nalgebra-sparse-linalg

Sparse linear algebra iterative solvers for nalgebra_sparse.

Overview

nalgebra-sparse-linalg provides iterative methods for solving large, sparse linear systems of equations, with a focus on compatibility with the nalgebra_sparse crate. The library currently includes Jacobi and Conjugate Gradient iterative solvers for sparse matrices.

Features

Jacobi iterative solver for sparse matrices in CSR format.
Conjugate Gradient solver for symmetric positive-definite matrices in CSR and CSC formats.
BiConjugate Gradient solver for general (possibly non-symmetric)
Generic over scalar types (e.g., f32, f64).
Simple API compatible with nalgebra_sparse's matrix and vector types.

Usage

Add this to your Cargo.toml:

[dependencies]
nalgebra-sparse-linalg = "0.1"
nalgebra-sparse = "0.9"

Example (Jacobi, CSR):

use nalgebra_sparse::{na::DVector, CsrMatrix};
use nalgebra_sparse_linalg::iteratives::jacobi::solve;

let a = CsrMatrix::identity(3);
let b = DVector::from_vec(vec![1.0; 3]);
let result = solve(&a, &b, 100, 1e-10);
assert!(result.is_some());

Exxample (Gauss-Seidel, CSR):

use nalgebra_sparse::{na::DVector, CsrMatrix};
use nalgebra_sparse_linalg::iteratives::gauss_seidel::solve;

let a = CsrMatrix::identity(3);
let b = DVector::from_vec(vec![1.0; 3]);
let result = solve(&a, &b, 100, 1e-10);
assert!(result.is_some());

Example (Relaxation, CSR):

use nalgebra_sparse::{na::DVector, CsrMatrix};
use nalgebra_sparse_linalg::iteratives::relaxation::solve;

let a = CsrMatrix::identity(3);
let b = DVector::from_vec(vec![1.0; 3]);
let result = solve(&a, &b, 100, 0.8, 1e-10);
assert!(result.is_some());

Example (Conjugate Gradient, CSC or CSR):

use nalgebra_sparse::{na::DVector, CsrMatrix};
use nalgebra_sparse_linalg::iteratives::conjugate_gradient::solve;

let a = CsrMatrix::identity(3);
let b = DVector::from_vec(vec![2.0; 3]);
let result = solve(&a, &b, 100, 1e-10);
assert!(result.is_some());

Example (BiConjugate Gradient, CSR or CSC):

use nalgebra_sparse::{na::DVector, CsrMatrix};
use nalgebra_sparse_linalg::iteratives::biconjugate_gradient::solve;

let a = CsrMatrix::identity(3);
let b = DVector::from_vec(vec![2.0; 3]);
let result = solve(&a, &b, 100, 1e-10);
assert!(result.is_some());

Documentation

See docs.rs for full API documentation.

License

Licensed under either of

Apache License, Version 2.0
MIT license