feral-amf

Approximate Minimum Fill (AMF / HAMF4) fill-reducing ordering for sparse symmetric matrices, implemented in pure Rust on the quotient-graph framework of Amestoy (1999).

• License: MIT
• Dependencies: feral-ordering-core only.
• MSRV: stable Rust, edition 2021. No unsafe.

What AMF does

AMF is a quotient-graph greedy ordering closely related to AMD (feral-amd), but the per-pivot scoring metric is the approximate fill introduced by selecting that pivot rather than the approximate degree. Empirically this produces lower-fill permutations than AMD on a substantial fraction of structurally unsymmetric or arrow-shaped matrices, at modest extra cost per pivot. The HAMF4 variant inherits AMD's mass elimination, supervariable detection, aggressive absorption, and dense-row deferral.

Reference

• Amestoy, P. R. (1999). Recent progress in parallel multifrontal solvers. Proceedings of the Fifteenth World Congress on Scientific Computation, Modelling and Applied Mathematics (IMACS-15). The HAMF / HAMF4 algorithm.

Full BibTeX in dev/references.bib of the parent repository.

Contract

feral-amf conforms to the FERAL ordering-crate contract defined by feral-ordering-core. Input is a borrowed full-symmetric CscPattern<'_>; output is a Vec<i32> permutation plus shared and crate-specific stats.

use feral_amf::{amf_order, CscPattern};

let col_ptr = [0, 2, 5, 8, 10];
let row_idx = [0, 1,  0, 1, 2,  1, 2, 3,  2, 3];
let pattern = CscPattern::new(4, &col_ptr, &row_idx).expect("valid CSC");
let perm = amf_order(&pattern).expect("amf_order");

See feral-amd's README for a fuller worked example; the API shape is identical.

License

MIT.