scipy.linalg.cholesky

scipy.linalg.cholesky(a, lower=False, overwrite_a=False, check_finite=True)

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

lower : bool, optional

Whether to compute the upper or lower triangular Cholesky factorization. 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 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.

Examples

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