torch.lu_unpack

torch.lu_unpack(LU_data: torch.Tensor, LU_pivots: torch.Tensor, unpack_data: bool = True, unpack_pivots: bool = True) → Tuple[Optional[torch.Tensor], Optional[torch.Tensor], Optional[torch.Tensor]]

Unpacks the data and pivots from a LU factorization of a tensor.

Returns a tuple of tensors as (the pivots, the L tensor, the U tensor).

Parameters

• LU_data (Tensor) – the packed LU factorization data

• LU_pivots (Tensor) – the packed LU factorization pivots

• unpack_data (bool) – flag indicating if the data should be unpacked

• unpack_pivots (bool) – flag indicating if the pivots should be unpacked

Examples:

>>> A = torch.randn(2, 3, 3)
>>> A_LU, pivots = A.lu()
>>> P, A_L, A_U = torch.lu_unpack(A_LU, pivots)
>>>
>>> # can recover A from factorization
>>> A_ = torch.bmm(P, torch.bmm(A_L, A_U))

>>> # LU factorization of a rectangular matrix:
>>> A = torch.randn(2, 3, 2)
>>> A_LU, pivots = A.lu()
>>> P, A_L, A_U = torch.lu_unpack(A_LU, pivots)
>>> P
tensor([[[1., 0., 0.],
         [0., 1., 0.],
         [0., 0., 1.]],

        [[0., 0., 1.],
         [0., 1., 0.],
         [1., 0., 0.]]])
>>> A_L
tensor([[[ 1.0000,  0.0000],
         [ 0.4763,  1.0000],
         [ 0.3683,  0.1135]],

        [[ 1.0000,  0.0000],
         [ 0.2957,  1.0000],
         [-0.9668, -0.3335]]])
>>> A_U
tensor([[[ 2.1962,  1.0881],
         [ 0.0000, -0.8681]],

        [[-1.0947,  0.3736],
         [ 0.0000,  0.5718]]])
>>> A_ = torch.bmm(P, torch.bmm(A_L, A_U))
>>> torch.norm(A_ - A)
tensor(2.9802e-08)