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. Default is upper-triangular.

overwrite_abool, optional

Whether to overwrite data in a (may improve performance).

check_finitebool, 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
LinAlgErrorif decomposition fails.

Examples

>>> 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]])


scipy.linalg.ldl

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scipy.linalg.cholesky_banded