torch-sla (Torch Sparse Linear Algebra) is a Python library that provides differentiable sparse linear equation solvers for PyTorch. It solves systems of the form Ax = b where A is a sparse matrix, with full support for automatic differentiation (autograd) and GPU acceleration via CUDA.

How do I solve a sparse linear system in PyTorch?

Use torch-sla's SparseTensor class: from torch_sla import SparseTensor; A = SparseTensor(values, row, col, shape); x = A.solve(b). This works on both CPU and GPU, and supports gradient computation.

What sparse solvers does torch-sla support?

torch-sla supports multiple backends: CPU solvers include SciPy (LU, UMFPACK, CG, BiCGStab, GMRES, MINRES) and PyTorch-native (CG, BiCGStab, GMRES, MINRES). GPU solvers include PyTorch-native (CG, BiCGStab, GMRES, MINRES) and cuDSS (LU, Cholesky, LDLT). The library automatically selects the best solver based on hardware and matrix properties.

Can I compute gradients through sparse solve in PyTorch?

Yes, torch-sla fully supports PyTorch autograd. You can set requires_grad=True on your sparse matrix values, solve the system, compute a loss, and call backward() to get gradients with respect to the matrix values and right-hand side.

How do I solve batched sparse systems in PyTorch?

torch-sla supports batched solving for matrices with the same sparsity pattern. Create a SparseTensor with batched values of shape [batch_size, nnz] and solve all systems in parallel. For matrices with different patterns, use SparseTensorList.

How do I use torch-sla on GPU?

Simply call .cuda() on your SparseTensor: A_cuda = A.cuda(); x = A_cuda.solve(b.cuda()). The library automatically uses cuDSS for GPU-accelerated solving.

What is the difference between torch-sla and scipy.sparse?

torch-sla offers native PyTorch integration, GPU support via CUDA, full autograd gradient support, and batched solving. scipy.sparse is CPU-only, requires data copying to/from PyTorch, and doesn't support automatic differentiation.