dpnp.linalg.lu_solve

dpnp.linalg.lu_solve(lu_and_piv, b, trans=0, overwrite_b=False, check_finite=True)

Solve a linear system, \(a x = b\), given the LU factorization of a.

For full documentation refer to scipy.linalg.lu_solve.

Parameters:

• lu ({tuple of dpnp.ndarrays or usm_ndarrays}) -- LU factorization of matrix a (M, M) together with pivot indices.

• piv ({tuple of dpnp.ndarrays or usm_ndarrays}) -- LU factorization of matrix a (M, M) together with pivot indices.

• b ({(M,), (..., M, K)} {dpnp.ndarray, usm_ndarray}) -- Right-hand side

• trans ({0, 1, 2} , optional) --

  Type of system to solve:

  trans	system
  0	\(a x = b\)
  1	\(a^T x = b\)
  2	\(a^H x = b\)

  Default: 0.

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

  Whether to overwrite data in b (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:

x -- Solution to the system

Return type:

{(M,), (M, K)} dpnp.ndarray

Warning

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

See also

dpnp.linalg.lu_factor

LU factorize a matrix.

Examples

>>> import dpnp as np
>>> A = np.array([[2, 5, 8, 7], [5, 2, 2, 8], [7, 5, 6, 6], [5, 4, 4, 8]])
>>> b = np.array([1, 1, 1, 1])
>>> lu, piv = np.linalg.lu_factor(A)
>>> x = np.linalg.lu_solve((lu, piv), b)
>>> np.allclose(A @ x - b, np.zeros((4,)))
array(True)