Peroxide

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

Quickstart

cargo add peroxide   # default profile is pure Rust, no system libraries needed

#[macro_use]
extern crate peroxide;
use peroxide::fuga::*;

fn main() {
    // R / MATLAB-style matrix literals
    let a = ml_matrix("1 2; 3 4");
    let b = c!(5, 6);

    // matrix-vector product (BLAS-dispatched when an `O3-*` feature is on)
    let c = &a * &b;

    a.print(); // pretty-formatted matrix
    c.print(); // [17, 39]
    a.det().print(); // -2
    a.inv().print();
}

For accelerated linear algebra, plotting, or DataFrame I/O, enable the matching feature flag (see Install and Available features).

Table of Contents

• Peroxide
• Table of Contents
• Why Peroxide?
  • 1. Customize features
  • 2. Easy to optimize
  • 3. Friendly syntax
  • 4. Can choose two different coding styles.
  • 5. Batteries included
  • 6. Compatible with Mathematics
  • 7. Written in Rust
• Pre-requisite
• Install
  • Most common combinations
  • Available features
• Examples
• Release notes
• Contributing
• License
• Cite Peroxide

Why Peroxide?

1. Customize features

Peroxide provides various features.

• default - Pure Rust (No dependencies of architecture - Perfect cross compilation)
• O3 - BLAS & LAPACK (Perfect performance but little bit hard to set-up - Strongly recommend to look Peroxide with BLAS)
• plot - With matplotlib of python, we can draw any plots.
• complex - With complex numbers (vector, matrix and integral)
• parallel - With some parallel functions
• nc - To handle netcdf file format with DataFrame
• csv - To handle csv file format with Matrix or DataFrame
• parquet - To handle parquet file format with DataFrame
• serde - serialization with Serde.
• rkyv - serialization with rkyv.

If you want to do high performance computation and more linear algebra, then choose O3 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 a 1D data structure to represent matrices, making it straightforward to integrate with BLAS (Basic Linear Algebra Subprograms). This means that Peroxide can guarantee excellent performance for linear algebraic computations by leveraging the optimized routines provided by BLAS.

3. Friendly syntax

For users familiar with numerical computing libraries like NumPy, MATLAB, or R, Rust's syntax might seem unfamiliar at first. This can make it more challenging to learn and use Rust libraries that heavily rely on Rust's unique features and syntax.

However, Peroxide aims to bridge this gap by providing a syntax that resembles the style of popular numerical computing environments. With Peroxide, you can perform complex computations using a syntax similar to that of R, NumPy, or MATLAB, making it easier for users from these backgrounds to adapt to Rust and take advantage of its performance benefits.

For example,

#[macro_use]
extern crate peroxide;
use peroxide::prelude::*;

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().print();

    // and etc.
}

4. Can choose two different coding styles.

In peroxide, there are two different options.

• prelude: To simple use.
• fuga: To choose numerical algorithms explicitly.

For examples, let's see norm.

In prelude, use norm is simple: a.norm(). But it only uses L2 norm for Vec<f64>. (For Matrix, Frobenius norm.)

#[macro_use]
extern crate peroxide;
use peroxide::prelude::*;

fn main() {
    let a = c!(1, 2, 3);
    let l2 = a.norm();      // L2 is default vector norm

    assert_eq!(l2, 14f64.sqrt());
}

In fuga, use various norms. But you should write a little bit longer than prelude.

#[macro_use]
extern crate peroxide;
use peroxide::fuga::*;

fn main() {
    let a = c!(1, 2, 3);
    let l1 = a.norm(Norm::L1);
    let l2 = a.norm(Norm::L2);
    let l_inf = a.norm(Norm::LInf);
    assert_eq!(l1, 6f64);
    assert_eq!(l2, 14f64.sqrt());
    assert_eq!(l_inf, 3f64);
}

5. Batteries included

Peroxide can do many things.

• Linear Algebra: effective Matrix structure, LU / QR / SVD / Cholesky decompositions (O3 feature for the last three), determinant, inverse, block partitioning, reduced row echelon form, eigenvalue & eigenvector
• Functional Programming: easier functional programming with Vec<f64>; matrix maps (fmap, col_map, row_map)
• Automatic Differentiation: const-generic Jet<N> for arbitrary-order forward AD (Dual, HyperDual aliases), #[ad_function] proc macro, exact Jacobian via jacobian(), Real trait over f64 and Jet<N>
• Numerical Analysis
• Interpolation & splines: Lagrange interpolation, Cubic / Cubic Hermite (Akima, quadratic slope estimation) / B-Spline
• Non-linear regression: Gradient Descent, Levenberg-Marquardt
• ODE (trait-based since v0.36.0): explicit (Ralston 3rd & 4th, Runge-Kutta 4th & 5th), embedded (Bogacki-Shampine 3(2), Runge-Kutta-Fehlberg 5(4) & 8(7), Dormand-Prince 5(4), Tsitouras 5(4)), implicit (Gauss-Legendre 4th)
• Numerical integration: Newton-Cotes, Gauss-Legendre (up to 30th order), adaptive Gauss-Kronrod (G7K15 through G30K61, absolute & relative tolerance variants)
• Root finding (trait-based since v0.37.0): Bisection, False Position, Secant, Newton, Broyden
• Statistics: probability distributions (Bernoulli, Uniform, Binomial, Normal, Gamma, Beta, Student's-t, LogNormal, Weighted Uniform), RNG algorithms (Acceptance-Rejection, Marsaglia Polar, Ziggurat, Piecewise Rejection Sampling), ordered statistics (median, R-compatible quantile), confusion matrix & metrics
• Special functions: wrapper of the pure-Rust puruspe crate
• Utils: R / MATLAB / NumPy / Julia style macros & functions
• Plotting: matplotlib-based Plot2D via pyo3 (plot feature)
• DataFrame: mixed-type columns; CSV / NetCDF / Parquet I/O (csv / nc / parquet features); shape & info, row / column operations, series & frame statistics (describe, mean, ...)

6. Compatible with Mathematics

After 0.23.0, peroxide is compatible with mathematical structures. Matrix, Vec<f64>, f64 are considered as inner product vector spaces. And Matrix, Vec<f64> are linear operators - Vec<f64> to Vec<f64> and Vec<f64> to f64. For future, peroxide will include more & more mathematical concepts. (But still practical.)

7. Written in Rust

Rust provides a strong type system, ownership concepts, borrowing rules, and other features that enable developers to write safe and efficient code. It also offers modern programming techniques like trait-based abstraction and convenient error handling. Peroxide is developed to take full advantage of these strengths of Rust.

The example code demonstrates how Peroxide can be used to simulate the Lorenz attractor and visualize the results. It showcases some of the powerful features provided by Rust, such as the ? operator for streamlined error handling and the ODEProblem trait for abstracting ODE problems.

use peroxide::fuga::*;

fn main() -> Result<(), Box<dyn Error>> {
    let initial_conditions = vec![10f64, 1f64, 1f64];
    let rkf45 = RKF45::new(1e-4, 0.9, 1e-6, 1e-2, 100);
    let basic_ode_solver = BasicODESolver::new(rkf45);
    let (_, y_vec) = basic_ode_solver.solve(
        &Lorenz,
        (0f64, 100f64),
        1e-2,
        &initial_conditions,
    )?; // Error handling with `?` - can check constraint violation and etc.
    let y_mat = py_matrix(y_vec);
    let y0 = y_mat.col(0);
    let y2 = y_mat.col(2);

    // Simple but effective plotting
    let mut plt = Plot2D::new();
    plt
        .set_domain(y0)
        .insert_image(y2)
        .set_xlabel(r"$y_0$")
        .set_ylabel(r"$y_2$")
        .set_style(PlotStyle::Nature)
        .tight_layout()
        .set_dpi(600)
        .set_path("example_data/lorenz_rkf45.png")
        .savefig()?;

    Ok(())
}

struct Lorenz;

impl ODEProblem for Lorenz {
    fn rhs(&self, t: f64, y: &[f64], dy: &mut [f64]) -> anyhow::Result<()> {
        dy[0] = 10f64 * (y[1] - y[0]);
        dy[1] = 28f64 * y[0] - y[1] - y[0] * y[2];
        dy[2] = -8f64 / 3f64 * y[2] + y[0] * y[1];
        Ok(())
    }
}

Running the code produces the following visualization of the Lorenz attractor:

Peroxide strives to leverage the benefits of the Rust language while providing a user-friendly interface for numerical computing and scientific simulations.

Pre-requisite

Most features are pure Rust and require no system setup. The three groups below depend on external libraries or runtimes; install the relevant prerequisites before enabling the corresponding feature flag.

O3: BLAS + LAPACK

O3 enables hardware-accelerated linear algebra (LU, QR, SVD, Cholesky, GEMV/GEMM dispatch) through the blas and lapack FFI crates. Those crates only provide function signatures, so the link backend that supplies the actual dgemv_ / dpotrf_ / ... symbols must be selected separately. The simplest path is to enable one of the convenience flags below; each pulls in blas-src and lapack-src with the matching backend.

If you need a backend not in the list above (for example BLIS or R's BLAS), enable the bare O3 flag and add blas-src / lapack-src to your downstream binary's Cargo.toml with the appropriate features yourself.

System libraries still need to be present on the host for O3-openblas and O3-netlib; install them with:

O3-accelerate and O3-mkl ship their own backend (Apple's framework and Intel's redistributable, respectively), so they need no further system packages.

Note: O3-accelerate only builds on Apple targets. Enabling it on Linux or Windows fails while compiling accelerate-src with error: library kind `framework` is only supported on Apple targets; pick O3-openblas, O3-mkl, or O3-netlib instead. For the same reason, exclude O3-accelerate (and O3-mkl / O3-netlib unless their toolchains are installed) when running tools like cargo hack --each-feature on Linux.

plot / pyo3: Python 3 + matplotlib

plot enables the high-level Plot2D API, which renders figures by delegating to matplotlib through pyo3. Python 3 with development headers is required at build time, and matplotlib is required at runtime.

If you use a virtual environment, activate it before building so that pyo3 resolves to