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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
```