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Classe « Covariance »

Méthode scipy.stats.Covariance.from_diagonal

Signature de la méthode from_diagonal

def from_diagonal(diagonal) 

Description

help(Covariance.from_diagonal)

Return a representation of a covariance matrix from its diagonal.

Parameters
----------
diagonal : array_like
    The diagonal elements of a diagonal matrix.

Notes
-----
Let the diagonal elements of a diagonal covariance matrix :math:`D` be
stored in the vector :math:`d`.

When all elements of :math:`d` are strictly positive, whitening of a
data point :math:`x` is performed by computing
:math:`x \cdot d^{-1/2}`, where the inverse square root can be taken
element-wise.
:math:`\log\det{D}` is calculated as :math:`-2 \sum(\log{d})`,
where the :math:`\log` operation is performed element-wise.

This `Covariance` class supports singular covariance matrices. When
computing ``_log_pdet``, non-positive elements of :math:`d` are
ignored. Whitening is not well defined when the point to be whitened
does not lie in the span of the columns of the covariance matrix. The
convention taken here is to treat the inverse square root of
non-positive elements of :math:`d` as zeros.

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 = np.diag(rng.random(n))
>>> x = rng.random(size=n)

Extract the diagonal from ``A`` and create the `Covariance` object.

>>> d = np.diag(A)
>>> cov = stats.Covariance.from_diagonal(d)

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

>>> res = cov.whiten(x)
>>> ref = np.diag(d**-0.5) @ x
>>> np.allclose(res, ref)
True
>>> res = cov.log_pdet
>>> ref = np.linalg.slogdet(A)[-1]
>>> np.allclose(res, ref)
True

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