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rslab (Python bindings)

NumPy/SciPy bindings for RSLAB, a pure-Rust sparse direct solver and preconditioner: complex/real symmetric LDL^T (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 LDL^T or LU path
ldlt(A, **kw) -> Ldlt factor a real/complex symmetric matrix (Bunch-Kaufman LDL^T)
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) yes yes yes solve one RHS, optional iterative-refinement steps against the original A
solve_many(B) yes yes yes solve n x nrhs RHS in one batched pass
solve_transpose(b) - - yes solve A^T y = b on the same factors (plain transpose, not conjugate)
refactor(data) - - yes 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) yes yes yes GMRES with this factor as preconditioner
gmres_block(B, tol=1e-8, maxit=400, restart=None, x0=None) yes yes yes block GMRES for multiple RHS
recycle(k) yes yes yes a Recycle workspace holding up to k deflation vectors across gmres calls
n, factor_nnz, n_perturbed, dtype yes yes yes dimension, stored factor entries, perturbed pivots (always 0 for Klu), NumPy dtype name
inertia yes - - (n_pos, n_neg, n_zero) eigenvalue counts from LDL^T
n_blocks - - yes number of BTF diagonal blocks

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

License

MIT.

Release files for rslab 0.29.0

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rslab-0.29.0-cp39-abi3-macosx_10_12_x86_64.whl CPython 3.9 abi3 macOS 10.12+ x86-64 Details

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