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Module « scipy.linalg »

Fonction cholesky - module scipy.linalg

Signature de la fonction cholesky

def cholesky(a, lower=False, overwrite_a=False, check_finite=True) 

Description

help(scipy.linalg.cholesky)

Compute the Cholesky decomposition of a matrix.

Returns the Cholesky decomposition, :math:`A = L L^*` or
:math:`A = U^* U` of a Hermitian positive-definite matrix A.

Parameters
----------
a : (M, M) array_like
    Matrix to be decomposed
lower : bool, optional
    Whether to compute the upper- or lower-triangular Cholesky
    factorization. During decomposition, only the selected half of the
    matrix is referenced. Default is upper-triangular.
overwrite_a : bool, optional
    Whether to overwrite data in `a` (may improve performance).
check_finite : bool, optional
    Whether to check that the entire input matrix contains only finite numbers.
    Disabling may give a performance gain, but may result in problems
    (crashes, non-termination) if the inputs do contain infinities or NaNs.

Returns
-------
c : (M, M) ndarray
    Upper- or lower-triangular Cholesky factor of `a`.

Raises
------
LinAlgError : if decomposition fails.

Notes
-----
During the finiteness check (if selected), the entire matrix `a` is
checked. During decomposition, `a` is assumed to be symmetric or Hermitian
(as applicable), and only the half selected by option `lower` is referenced.
Consequently, if `a` is asymmetric/non-Hermitian, `cholesky` may still
succeed if the symmetric/Hermitian matrix represented by the selected half
is positive definite, yet it may fail if an element in the other half is
non-finite.

Examples
--------
>>> import numpy as np
>>> from scipy.linalg import cholesky
>>> a = np.array([[1,-2j],[2j,5]])
>>> L = cholesky(a, lower=True)
>>> L
array([[ 1.+0.j,  0.+0.j],
       [ 0.+2.j,  1.+0.j]])
>>> L @ L.T.conj()
array([[ 1.+0.j,  0.-2.j],
       [ 0.+2.j,  5.+0.j]])

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