scipy.linalg.cholesky

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

Compute the Cholesky decomposition of a matrix.

Returns the Cholesky decomposition, :lm:`A = L L^*` or :lm:`A = U^* U` of a Hermitian positive-definite matrix :lm:`A`.

Parameters :

a : array, shape (M, M)

Matrix to be decomposed

lower : boolean

Whether to compute the upper or lower triangular Cholesky factorization (Default: upper-triangular)

overwrite_a : boolean

Whether to overwrite data in a (may improve performance)

Returns :

c : array, 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]])