Crate numra_linalg 

Linear algebra abstractions for Numra.

This crate provides matrix operations and linear solvers built on faer.

Design

The Matrix trait provides a backend-agnostic interface for matrix operations. The primary implementation wraps faer’s Mat<S> type.

Example

use numra_linalg::{Matrix, DenseMatrix};

// Create a 3x3 matrix
let mut a: DenseMatrix<f64> = DenseMatrix::zeros(3, 3);
a.set(0, 0, 2.0);
a.set(1, 1, 3.0);
a.set(2, 2, 4.0);

// Solve Ax = b
let b = vec![1.0, 2.0, 3.0];
let x = a.solve(&b).unwrap();

assert!((x[0] - 0.5).abs() < 1e-10);
assert!((x[1] - 2.0/3.0).abs() < 1e-10);
assert!((x[2] - 0.75).abs() < 1e-10);

Author: Moussa Leblouba Date: 9 February 2026 Modified: 2 May 2026

Re-exports

pub use iterative::bicgstab;

pub use iterative::cg;

pub use iterative::gmres;

pub use iterative::minres;

pub use iterative::pcg;

pub use iterative::IterativeOptions;

pub use iterative::IterativeResult;

pub use preconditioner::IdentityPreconditioner;

pub use preconditioner::Ilu0;

pub use preconditioner::Jacobi;

pub use preconditioner::Preconditioner;

pub use preconditioner::Ssor;

Modules

iterative

Iterative (Krylov) linear solvers for sparse systems.

preconditioner

Preconditioners for iterative linear solvers.

Structs

CholeskyFactorization

Cholesky factorization A = L L^T for symmetric positive-definite matrices.

DenseMatrix

Dense matrix backed by faer.

EigenDecomposition

General eigendecomposition (complex eigenvalues for real matrices).

LUFactorization

LU factorization of a matrix.

QRFactorization

QR factorization of a matrix.

SparseCholesky

Sparse Cholesky factorization for SPD systems.

SparseLU

Sparse LU factorization for solving Ax = b.

SparseMatrix

CSC sparse matrix wrapping faer’s SparseColMat.

SvdDecomposition

Full SVD decomposition: A = U * diag(S) * V^T.

SymEigenDecomposition

Symmetric/Hermitian eigendecomposition (real eigenvalues).

ThinSvdDecomposition

Thin SVD decomposition: A = U * diag(S) * V^T.

Enums

LinalgError

Linear algebra specific errors.

Traits

LUSolver

Trait for types that can solve linear systems.

Matrix

Trait for matrix types.

Scalar

A real scalar type suitable for numerical computation.