torch.lu — PyTorch 2.7 documentation (original) (raw)

torch.lu(*args, **kwargs)[source]¶

Computes the LU factorization of a matrix or batches of matricesA. Returns a tuple containing the LU factorization and pivots of A. Pivoting is done if pivot is set toTrue.

Warning

torch.lu() is deprecated in favor of torch.linalg.lu_factor()and torch.linalg.lu_factor_ex(). torch.lu() will be removed in a future PyTorch release.LU, pivots, info = torch.lu(A, compute_pivots) should be replaced with

LU, pivots = torch.linalg.lu_factor(A, compute_pivots)

LU, pivots, info = torch.lu(A, compute_pivots, get_infos=True) should be replaced with

LU, pivots, info = torch.linalg.lu_factor_ex(A, compute_pivots)

Note

• The returned permutation matrix for every matrix in the batch is represented by a 1-indexed vector of size min(A.shape[-2], A.shape[-1]).pivots[i] == j represents that in the i-th step of the algorithm, the i-th row was permuted with the j-1-th row.
• LU factorization with pivot = False is not available for CPU, and attempting to do so will throw an error. However, LU factorization with pivot = False is available for CUDA.
• This function does not check if the factorization was successful or not if get_infos is True since the status of the factorization is present in the third element of the return tuple.
• In the case of batches of square matrices with size less or equal to 32 on a CUDA device, the LU factorization is repeated for singular matrices due to the bug in the MAGMA library (see magma issue 13).
• L, U, and P can be derived using torch.lu_unpack().

Warning

The gradients of this function will only be finite when A is full rank. This is because the LU decomposition is just differentiable at full rank matrices. Furthermore, if A is close to not being full rank, the gradient will be numerically unstable as it depends on the computation of L−1L^{-1} and U−1U^{-1}.

Parameters

• A (Tensor) – the tensor to factor of size (∗,m,n)(*, m, n)
• pivot (bool, optional) – controls whether pivoting is done. Default: True
• get_infos (bool, optional) – if set to True, returns an info IntTensor. Default: False
• out (tuple, optional) – optional output tuple. If get_infos is True, then the elements in the tuple are Tensor, IntTensor, and IntTensor. If get_infos is False, then the elements in the tuple are Tensor, IntTensor. Default: None

Returns

A tuple of tensors containing

• factorization (Tensor): the factorization of size (∗,m,n)(*, m, n)
• pivots (IntTensor): the pivots of size (∗,min(m,n))(*, \text{min}(m, n)).pivots stores all the intermediate transpositions of rows. The final permutation perm could be reconstructed by applying swap(perm[i], perm[pivots[i] - 1]) for i = 0, ..., pivots.size(-1) - 1, where perm is initially the identity permutation of mm elements (essentially this is what torch.lu_unpack() is doing).
• infos (IntTensor, optional): if get_infos is True, this is a tensor of size (∗)(*) where non-zero values indicate whether factorization for the matrix or each minibatch has succeeded or failed

Return type

(Tensor, IntTensor, IntTensor (optional))

Example:

A = torch.randn(2, 3, 3) A_LU, pivots = torch.lu(A) A_LU tensor([[[ 1.3506, 2.5558, -0.0816], [ 0.1684, 1.1551, 0.1940], [ 0.1193, 0.6189, -0.5497]],

    [[ 0.4526,  1.2526, -0.3285],
     [-0.7988,  0.7175, -0.9701],
     [ 0.2634, -0.9255, -0.3459]]])

pivots tensor([[ 3, 3, 3], [ 3, 3, 3]], dtype=torch.int32) A_LU, pivots, info = torch.lu(A, get_infos=True) if info.nonzero().size(0) == 0: ... print('LU factorization succeeded for all samples!') LU factorization succeeded for all samples!