/
covariance-matrix.sql
52 lines (46 loc) · 1.59 KB
/
covariance-matrix.sql
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
-- This exmaple illustrates how we can calculate covariance matrix of a given dataset in a very definite manner. In other words, this example is not dimension-agnostic and you have to know the exact number of columns of your dataset before applying this.
-- author: saif, a. (2k19)
-- define some data (3 dimensional in this case, it can be n-dimensional)
with data as (
select 1 as a, 2 as b, 3 as c
union all
select 12,5,6
union all
select 2,8,9
union all
select 2,11,12
union all
select 3,14,15
union all
select 16,17,18
),
-- pre-establish the length of your dataset
allc as (
select count(*) allc from data
),
-- pre-establish dimensional means
avgs as (
select avg(a) as avga, avg(b) as avgb, avg(c) as avgc from data
)
select
round(items.f1/allc.allc, 2) as x1,
round(items.f2/allc.allc,2) as x2,
round(items.f3/allc.allc,2) as x3
from (
-- since we have 3 dimensions, you see three select statements in here. You can change it based on your dataset to have n of these.
select
struct(sum((a-avgs.avga)*(a-avgs.avga)) as f1, sum((a-avgs.avga)*(b-avgs.avgb)) as f2, sum((a-avgs.avga)*(c-avgs.avgc)) as f3) as items
from data
left join avgs on 1=1
union all
select
struct(sum((b-avgs.avgb)*(a-avgs.avga)) as f1, sum((b-avgs.avgb)*(b-avgs.avgb)) as f2, sum((b-avgs.avgb)*(c-avgs.avgc)) as f3) as items
from data
left join avgs on 1=1
union all
select
struct(sum((c-avgs.avgc)*(a-avgs.avga)) as f1, sum((c-avgs.avgc)*(b-avgs.avgb)) as f2, sum((c-avgs.avgc)*(c-avgs.avgc)) as f3) as items
from data
left join avgs on 1=1
)
left join allc on 1=1