#Numeric #Science #Plot #Dataframe #LinearAlgebra

peroxide

Rust comprehensive scientific computation library contains linear algebra, numerical analysis, statistics and machine learning tools with farmiliar syntax

134 releases (20 breaking)

new 0.21.5 Apr 1, 2020
0.21.4 Mar 21, 2020
0.21.0 Feb 29, 2020
0.19.3 Dec 21, 2019
0.6.6 Nov 29, 2018

#5 in Science

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BSD-3-Clause

415KB
9K SLoC

Peroxide

On crates.io On docs.rs

builds.sr.ht status travis github

maintenance

Rust numeric library contains linear algebra, numerical analysis, statistics and machine learning tools with R, MATLAB, Python like macros.

Why Peroxide?

1. Customize features

Peroxide provides various features.

  • default - Pure Rust (No dependencies of architecture - Perfect cross compilation)
  • O3 - SIMD + OpenBLAS (Perfect performance but hard to set-up - Strongly recommend to read OpenBLAS for Rust)
  • plot - With matplotlib of python, we can draw any plots.
  • dataframe - Dataframe & netcdf
  • serde - serialization with Serde.

If you want to do high performance computation, then choose openblas feature. If you don't want to depend C/C++ or Fortran libraries, then choose default feature. If you want to draw plot with some great templates, then choose plot feature.

You can choose any features simultaneously.

2. Easy to optimize

Peroxide uses 1D data structure to describe matrix. So, it's too easy to integrate BLAS & SIMD. It means peroxide guarantees perfect performance for linear algebraic computations.

3. Friendly syntax

Rust is so strange for Numpy, MATLAB, R users. Thus, it's harder to learn the more rusty libraries. With peroxide, you can do heavy computations with R, Numpy, MATLAB like syntax.

For example,

extern crate peroxide;
use peroxide::*;

fn main() {
    // MATLAB like matrix constructor
    let a = ml_matrix("1 2;3 4");

    // R like matrix constructor (default)
    let b = matrix(c!(1,2,3,4), 2, 2, Row);

    // Or use zeros
    let mut z = zeros(2, 2);
    z[(0,0)] = 1.0;
    z[(0,1)] = 2.0;
    z[(1,0)] = 3.0;
    z[(1,1)] = 4.0;
    
    // Simple but effective operations
    let c = a * b; // Matrix multiplication (BLAS integrated)

    // Easy to pretty print
    c.print();
    //       c[0] c[1]
    // r[0]     1    3
    // r[1]     2    4

    // Easy to do linear algebra
    c.det().print();
    c.inv().unwrap().print();

    // and etc.
}

4. Batteries included

Peroxide can do many things.

  • Linear Algebra
    • Effective Matrix structure
    • Transpose, Determinant, Diagonal
    • LU Decomposition, Inverse matrix, Block partitioning
    • Column, Row operations
    • Eigenvalue, Eigenvector
  • Functional Programming
    • More easy functional programming with Vec<f64>
    • For matrix, there are three maps
      • fmap : map for all elements
      • col_map : map for column vectors
      • row_map : map for row vectors
  • Automatic Differentiation
    • Dual number system - for 1st order AD
    • Hyper dual number system - for 2nd order AD
    • Exact jacobian
    • Real trait to constrain for f64 and Dual
    • Number structure to unify f64 and Dual
  • Numerical Analysis
    • Lagrange interpolation
    • Cubic spline
    • Non-linear regression
      • Gradient Descent
      • Gauss Newton
      • Levenberg Marquardt
    • Ordinary Differential Equation
      • Euler
      • Runge Kutta 4th order
      • Backward Euler
      • Gauss Legendre 4th order
    • Numerical Integration
      • Gauss-Legendre Quadrature
  • Statistics
    • More easy random with rand crate
    • Ordered Statistics
      • Median
      • Quantile (Matched with R quantile)
    • Probability Distributions
      • Bernoulli
      • Uniform
      • Normal
      • Gamma
      • Beta
      • Student's-t
    • RNG algorithms
      • Acceptance Rejection
      • Marsaglia Polar
      • Ziggurat
      • Wrapper for rand-dist crate
  • Special functions
    • Wrapper for pururspe crate (pure rust)
  • Utils
    • R-like macro & functions
    • Matlab-like macro & functions
    • Numpy-like macro & functions
    • Julia-like macro & functions
  • Plotting
    • With pyo3 & matplotlib
  • DataFrame
    • Convert with Matrix
    • Read & Write csv files
    • Read & Write netcdf files

5. Written in Rust

Rust & Cargo are awesome for scientific computations. You can use any external packages easily with Cargo, not make. And default runtime performance of Rust is also great. If you use many iterations for computations, then Rust become great choice.

Latest README version

Corresponding to 0.21.4

Pre-requisite

  • For O3 feature - Need OpenBLAS
  • For plot feature - Need matplotlib of python
  • For dataframe feature - Need netcdf

Install

  • Add next block to your cargo.toml
  1. Default
    [dependencies]
    peroxide = "0.21"
    
  2. OpenBLAS + SIMD
    [dependencies.peroxide]
    version = "0.21"
    default-features = false
    features = ["O3"] 
    
  3. Plot
    [dependencies.peroxide]
    version = "0.21"
    default-features = false
    features = ["plot"] 
    
  4. DataFrame
    [dependencies.peroxide]
    version = "0.21"
    default-features = false
    features = ["dataframe"]
    
  5. OpenBLAS + SIMD & Plot & DataFrame
    [dependencies.peroxide]
    version = "0.21"
    default-features = false
    features = ["O3", "plot", "dataframe"] 
    

Useful tips for features

  • After 0.21.4, if size of matrix is smaller than 1000 x 1000, default is more effective than O3 feature.
  • To plot, use dataframe to export data as netcdf format and use python to draw plot.
    • plot feature has limited plot abilities.
    • There is a template of python code. - Socialst

Module Structure

Documentation

  • On docs.rs

Example

Peroxide Gallery

Basic Runge-Kutta 4th order with inline-python

#![feature(proc_macro_hygiene)]
extern crate peroxide;
extern crate inline_python;
use peroxide::*;
use inline_python::python;

fn main() {
    // Initial condition
    let init_state = State::<f64>::new(0f64, c!(1), c!(0));

    let mut ode_solver = ExplicitODE::new(test_fn);

    ode_solver
        .set_method(ExMethod::RK4)
        .set_initial_condition(init_state)
        .set_step_size(0.01)
        .set_times(1000);

    let result = ode_solver.integrate();

    let x = result.col(0);
    let y = result.col(1);

    // Plot (Thanks to inline-python)
    python! {
        import matplotlib.pyplot as plt
        plt.plot('x, 'y)
        plt.show()
    }
}

// dy/dx = (5x^2 - y) / e^(x+y)
fn test_fn(st: &mut State<f64>) {
    let x = st.param;
    let y = &st.value;
    let dy = &mut st.deriv;
    dy[0] = (5f64 * x.powi(2) - y[0]) / (x + y[0]).exp();
}

Basic Runge-Kutta 4th order with advanced plotting

extern crate peroxide;
use peroxide::*;

fn main() {
    let init_state = State::<f64>::new(0f64, c!(1), c!(0));

    let mut ode_solver = ExplicitODE::new(test_fn);

    ode_solver
        .set_method(ExMethod::RK4)
        .set_initial_condition(init_state)
        .set_step_size(0.01)
        .set_times(1000);

    let result = ode_solver.integrate();

    let x = result.col(0);
    let y = result.col(1);

    // Plot (using python matplotlib)
    let mut plt = Plot2D::new();
    plt.set_domain(x)
        .insert_image(y)
        .set_title("Test Figure")
        .set_fig_size((10, 6))
        .set_dpi(300)
        .set_legend(vec!["RK4"])
        .set_path("example_data/test_plot.png");

    // Remove below comments to activate
    //plt.savefig();
}

fn test_fn(st: &mut State<f64>) {
    let x = st.param;
    let y = &st.value;
    let dy = &mut st.deriv;
    dy[0] = (5f64 * x.powi(2) - y[0]) / (x + y[0]).exp();
}

Basic Runge-Kutta 4th order with exporting netcdf (Recommended)

extern crate peroxide;
use peroxide::*;

fn main() {
    let init_state = State::<f64>::new(0f64, c!(1), c!(0));

    let mut ode_solver = ExplicitODE::new(test_fn);

    ode_solver
        .set_method(ExMethod::RK4)
        .set_initial_condition(init_state)
        .set_step_size(0.01)
        .set_times(1000);

    let result = ode_solver.integrate();

    let x = result.col(0);
    let y = result.col(1);

    // Construct DataFrame
    let mut df = DataFrame::with_headers(vec!["x", "y"]);
    df["x"] = x;
    df["y"] = y;

    // Write netcdf (Remove below comment)
    //df.write_nc("example_data/rk4_test.nc").expect("Can't write nc files");
}

fn test_fn(st: &mut State<f64>) {
    let x = st.param;
    let y = &st.value;
    let dy = &mut st.deriv;
    dy[0] = (5f64 * x.powi(2) - y[0]) / (x + y[0]).exp();
}

Basic Runge-Kutta 4th order with Stop condition

extern crate peroxide;
use peroxide::*;

fn main() {
    let init_state = State::<f64>::new(0f64, c!(1), c!(0));

    let mut ode_solver = ExplicitODE::new(test_fn);

    ode_solver
        .set_method(ExMethod::RK4)
        .set_initial_condition(init_state)
        .set_step_size(0.01)
        .set_stop_condition(stop)        // Add stop condition
        .set_times(1000);

    let result = ode_solver.integrate();

    let x = result.col(0);
    let y = result.col(1);

    let mut plt = Plot2D::new();
    plt.set_domain(x)
        .insert_image(y)
        .set_title("Test Figure")
        .set_fig_size((10, 6))
        .set_dpi(300)
        .set_legend(vec!["RK4"])
        .set_path("example_data/test_plot.png");

    plt.savefig();
}

fn test_fn(st: &mut State<f64>) {
    let x = st.param;
    let y = &st.value;
    let dy = &mut st.deriv;
    dy[0] = (5f64 * x.powi(2) - y[0]) / (x + y[0]).exp();
}

fn stop(st: &ExplicitODE) -> bool {
    let y = &st.get_state().value[0];
    (*y - 2.4).abs() < 0.01
}

Example image

Multi-Layer Perceptron (from scratch)

extern crate peroxide;
use peroxide::*;

// x : n x L
// xb: n x (L+1)
// v : (L+1) x M
// a : n x M
// ab: n x (M+1)
// w : (M+1) x n
// wb: M x N
// y : n x N
// t : n x N
// dh: n x M
// do: n x N

fn main() {
    let v = weights_init(3, 2);
    let w = weights_init(3, 1);

    let x = ml_matrix("0 0; 0 1; 1 0; 1 1");
    let t = ml_matrix("0;1;1;0");

    let y = train(v, w, x, t, 0.25, 5000);
    y.print();
}

fn weights_init(m: usize, n: usize) -> Matrix {
    rand(m, n) * 2f64 - 1f64
}

fn sigmoid(x: f64) -> f64 {
    1f64 / (1f64 + (-x).exp())
}

fn forward(weights: Matrix, input_bias: Matrix) -> Matrix {
    let s = input_bias * weights;
    s.fmap(|x| sigmoid(x))
}

fn add_bias(input: Matrix, bias: f64) -> Matrix {
    let b = matrix(vec![bias; input.row], input.row, 1, Col);
    cbind(b, input)
}

fn hide_bias(weight: Matrix) -> Matrix {
    weight.skip(1, Row)
}

fn train(
    weights1: Matrix,
    weights2: Matrix,
    input: Matrix,
    answer: Matrix,
    eta: f64,
    times: usize,
) -> Matrix {
    let x = input;
    let mut v = weights1;
    let mut w = weights2;
    let t = answer;
    let xb = add_bias(x.clone(), -1f64);

    for _i in 0..times {
        let a = forward(v.clone(), xb.clone());
        let ab = add_bias(a.clone(), -1f64);
        let y = forward(w.clone(), ab.clone());
        //        let err = (y.clone() - t.clone()).t() * (y.clone() - t.clone());
        let wb = hide_bias(w.clone());
        let delta_o = (y.clone() - t.clone()) * y.clone() * (1f64 - y.clone());
        let delta_h = (delta_o.clone() * wb.t()) * a.clone() * (1f64 - a.clone());

        w = w.clone() - eta * (ab.t() * delta_o);
        v = v.clone() - eta * (xb.t() * delta_h);
    }

    let a = forward(v, xb);
    let ab = add_bias(a, -1f64);
    let y = forward(w, ab);

    y
}

Levenberg-Marquardt Algorithm (refer to lm.pdf)

extern crate peroxide;
use peroxide::*;

fn main() {
    let noise = Normal(0., 0.5);
    let p_true: Vec<Number> = NumberVector::from_f64_vec(vec![20f64, 10f64, 1f64, 50f64]);
    let p_init = vec![5f64, 2f64, 0.2f64, 10f64];
    let domain = seq(0, 99, 1);
    let real = f(&domain, p_true.clone()).to_f64_vec();
    let y = zip_with(|x, y| x + y, &real, &noise.sample(100));
    let data = hstack!(domain.clone(), y.clone());

    let mut opt = Optimizer::new(data, f);
    let p = opt
        .set_init_param(p_init)
        .set_max_iter(100)
        .set_method(LevenbergMarquardt)
        .optimize();
    p.print();
    opt.get_error().print();

    let mut plt = Plot2D::new();
    plt.set_domain(domain)
        .insert_image(y)
        .insert_image(p)
        .set_legend(vec!["real", "fit"])
        .set_title("Levenberg-Marquardt Algorithm")
        .set_path("example_data/lm_test.png")
        .set_marker(vec![Point, Line])
        .savefig()
        .expect("Can't draw a plot");
}

fn f(domain: &Vec<f64>, p: Vec<Number>) -> Option<Vec<Number>> {
    Some(
        domain.clone().into_iter()
            .map(|t| Number::from_f64(t))
            .map(|t| p[0] * (-t / p[1]).exp() + p[2] * t * (-t / p[3]).exp())
            .collect()
    )
}

LM

Version Info

To see RELEASES.md

Contributes Guide

See CONTRIBUTES.md

TODO

To see TODO.md

Dependencies

~2.1–3.5MB
~60K SLoC