rslab (Python bindings)

NumPy/SciPy bindings for RSLAB, a pure-Rust sparse direct solver and preconditioner: complex/real symmetric LDLᵀ (Bunch-Kaufman), unsymmetric LU, and a KLU-style path for circuit-shaped matrices. A thin wrapper, all numeric work happens in Rust.

Install

pip install rslab

Usage

import numpy as np
import scipy.sparse as sp
import rslab

# Symmetric system (real or complex; the dtype selects the path).
A = sp.random(5000, 5000, density=1e-3, format="csc") + sp.eye(5000) * 10
A = A + A.T
b = np.random.rand(5000)

# One-shot solve.
x = rslab.spsolve(A, b)

# Factor once, solve many right-hand sides.
f = rslab.ldlt(A)
x1 = f.solve(b)
X = f.solve_many(np.random.rand(5000, 8))   # n x nrhs

print(f.n, f.factor_nnz, f.inertia, f.dtype)

Complex-symmetric matrices (EM/FEM, PARDISO mtype 6) work identically:

A = A.astype(np.complex128); A.data += 1j * 0.3 * A.data.real
x = rslab.ldlt(A).solve(np.ones(A.shape[0], dtype=np.complex128))

Unsymmetric matrices use the LU path:

f = rslab.lu(A_general)
x = f.solve(b)

Circuit-shaped matrices (MNA / SPICE-class: very sparse, unsymmetric, near-triangularizable) use the KLU path, bit-deterministic, with a numeric-only refactor for fixed-pattern sweeps:

f = rslab.klu(A_circuit)
x = f.solve(b)
A_circuit.data *= 1.5            # frequency sweep: same pattern, new values
f.refactor(A_circuit.data)       # no symbolic work, no pivot search
x2 = f.solve(b)
y = f.solve_transpose(b)         # A.T @ y = b on the same factors (adjoint)

solve_transpose is the plain transpose; for the conjugate-transpose adjoint use f.solve_transpose(b.conj()).conj().

Preconditioner mode

Never-fail static pivoting plus iterative refinement for hard/indefinite systems:

f = rslab.ldlt(A, preconditioner=1e-4)
x = f.solve(b, refine=20)        # refine against the original A

Configuration (keyword arguments)

By default ldlt, lu and spsolve use RSLAB's deterministic heuristic pick, the adaptive ordering plus an exact nested-dissection bakeoff on large systems (adopted only on a clear predicted win with no fill/memory regression). A one-time rslab.install_diagnose() measures this machine's throughput and speedup curve and caches it; afterwards the default also picks its worker count from the calibration (until then the conservative capped default applies). Keyword arguments override the pick:

kwarg	default	meaning
`threads`	`None` (auto)	`None` = calibrated/structural per-matrix pick; int = fixed (`0` = all)
`preconditioner`	`None`	static-pivot floor (e.g. `1e-4`); never-fail, refine to solve
`drop_tol`	`None`	incomplete-factor threshold (preconditioner)
`method`	`"left_looking"`	`"left_looking"` or `"multifrontal"`
`memory`	`"low"`	`"low"` or `"eager"` factor emit strategy
`force_accept`	`False`	accept tiny pivots in exact mode instead of failing

klu accepts:

kwarg	default	meaning
`pivot_tol`	`1e-3`	diagonal-preference threshold; `1.0` = plain partial pivoting
`row_scaling`	`True`	divide each row by its max-magnitude entry before factoring
`btf`	`True`	permute to block upper triangular form first (keep it on)
`parallel`	`None`	per-block parallel factor/refactor over the BTF blocks; `None` = auto gate (≥4 blocks, ≥8000 nnz, no dominant block), `True`/`False` force on/off; bit-identical result in every mode

Supported dtypes: float64, float32, complex128, complex64.

API

Everything ships in the flat rslab namespace; full parameter documentation lives in the docstrings (help(rslab.klu) etc.).

Functions

function	meaning
`spsolve(A, b, **kw)`	one-shot factor-and-solve; detects symmetry and picks the LDLᵀ or LU path
`ldlt(A, **kw) -> Ldlt`	factor a real/complex symmetric matrix (Bunch-Kaufman LDLᵀ)
`lu(A, **kw) -> Lu`	factor a general unsymmetric matrix (supernodal multifrontal LU)
`klu(A, **kw) -> Klu`	factor a circuit-shaped matrix (BTF + per-block Gilbert-Peierls LU)
`install_diagnose()`	one-time machine calibration; caches the measured thread-speedup curve

Factor handles — factor once, then:

method / attribute	`Ldlt`	`Lu`	`Klu`	meaning
`solve(b, refine=0)`	✓	✓	✓	solve one RHS, optional iterative-refinement steps against the original `A`
`solve_many(B)`	✓	✓	✓	solve `n × nrhs` RHS in one batched pass
`solve_transpose(b)`	–	–	✓	solve `Aᵀ y = b` on the same factors (plain transpose, not conjugate)
`refactor(data)`	–	–	✓	numeric-only re-factorization for new values on the same pattern (no symbolic work, no pivot search)
`gmres(b, tol=1e-8, maxit=400, restart=None, x0=None, recycle=None)`	✓	✓	✓	GMRES with this factor as preconditioner
`gmres_block(B, tol=1e-8, maxit=400, restart=None, x0=None)`	✓	✓	✓	block GMRES for multiple RHS
`recycle(k)`	✓	✓	✓	a `Recycle` workspace holding up to `k` deflation vectors across `gmres` calls
`n`, `factor_nnz`, `n_perturbed`, `dtype`	✓	✓	✓	dimension, stored factor entries, perturbed pivots (always `0` for `Klu`), NumPy dtype name
`inertia`	✓	–	–	`(n_pos, n_neg, n_zero)` eigenvalue counts from LDLᵀ
`n_blocks`	–	–	✓	number of BTF diagonal blocks

Recycle — deflation-subspace carrier for sweeps: attributes k, active, dtype; clear() resets it.

License

MIT.

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rslab 0.27.0

rslab (Python bindings)

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