Let’s say I have a sparse set of matrices A1, A2, ... An, each of type CuSparseMatrixCSC{Float32, Int32} along with associated RHS vectors b1, b2, ... bn. Is there some watch to do a batch LU solve on the GPU with CUDA.jl?
If the matrices are dense, getrf_batched! works fine to get the LU factors. Is there some way to do batch solves/factorizations with sparse matrices @maleadt?
how big are the a matrices? you might just want to treat them as dense
The matrices are large network matrices (e.g., 10k x 10k), and they are extremely sparse (e.g., 99.99%). So leaving them dense is not an option, sadly!
LinearSolve.jl’s SimpleGMRES has optimizations for batched solving and is compatible with GPUs. That’s likely to be the best option here, though if you can supply a good preconditioner that would be helpful.
Thanks @ChrisRackauckas! Big fan of LinearSolve.jl. Unfortunately, I am solving linear systems within the context of a nonlinear optimization problem (interior point method), where the associated matrices sequentially have worse and worse condition numbers as convergence is approached (10^20 even). Thus, iterative methods (GMRES et al.) are well-known to cause slow convergence or divergence, so they are not a great choice here. If there is a GPU-batched LU/QR solver in LinearSolve.jl, I would love to hear about it. If not, maybe I can help develop it in the future.
@schev I suggest to try CUDSS.jl (GitHub - exanauts/CUDSS.jl).
It provides an interface to the new sparse linear solvers of NVIDIA.
They don’t provide a routine for solving batched sparse linear systems but you can create one big sparse block diagonal matrix diag(A1, A2, …, An) with the right-hand side [b1; b2; …; bn].