scipy.linalg.cho_factor

scipy.linalg.cho_factor(a, lower=False, overwrite_a=False, check_finite=True)

Compute the Cholesky decomposition of a matrix, to use in cho_solve

Returns a matrix containing the Cholesky decomposition, A = L L* or A = U* U of a Hermitian positive-definite matrix a. The return value can be directly used as the first parameter to cho_solve.

Warning

The returned matrix also contains random data in the entries not used by the Cholesky decomposition. If you need to zero these entries, use the function cholesky instead.

Parameters:

a : (M, M) array_like

Matrix to be decomposed

lower : bool, optional

Whether to compute the upper or lower triangular Cholesky factorization (Default: 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 : (M, M) ndarray

Matrix whose upper or lower triangle contains the Cholesky factor of a. Other parts of the matrix contain random data.

lower : bool

Flag indicating whether the factor is in the lower or upper triangle

Raises:

LinAlgError

Raised if decomposition fails.

See also

cho_solve

Solve a linear set equations using the Cholesky factorization of a matrix.

Examples

>>> from scipy.linalg import cho_factor
>>> A = np.array([[9, 3, 1, 5], [3, 7, 5, 1], [1, 5, 9, 2], [5, 1, 2, 6]])
>>> c, low = cho_factor(A)
>>> c
array([[3.        , 1.        , 0.33333333, 1.66666667],
       [3.        , 2.44948974, 1.90515869, -0.27216553],
       [1.        , 5.        , 2.29330749, 0.8559528 ],
       [5.        , 1.        , 2.        , 1.55418563]])
>>> np.allclose(np.triu(c).T @ np. triu(c) - A, np.zeros((4, 4)))
True