3 releases
0.1.2 | Jun 10, 2023 |
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0.1.1 | Jun 10, 2023 |
0.1.0 | Jun 3, 2023 |
#631 in Math
91KB
2.5K
SLoC
A mathematics library for embedded scientific computation
Note: This library is in no way ready for even limited use. Use num-traits, num-complex, and nalgebra if you need a proper math library.
This repository contains Talrost, an experimental library with the goal of providing an ergonomic, expedient, and embedded-ready numerical tower existing at the edges of Rust’s limitations on specialization and type coercion. Will likely require libm
, currently requires std
.
Examples of use
Warning: Most features are not remotely close to being properly implemented. Do not expect to be able to use this library at this time.
Algebraic traits
Loosely selected algebraic structures:
trait Element: Sized + Copy + Clone + core::fmt::Display + Debug {}
trait Monoid: Element + Add<Output = Self> + AddAssign { const ZERO: Self; }
trait Group: Monoid + Sub<Output = Self> + SubAssign + Neg<Output = Self> { fn Neg(self) -> Self; }
trait Semiring: Monoid + Mul<Output = Self> + MulAssign { const ONE: Self; }
trait Ring: Group + Semiring {}
trait Field: Ring + Div<Output = Self> + DivAssign { fn recip(self) -> Self; }
and then composes them to build a numerical tower accordingly:
trait Natural: Semiring + PartialOrd + PartialEq { ... } // unsigned ints
trait Integer: Ring + Natural { ... } // signed ints
trait Float: Field + Natural { ... } // standard floats & (currently) complex numbers
Complex arithmetic
Implements Float
, exposed as c32
and c64
with like-basis interoperability with f32
and f64
accordingly.
use talrost::complex::*;
let a: f64 = 0.25;
let mut b: c64 = (0.75, 1.0).into();
b += a;
b /= c64::new([0.5, 0.5]);
assert_eq!(b, "2 + 0i".into());
Polynomials
Supports polynomials in $\mathbb{R}$ (working) and $\mathbb{C}$ (broken).
use talrost::polynomial::*;
let tol = f64::EPSILON;
// p(x) = 1x^3 + 5x^2 + -14x + 0, has roots -7, 0, 2
let p = Polynomial::new([1.0, 5.0, -14.0, 0.0]);
let y = p.eval(4.0);
assert_eq!(y, 88.0); // p(4) = 88
let r = solvers::yuksel::roots_cubic(&p, tol);
assert_eq!(r.len(), 3); // count roots
assert_eq!(r, [-7.0, 0.0, 2.0]); // verify ordered roots
Vectors and Matrices
Vectors are supported over $\mathbb{R^n}$ and $\mathbb{C^n}$, with explicit coercion to row and column matrix types.
use talrost::{vector::*, matrix::*};
let v1 = Vector::new([1., 2., 3.]);
let v2 = Vector::new([4., 5., 6.]);
assert_eq!(v1.magnitude(), 14_f64.sqrt());
assert_eq!(v1.normalize().magnitude(), 1.);
assert_eq!(v1.row(), Matrix::new([[1., 2., 3.]]));
assert_eq!(v1.column(), Matrix::new([[1.], [2.], [3.]]));
assert_eq!(v1 + v2, Vector::new([5., 7., 9.]));
assert_eq!(v1 - v2, Vector::new([-3., -3., -3.]));
assert_eq!(v1 * 2., Vector::new([2., 4., 6.]));
assert_eq!(2. * v2, Vector::new([8., 10., 12.]));
let vec_real = Vector::new([1.0, 2.0]);
let vec_complex = Vector::new([c64::new(1.0, 0.0), c64::new(2.0, 0.0)]);
assert_eq!(vec_real.magnitude(), 5_f64.sqrt());
assert_eq!(vec_complex.magnitude(), 5_f64.sqrt().into());
$M \times N$ matrices are supported over $\mathbb{R^n}$ and $\mathbb{C^n}$.
use talrost::matrix::*;
let x = Matrix::<f32, 2, 3>::new([[1., 2.], [3., 4.], [5., 6.]]);
assert_eq!((x + Matrix::ZERO), x);
let y = Matrix::new([[1., 2.], [3., 4.]]);
assert_eq!((y * Matrix::<_, 2, _>::IDENTITY).determinant(), -2.0);
let a = Matrix::new([
[1., 2., 3., 4.],
[5., 6., 7., 8.],
[9., 10., 11., 12.],
[13., 14., 15., 16.],
]);
let b = Matrix::new([
[17., 18., 19., 20.],
[21., 22., 23., 24.],
[25., 26., 27., 28.],
[29., 30., 31., 32.],
]);
let c = Matrix::new([
[250., 260., 270., 280.],
[618., 644., 670., 696.],
[986., 1028., 1070., 1112.],
[1354., 1412., 1470., 1528.],
]);
assert_eq!(a * b, c);