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# torch.lu_unpack¶

torch.lu_unpack(LU_data, LU_pivots, unpack_data=True, unpack_pivots=True, *, out=None)

Unpacks the data and pivots from a LU factorization of a tensor into tensors L and U and a permutation tensor P such that LU_data, LU_pivots = (P @ L @ U).lu().

Returns a tuple of tensors as (the P tensor (permutation matrix), the L tensor, the U tensor).

Note

P.dtype == LU_data.dtype and P.dtype is not an integer type so that matrix products with P are possible without casting it to a floating type.

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. If False, then the returned L and U are None. Default: True

• unpack_pivots (bool) – flag indicating if the pivots should be unpacked into a permutation matrix P. If False, then the returned P is None. Default: True

• out (tuple, optional) – a tuple of three tensors to use for the outputs (P, L, U).

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)


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