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doc/07_gravity.md
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doc/07_gravity.md
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## Gravity Model
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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)
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**CDB_Gravity** is based on the model defined in *Huff's Law of Shopper attraction (1963)*
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### 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)
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#### Arguments
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| Name | Type | Description |
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|------|------|-------------|
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| t_id | bigint[] | Array of targets ID |
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| t_geom | geometry[] | Array of targets' geometries |
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| t_weight | numeric[] | Array of targets's weights |
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| s_id | bigint[] | Array of sources ID |
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| s_geom | geometry[] | Array of sources' geometries |
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| s_pop | numeric[] | Array of sources's population |
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| target | bigint | ID of the target under study |
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| radius | integer | Radius in meters around the target under study that will be taken into account|
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| minval (optional) | numeric | Lowest accepted value of weight, defaults to numeric min_value |
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### CDB_Gravity( target_query text, weight_column text, source_query text, pop_column text, target bigint, radius integer, minval numeric DEFAULT -10e307)
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#### Arguments
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| Name | Type | Description |
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|------|------|-------------|
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| target_query | text | Query that defines targets |
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| weight_column | text | Column name of weights |
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| source_query | text | Query that defines sources |
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| pop_column | text | Column name of population |
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| target | bigint | cartodb_id of the target under study |
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| radius | integer | Radius in meters around the target under study that will be taken into account|
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| minval (optional) | numeric | Lowest accepted value of weight, defaults to numeric min_value |
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### Returns
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| Column Name | Type | Description |
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|-------------|------|-------------|
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| the_geom | geometry | Geometries of the sources within the radius |
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| source_id | bigint | ID of the source |
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| target_id | bigint | Target ID from input |
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| dist | numeric | Distance in meters source to target (if not points, distance between centroids) |
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| h | numeric | Probability of patronage |
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| hpop | numeric | Patronaging population |
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#### Example Usage
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```sql
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with t as (
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SELECT
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array_agg(cartodb_id::bigint) as id,
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array_agg(the_geom) as g,
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array_agg(coalesce(gla,0)::numeric) as w
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FROM
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abel.centros_comerciales_de_madrid
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WHERE not no_cc
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),
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s as (
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SELECT
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array_agg(cartodb_id::bigint) as id,
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array_agg(center) as g,
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array_agg(coalesce(t1_1, 0)::numeric) as p
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FROM
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sscc_madrid
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)
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select
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g.the_geom,
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trunc(g.h,2) as h,
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round(g.hpop) as hpop,
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trunc(g.dist/1000,2) as dist_km
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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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```
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115
src/pg/sql/07_gravity.sql
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src/pg/sql/07_gravity.sql
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CREATE OR REPLACE FUNCTION CDB_Gravity(
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IN target_query text,
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IN weight_column text,
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IN source_query text,
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IN pop_column text,
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IN target bigint,
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IN radius integer,
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IN minval numeric DEFAULT -10e307
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)
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RETURNS TABLE(
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the_geom geometry,
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source_id bigint,
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target_id bigint,
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dist numeric,
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h numeric,
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hpop numeric) AS $$
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DECLARE
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t_id bigint[];
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t_geom geometry[];
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t_weight numeric[];
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s_id bigint[];
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s_geom geometry[];
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s_pop numeric[];
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BEGIN
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EXECUTE 'WITH foo as('+target_query+') SELECT array_agg(cartodb_id), array_agg(the_geom), array_agg(' || weight_column || ') FROM foo' INTO t_id, t_geom, t_weight;
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EXECUTE 'WITH foo as('+source_query+') SELECT array_agg(cartodb_id), array_agg(the_geom), array_agg(' || pop_column || ') FROM foo' INTO s_id, s_geom, s_pop;
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RETURN QUERY
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SELECT g.* FROM t, s, CDB_Gravity(t_id, t_geom, t_weight, s_id, s_geom, s_pop, target, radius, minval) g;
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END;
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$$ language plpgsql;
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CREATE OR REPLACE FUNCTION CDB_Gravity(
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IN t_id bigint[],
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IN t_geom geometry[],
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IN t_weight numeric[],
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IN s_id bigint[],
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IN s_geom geometry[],
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IN s_pop numeric[],
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IN target bigint,
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IN radius integer,
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IN minval numeric DEFAULT -10e307
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)
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RETURNS TABLE(
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the_geom geometry,
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source_id bigint,
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target_id bigint,
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dist numeric,
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h numeric,
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hpop numeric) AS $$
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DECLARE
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t_type text;
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s_type text;
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t_center geometry[];
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s_center geometry[];
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BEGIN
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t_type := GeometryType(t_geom[1]);
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s_type := GeometryType(s_geom[1]);
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IF t_type = 'POINT' THEN
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t_center := t_geom;
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ELSE
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WITH tmp as (SELECT unnest(t_geom) as g) SELECT array_agg(ST_Centroid(g)) INTO t_center FROM tmp;
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END IF;
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IF s_type = 'POINT' THEN
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s_center := s_geom;
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ELSE
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WITH tmp as (SELECT unnest(s_geom) as g) SELECT array_agg(ST_Centroid(g)) INTO s_center FROM tmp;
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END IF;
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RETURN QUERY
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with target0 as(
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SELECT unnest(t_center) as tc, unnest(t_weight) as tw, unnest(t_id) as td
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),
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source0 as(
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SELECT unnest(s_center) as sc, unnest(s_id) as sd, unnest (s_geom) as sg, unnest(s_pop) as sp
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),
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prev0 as(
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SELECT
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source0.sg,
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source0.sd as sourc_id,
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coalesce(source0.sp,0) as sp,
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target.td as targ_id,
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coalesce(target.tw,0) as tw,
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GREATEST(1.0,ST_Distance(geography(target.tc), geography(source0.sc)))::numeric as distance
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FROM source0
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CROSS JOIN LATERAL
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(
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SELECT
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*
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FROM target0
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WHERE tw > minval
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AND ST_DWithin(geography(source0.sc), geography(tc), radius)
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) AS target
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),
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deno as(
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SELECT
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sourc_id,
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sum(tw/distance) as h_deno
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FROM
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prev0
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GROUP BY sourc_id
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)
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SELECT
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p.sg as the_geom,
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p.sourc_id as source_id,
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p.targ_id as target_id,
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case when p.distance > 1 then p.distance else 0.0 end as dist,
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100*(p.tw/p.distance)/d.h_deno as h,
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p.sp*(p.tw/p.distance)/d.h_deno as hpop
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FROM
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prev0 p,
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deno d
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WHERE
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p.targ_id = target AND
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p.sourc_id = d.sourc_id;
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END;
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$$ language plpgsql;
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11
src/pg/test/expected/07_gravity_test.out
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src/pg/test/expected/07_gravity_test.out
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the_geom | h | hpop | dist
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--------------------------------------------+-------------------------+--------------------------+----------------
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01010000001361C3D32B650140DD24068195B34440 | 1.51078258369747945249 | 12.08626066957983561994 | 4964.714459152
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01010000002497FF907EFB0040713D0AD7A3B04440 | 98.29730954183620807430 | 688.08116679285345652007 | 99.955141922
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0101000000A167B3EA733501401D5A643BDFAF4440 | 63.70532894711274639196 | 382.23197368267647835174 | 2488.330566505
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010100000062A1D634EF380140BE9F1A2FDDB44440 | 35.35415870080995954879 | 176.77079350404979774397 | 4359.370460594
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010100000052B81E85EB510140355EBA490CB24440 | 33.12290506987740864904 | 132.49162027950963459615 | 3703.664449828
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0101000000C286A757CA320140736891ED7CAF4440 | 65.45251754279248087849 | 196.35755262837744263547 | 2512.092358644
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01010000007DD0B359F5390140C976BE9F1AAF4440 | 62.83927792471345639225 | 125.67855584942691278449 | 2926.25725244
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0101000000D237691A140D01407E6FD39FFDB44440 | 53.54905726651871279586 | 53.54905726651871279586 | 3744.515577777
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(8 rows)
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21
src/pg/test/sql/07_gravity_test.sql
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WITH t AS (
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SELECT
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ARRAY[1,2,3] AS id,
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ARRAY[7.0,8.0,3.0] AS w,
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ARRAY[ST_GeomFromText('POINT(2.1744 41.4036)'),ST_GeomFromText('POINT(2.1228 41.3809)'),ST_GeomFromText('POINT(2.1511 41.3742)')] AS g
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),
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s AS (
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SELECT
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ARRAY[10,20,30,40,50,60,70,80] AS id,
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ARRAY[800, 700, 600, 500, 400, 300, 200, 100] AS p,
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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
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)
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SELECT
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g.the_geom,
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g.h,
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g.hpop,
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g.dist
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FROM
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t,
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s,
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CDB_Gravity(t.id, t.g, t.w, s.id, s.g, s.p, 2, 100000, 3) g;
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