`scipy.stats._covariance:Covariance.from_cholesky`

source: /scipy/stats/_covariance.py :194

Signature

staticmethod def from_cholesky ( cholesky )

Summary

Representation of a covariance provided via the (lower) Cholesky factor

Parameters

cholesky : array_like: The lower triangular Cholesky factor of the covariance matrix.

Notes

Let the covariance matrix be $A$ and $L$ be the lower Cholesky factor such that $L L^{T} = A$ . Whitening of a data point $x$ is performed by computing $L^{- 1} x$ . $lo g det A$ is calculated as $2 t r (lo g L)$ , where the $lo g$ operation is performed element-wise.

This Covariance class does not support singular covariance matrices because the Cholesky decomposition does not exist for a singular covariance matrix.

Examples

Prepare a symmetric positive definite covariance matrix ``A`` and a data point ``x``.

import numpy as np
from scipy import stats
rng = np.random.default_rng()
n = 5
A = rng.random(size=(n, n))
A = A @ A.T  # make the covariance symmetric positive definite
x = rng.random(size=n)

✓

Perform the Cholesky decomposition of ``A`` and create the `Covariance` object.

L = np.linalg.cholesky(A)
cov = stats.Covariance.from_cholesky(L)

✓

Compare the functionality of the `Covariance` object against reference implementation.

from scipy.linalg import solve_triangular
res = cov.whiten(x)
ref = solve_triangular(L, x, lower=True)
np.allclose(res, ref)
res = cov.log_pdet
ref = np.linalg.slogdet(A)[-1]
np.allclose(res, ref)

✓

Aliases

scipy.stats.Covariance.from_cholesky