axb

A lightweight, zero-dependency linear algebra library for Rust with compile-time dimension checking using const generics.

Features

🔒 Compile-time dimension checking - Catch dimension mismatches at compile time
📦 Zero dependencies - No external dependencies for the core library
🛡️ Result-based error handling - No panics, all errors are returned as Result
➕ Operator overloading - Natural syntax with +, -, * operators
📐 Matrix factorizations - QR, LU, and LDU decompositions
🧮 Comprehensive operations - Determinant, inverse, transpose, trace, rank, and more

Installation

Add this to your Cargo.toml:

[dependencies]
axb = "0.2"

Quick Start

use axb::matrix::Matrix;

fn main() {
    // Create matrices
    let a = Matrix::<2, 2>::new([[1.0, 2.0], [3.0, 4.0]]);
    let b = Matrix::<2, 2>::new([[5.0, 6.0], [7.0, 8.0]]);

    // Arithmetic operations
    let sum = (&a + &b).unwrap();
    let diff = (&a - &b).unwrap();
    let product = (&a * &b).unwrap();
    let scaled = &a * 2.0;

    // Matrix operations
    let det = a.determinant().unwrap();      // -2.0
    let inv = a.inverse().unwrap();
    let transposed = a.transpose();
    let trace = a.trace();                    // 5.0

    // Indexing
    let element = a[(0, 1)];                  // 2.0
    
    println!("Determinant: {}", det);
    println!("Inverse:\n{}", inv);
}

Constructors

use axb::matrix::Matrix;

// From 2D array
let m = Matrix::<2, 3>::new([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]]);

// From nested Vec
let v = vec![vec![1.0, 2.0], vec![3.0, 4.0]];
let m = Matrix::<2, 2>::from_vec(v);

// Special matrices
let zeros = Matrix::<3, 3>::zeros();
let identity = Matrix::<3, 3>::identity();
let diagonal = Matrix::<3, 3>::diagonal(&[1.0, 2.0, 3.0]);
let filled = Matrix::<2, 2>::fill(5.0);

Matrix Factorizations

use axb::matrix::Matrix;

let m = Matrix::<3, 3>::new([
    [1.0, 2.0, 3.0],
    [4.0, 5.0, 6.0],
    [7.0, 8.0, 10.0],
]);

// QR Factorization (A = QR)
let (q, r) = m.qr().unwrap();

// LU Factorization (A = LU)
let (l, u) = m.lu().unwrap();

// LDU Factorization (A = LDU)
let (l, d, u) = m.ldu().unwrap();

Solving Linear Systems

use axb::matrix::Matrix;

// Solve Ax = b
let a = Matrix::<2, 2>::new([[2.0, 1.0], [1.0, 3.0]]);
let b = Matrix::<2, 1>::new([[5.0], [10.0]]);

let x = a.solve(&b).unwrap();
// x ≈ [1.0, 3.0]

Vector Operations

use axb::matrix::Matrix;

let v1 = Matrix::<3, 1>::new([[1.0], [2.0], [3.0]]);
let v2 = Matrix::<3, 1>::new([[4.0], [5.0], [6.0]]);

let dot = v1.dot(&v2);           // 32.0
let norm = v1.norm();            // √14
let unit = v1.normalize().unwrap();
let cross = v1.cross(&v2);       // 3D cross product

Matrix Properties

use axb::matrix::Matrix;

let m = Matrix::<3, 3>::new([
    [1.0, 2.0, 3.0],
    [2.0, 4.0, 5.0],
    [3.0, 5.0, 6.0],
]);

m.is_symmetric();     // true
m.is_orthogonal();    // false
m.is_projection();    // false
m.rank();             // matrix rank
m.frobenius_norm();   // Frobenius norm

Error Handling

All fallible operations return Result<T, MatrixError>:

use axb::matrix::{Matrix, MatrixError};

let singular = Matrix::<2, 2>::new([[1.0, 2.0], [2.0, 4.0]]);

match singular.inverse() {
    Ok(inv) => println!("Inverse: {}", inv),
    Err(MatrixError::NotInvertible) => println!("Matrix is singular"),
    Err(e) => println!("Error: {}", e),
}

// Non-square matrix operations
let rect = Matrix::<2, 3>::new([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]]);
assert!(rect.determinant().is_err()); // NonSquare error

API Reference

Basic Operations

Method	Description
`new(arr)`	Create from 2D array
`from_vec(v)`	Create from nested Vec
`zeros()`	Create zero matrix
`identity()`	Create identity matrix
`diagonal(values)`	Create diagonal matrix
`transpose()`	Transpose matrix
`determinant()`	Compute determinant
`inverse()`	Compute inverse
`trace()`	Sum of diagonal elements
`rank()`	Compute matrix rank
`pow(n)`	Matrix exponentiation

Factorizations

Method	Description
`qr()`	QR factorization
`lu()`	LU factorization
`ldu()`	LDU factorization

Vector Operations (for `Matrix<R, 1>`)

Method	Description
`norm()`	Euclidean norm
`normalize()`	Unit vector
`dot(other)`	Dot product
`cross(other)`	Cross product (3D only)

Properties

Method	Description
`is_symmetric()`	Check if A = A^T
`is_orthogonal()`	Check if A * A^T = I
`is_projection()`	Check if P² = P
`frobenius_norm()`	Frobenius norm

Minimum Supported Rust Version

This crate requires Rust 1.51 or later (for const generics).

License

Licensed under either of:

Apache License, Version 2.0 (LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)
MIT license (LICENSE-MIT or http://opensource.org/licenses/MIT)

at your option.

Contributing

Contributions are welcome! Please feel free to submit a Pull Request.

axb 0.2.1

axb