torch.lu_unpack

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

Unpacks the LU decomposition returned by lu_factor() into the P, L, U matrices.

See also

lu() returns the matrices from the LU decomposition. Its gradient formula is more efficient than that of doing lu_factor() followed by lu_unpack().

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 empty tensors. 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 an empty tensor. Default: True

Keyword Arguments:

out (tuple, optional) – output tuple of three tensors. Ignored if None.

Returns:

A namedtuple (P, L, U)

Examples:

>>> A = torch.randn(2, 3, 3)
>>> LU, pivots = torch.linalg.lu_factor(A)
>>> P, L, U = torch.lu_unpack(LU, pivots)
>>> # We can recover A from the factorization
>>> A_ = P @ L @ U
>>> torch.allclose(A, A_)
True

>>> # LU factorization of a rectangular matrix:
>>> A = torch.randn(2, 3, 2)
>>> LU, pivots = torch.linalg.lu_factor(A)
>>> P, L, U = torch.lu_unpack(LU, pivots)
>>> # P, L, U are the same as returned by linalg.lu
>>> P_, L_, U_ = torch.linalg.lu(A)
>>> torch.allclose(P, P_) and torch.allclose(L, L_) and torch.allclose(U, U_)
True