Native SuperLU bridge

The native bridge solves general SciPy sparse matrices with SuperLU on the host CPU. It is an explicit escape hatch for systems that do not fit SOLVAX’s JAX structured or matrix-free methods.

Install the optional dependency:

pip install "solvax[native]"

Factor once

import scipy.sparse as sp

A = sp.csr_matrix(...)
factorization = sx.SpluFactorization(A)
x1 = factorization.solve(b1)
x2 = factorization.solve(b2)

One-shot solve

x = sx.splu_solve(A, b)

Execution model

The sparse matrix and solve execute through SciPy/SuperLU, outside the JAX trace. Returned values are converted to JAX arrays for convenience, but the operation is not:

• JIT compilable;

• vectorizable with jax.vmap;

• differentiable with jax.grad;

• accelerator resident.

Runtime guards raise a clear error if traced values are passed. Do not hide the bridge inside a jitted outer function.

When to use it

• a general sparse CPU system needs robust pivoted LU;

• factorization reuse is important;

• the solve is outside optimization/adjoint traces;

• a structured JAX solver is unavailable or insufficiently robust.

Comparison with JAX-native methods

Property	SuperLU bridge	FGMRES	structured direct
matrix representation	SciPy sparse	callable	bands/blocks
pivoting	sparse pivoted LU	not applicable	method dependent
accelerator	no	yes	yes
jit/vmap/grad	no	yes	yes
repeated RHS	excellent after factorization	repeated iteration	excellent after factorization

Sparse LU fill-in can dominate memory even when the input matrix is sparse. For large PDEs, a matrix-free Krylov method with a structured preconditioner may scale better. For small-to-moderate difficult CPU systems, SuperLU is often the more robust engineering choice.

API summary

• solvax.native.SpluFactorization

• solvax.native.splu_solve()

Runnable counterpart: examples/13_native_splu.py.