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

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.

Raises

LinAlgError : if decomposition fails.

Returns

c : (M, M) ndarray

Upper- or lower-triangular Cholesky factor of a.

Compute the Cholesky decomposition of a matrix.

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]])

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.linalg._decomp_ldl.ldl scipy.linalg._decomp_cholesky.cholesky

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GitHub : /scipy/linalg/_decomp_cholesky.py#45
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