let A=[[3,2],[1,-3]] and B=[[3],[-10]]
and solve equation AX=B by using torch.solve:
X, LU = torch.solve(B,A)
Then I got X=[[-1],[3]] and LU=[[3,2],[0.333,-3.666]].
According to definition of LU decompose, LU must be same as A, however they aren't same.
Can anyone explain this???
Thank you
The representation you got is a compact way of representing the lower trainagular matrix L and the upper trainagular matrix U. You can use torch.tril and torch.triu to get these matrices explicitly:
L = torch.tril(LU, -1) + torch.eye(LU.shape[-1])
U = torch.triu(LU)
verify:
In [*]: L Out[*]: tensor([[1.0000, 0.0000], [0.3333, 1.0000]])
In [*]: U Out[*]: tensor([[ 3.0000, 2.0000], [ 0.0000, -3.6667]])
And the product is indeed equal to A:
In [*]: torch.dist(L @ U , A) Out[*]: tensor(0.)