Vous êtes un professionnel et vous avez besoin d'une formation ? Mise en oeuvre d'IHM
avec Qt et PySide6 Voir le programme détaillé

Classe « Covariance »

Méthode scipy.stats.Covariance.from_precision

Signature de la méthode from_precision

def from_precision(precision, covariance=None) 

Description

help(Covariance.from_precision)

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 :math:`A`, its precision matrix be
:math:`P = A^{-1}`, and :math:`L` be the lower Cholesky factor such
that :math:`L L^T = P`.
Whitening of a data point :math:`x` is performed by computing
:math:`x^T L`. :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 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)
True
>>> res = cov.log_pdet
>>> ref = -np.linalg.slogdet(P)[-1]
>>> np.allclose(res, ref)
True

Vous êtes un professionnel et vous avez besoin d'une formation ? Mise en oeuvre d'IHM
avec Qt et PySide6 Voir le programme détaillé