symjax.tensor.linalg.cholesky

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

Compute the Cholesky decomposition of a matrix.

LAX-backend implementation of cholesky(). Original docstring below.

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 – Upper- or lower-triangular Cholesky factor of a.
Return type:

(M, M) ndarray
Raises:

LinAlgError : if 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]])