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Classe « Covariance »

Méthode scipy.stats.Covariance.from_cholesky

Signature de la méthode from_cholesky

def from_cholesky(cholesky) 

Description

help(Covariance.from_cholesky)

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 :math:`A` and :math:`L` be the lower
Cholesky factor such that :math:`L L^T = A`.
Whitening of a data point :math:`x` is performed by computing
:math:`L^{-1} x`. :math:`\log\det{A}` is calculated as
:math:`2tr(\log{L})`, where the :math:`\log` 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)
True
>>> res = cov.log_pdet
>>> ref = np.linalg.slogdet(A)[-1]
>>> np.allclose(res, ref)
True

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