RSLAB

A sparse direct solver in pure Rust. PARDISO-style, embeddable, deterministic.

RSLAB is a sparse direct solver for real and complex matrices in pure Rust with no BLAS, LAPACK, or MKL dependency. It started from the feral project, made generic over the scalar type (f64, f32, and their complex counterparts), and grew into three factorization paths matched to their operator classes: symmetric LDLT with Bunch-Kaufman pivoting, threshold-pivoted unsymmetric LU, and a KLU path for circuit-shaped matrices (BTF block structure, per-block AMD, Gilbert-Peierls LU).

Built for solver-in-the-loop

The design target is a solver that sits inside an engine, not on a cluster queue. The numeric factor is bit-identical across thread counts. Peak memory and runtime are predicted exactly from the symbolic structure before any numeric work. Fixed-pattern sequences (frequency sweeps, Newton steps) refactor numeric-only on frozen pivots, and solve_transpose reuses the same factors for adjoint and sensitivity solves. Mixed-precision solves factor in single precision, refine against the double-precision original, and return a backward-error certificate. Where a matrix is outside the target class, RSLAB declines rather than returning a degraded solution.

Configuration is a deterministic heuristic: adaptive ordering, an exact nested-dissection bakeoff on large systems, and a worker count from a one-time cached hardware calibration. The solvers never measure implicitly.

Benchmarks

All cross-solver figures come from one benchmark engine over a complete-distribution corpus: structured-grid generators (curl-curl Maxwell, shifted Helmholtz, Stokes/KKT, convection-diffusion, BEM/MoM kernels) plus the complex SuiteSparse matrices, measured in a single run. Geomean over 63 sizes per path: 6.7x faster factor than faer on the symmetric class, 2.7x on the unsymmetric class, within 5.1-5.6x of MKL PARDISO. On the circuit class the KLU path factors 5-12x faster than the general LU, and same-pattern sweeps run 10-40x faster end to end. Accuracy: 24 of 31 complex SuiteSparse matrices below 1e-8 relative residual, matching PARDISO and ahead of faer.

History

RSLAB started in late June 2026 from feral, driven directly by what SANE and RapidMoM need from their linear algebra. Along the way I experimented with an MLP cost-model auto-tuner for picking solver configurations and discarded it: the deterministic heuristic is simpler, reproducible, and holds up. The repository ships a technical report that derives the algorithms and carries the full evaluation; every benchmark reruns with one command.