torch.lu¶

torch.
lu
(*args, **kwargs)¶ Computes the LU factorization of a matrix or batches of matrices
A
. Returns a tuple containing the LU factorization and pivots ofA
. Pivoting is done ifpivot
is set toTrue
.Note
The returned permutation matrix for every matrix in the batch is represented by a 1indexed vector of size
min(A.shape[2], A.shape[1])
.pivots[i] == j
represents that in thei
th step of the algorithm, thei
th row was permuted with thej1
th row.LU factorization with
pivot
=False
is not available for CPU, and attempting to do so will throw an error. However, LU factorization withpivot
=False
is available for CUDA.This function does not check if the factorization was successful or not if
get_infos
isTrue
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
, andP
can be derived usingtorch.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, ifA
is close to not being full rank, the gradient will be numerically unstable as it depends on the computation of $L^{1}$ and $U^{1}$. Parameters
A (Tensor) – the tensor to factor of size $(*, m, n)$
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
isTrue
, then the elements in the tuple are Tensor, IntTensor, and IntTensor. Ifget_infos
isFalse
, then the elements in the tuple are Tensor, IntTensor. Default:None
 Returns
A tuple of tensors containing
factorization (Tensor): the factorization of size $(*, m, n)$
pivots (IntTensor): the pivots of size $(*, \text{min}(m, n))$.
pivots
stores all the intermediate transpositions of rows. The final permutationperm
could be reconstructed by applyingswap(perm[i], perm[pivots[i]  1])
fori = 0, ..., pivots.size(1)  1
, whereperm
is initially the identity permutation of $m$ elements (essentially this is whattorch.lu_unpack()
is doing).infos (IntTensor, optional): if
get_infos
isTrue
, this is a tensor of size $(*)$ where nonzero 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!