Peroxide

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

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
    • Hello, Peroxide
    • 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
  • Transpose, Determinant, Diagonal
  • LU Decomposition, Inverse matrix, Block partitioning
  • QR Decomposition (O3 feature)
  • Singular Value Decomposition (SVD) (O3 feature)
  • Cholesky Decomposition (O3 feature)
  • Reduced Row Echelon form
  • Column, Row operations
  • Eigenvalue, Eigenvector
• Functional Programming
  • Easier 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
  • Const-generic Jet<N> type for arbitrary-order forward AD
  • Type aliases: Dual (1st order), HyperDual (2nd order)
  • Normalized Taylor coefficients (no binomial overhead)
  • #[ad_function] proc macro for automatic gradient/hessian generation
  • Exact Jacobian via jacobian() function
  • Real trait to constrain for f64 and Jet<N>
• Numerical Analysis
  • Lagrange interpolation
  • Splines
    • Cubic Spline
    • Cubic Hermite Spline
      • Estimate slope via Akima
      • Estimate slope via Quadratic interpolation
    • B-Spline
  • Non-linear regression
    • Gradient Descent
    • Levenberg Marquardt
  • Ordinary Differential Equation (trait-based since v0.36.0)
    • Explicit: Ralston 3rd / Runge-Kutta 4th / Ralston 4th / Runge-Kutta 5th
    • Embedded: Bogacki-Shampine 3(2) / Runge-Kutta-Fehlberg 5(4) / Dormand-Prince 5(4) / Tsitouras 5(4) / Runge-Kutta-Fehlberg 8(7)
    • Implicit: Gauss-Legendre 4th order
  • Numerical Integration
    • Newton-Cotes Quadrature
    • Gauss-Legendre Quadrature (up to 30 order)
    • Gauss-Kronrod Quadrature, adaptive: G7K15 / G10K21 / G15K31 / G20K41 / G25K51 / G30K61
    • Gauss-Kronrod Quadrature, relative tolerance: G7K15R / G10K21R / G15K31R / G20K41R / G25K51R / G30K61R
  • Root Finding (trait-based since v0.37.0): Bisection / False Position / Secant / Newton / Broyden
• Statistics
  • More easy random with rand crate
  • Ordered Statistics
    • Median
    • Quantile (Matched with R quantile)
  • Probability Distributions
    • Bernoulli
    • Uniform
    • Binomial
    • Normal
    • Gamma
    • Beta
    • Student's-t
    • Weighted Uniform
    • LogNormal
  • RNG algorithms
    • Acceptance Rejection
    • Marsaglia Polar
    • Ziggurat
    • Wrapper for rand-dist crate
    • Piecewise Rejection Sampling
  • Confusion Matrix & Metrics
• Special functions
  • Wrapper for puruspe 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
  • Support various types simultaneously
  • Read & Write csv files (csv feature)
  • Read & Write netcdf files (nc feature)
  • Read & Write parquet files (parquet feature)
  • Shape & info: nrow, ncol, shape, dtypes, is_empty, contains
  • Row operations: head, tail, slice
  • Column operations: select, rename, column_names, select_dtypes
  • Series statistics: sum, mean, var, sd, min, max
  • DataFrame statistics: describe, sum, 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.

Convenience flag	Backend	Typical platform / use case
O3-openblas	OpenBLAS	Linux, Windows, macOS via Homebrew
O3-accelerate	Apple Accelerate	macOS (no extra system install)
O3-mkl	Intel MKL	Intel CPUs, vendor-tuned performance
O3-netlib	Netlib reference	Portability, lowest performance

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:

Platform	Install
Debian / Ubuntu	sudo apt install libopenblas-dev liblapack-dev
Fedora / RHEL	sudo dnf install openblas-devel lapack-devel
Arch Linux	sudo pacman -S openblas lapack
macOS (Homebrew)	brew install openblas lapack

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

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.

Step	Command
Install Python 3 + dev headers (Debian)	sudo apt install python3 python3-dev
Install Python 3 + dev headers (Fedora)	sudo dnf install python3 python3-devel
Install matplotlib	pip install matplotlib
(Optional) Publication-quality styles	pip install scienceplots

If you use a virtual environment, activate it before building so that pyo3 resolves to the intended interpreter (e.g. source .venv/bin/activate). The plain pyo3 flag enables the Python interop layer without pulling in the Plot2D API.

nc / netcdf: HDF5 + netCDF-C

nc (alias netcdf) enables NetCDF I/O for DataFrame via the netcdf crate, which links against the system HDF5 and netCDF-C libraries.

Platform	Install
Debian / Ubuntu	sudo apt install libnetcdf-dev libhdf5-dev
Fedora / RHEL	sudo dnf install netcdf-devel hdf5-devel
Arch Linux	sudo pacman -S netcdf hdf5
macOS (Homebrew)	brew install netcdf hdf5

Note: Peroxide currently pins netcdf = "0.7", which transitively uses hdf5-sys 0.8.x. That hdf5-sys only recognizes the HDF5 1.x version string and rejects HDF5 2.x with Invalid H5_VERSION. If your distribution ships HDF5 2.x (e.g. recent rolling-release Linux), install an HDF5 1.14.x package alongside (Debian/Ubuntu LTS releases still default to 1.10/1.14) or wait for the planned bump to netcdf 0.12. The nc build will succeed against any HDF5 1.x.

Install

Peroxide builds on stable Rust 1.91 or later. The default profile is pure Rust; system libraries are only needed for the features listed in the Pre-requisite section.

cargo add peroxide                              # default (pure Rust)
cargo add peroxide --features "<FEATURES>"      # opt-in features

Most common combinations

Goal	Command
Linear algebra on Linux / Windows	cargo add peroxide --features O3-openblas
Linear algebra on macOS	cargo add peroxide --features O3-accelerate
Plotting via Python / matplotlib	cargo add peroxide --features plot
DataFrame + Parquet I/O	cargo add peroxide --features parquet
Full Linux scientific stack	cargo add peroxide --features "O3-openblas plot nc csv parquet serde"
Full macOS scientific stack	cargo add peroxide --features "O3-accelerate plot nc csv parquet serde"

Hello, Peroxide

#[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();
    a.inv().print();
}

Available features

Most users only need the composite flags in the first table. The remaining single-crate flags exist so advanced users can pull in just one optional dependency without enabling the rest.

Composite flags (recommended)

Flag	Requires	Purpose
O3-openblas	OpenBLAS	BLAS / LAPACK accelerated linear algebra (Linux / Windows)
O3-accelerate	Apple Accelerate	Same, using the Accelerate framework on macOS
O3-mkl	Intel MKL	Same, using Intel MKL
O3-netlib	Netlib	Same, using the reference Netlib BLAS
plot	Python 3 + matplotlib	High-level Plot2D API
nc	HDF5 + netCDF-C	NetCDF I/O for DataFrame
parquet	(pure Rust)	Parquet I/O for DataFrame (pulls in arrow, indexmap)
complex	(pure Rust)	Complex vectors / matrices + cgemm matmul
parallel	(pure Rust)	Parallel iterators on vectors / matrices
csv	(pure Rust)	CSV I/O for DataFrame
json	(pure Rust)	JSON I/O for DataFrame
serde	(pure Rust)	serde (de)serialization
rkyv	(pure Rust)	rkyv zero-copy (de)serialization

Advanced: single-crate flags

These flags enable one optional dependency in isolation. Use them only if you want to depend on the underlying crate without the surrounding Peroxide API.

Flag	Underlying crate	Notes
O3	blas, lapack	Bare BLAS / LAPACK FFI; bring your own blas-src / lapack-src
blas	blas	Raw BLAS bindings only
lapack	lapack	Raw LAPACK bindings only
pyo3	pyo3	Python 3 interop without the Plot2D API
netcdf	netcdf	Alias for nc
num-complex	num-complex	Raw complex-number dependency only
rayon	rayon	Raw rayon dependency only
arrow	arrow	Raw arrow dependency only
indexmap	indexmap	Raw indexmap dependency only

Examples

Runnable programs covering every component live in examples/, with longer worked notebooks in the companion Peroxide_Gallery repository. API reference and feature-specific guidance are published on docs.rs/peroxide.

Release notes

See RELEASES.md.

Contributing

See CONTRIBUTING.md.

License

Peroxide is licensed under dual licenses: Apache License 2.0 and MIT License.

Cite Peroxide

Hey there! If you're using Peroxide in your research or project, you're not required to cite us. But if you do, we'd be really grateful! 😊

To make citing Peroxide easy, we've created a DOI through Zenodo. Just click on this badge:

This will take you to the Zenodo page for Peroxide. At the bottom, you'll find the citation information in various formats like BibTeX, RIS, and APA.

So, if you want to acknowledge the work we've put into Peroxide, citing us would be a great way to do it! Thanks for considering it, we appreciate your support! 👍