I’ve released an open-source Python package for computing selected inverse blocks of sparse block-structured matrices without forming the dense inverse.
It supports PyTorch autograd, sparse solves, log-determinants, Gaussian sampling, and marginal covariance calculations for Gaussian Markov random fields.
The underlying algorithms are classical (Takahashi/Erisman–Tinney). This is a PyTorch-oriented reference implementation, not a replacement for high-performance sparse-direct libraries such as CHOMPACK or CHOLMOD.
I’d really welcome feedback from anyone working with sparse Gaussian models, differentiable linear algebra, or structured probabilistic inference.