scipy.linalg.

cholesky#

scipy.linalg.cholesky(a, lower=False, overwrite_a=False, check_finite=True)[source]#

Compute the Cholesky decomposition of a matrix.

Returns the Cholesky decomposition, \(A = L L^*\) or \(A = U^* U\) of a Hermitian positive-definite matrix A.

Parameters:

a(M, M) array_like: Matrix to be decomposed
lowerbool, 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_abool, optional: Whether to overwrite data in a (may improve performance).
check_finitebool, 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:

LinAlgErrorif 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]])