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78
doc/07_gravity.md
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## Gravity Model
Gravity Models are derived from Newton's Law of Gravity and are used to predict the interaction between a group of populated areas (sources) and a specific target among a group of potential targets, in terms of an attraction factor (weight)
**CDB_Gravity** is based on the model defined in *Huff's Law of Shopper attraction (1963)*
### CDB_Gravity(t_id bigint[], t_geom geometry[], t_weight numeric[], s_id bigint[], s_geom geometry[], s_pop numeric[], target bigint, radius integer, minval numeric DEFAULT -10e307)
#### Arguments
| Name | Type | Description |
|------|------|-------------|
| t_id | bigint[] | Array of targets ID |
| t_geom | geometry[] | Array of targets' geometries |
| t_weight | numeric[] | Array of targets's weights |
| s_id | bigint[] | Array of sources ID |
| s_geom | geometry[] | Array of sources' geometries |
| s_pop | numeric[] | Array of sources's population |
| target | bigint | ID of the target under study |
| radius | integer | Radius in meters around the target under study that will be taken into account|
| minval (optional) | numeric | Lowest accepted value of weight, defaults to numeric min_value |
### CDB_Gravity( target_query text, weight_column text, source_query text, pop_column text, target bigint, radius integer, minval numeric DEFAULT -10e307)
#### Arguments
| Name | Type | Description |
|------|------|-------------|
| target_query | text | Query that defines targets |
| weight_column | text | Column name of weights |
| source_query | text | Query that defines sources |
| pop_column | text | Column name of population |
| target | bigint | cartodb_id of the target under study |
| radius | integer | Radius in meters around the target under study that will be taken into account|
| minval (optional) | numeric | Lowest accepted value of weight, defaults to numeric min_value |
### Returns
| Column Name | Type | Description |
|-------------|------|-------------|
| the_geom | geometry | Geometries of the sources within the radius |
| source_id | bigint | ID of the source |
| target_id | bigint | Target ID from input |
| dist | numeric | Distance in meters source to target (if not points, distance between centroids) |
| h | numeric | Probability of patronage |
| hpop | numeric | Patronaging population |
#### Example Usage
```sql
with t as (
SELECT
array_agg(cartodb_id::bigint) as id,
array_agg(the_geom) as g,
array_agg(coalesce(gla,0)::numeric) as w
FROM
abel.centros_comerciales_de_madrid
WHERE not no_cc
),
s as (
SELECT
array_agg(cartodb_id::bigint) as id,
array_agg(center) as g,
array_agg(coalesce(t1_1, 0)::numeric) as p
FROM
sscc_madrid
)
select
g.the_geom,
trunc(g.h,2) as h,
round(g.hpop) as hpop,
trunc(g.dist/1000,2) as dist_km
FROM t, s, CDB_Gravity1(t.id, t.g, t.w, s.id, s.g, s.p, newmall_ID, 100000, 5000) g
```

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src/pg/sql/07_gravity.sql
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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;
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;

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src/pg/test/expected/07_gravity_test.out
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the_geom | h | hpop | dist
--------------------------------------------+-------------------------+--------------------------+----------------
01010000001361C3D32B650140DD24068195B34440 | 1.51078258369747945249 | 12.08626066957983561994 | 4964.714459152
01010000002497FF907EFB0040713D0AD7A3B04440 | 98.29730954183620807430 | 688.08116679285345652007 | 99.955141922
0101000000A167B3EA733501401D5A643BDFAF4440 | 63.70532894711274639196 | 382.23197368267647835174 | 2488.330566505
010100000062A1D634EF380140BE9F1A2FDDB44440 | 35.35415870080995954879 | 176.77079350404979774397 | 4359.370460594
010100000052B81E85EB510140355EBA490CB24440 | 33.12290506987740864904 | 132.49162027950963459615 | 3703.664449828
0101000000C286A757CA320140736891ED7CAF4440 | 65.45251754279248087849 | 196.35755262837744263547 | 2512.092358644
01010000007DD0B359F5390140C976BE9F1AAF4440 | 62.83927792471345639225 | 125.67855584942691278449 | 2926.25725244
0101000000D237691A140D01407E6FD39FFDB44440 | 53.54905726651871279586 | 53.54905726651871279586 | 3744.515577777
(8 rows)

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src/pg/test/sql/07_gravity_test.sql
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WITH t AS (
SELECT
ARRAY[1,2,3] AS id,
ARRAY[7.0,8.0,3.0] AS w,
ARRAY[ST_GeomFromText('POINT(2.1744 41.4036)'),ST_GeomFromText('POINT(2.1228 41.3809)'),ST_GeomFromText('POINT(2.1511 41.3742)')] AS g
),
s AS (
SELECT
ARRAY[10,20,30,40,50,60,70,80] AS id,
ARRAY[800, 700, 600, 500, 400, 300, 200, 100] AS p,
ARRAY[ST_GeomFromText('POINT(2.1744 41.403)'),ST_GeomFromText('POINT(2.1228 41.380)'),ST_GeomFromText('POINT(2.1511 41.374)'),ST_GeomFromText('POINT(2.1528 41.413)'),ST_GeomFromText('POINT(2.165 41.391)'),ST_GeomFromText('POINT(2.1498 41.371)'),ST_GeomFromText('POINT(2.1533 41.368)'),ST_GeomFromText('POINT(2.131386 41.41399)')] AS g
)
SELECT
g.the_geom,
g.h,
g.hpop,
g.dist
FROM
t,
s,
CDB_Gravity(t.id, t.g, t.w, s.id, s.g, s.p, 2, 100000, 3) g;