# torch.lu_solve¶

torch.lu_solve(input, LU_data, LU_pivots, *, out=None) → Tensor

Returns the LU solve of the linear system $Ax = b$ using the partially pivoted LU factorization of A from torch.lu().

Parameters
• b (Tensor) – the RHS tensor of size $(*, m, k)$ , where $*$ is zero or more batch dimensions.

• LU_data (Tensor) – the pivoted LU factorization of A from torch.lu() of size $(*, m, m)$ , where $*$ is zero or more batch dimensions.

• LU_pivots (IntTensor) – the pivots of the LU factorization from torch.lu() of size $(*, m)$ , where $*$ is zero or more batch dimensions. The batch dimensions of LU_pivots must be equal to the batch dimensions of LU_data.

Keyword Arguments

out (Tensor, optional) – the output tensor.

Example:

>>> A = torch.randn(2, 3, 3)
>>> b = torch.randn(2, 3, 1)
>>> A_LU = torch.lu(A)
>>> x = torch.lu_solve(b, *A_LU)
>>> torch.norm(torch.bmm(A, x) - b)
tensor(1.00000e-07 *
2.8312)