dpnp.scipy.linalg.cho_factor¶

dpnp.scipy.linalg.cho_factor(a, lower=False, overwrite_a=False, check_finite=True)[source]¶

Compute the Cholesky decomposition of a matrix, to use in dpnp.scipy.linalg.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 dpnp.scipy.linalg.cho_solve.

For full documentation refer to scipy.linalg.cho_factor.

Parameters:

a(..., M, M) {dpnp.ndarray, usm_ndarray}

Matrix to be decomposed.

lower{bool, array_like of bool}, optional

Whether to compute the upper or lower triangular Cholesky factorization. An array or a sequence is accepted if all its values are equal.

Default: False.

overwrite_abool, optional

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

Default: False.

check_finitebool, 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.

Default: True.

Returns:

c(..., M, M) dpnp.ndarray: Matrix whose upper or lower triangle contains the Cholesky factor of a. If a is not overwritten, the other triangle is zeroed, otherwise it contains the data of a not used by the decomposition.
lowerbool: Flag indicating whether the factor is in the lower or upper triangle. Unlike SciPy, which returns it as an array tiled to the batch shape, a Python bool is returned.

Raises:

dpnp.linalg.LinAlgError: If the decomposition fails.
ValueError: If a is not square, if lower is empty or its values are not all equal, or if check_finite=True and a contains infinities or NaNs.

Warning

This function synchronizes in order to validate array elements when check_finite=True, and to check the factorization status.

See also

dpnp.scipy.linalg.cho_solve(): Solve a linear set equations using the Cholesky factorization of a matrix.
dpnp.linalg.cholesky(): Cholesky decomposition of a matrix.

Notes

During the finiteness check (if selected), the entire matrix a is checked. During decomposition, a is assumed to be symmetric or Hermitian (as applicable), and only the half selected by option lower is referenced.

Examples

>>> import dpnp as np
>>> A = np.array([[9., 3., 1., 5.], [3., 7., 5., 1.],
...               [1., 5., 9., 2.], [5., 1., 2., 6.]])
>>> c, low = np.scipy.linalg.cho_factor(A)
>>> c
array([[ 3.        ,  1.        ,  0.33333333,  1.66666667],
       [ 0.        ,  2.44948974,  1.90515869, -0.27216553],
       [ 0.        ,  0.        ,  2.29330749,  0.8559528 ],
       [ 0.        ,  0.        ,  0.        ,  1.55418563]])
>>> np.allclose(c.T @ c, A)
array(True)

Batched input:

>>> B = np.stack([A, 2 * A])
>>> c, low = np.scipy.linalg.cho_factor(B, lower=True)
>>> np.allclose(c @ c.mT, B)
array(True)