covarPopMatrix

Returns the population covariance matrix over N variables.

Syntax

covarPopMatrix(x[, ...])

Arguments

x — a variable number of parameters. (U)Int*, Float*, Decimal.

Returned Value

Population covariance matrix. Array(Array(Float64)).

Example

Query:

DROP TABLE IF EXISTS test;
CREATE TABLE test
(
    a UInt32,
    b Float64,
    c Float64,
    d Float64
)
ENGINE = Memory;
INSERT INTO test(a, b, c, d) VALUES (1, 5.6, -4.4, 2.6), (2, -9.6, 3, 3.3), (3, -1.3, -4, 1.2), (4, 5.3, 9.7, 2.3), (5, 4.4, 0.037, 1.222), (6, -8.6, -7.8, 2.1233), (7, 5.1, 9.3, 8.1222), (8, 7.9, -3.6, 9.837), (9, -8.2, 0.62, 8.43555), (10, -3, 7.3, 6.762);

SELECT arrayMap(x -> round(x, 3), arrayJoin(covarPopMatrix(a, b, c, d))) AS covarPopMatrix
FROM test;

Result:

   ┌─covarPopMatrix────────────┐
1. │ [8.25,-1.76,4.08,6.748]   │
2. │ [-1.76,41.07,6.486,2.132] │
3. │ [4.08,6.486,34.21,4.755]  │
4. │ [6.748,2.132,4.755,9.93]  │
   └───────────────────────────┘

covarPopMatrix

Introduced in: v23.2

Returns the population covariance matrix over N variables.

Syntax

covarPopMatrix(x1[, x2, ...])

Arguments

x1[, x2, ...] — A variable number of parameters. (U)Int* or Float* or Decimal

Returned value

Returns the population covariance matrix. Array(Array(Float64))

Examples

Basic population covariance matrix calculation

DROP TABLE IF EXISTS test;
CREATE TABLE test
(
    a UInt32,
    b Float64,
    c Float64,
    d Float64
)
ENGINE = Memory;
INSERT INTO test(a, b, c, d) VALUES (1, 5.6, -4.4, 2.6), (2, -9.6, 3, 3.3), (3, -1.3, -4, 1.2), (4, 5.3, 9.7, 2.3), (5, 4.4, 0.037, 1.222), (6, -8.6, -7.8, 2.1233), (7, 5.1, 9.3, 8.1222), (8, 7.9, -3.6, 9.837), (9, -8.2, 0.62, 8.43555), (10, -3, 7.3, 6.762);

SELECT arrayMap(x -> round(x, 3), arrayJoin(covarPopMatrix(a, b, c, d))) AS covarPopMatrix
FROM test

┌─covarPopMatrix────────────┐
│ [8.25,-1.76,4.08,6.748]   │
│ [-1.76,41.07,6.486,2.132] │
│ [4.08,6.486,34.21,4.755]  │
│ [6.748,2.132,4.755,9.93]  │
└───────────────────────────┘

covarPopMatrix​

covarPopMatrix