#linear-algebra #matrix-vector #robotics #matrix #vector #vector-math

no-std stack-algebra

Stack-allocated lightweight algebra for bare-metal rust

1 unstable release

0.1.0 Dec 30, 2022

#918 in Math

MIT/Apache

82KB
1.5K SLoC

stack-algebra

A stack-allocated lightweight algebra library for bare-metal applications.

Overview

This crate provides a stack-allocated matrix type with constant size determined at compile time. The primary goal for this library is to be useful in building robotics applications in rust. This means several things:

  1. Target platform is often bare-metal
  2. Size of the matrices can usually be defined at compile-time
  3. Problem solving does not require large matrices or heavy optimization
  4. Users are not experts in rust but often familiar with scientific tools (e.g. python or matlab)

Implementing numerical algorithms in rust can be made much more productive and ergonomic if simple abstractions and necessary algebra routines are available. This library is a growing collection of addressing those needs. It is heavily based on vectrix for core implementations.

Install

Use cargo to add to your project (or add manually to your Cargo.toml)

cargo add stack-algebra

Then import to your module by using

use stack_algebra::*; // or import just the items you need

Usage

  • matrix! macro can be used to create a new matrix

    // 2-by-3 matrix 
    let m = matrix![
        1.0, 2.0, 3.0;
        4.0, 5.0, 6.0; // Semicolon here is optional
    ]; 
    
  • vector! macro can be used to create a row/column vector

    // 1-by-3 row vector
    let r = vector![1.0, 2.0, 3.0]; 
    
    // 3-by-1 column vector
    let c = vector![1.0; 2.0; 3.0]; 
    
    // Vector to tuple conversion (for 3 or 4 element vectors)
    let (x, y, z) = r.into();
    
  • eye! for creating square identity matrix

    let m = eye!(2); 
    let exp = matrix![
      1.0, 0.0;
      0.0, 1.0
    ];
    assert_eq!(m, exp);
    
  • zeros! for creating zero-valued matrix

    let m = zeros!(2); // Square 2-by-2 matrix
    let exp = matrix![
      0.0, 0.0;
      0.0, 0.0
    ];
    assert_eq!(m, exp);
    
    let m = zeros!(2,3); // 2-by-3 matrix
    let exp = matrix![
      0.0, 0.0, 0.0;
      0.0, 0.0, 0.0
    ];
    assert_eq!(m, exp);
    
  • ones! for creating matrix with 1.0s (same as zeros! for usage)

  • diag! for creating a diagonal matrix with given entries (up to 6-by-6 size)

    let m = diag!(1.0, 2.0, 3.0);
    let exp = matrix![
      1.0, 0.0, 0.0;
      0.0, 2.0, 0.0;
      0.0, 0.0, 3.0
    ];
    assert_eq!(m, exp);
    
  • [i] or [(r,c)] to access individual elements

    let m = matrix![
        1.0, 2.0, 3.0;
        4.0, 5.0, 6.0
    ]; 
    
    assert_eq!(m[1], 4.0); // Using a single index assumes column-major order
    assert_eq!(m[(1,2)], 6.0);
    
  • *, /, +, - for matrix arithmatics

    let m = matrix![
        1.0, 2.0;
        3.0, 4.0
    ];
    
    let exp = matrix![
        2.0, 4.0;
        6.0, 8.0
    ];
    
    assert_eq!(m + m, exp); // Add matrices
    
    let exp = matrix![
        2.0, 3.0;
        4.0, 5.0
    ];
    
    assert_eq!(m + 1.0, exp); // Add scalar to matrix (note scalar has to be behind the operator)
    
  • .T() for matrix transpose

    let m = matrix![
        1.0, 2.0;
        3.0, 4.0
    ];
    
    let exp = matrix![
        1.0, 3.0;
        2.0, 4.0
    ];
    
    assert_eq!(m.T(), exp); 
    
    
  • .norm() for computing the Frobenius norm

      let m = matrix![
        1.0,-2.0;
       -3.0, 6.0;
      ];
      assert_relative_eq!(m.norm(), 7.0710678, max_relative = 1e-6);
    
  • .trace() for sum of diagonal elements of a sqaure matrix

      let m = matrix![
        9.0, 8.0, 7.0;
        6.0, 5.0, 4.0;
        3.0, 2.0, 1.0;
      ];
      assert_eq!(m.trace(), 15.0);
    
  • .det() for determinant (only available for square matrix)

      let m = matrix![
        3.0, 7.0;
        1.0, -4.0;
      ];
      assert_eq!(m.det(), -19.0); 
    
  • .inv() for inverse of a matrix (for square invertible matrix)

      let m = matrix![
        6.0, 2.0, 3.0;
        1.0, 1.0, 1.0;
        0.0, 4.0, 9.0;
      ];
      let exp = matrix![
        0.20833333, -0.25, -0.04166667;
            -0.375,  2.25,      -0.125;
        0.16666667,  -1.0,  0.16666667;
      ];
      assert_relative_eq!(m.inv().unwrap(), exp, max_relative = 1e-6);
    

License

This project is distributed under the terms of both the MIT license and the Apache License (Version 2.0).

See LICENSE-APACHE and LICENSE-MIT for details.

Dependencies

~2MB
~49K SLoC