Crate mathru

mathru

A crate that provides mathematics functions implemented entirely in Rust.

Usage

The library usage is described well in the API documentation - including example code.

Add this to your Cargo.toml:

[dependencies]
mathru = "0.6.*"

Then it is ready to be used:

 use mathru::algebra::linear::{Vector, Matrix};
 use mathru::algebra::linear::matrix::{Substitute};

 // Compute the LU decomposition of a 2x2 matrix
 let a: Matrix<f64> = Matrix::new(2, 2, vec![1.0, 2.0, -3.0, -7.0]);
 let b: Vector<f64> = vector![1.0; 3.0];

 let (l, u, p): (Matrix<f64>, Matrix<f64>, Matrix<f64>) = a.dec_lu().lup();

 let b_hat = &p * &b;

 let y = u.substitute_backward(b_hat);

 let x = p * l.substitute_forward(y);

 println!("{}", x);

 use mathru::*;
 use mathru::algebra::linear::{Vector, Matrix};
 use mathru::statistics::distrib::{Distribution, Normal};
 use mathru::optimization::{Optim, LevenbergMarquardt};


 //y = a + b * exp(c * t) = f(t)
 pub struct Example
 {
		x: Vector<f64>,
		y: Vector<f64>
 }

 impl Example
 {
		pub fn new(x: Vector<f64>, y: Vector<f64>) -> Example
		{
			Example
			{
				x: x,
				y: y
			}
		}

		pub fn function(x: f64, beta: &Vector<f64>) -> f64
		{
			let beta_0: f64 = *beta.get(0);
			let beta_1: f64 = *beta.get(1);
			let beta_2: f64 = *beta.get(2);
			let f_x: f64 = beta_0 + beta_1 * (beta_2 * x).exp();

			return f_x;
		}
 }

 impl Optim<f64> for Example
 {
		// y(x_i) - f(x_i)
		fn eval(self: &Self, beta: &Vector<f64>) -> Vector<f64>
		{
			let f_x = self.x.clone().apply(&|x: &f64| Example::function(*x, beta));
			let r: Vector<f64> = &self.y - &f_x;
			return vector![r.dotp(&r)]
		}

		fn jacobian(self: &Self, beta: &Vector<f64>) -> Matrix<f64>
		{
			let (x_m, _x_n) = self.x.dim();
			let (beta_m, _beta_n) = beta.dim();

			let mut jacobian_f: Matrix<f64> = Matrix::zero(x_m, beta_m);

			let f_x = self.x.clone().apply(&|x: &f64| Example::function(*x, beta));
			let residual: Vector<f64> = &self.y - &f_x;

			for i in 0..x_m
			{
				//let beta_0: f64 = *beta.get(0);
				let beta_1: f64 = *beta.get(1);
				let beta_2: f64 = *beta.get(2);

				let x_i: f64 = *self.x.get(i);

				*jacobian_f.get_mut(i, 0) = 1.0;
				*jacobian_f.get_mut(i, 1) = (beta_2 * x_i).exp();
				*jacobian_f.get_mut(i, 2) = beta_1 * x_i * (beta_2 * x_i).exp();

			}

			let jacobian: Matrix<f64> = (residual.transpose() * jacobian_f * -2.0).into();
			return jacobian;
		}
 }


 fn main()
 {
		let num_samples: usize = 100;

		let noise: Normal<f64> = Normal::new(0.0, 0.05);

		let mut t_vec: Vec<f64> = Vec::with_capacity(num_samples);

		// Start time
		let t_0 = 0.0f64;
		// End time
		let t_1 = 5.0f64;

		let mut y_vec: Vec<f64> = Vec::with_capacity(num_samples);

		// True function parameters
		let beta: Vector<f64> = vector![0.5; 5.0; -1.0];

		for i in 0..num_samples
		{
			let t_i: f64 = (t_1 - t_0) / (num_samples as f64) * (i as f64);

			//Add some noise
			y_vec.push(Example::function(t_i, &beta) + noise.random());

			t_vec.push(t_i);
		}

		let t: Vector<f64> = Vector::new_column(num_samples, t_vec.clone());
		let y: Vector<f64> = Vector::new_column(num_samples, y_vec.clone());

		let example_function = Example::new(t, y);

		let optim: LevenbergMarquardt<f64> = LevenbergMarquardt::new(100, 0.3, 0.95);

		let beta_0: Vector<f64> = vector![-1.5; 1.0; -2.0];
		let beta_opt: Vector<f64> = optim.minimize(&example_function, &beta_0).arg();

 	println!("{}", beta_opt);
	}

Modules

algebra	Algebra
analysis	Analysis
elementary	Elementary functions
num
optimization	Optimization
special	Special functions
statistics	Statistics

Macros

Complex
Complex32
Complex64
matrix	Macro to construct matrices
vector	Macro to construct vectors