Peroxide

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)
• oxidize - No pain, no gain - 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.

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 openblas & plot 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,

```rust 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
• 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
  • Probability Distributions
    • Bernoulli
    • Uniform
    • Normal
    • Gamma
    • Beta
  • RNG algorithms
    • Acceptance Rejection
    • Marsaglia Polar
    • Ziggurat
• Special functions
  • Wrapper for special crate
• Utils
  • R-like macro & functions
  • Matlab-like macro & functions
  • Numpy-like macro & functions
  • Julia-like macro & functions
• Plotting
  • With pyo3 & matplotlib

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 0.15.3

Pre-requisite

• oxidize feature - Need OpenBLAS
• plot feature - Need matplotlib of python

Install

• Add next block to your cargo.toml

1. Default toml [dependencies] peroxide = "0.15"
2. OpenBLAS + SIMD toml [dependencies.peroxide] version = "0.15" default-features = false features = ["oxidize"]
3. Plot toml [dependencies.peroxide] version = "0.15" default-features = false features = ["plot"]
4. OpenBLAS + SIMD & Plot toml [dependencies.peroxide] version = "0.15" default-features = false features = ["oxidize", "plot"]

Module Structure

• src
  • lib.rs : mod and re-export
  • macros : Macro files
  • juliamacro.rs : Julia like macro
  • matlabmacro.rs : MATLAB like macro
  • mod.rs
  • rmacro.rs : R like macro
  • ml : For machine learning (Beta)
    • mod.rs
    • reg.rs : Regression tools
  • numerical : To do numerical things
  • bdf.rs : Backward Differentiation Formula
  • gausslegendre.rs : Gauss-Legendre 4th order
  • interp.rs : Interpolation
  • mod.rs
  • newton.rs : Newton's Method
  • ode.rs : Main ODE solver
  • optimize.rs : Non-linear regression
  • spline.rs : Natural Spline
  • utils.rs : Utils to do numerical things (e.g. jacobian)
  • operation : To define general operations
  • extraops.rs : Missing operations & Real Trait
  • mutops.rs : Mutable operations
  • mod.rs
  • number.rs : Number type (include f64, Dual)
  • special : Wrapper for special crate
  • mod.rs
  • function.rs : Special functions
  • statistics : Statistical Tools
  • mod.rs
  • dist.rs : Probability distributions
  • ops.rs : Some probabilistic operations
  • rand.rs : Wrapper for rand crate
  • stat.rs : Statistical tools
  • structure : Fundamental data structures
  • dataframe.rs : Not yet implemented
  • dual.rs : Dual number system for automatic differentiation
  • hyperdual.rs : Hyper dual number system for automatic differentiation
  • matrix.rs : Matrix
  • multinomial.rs : For multinomial (Beta)
  • mod.rs
  • polynomial.rs : Polynomial
  • vector.rs : Extra tools for Vec<f64>
  • util
  • mod.rs
  • api.rs : Matrix constructor for various language style
  • nonmacro.rs : Primordial version of macros
  • pickle.rs : To handle pickle data structure
  • plot.rs : To draw plot (using pyo3)
  • print.rs : To print conveniently
  • useful.rs : Useful utils to implement library
  • writer.rs : More convenient write system

Documentation

Example

Basic Runge-Kutta 4th order with inline-python

```rust

![feature(procmacrohygiene)]

extern crate peroxide; extern crate inlinepython; use peroxide::*; use inlinepython::python;

fn main() { // Initial condition let init_state = State::::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 pylab as plt
    plt.plot('x, 'y)
    plt.show()
}

}

// dy/dx = (5x^2 - y) / e^(x+y) fn test_fn(st: &mut State) { 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

```rust extern crate peroxide; use peroxide::*;

fn main() { let init_state = State::::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");

plt.savefig();

}

fn test_fn(st: &mut State) { 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

```rust extern crate peroxide; use peroxide::*;

fn main() { let init_state = State::::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) { 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 } ```

Multi-Layer Perceptron (from scratch)

```rust 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 = weightsinit(3, 2); let w = weightsinit(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, inputbias: Matrix) -> Matrix { let s = inputbias * 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)

```rust extern crate peroxide; use peroxide::*;

fn main() { let noise = Normal(0., 0.5); let ptrue: Vec = NumberVector::fromf64vec(vec![20f64, 10f64, 1f64, 50f64]); let pinit = vec![5f64, 2f64, 0.2f64, 10f64]; let domain = seq(0, 99, 1); let real = f(&domain, ptrue.clone()).tof64vec(); let y = zipwith(|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();

}

fn f(domain: &Vec, p: Vec) -> Vec { domain.clone().intoiter() .map(|t| Number::fromf64(t)) .map(|t| p[0] * (-t / p[1]).exp() + p[2] * t * (-t / p[3]).exp()) .collect() } ```

Version Info

To see RELEASES.md

TODO

To see TODO.md