i::numeric * diff;
reply = array_append(reply, tmp_val);
i := i+1;
ELSE
reply = array_append(reply, max_val);
EXIT;
END IF;
END LOOP;
RETURN reply;
END;
$$ language plpgsql IMMUTABLE PARALLEL SAFE;
--
-- Determine the Heads/Tails classifications from a numeric array
--
-- @param in_array A numeric array of numbers to determine the best
-- bins based on the Heads/Tails method.
--
-- @param breaks The number of bins you want to find.
--
--
CREATE OR REPLACE FUNCTION CDB_HeadsTailsBins ( in_array NUMERIC[], breaks INT) RETURNS NUMERIC[] as $$
DECLARE
element_count INT4;
arr_mean numeric;
i INT := 2;
reply numeric[];
BEGIN
-- get the total size of our row
element_count := array_upper(in_array, 1) - array_lower(in_array, 1);
-- ensure the ordering of in_array
SELECT array_agg(e) INTO in_array FROM (SELECT unnest(in_array) e ORDER BY e) x;
-- stop if no rows
IF element_count IS NULL THEN
RETURN NULL;
END IF;
-- stop if our breaks are more than our input array size
IF element_count < breaks THEN
RETURN in_array;
END IF;
-- get our mean value
SELECT avg(v) INTO arr_mean FROM ( SELECT unnest(in_array) as v ) x;
reply = Array[arr_mean];
-- slice our bread
LOOP
IF i > breaks THEN EXIT; END IF;
SELECT avg(e) INTO arr_mean FROM ( SELECT unnest(in_array) e) x WHERE e > reply[i-1];
IF arr_mean IS NOT NULL THEN
reply = array_append(reply, arr_mean);
END IF;
i := i+1;
END LOOP;
RETURN reply;
END;
$$ language plpgsql IMMUTABLE PARALLEL SAFE;
--
-- Determine the Jenks classifications from a numeric array
--
-- @param in_array A numeric array of numbers to determine the best
-- bins based on the Jenks method.
--
-- @param breaks The number of bins you want to find.
--
-- @param iterations The number of different starting positions to test.
--
-- @param invert Optional wheter to return the top of each bin (default)
-- or the bottom. BOOLEAN, default=FALSE.
--
--
CREATE OR REPLACE FUNCTION CDB_JenksBins ( in_array NUMERIC[], breaks INT, iterations INT DEFAULT 5, invert BOOLEAN DEFAULT FALSE) RETURNS NUMERIC[] as $$
DECLARE
element_count INT4;
arr_mean NUMERIC;
bot INT;
top INT;
tops INT[];
classes INT[][];
i INT := 1; j INT := 1;
curr_result NUMERIC[];
best_result NUMERIC[];
seedtarget TEXT;
quant NUMERIC[];
shuffles INT;
BEGIN
-- get the total size of our row
element_count := array_length(in_array, 1); --array_upper(in_array, 1) - array_lower(in_array, 1);
-- ensure the ordering of in_array
SELECT array_agg(e) INTO in_array FROM (SELECT unnest(in_array) e ORDER BY e) x;
-- stop if no rows
IF element_count IS NULL THEN
RETURN NULL;
END IF;
-- stop if our breaks are more than our input array size
IF element_count < breaks THEN
RETURN in_array;
END IF;
shuffles := LEAST(GREATEST(floor(2500000.0/(element_count::float*iterations::float)), 1), 750)::int;
-- get our mean value
SELECT avg(v) INTO arr_mean FROM ( SELECT unnest(in_array) as v ) x;
-- assume best is actually Quantile
SELECT cdb_crankshaft.CDB_QuantileBins(in_array, breaks) INTO quant;
-- if data is very very large, just return quant and be done
IF element_count > 5000000 THEN
RETURN quant;
END IF;
-- change quant into bottom, top markers
LOOP
IF i = 1 THEN
bot = 1;
ELSE
-- use last top to find this bot
bot = top+1;
END IF;
IF i = breaks THEN
top = element_count;
ELSE
SELECT count(*) INTO top FROM ( SELECT unnest(in_array) as v) x WHERE v <= quant[i];
END IF;
IF i = 1 THEN
classes = ARRAY[ARRAY[bot,top]];
ELSE
classes = ARRAY_CAT(classes,ARRAY[bot,top]);
END IF;
IF i > breaks THEN EXIT; END IF;
i = i+1;
END LOOP;
best_result = cdb_crankshaft.CDB_JenksBinsIteration( in_array, breaks, classes, invert, element_count, arr_mean, shuffles);
--set the seed so we can ensure the same results
SELECT setseed(0.4567) INTO seedtarget;
--loop through random starting positions
LOOP
IF j > iterations-1 THEN EXIT; END IF;
i = 1;
tops = ARRAY[element_count];
LOOP
IF i = breaks THEN EXIT; END IF;
SELECT array_agg(distinct e) INTO tops FROM (SELECT unnest(array_cat(tops, ARRAY[floor(random()*element_count::float)::int])) as e ORDER BY e) x WHERE e != 1;
i = array_length(tops, 1);
END LOOP;
i = 1;
LOOP
IF i > breaks THEN EXIT; END IF;
IF i = 1 THEN
bot = 1;
ELSE
bot = top+1;
END IF;
top = tops[i];
IF i = 1 THEN
classes = ARRAY[ARRAY[bot,top]];
ELSE
classes = ARRAY_CAT(classes,ARRAY[bot,top]);
END IF;
i := i+1;
END LOOP;
curr_result = cdb_crankshaft.CDB_JenksBinsIteration( in_array, breaks, classes, invert, element_count, arr_mean, shuffles);
IF curr_result[1] > best_result[1] THEN
best_result = curr_result;
j = j-1; -- if we found a better result, add one more search
END IF;
j = j+1;
END LOOP;
RETURN (best_result)[2:array_upper(best_result, 1)];
END;
$$ language plpgsql VOLATILE PARALLEL RESTRICTED;
--
-- Perform a single iteration of the Jenks classification
--
CREATE OR REPLACE FUNCTION CDB_JenksBinsIteration ( in_array NUMERIC[], breaks INT, classes INT[][], invert BOOLEAN, element_count INT4, arr_mean NUMERIC, max_search INT DEFAULT 50) RETURNS NUMERIC[] as $$
DECLARE
tmp_val numeric;
new_classes int[][];
tmp_class int[];
i INT := 1;
j INT := 1;
side INT := 2;
sdam numeric;
gvf numeric := 0.0;
new_gvf numeric;
arr_gvf numeric[];
class_avg numeric;
class_max_i INT;
class_min_i INT;
class_max numeric;
class_min numeric;
reply numeric[];
BEGIN
-- Calculate the sum of squared deviations from the array mean (SDAM).
SELECT sum((arr_mean - e)^2) INTO sdam FROM ( SELECT unnest(in_array) as e ) x;
--Identify the breaks for the lowest GVF
LOOP
i = 1;
LOOP
-- get our mean
SELECT avg(e) INTO class_avg FROM ( SELECT unnest(in_array[classes[i][1]:classes[i][2]]) as e) x;
-- find the deviation
SELECT sum((class_avg-e)^2) INTO tmp_val FROM ( SELECT unnest(in_array[classes[i][1]:classes[i][2]]) as e ) x;
IF i = 1 THEN
arr_gvf = ARRAY[tmp_val];
-- init our min/max map for later
class_max = arr_gvf[i];
class_min = arr_gvf[i];
class_min_i = 1;
class_max_i = 1;
ELSE
arr_gvf = array_append(arr_gvf, tmp_val);
END IF;
i := i+1;
IF i > breaks THEN EXIT; END IF;
END LOOP;
-- calculate our new GVF
SELECT sdam-sum(e) INTO new_gvf FROM ( SELECT unnest(arr_gvf) as e ) x;
-- if no improvement was made, exit
IF new_gvf < gvf THEN EXIT; END IF;
gvf = new_gvf;
IF j > max_search THEN EXIT; END IF;
j = j+1;
i = 1;
LOOP
--establish directionality (uppward through classes or downward)
IF arr_gvf[i] < class_min THEN
class_min = arr_gvf[i];
class_min_i = i;
END IF;
IF arr_gvf[i] > class_max THEN
class_max = arr_gvf[i];
class_max_i = i;
END IF;
i := i+1;
IF i > breaks THEN EXIT; END IF;
END LOOP;
IF class_max_i > class_min_i THEN
class_min_i = class_max_i - 1;
ELSE
class_min_i = class_max_i + 1;
END IF;
--Move from higher class to a lower gid order
IF class_max_i > class_min_i THEN
classes[class_max_i][1] = classes[class_max_i][1] + 1;
classes[class_min_i][2] = classes[class_min_i][2] + 1;
ELSE -- Move from lower class UP into a higher class by gid
classes[class_max_i][2] = classes[class_max_i][2] - 1;
classes[class_min_i][1] = classes[class_min_i][1] - 1;
END IF;
END LOOP;
i = 1;
LOOP
IF invert = TRUE THEN
side = 1; --default returns bottom side of breaks, invert returns top side
END IF;
reply = array_append(reply, in_array[classes[i][side]]);
i = i+1;
IF i > breaks THEN EXIT; END IF;
END LOOP;
RETURN array_prepend(gvf, reply);
END;
$$ language plpgsql IMMUTABLE PARALLEL SAFE;
--
-- Determine the Quantile classifications from a numeric array
--
-- @param in_array A numeric array of numbers to determine the best
-- bins based on the Quantile method.
--
-- @param breaks The number of bins you want to find.
--
--
CREATE OR REPLACE FUNCTION CDB_QuantileBins ( in_array NUMERIC[], breaks INT) RETURNS NUMERIC[] as $$
DECLARE
element_count INT4;
break_size numeric;
tmp_val numeric;
i INT := 1;
reply numeric[];
BEGIN
-- sort our values
SELECT array_agg(e) INTO in_array FROM (SELECT unnest(in_array) e ORDER BY e ASC) x;
-- get the total size of our data
element_count := array_length(in_array, 1);
break_size := element_count::numeric / breaks;
-- slice our bread
LOOP
IF i < breaks THEN
IF break_size * i % 1 > 0 THEN
SELECT e INTO tmp_val FROM ( SELECT unnest(in_array) e LIMIT 1 OFFSET ceil(break_size * i) - 1) x;
ELSE
SELECT avg(e) INTO tmp_val FROM ( SELECT unnest(in_array) e LIMIT 2 OFFSET ceil(break_size * i) - 1 ) x;
END IF;
ELSIF i = breaks THEN
-- select the last value
SELECT max(e) INTO tmp_val FROM ( SELECT unnest(in_array) e ) x;
ELSE
EXIT;
END IF;
reply = array_append(reply, tmp_val);
i := i+1;
END LOOP;
RETURN reply;
END;
$$ language plpgsql IMMUTABLE STRICT PARALLEL SAFE;
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