linear algebra package for rust
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README.md

linxal

Status

Crate Version Build Status Documentation

Description

linxal is a linear algebra package for rust. linxal uses LAPACK as a backend, (specifically with the lapack package) to execute linear algebra routines with rust-ndarray as inputs and outputs.

Installation / Usage

linxal is available on crates.io and can be installed via cargo. In your Cargo.toml file, you can use.

[dependencies]
....
linxal = "0.5"

Features

linxal exposes features to choose the underlying LAPACK / BLAS source. By default, linxal enables the openblas feature, which compiles LAPACK and BLAS from the OpenBLAS distribution via openblas-src. You can use netlib LAPACK instead, via:

...
[dependencies.linxal]
version = "0.5"
default-features = false
features = ["netlib"]

Other possible features are openblas-system and netlib-system. These are similar to openblas and netlib, execpt that they use the installed shared libraries on your system instead of compiling them from source.

Documentation

Documentation can be found at https://github.masonium.io/rustdoc/linxal/.

Example

#[macro_use]
extern crate linxal;
extern crate ndarray;

use linxal::types::{c32, LinxalMatrix};
use ndarray::{arr1, arr2};

fn main() {
	let m = arr2(&[[1.0f32, 2.0],
				   [-2.0, 1.0]]);

	let r = m.eigenvalues(false, false);
	assert!(r.is_ok());

	let r = r.unwrap();
	let true_evs = arr1(&[c32::new(1.0, 2.0), c32::new(1.0, -2.0)]);
	assert_eq_within_tol!(true_evs, r.values, 0.01);

	let b = arr1(&[-1.0, 1.0]);
	let x = m.solve_linear(&b).unwrap();
	let true_x = arr1(&[-0.6, -0.2]);
	assert_eq_within_tol!(x, true_x, 0.0001);
}

Priorities

  • Correctness: linxal will strive for correctness in all cases. Any function returning a non-Err result should return a correct result.

  • Ease of Use: linxal will provide a consistent interface and should require minimal setup. Most routine should be high-level and should require no knowledge of the underlying LAPACK routines.

    linxal will minimize surprising behaviour.

  • Documentation: linxal will strive to provide documentation for all functionality. Undocumented public features are a bug.

  • Ergonomics: linxal will try to minimize boilerplate whenever appropriate.

  • Speed

Non-Goals

  • Low-dimension arithmetic: linxal is not specifically designed or optimized for {2,3,4}-D problems, as you would encounter in computer graphics, physics, or other domains. There are libraries such as nalgebra and cgmath that specialize in low-dimensional algorithms.

  • Representation flexibility: ndarray is the only for standard matrices, and future representations of specialized formats (packed triangular, banded, tridiagonal, etc.) will probably not allow for user-defined formats.

Goals

  • Major linear algebra routines
    • Eigenvalues
    • Singular Value
    • Linear Solvers
    • Linear Least-Squares
    • Matrix Factorizations (QR, LU, etc.)
      • QR
      • LU
      • Cholesky
      • Schur
    • Inversion
    • Generalized Eigenvalues
    • Generalized Singular Value Decomposition
  • Multiple matrix formats
    • General (direct via ndarray)
    • Symmetric / Hermitian
    • Banded (Packed)
  • Random matrix generation
    • General
    • Symmetric / Hermitian
    • Positive
    • Unitary

Contributing

Pull requests of all kinds (code, documentation, formatting, spell-checks) are welcome!