peroxide

Peroxide is a comprehensive numerical library including:

• Linear Algebra: Matrix structures, LU/QR/SVD/Cholesky decompositions, eigenvalues/vectors, and determinants.
• Automatic Differentiation: Forward AD using Jet<N> (aliases Dual, HyperDual) and the #[ad_function] macro.
• Numerical Analysis: Interpolation (Lagrange, Splines), Non-linear regression (Gradient Descent, Levenberg-Marquardt), ODE solvers (Explicit/Implicit), and Root finding.
• Statistics: Probability distributions, RNG algorithms, and ordered statistics.
• DataFrame: Mixed-type columns with support for CSV, NetCDF, and Parquet I/O.
• Functional Programming: Matrix mapping via fmap, col_map, and row_map.

Peroxide is an integrated numerical computing library that covers eight primary domains in a single crate:

• Linear Algebra: Matrix operations and storage.
• ODE Solvers: Ordinary Differential Equation integration (including fixed-step, adaptive pairs, and implicit methods).
• Adaptive Quadrature: Numerical integration.
• Spline Interpolation: Cubic, cubic Hermite, and B-spline interpolation with exact polynomial calculus.
• Root-finding: Solving for roots in univariate and multivariate systems.
• Automatic Differentiation (AD): High-order forward-mode AD using Taylor-mode propagation.
• Statistics: Probability distributions with sample, pdf, and cdf methods.
• DataFrame I/O: Multi-format support for CSV, NetCDF, and Parquet.

The peroxide-num crate provides a set of traits for mathematical computations, enabling generic programming for numeric types. It covers basic arithmetic, powers, trigonometry, and exponential/logarithmic functions.

Key traits include:

• PowOps: Operations for powers and roots (e.g., powi, powf, pow, sqrt).
• TrigOps: Trigonometric functions (e.g., sin, cos).
• ExpLogOps: Exponential and logarithmic functions.
• Float: A trait to define custom floating-point types (standard f32 and f64 are provided by default).
• Numeric: A comprehensive trait that aggregates all the above traits along with standard arithmetic operations (Add, Sub, Mul, Div, Neg).

Peroxide provides cubic, cubic Hermite, and B-spline interpolation. Unlike many other libraries, it supports exact symbolic calculus on these splines:

• PolynomialSpline trait: Exposes the polynomial_at(x) method, which returns the specific Polynomial governing a given interval.
• Calculus trait: Enables symbolic operations on splines. You can call .derivative() to return a new spline representing the analytic derivative, or .integrate((a, b)) to evaluate the exact definite integral via antidifferentiation rather than finite differencing.

Peroxide implements high-order forward-mode automatic differentiation using the Jet<N> type.

• Jet<N>: A const generic type that stores a function value $c_0 = f(a)$ and $N$ normalized Taylor coefficients $c_k = f^{(k)}(a)/k!$.
• Efficiency: By storing pre-divided coefficients, Peroxide achieves $O(N^2)$ Taylor-mode propagation and avoids factorial overflow at higher orders.
• #[ad_function] macro: Provided by the peroxide-ad crate, this procedural macro transforms a standard function fn(f64) -> f64 into versions that accept Jet<N>, automatically generating first- and second-derivative functions.
• Real trait: This trait abstracts over f64 and AD (e.g., Jet<2>), allowing the same function code to compute both values and derivatives seamlessly.

Peroxide provides R and MATLAB-style macros for easy matrix construction and arithmetic. Use #[macro_use] extern crate peroxide; to enable these macros.

Key functions:

• ml_matrix("..."): Creates a matrix from a string literal (MATLAB/R style).
• c!(...): Creates a vector or matrix from a list of elements.
• .print(): Pretty-prints the matrix or vector to the console.
• .det(): Calculates the determinant.
• .inv(): Calculates the inverse.

#! [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
    let c = &a * &b;

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

If you use Peroxide in your research or projects, you can cite the project using its DOI via Zenodo. Citation information is available in BibTeX, RIS, and APA formats on the Zenodo page.

https://doi.org/10.5281/zenodo.10815823