Mathru

Mathru is a numeric library containing algorithms for linear algebra, analysis ,statistics and optimization written in pure Rust with optional BLAS/LAPACK as backend.

Features

The following features are implemented in this create:

• Algebra

  • Abstract
    • Polynomial
      • Legendre polynomial
      • Chebyshev polynomial first & second kind
      • Bernstein polynomial
      • Bessel polynomial
  • Linear algebra
    • Vector
    • Matrix
      • Basic matrix operations(+,-,*)
      • Transposition (In-place)
      • LU decomposition
      • QR decomposition
      • Hessenberg decomposition
      • Cholesky decomposition
      • Eigen decomposition
      • Singular value decomposition
      • Inverse
      • Pseudo inverse
      • Determinant
      • Trace
      • Solve linear system

• Analysis

  • Integration
    • Newton-Cotes
    • Gauss-Legendre
  • Ordinary differential equation (ODE)
    • Explicit methods
      • Euler method
      • Heun's 2nd order method
      • Midpoint method
      • Ralston's 2nd order method
      • Kutta 3rd order
      • Heun's 3rd order method
      • Ralston's 3rd order method
      • Runge-Kutta 4th order
      • Runge-Kutta-Felhberg
      • Dormand-Prince
      • Cash-Karp
      • Bogacki-Shampine
      • Adams-Bashforth
    • Automatic step size control with starting step size
    • Implicit methods
      • Implicit Euler
      • Backward differentiation formula (BDF)
  • Interpolation
    • Cubic spline

• Optimization

  • Gauss-Newton algorithm
  • Gradient descent
  • Newton method
  • Levenberg-Marquardt algorithm
  • Conjugate gradient method

• Statistics

  • Probability distribution
    • Bernoulli
    • Beta
    • Binomial
    • Exponential
    • Gamma
    • Chi-squared
    • Normal
    • Log-Normal
    • Poisson
    • Raised cosine
    • Student-t
    • Uniform
  • Test
    • Chi-squared
    • G
    • Student-t

• Elementary functions

  • trigonometric functions
  • hyperbolic functions
  • exponential functions
  • power functions
  • trigonometric functions

• Special functions

  • gamma functions
    • gamma function
    • log-gamma function
    • digamma function
    • upper incomplete gamma function
    • upper incomplete regularized gamma function
    • inverse upper incomplete regularized gamma function
    • lower incomplete gamma function
    • lower regularized incomplete gamma function
    • inverse lower regularized incomplete gamma function
  • beta functions
    • beta function
    • incomplete beta function
    • incomplete regularized beta function
  • error functions
    • error function
    • complementary error function
    • inverse error function
    • inverse complementary error function
  • hypergeometric functions

Usage

Add this to your Cargo.toml for the native Rust implementation:

[dependencies.mathru]
version = "0.15"

Add the following lines to 'Cargo.toml' if the openblas library should be used:

[dependencies.mathru]
version = "0.15"
default-features = false
features = "openblas"

One of the following implementations for linear algebra can be activated as a feature:

• native: Native Rust implementation(activated by default)
• openblas: Optimized BLAS library
• netlib: Collection of mathematical software, papers, and databases
• intel-mkl: Intel Math Kernel Library
• accelerate Make large-scale mathematical computations and image calculations, optimized for high performance and low-energy consumption.(macOS only)

Solve a system of linear equations

use mathru::{
    algebra::linear::{
        matrix::{LUDec, Solve},
        General, Vector,
    },
    matrix, vector,
};

/// Solves a system of linear equations
fn main()
{
    let a: General<f64> = matrix![6.0, 2.0, -1.0;
                                -3.0, 5.0, 3.0; 
                                -2.0, 1.0, 3.0];
                                
    let b: Vector<f64> = vector![48.0; 
                                49.0; 
                                24.0];

    // Decompose a into a lower and upper matrix
    let lu_dec: LUDec<f64> = a.dec_lu().unwrap();

    // Solve the system of linear equations with the decomposed matrix
    let _x1: Vector<f64> = lu_dec.solve(&b).unwrap();

    // Solve it directly
    let _x2: Vector<f64> = a.solve(&b).unwrap();
}

Solve ordinary differential equation with the Dormand-Prince algorithm

use mathru::{
    algebra::linear::vector::Vector,
    analysis::differential_equation::ordinary::{problem, DormandPrince54, ExplicitODE},
};

fn main()
{
    // Create an ODE instance
    let problem: problem::Euler<f64> = problem::Euler::default();

    let (x_start, x_end) = problem.time_span();

    // Create a ODE solver instance
    let h_0: f64 = 0.0001;
    let n_max: u32 = 800;
    let abs_tol: f64 = 10e-7;

    let solver: DormandPrince54<f64> = DormandPrince54::new(abs_tol, h_0, n_max);

    // Solve ODE
    let (x, y): (Vec<f64>, Vec<Vector<f64>>) = solver.solve(&problem).unwrap();
}

Further examples

For further examples, see project page

Documentation

See project page for more information and examples. The API is documented on docs.rs.

License

Licensed under

• MIT license (LICENSE-MIT or http://opensource.org/licenses/MIT)

Contribution

Any contribution is welcome!