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"""
Interface of the SciPy-compatible Linear Algebra subset for DPNP.
Notes
-----
This module exposes the public API for ``dpnp.scipy.linalg``.
It contains:
- SciPy-like interface functions
- documentation for the functions
"""
import dpnp
from dpnp.linalg.dpnp_utils_linalg import (
assert_stacked_2d,
assert_stacked_square,
)
from ._utils import (
dpnp_lu_factor,
dpnp_lu_solve,
)
__all__ = [
"lu_factor",
"lu_solve",
]
[docs]
def 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 :obj:`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``.
See Also
--------
:obj:`dpnp.scipy.linalg.lu_solve` : Solve an equation system using
the LU factorization of `a` matrix.
Examples
--------
>>> import dpnp as np
>>> a = np.array([[4., 3.], [6., 3.]])
>>> lu, piv = np.scipy.linalg.lu_factor(a)
>>> lu
array([[6. , 3. ],
[0.66666667, 1. ]])
>>> piv
array([1, 1])
"""
dpnp.check_supported_arrays_type(a)
assert_stacked_2d(a)
return dpnp_lu_factor(a, overwrite_a=overwrite_a, check_finite=check_finite)
[docs]
def lu_solve(lu_and_piv, b, trans=0, overwrite_b=False, check_finite=True):
"""
Solve a linear system, :math:`a x = b`, given the LU factorization of `a`.
For full documentation refer to :obj:`scipy.linalg.lu_solve`.
Parameters
----------
lu, 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 :math:`a x = b`
1 :math:`a^T x = b`
2 :math:`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 : {(M,), (..., M, K)} dpnp.ndarray
Solution to the system
Warning
-------
This function synchronizes in order to validate array elements
when ``check_finite=True``.
See Also
--------
:obj:`dpnp.scipy.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.scipy.linalg.lu_factor(A)
>>> x = np.scipy.linalg.lu_solve((lu, piv), b)
>>> np.allclose(A @ x - b, np.zeros((4,)))
array(True)
"""
(lu, piv) = lu_and_piv
dpnp.check_supported_arrays_type(lu, piv, b)
assert_stacked_2d(lu)
assert_stacked_square(lu)
return dpnp_lu_solve(
lu,
piv,
b,
trans=trans,
overwrite_b=overwrite_b,
check_finite=check_finite,
)