dpnp.linalg.lu_factor

dpnp.linalg.lu_factor(a, overwrite_a=False, check_finite=True)

Compute the pivoted LU decomposition of a matrix.

The decomposition is:

A = P @ L @ U

where P is a permutation matrix, L is lower triangular with unit diagonal elements, and U is upper triangular.

For full documentation refer to scipy.linalg.lu_factor.

Parameters:

• a ((..., M, N) {dpnp.ndarray, usm_ndarray}) -- Input array to decompose.

• overwrite_a ({None, bool}, optional) --

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

  Default: False.

• check_finite ({None, 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.

  Default: True.

Returns:

• lu ((..., M, N) dpnp.ndarray) -- Matrix containing U in its upper triangle, and L in its lower triangle. The unit diagonal elements of L are not stored.

• piv ((..., K) dpnp.ndarray) -- Pivot indices representing the permutation matrix P: row i of matrix was interchanged with row piv[i]. Where K = min(M, N).

Warning

This function synchronizes in order to validate array elements when check_finite=True.

Examples

>>> import dpnp as np
>>> a = np.array([[4., 3.], [6., 3.]])
>>> lu, piv = np.linalg.lu_factor(a)
>>> lu
array([[6.        , 3.        ],
       [0.66666667, 1.        ]])
>>> piv
array([1, 1])