cholesky — SciPy v1.15.2 Manual (original) (raw)

scipy.linalg.

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]])