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

• 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
  • Latest README version
  • Pre-requisite
  • Install
    • Basic Installation
    • Featured Installation
    • Available Features
    • Install Examples
  • Useful tips for features
  • Module Structure
  • Documentation
  • Examples
  • Release Info
  • Contributes Guide
  • LICENSE
  • TODO
  • Cite Peroxide

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 lookPeroxide 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 withSerde.
• rkyv - serialization withrkyv.

If you want to do high performance computation and more linear algebra, then chooseO3 feature.If you don't want to depend C/C++ or Fortran libraries, then choosedefault feature.If you want to draw plot with some great templates, then chooseplot feature.

You can choose any features simultaneously.

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.

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]externcrate peroxide;use peroxide::prelude::*;fnmain(){// MATLAB like matrix constructorlet 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 zerosletmut 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 operationslet 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.}

In peroxide, there are two different options.

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

For examples, let's see norm.

Inprelude, usenorm is simple:a.norm(). But it only uses L2 norm forVec<f64>. (ForMatrix, Frobenius norm.)

#[macro_use]externcrate peroxide;use peroxide::prelude::*;fnmain(){let a =c!(1,2,3);let l2 = a.norm();// L2 is default vector normassert_eq!(l2,14f64.sqrt());}

Infuga, use various norms. But you should write a little bit longer thanprelude.

#[macro_use]externcrate peroxide;use peroxide::fuga::*;fnmain(){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);}

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 withVec<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
  • Taylor mode Forward AD - for nth order AD
  • Exact jacobian
  • Real trait to constrain forf64 andAD (for ODE)
• 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 ODE solver (afterv0.36.0)
    • Explicit integrator
      • Ralston's 3rd order
      • Runge-Kutta 4th order
      • Ralston's 4th order
      • Runge-Kutta 5th order
    • Embedded integrator
      • Bogacki-Shampine 3(2)
      • Runge-Kutta-Fehlberg 5(4)
      • Dormand-Prince 5(4)
      • Tsitouras 5(4)
      • Runge-Kutta-Fehlberg 8(7)
    • Implicit integrator
      • 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 root finding (afterv0.37.0)
    • Bisection
    • False Position
    • Secant
    • Newton
    • Broyden
• Statistics
  • More easy random withrand 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 forrand-dist crate
    • Piecewise Rejection Sampling
  • Confusion Matrix & Metrics
• Special functions
  • Wrapper forpuruspe crate (pure rust)
• Utils
  • R-like macro & functions
  • Matlab-like macro & functions
  • Numpy-like macro & functions
  • Julia-like macro & functions
• Plotting
  • Withpyo3 &matplotlib
• DataFrame
  • Support various types simultaneously
  • Read & Writecsv files (csv feature)
  • Read & Writenetcdf files (nc feature)
  • Read & Writeparquet files (parquet feature)

After0.23.0, peroxide is compatible with mathematical structures.Matrix,Vec<f64>,f64 are considered as inner product vector spaces.AndMatrix,Vec<f64> are linear operators -Vec<f64> toVec<f64> andVec<f64> tof64.For future, peroxide will include more & more mathematical concepts. (But still practical.)

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 theODEProblem trait for abstracting ODE problems.

use peroxide::fuga::*;fnmain() ->Result<(),Box<dynError>>{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 plottingletmut 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(())}structLorenz;implODEProblemforLorenz{fnrhs(&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.

How's that? Let me know if there's anything else you'd like me to improve!

Corresponding to0.38.0

• ForO3 feature - NeedOpenBLAS
• Forplot feature - Needmatplotlib and optionalscienceplots (for publication quality)
• Fornc feature - Neednetcdf

cargo add peroxide

cargo add peroxide --features"<FEATURES>"

• O3: Adds OpenBLAS support
• plot: Enables plotting functionality
• complex: Supports complex number operations
• parallel: Enables parallel processing capabilities
• nc: Adds NetCDF support for DataFrame
• csv: Adds CSV support for DataFrame
• parquet: Adds Parquet support for DataFrame
• serde: Enables serialization/deserialization for Matrix and polynomial

Single feature installation:

cargo add peroxide --features"plot"

Multiple features installation:

cargo add peroxide --features"O3 plot nc csv parquet serde"

• If you want to useQR,SVD, orCholesky Decomposition, you should use theO3 feature. These decompositions are not implemented in thedefault feature.

• If you want to save your numerical results, consider using theparquet ornc features, which correspond to theparquet andnetcdf file formats, respectively. These formats are much more efficient thancsv andjson.

• For plotting, it is recommended to use theplot feature. However, if you require more customization, you can use theparquet ornc feature to export your data in the parquet or netcdf format and then use Python to create the plots.

  • To read parquet files in Python, you can use thepandas andpyarrow libraries.

  • A template for Python code that works with netcdf files can be found in theSocialst repository.

• src
  • lib.rs :mod andre-export
  • complex: For complex vector, matrix & integrals.
    • mod.rs
    • integrate.rs : Complex integral
    • matrix.rs : Complex matrix
    • vector.rs : Complex vector
  • fuga : Fuga for controlling numerical algorithms.
    • mod.rs
  • macros : Macro files
    • julia_macro.rs : Julia like macro
    • matlab_macro.rs : MATLAB like macro
    • mod.rs
    • r_macro.rs : R like macro
  • ml : For machine learning (Beta)
    • mod.rs
    • reg.rs : Regression tools
  • numerical : To do numerical things
    • mod.rs
    • eigen.rs : Eigenvalue, Eigenvector algorithm
    • integral.rs : Numerical integration
    • interp.rs : Interpolation
    • newton.rs : Newton's Method
    • ode.rs : Main ODE solver with various algorithms
    • optimize.rs : Non-linear regression
    • root.rs : Root finding
    • spline.rs : Cubic spline, Cubic Hermite spline & B-Spline
    • utils.rs : Utils to do numerical things (e.g. jacobian)
  • prelude : Prelude for using simple
    • mod.rs
    • simpler.rs : Provides more simple api
  • special : Special functions written in pure Rust (Wrapper ofpuruspe)
    • mod.rs
    • function.rs : Special functions
  • statistics : Statistical Tools
    • mod.rs
    • dist.rs : Probability distributions
    • ops.rs : Some probabilistic operations
    • rand.rs : Wrapper forrand crate & Piecewise Rejection Sampling
    • stat.rs : Statistical tools
  • structure : Fundamental data structures
    • mod.rs
    • ad.rs : Automatic Differentation
    • dataframe.rs : Dataframe
    • matrix.rs : Matrix
    • polynomial.rs : Polynomial
    • sparse.rs : For sparse structure (Beta)
    • vector.rs : Extra tools forVec<f64>
  • traits
    • mod.rs
    • fp.rs : Functional programming toolbox
    • general.rs : General algorithms
    • math.rs : Mathematics
    • matrix.rs : Matrix traits
    • mutable.rs : Mutable toolbox
    • num.rs : Number, Real and more operations
    • pointer.rs : Matrix pointer and Vector pointer for convenience
    • stable.rs : Implement nightly-only features in stable
    • sugar.rs : Syntactic sugar for Vector
  • util
    • mod.rs
    • api.rs : Matrix constructor for various language style
    • low_level.rs : Low-level tools
    • non_macro.rs : Primordial version of macros
    • plot.rs : To draw plot (usingpyo3)
    • print.rs : To print conveniently
    • useful.rs : Useful utils to implement library
    • wrapper.rs : Wrapper for other crates (e.g. rand)
    • writer.rs : More convenient write system

• Inexamples directory, there are some examples.

• Intests directory, there are some useful tests.

• More examples are inPeroxide Gallery.

To seeRELEASES.md

SeeCONTRIBUTES.md

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

To seeTODO.md

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! 👍