Dear PyTorch people, what a dream of library this is!
I have a set of linear systems of the following form:
1A(v) • 1x = 1b(v)
2A(v) • 2x = 2b(v,1x)
3A(v) • 3x = 3b(v,1x,2x)
…
The nA matrices is constructed from several component nAi matrices multiplied by an element of vector v: 1A = 1Aa * va + 1Ab * vb + 1Ac * vc… The nAi matrices are large, sparse and there are many of them. I would thus like to store the matrices as sparse tensors. I was wondering whether there were any plans to implement a sparse linear solver (direct, since I guess iterative would be impossible) that was amenable to autograd? I need autograd to compute the Jacobian dx/dv in the end.
For now I have it working with dense systems, but I was wondering whether there would be a version of lu_solve that works with backpropagation, since I would like to store the factorization of A for use down the road. Discussed in issue: https://github.com/pytorch/pytorch/issues/22620 23