lu_solve¶

paddle.linalg. lu_solve ( b: Tensor, lu: Tensor, pivots: Tensor, trans: Literal[N, T, C] = 'N', name: str | None = None ) [source]

Computes the solution x to the system of linear equations $Ax = b$ , given LU decomposition $A$ and column vector $b$.

Parameters

• b (Tensor) – Column vector b in the above equation. It has shape $(*, m, k)$, where $*$ is batch dimensions, with data type float32, float64.

• lu (Tensor) – LU decomposition. It has shape $(*, m, m)$, where $*$ is batch dimensions, that can be decomposed into an upper triangular matrix U and a lower triangular matrix L, with data type float32, float64.

• pivots (Tensor) – Permutation matrix P of LU decomposition. It has shape $(*, m)$, where $*$ is batch dimensions, that can be converted to a permutation matrix P, with data type int32.

• trans (str, optional) – The transpose of the matrix A. It can be “N” , “T” or “C”, “N” means $Ax=b$, “T” means $A^Tx=b$, “C” means $A^Hx=b$, default is “N”.

• name (str|None, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

Tensor, the same data type as the b and lu.

Examples

>>> import paddle
>>> import numpy as np

>>> A = paddle.to_tensor([[3, 1], [1, 2]], dtype="float64")
>>> b = paddle.to_tensor([[9, 8], [9, 8]], dtype="float64")
>>> lu, p = paddle.linalg.lu(A)
>>> x = paddle.lu_solve(b, lu, p)
>>> paddle.allclose(A @ x, b)

>>> print(x)
Tensor(shape=[2, 2], dtype=float64, place=Place(cpu), stop_gradient=True,
[[1.80000000, 1.60000000],
[3.60000000, 3.20000000]])