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.