scipy.linalg.cholesky

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

Compute the Cholesky decomposition of a matrix.

Returns the Cholesky decomposition, or of a Hermitian positive-definite matrix A.

Parameters :

a : ndarray, shape (M, M)

Matrix to be decomposed

lower : bool

Whether to compute the upper or lower triangular Cholesky factorization. Default is upper-triangular.

overwrite_a : bool

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

Returns :

c : ndarray, shape (M, M)

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]])