Linear algebra

Decompositions, derived quantities, and matrix functions over FixedMatrix, each chained at the wide compute tier.

What it is

Three modules build on FixedMatrix: decompose (factorizations and the solvers built on them), derived (norms, inverses, condition numbers, least squares), and matrix_functions (exp, log, sqrt, pow of a matrix). Operation chains run through a ComputeMatrix at tier N+1 so the whole chain rounds once at the end rather than once per intermediate.

Usage

use g_math::fixed_point::{FixedMatrix, FixedVector, FixedPoint};
use g_math::fixed_point::imperative::decompose;

let a = FixedMatrix::from_slice(2, 2, &[
    FixedPoint::from_int(4), FixedPoint::from_int(3),
    FixedPoint::from_int(6), FixedPoint::from_int(3),
]);
let lu = decompose::lu_decompose(&a).unwrap();   // Doolittle, partial pivoting
let b = FixedVector::from_slice(&[FixedPoint::from_int(1), FixedPoint::from_int(2)]);
let x = lu.solve(&b).unwrap();                    // solve A x = b
let det = lu.determinant();

What's here

Decompositions (decompose): LU (Doolittle, partial pivoting), QR (Householder), Cholesky, SVD (Golub-Kahan), symmetric eigenvalues (Jacobi), Schur (Francis QR). Each returns a struct exposing solve / determinant / inverse where applicable, plus iterative refinement on LU.
Derived (derived): frobenius_norm, norm_1, norm_inf, solve, solve_spd, determinant, inverse, inverse_spd, pseudoinverse, rank, nullspace, least_squares, condition_number_1 / _2.
Matrix functions (matrix_functions): matrix_exp (Padé + scaling-and-squaring), matrix_sqrt (Denman-Beavers), matrix_log (inverse scaling-and-squaring), matrix_pow: all chained through ComputeMatrix.

Public API

See PUBLIC_API.md → Linear algebra and docs.rs.

Behaviour & limits

Solver and factor accuracy is validated against mpmath references combined with structural checks (PA=LU, QᵀQ=I, exp/log roundtrips).
Error in a solved system scales with the condition number of the matrix. An ill-conditioned system (e.g. a Hilbert matrix) amplifies input error by orders of magnitude in any finite precision; iterative refinement recovers the residual but not the lost input information. See the precision guide.

Determinism guarantees are in CONTRACT.md.

Disclaimer

This software is provided "as is", without warranty of any kind, express or implied. Use of this software is entirely at your own risk. In no event shall the author or contributors be held liable for any damages arising from the use or inability to use this software.

Built by Niels Erik Toren · support & donations.

gMath