Computes the LU factorization of a matrix or batches of matrices A. Returns a tuple containing the LU factorization and pivots of A. Pivoting is done if pivot is set to True.
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)
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 − 1 L^{-1} L−1 and U − 1 U^{-1} U−1.
>>> 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!
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