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## Gravity Model
## Gravity Model
### CDB_Gravity()
### 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)
The Gravity Model is derived from newtons law of gravity and is used to estimate the degree of interaction between two places
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)
#### Arguments
**CDB_Gravity** is based on the model defined in *Huff's Law of Shopper attraction (1963)*
| Name | Type | Description |
#### Arguments
| Name | Type | Description |
|------|------|-------------|
| t_id | bigint[] | |
| t_geom | geometry[] | |
| t_weight | numeric[] | |
| s_id | bigint[] | |
| s_geom | geometry[] | |
| s_pop | numeric[] | |
| target | bigint | |
| radius | integer | |
| minval | numeric | |
| 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 |
#### Returns
#### Returns
| Column Name | Type | Description |
|-------------|------|-------------|
| the_geom | Numeric | |
| source_id | bigint | |
| target_id | bigint | |
| dist | Numeric | |
| n | Numeric | |
| hpop | NUMERIC | |
| 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
SELECT CDB_GRAVITY ();
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
```