`scipy.stats._covariance:Covariance.from_precision`

source: /scipy/stats/_covariance.py :131

Signature

staticmethod def from_precision ( precision , covariance = None )

Summary

Return a representation of a covariance from its precision matrix.

Parameters

precision : array_like: The precision matrix; that is, the inverse of a square, symmetric, positive definite covariance matrix.
covariance : array_like, optional: The square, symmetric, positive definite covariance matrix. If not provided, this may need to be calculated (e.g. to evaluate the cumulative distribution function of scipy.stats.multivariate_normal) by inverting precision.

Notes

Let the covariance matrix be $A$ , its precision matrix be $P = A^{- 1}$ , and $L$ be the lower Cholesky factor such that $L L^{T} = P$ . Whitening of a data point $x$ is performed by computing $x^{T} L$ . $lo g det A$ 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 precision matrix does not exist for a singular covariance matrix.

Examples

Prepare a symmetric positive definite precision matrix ``P`` and a data point ``x``. (If the precision matrix is not already available, consider the other factory methods of the `Covariance` class.)

import numpy as np
from scipy import stats
rng = np.random.default_rng()
n = 5
P = rng.random(size=(n, n))
P = P @ P.T  # a precision matrix must be positive definite
x = rng.random(size=n)

✓

Create the `Covariance` object.

cov = stats.Covariance.from_precision(P)

✓

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

res = cov.whiten(x)
ref = x @ np.linalg.cholesky(P)
np.allclose(res, ref)
res = cov.log_pdet
ref = -np.linalg.slogdet(P)[-1]
np.allclose(res, ref)

✓

Aliases

scipy.stats.Covariance.from_precision