feral-solver 0.11.3

Sparse symmetric indefinite direct solver with certified inertia, in pure Rust.

feral-solver

Python bindings for feral, a pure-Rust sparse symmetric indefinite direct solver with certified inertia counts. Aimed at interior-point methods (the IPM in discopt is the primary consumer), but usable for any application that factors symmetric KKT-shaped systems.

Install

pip install feral-solver           # plain
pip install 'feral-solver[scipy]'  # with scipy.sparse adapters
uv add feral-solver                # via uv

Wheels are published for CPython 3.10+ on Linux x86_64/aarch64, macOS universal2, and Windows x86_64. abi3 means one wheel per platform/arch covers all supported Python minor versions.

Quickstart

import numpy as np
import feral

A = feral.CscMatrix.from_dense(np.array([
    [4.0, 1.0, 0.0],
    [1.0, 3.0, 2.0],
    [0.0, 2.0, 5.0],
]))

solver = feral.Solver()
status, inertia = solver.factor(A)
assert status == feral.FactorStatus.SUCCESS
print(inertia)                       # Inertia(n_pos=3, n_neg=0, n_zero=0)

b = np.array([1.0, 2.0, 3.0])
x = solver.solve(b)
print(np.allclose(A.symv(x), b))     # True

IPM use

The feral.ipm.KktSolver class wraps Solver with the Wächter–Biegler 2006 §3.1 perturbation-escalation loop. Symbolic analysis is cached; across an entire Newton run solver.symbolic_call_count stays at 1.

import feral
import feral.ipm

kkt_pattern = feral.CscMatrix.from_scipy(my_kkt)   # see scipy adapter
kkt = feral.ipm.KktSolver(
    kkt_pattern,
    expected_inertia=feral.Inertia(n_vars, n_equality_constraints),
)
for newton_iter in range(max_iter):
    report = kkt.factor(values_this_iter)          # auto-perturbs if needed
    if report.status != feral.FactorStatus.SUCCESS:
        break
    dx_aff, dx_corr = kkt.solve_pair(b_aff, b_corr)
    ...

See examples/discopt_ipm_kkt.py for an end-to-end Newton step against a small NLP.

Unsymmetric LU basis engine

LuFactor factors a general square matrix and solves A x = b (ftran) / Aᵀ y = c (btran), with simplex-style product-form updates. It auto-routes to a dense or sparse engine via the same should_use_dense_lu heuristic the Rust core uses; pass force_dense=True/False to override.

import numpy as np
import feral

A = np.array([[2.0, 1.0, 0.0], [0.0, 3.0, 1.0], [1.0, 0.0, 4.0]])
lu = feral.LuFactor(feral.LuMatrix.from_dense(A))
x = lu.ftran(np.array([1.0, 2.0, 3.0]))     # solve A x = b
y = lu.btran(np.array([1.0, 0.0, 0.0]))     # solve Aᵀ y = c
lu.update(1, np.array([0.0, 5.0, 1.0]))     # replace basis column 1
# P A Q = L U :  A[perm][:, qcol] == l_array() @ u_array()

A singular basis raises SingularBasisError (a FactorError); an exhausted update budget raises NeedsRefactorError — call lu.refactor(new_matrix).

Factor access and introspection

After Solver.factor, the assembled factor and its statistics are available without re-solving:

s = feral.Solver(ordering="amd", profiling=True)
s.factor(A_csc)

fac = s.factors()                  # Factors snapshot
indptr, indices, data = fac.l_csc()   # unit-lower L as CSC (factorization order)
d_diag, d_subdiag = fac.d_blocks()    # block-diagonal D (2×2 where d_subdiag != 0)
L_scipy = fac.to_scipy_l()            # optional scipy.sparse.csc_matrix

# Reconstruction identity (factorization order):
#   L @ D @ L.T  ==  P (S A S) Pᵀ
# with fac.perm and the per-row fac.scaling vector.

stats = s.last_factor_stats()      # nnz, fill_ratio, inertia, pivot range, ...
print(s.min_pivot_magnitude, s.max_pivot_magnitude)
print(s.scaling_info.kind)         # "applied" | "mc64_fallback_to_infnorm" | ...
print(s.profile_report())          # populated when profiling=True

Solver.symbolic() (and the standalone feral.analyze(A_csc, ordering=...), which runs no numeric factorization) return a SymbolicAnalysis with the resolved ordering, perm/perm_inv, num_supernodes, factor_nnz_estimate, col_counts, and the elimination-tree etree_parent array (roots marked -1).

New Solver(...) keyword arguments — all optional, defaulting to the prior behavior — expose the tuning knobs: ordering ("amd", "amf", "metis", "scotch", "kahip", "auto", "auto_race"), mc64_cache, profiling, partial_singular_warning, and auto_cascade_break.

Conversion conveniences

CscMatrix.to_dense() returns the full symmetric matrix as a 2-D numpy array; CscMatrix.from_dense(a, triangle="lower"|"upper"|"full") ingests either triangle; CscMatrix.symmetric_pattern() returns the full (indptr, indices) structural pattern.

Example notebooks

Runnable notebooks live in examples/notebooks/. Regenerate them from the reviewable _build_notebooks.py generator: python _build_notebooks.py re-executes each notebook and commits its cell outputs (the embedded assertions double as a smoke test), or pass --no-execute for source-only .ipynb when feral is not installed in the running interpreter.

• 01_basic_factor_solve — factor, certified inertia, solve, refine, reuse.
• 02_multi_rhs_batched — batched multi-RHS solve, motivated by a steady-state heat-conduction sweep, with a correctness check and a looped-vs-batched timing showing the per-RHS speedup (issue #57).
• 03_kkt_saddle_inertia — indefinite KKT system with certified inertia.
• 04_scipy_numpy_interop — scipy.sparse round-trip vs spsolve.
• 05_lu_and_introspection — the LU basis engine (ftran/btran, product-form updates, P A Q = L U), factor access (L/D reconstruction, feral.analyze), and introspection (knobs, factor stats, pivot range, scaling info) added in 0.11.0.

scipy.sparse interop

import scipy.sparse as sp
import feral

A_scipy = sp.csc_matrix(...)
A = feral.from_scipy(A_scipy, symmetric="full")    # reads lower triangle
# ... factor, solve ...
A_back = feral.to_scipy(A)                          # round-trips to scipy

Building from source

Requires a stable Rust toolchain (1.75+) and Python 3.10+.

git clone https://github.com/jkitchin/feral.git
cd feral/python
pip install maturin
maturin develop --release    # builds and installs into current venv
pytest tests/

License

MIT, same as the underlying Rust crate.