torch.lu_unpack (original) (raw)

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