# 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)`O3`

- OpenBLAS (Perfect performance but little bit hard to set-up - Strongly recommend to read OpenBLAS for Rust)`plot`

- With matplotlib of python, we can draw any plots.`nc`

- To handle netcdf file format with DataFrame`csv`

- To handle csv file format with Matrix or DataFrame`serde`

- serialization with Serde.

If you want to do high performance computation and more linear algebra, 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 any features simultaneously.

### 2. Easy to optimize

Peroxide uses 1D data structure to describe matrix. So, it's too easy to integrate BLAS. 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,

```
#[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 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) - Reduced Row Echelon form
- Column, Row operations
- Eigenvalue, Eigenvector

- 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

- More easy functional programming with
- Automatic Differentiation
- Taylor mode Forward AD - for nth order AD
- Exact jacobian
`Real`

trait to constrain for`f64`

and`AD`

(for ODE)

- Numerical Analysis
- Lagrange interpolation
- Cubic spline
- Non-linear regression
- Gradient Descent
- Levenberg Marquardt

- Ordinary Differential Equation
- Euler
- Runge Kutta 4th order
- Backward Euler (Implicit)
- Gauss Legendre 4th order (Implicit)

- Numerical Integration
- Newton-Cotes Quadrature
- Gauss-Legendre Quadrature (up to 30 order)
- Gauss-Kronrod Quadrature (Adaptive)
- G7K15, G10K21, G15K31, G20K41, G25K51, G30K61

- Root Finding
- Bisection
- False Position (Regula Falsi)
- Secant
- Newton

- 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

- RNG algorithms
- Acceptance Rejection
- Marsaglia Polar
- Ziggurat
- Wrapper for
`rand-dist`

crate

- More easy random with
- Special functions
- Wrapper for
`puruspe`

crate (pure rust)

- Wrapper for
- Utils
- R-like macro & functions
- Matlab-like macro & functions
- Numpy-like macro & functions
- Julia-like macro & functions

- Plotting
- With
`pyo3`

&`matplotlib`

- With
- DataFrame
- Support various types simultaneously
- Read & Write
`csv`

files (`csv`

feature) - Read & Write
`netcdf`

files (`nc`

feature)

### 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 & 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 `0.30.2`

## Pre-requisite

- For
`O3`

feature - Need`OpenBLAS`

- For
`plot`

feature - Need`matplotlib`

of python - For
`nc`

feature - Need`netcdf`

## Install

- Add next block to your
`cargo.toml`

- Default
[dependencies] peroxide = "0.30"

- OpenBLAS
[dependencies.peroxide] version = "0.30" default-features = false features = ["O3"]

- Plot
[dependencies.peroxide] version = "0.30" default-features = false features = ["plot"]

- NetCDF dependency for DataFrame
[dependencies.peroxide] version = "0.30" default-features = false features = ["nc"]

- CSV dependency for DataFrame
[dependencies.peroxide] version = "0.30" default-features = false features = ["csv"]

- OpenBLAS & Plot & NetCDF
[dependencies.peroxide] version = "0.30" default-features = false features = ["O3", "plot", "nc", "csv"]

## Useful tips for features

- If you want to use
`QR`

or`SVD`

then should use`O3`

feature (there are no implementations for these decompositions in`default`

) - If you want to write your numerical results, then use
`nc`

feature and`netcdf`

format. (It is much more effective than`csv`

and`json`

.) - To plot, use
`nc`

feature to export data as netcdf format and use python to draw plot.`plot`

feature has limited plot abilities.- There is a template of python code. - Socialst

## Module Structure

**src**- lib.rs :
`mod`

and`re-export`

**fuga**: Fuga for controlling numerical algorithms.**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*)**numerical**: To do numerical things- bdf.rs : Backward Differentiation Formula (deprecated)
- eigen.rs : Eigenvalue, Eigenvector algorithm
- interp.rs : Interpolation
- integral.rs : Numerical integration
- mod.rs
- newton.rs : Newton's Method
- ode.rs : Main ODE solver with various algorithms
- optimize.rs : Non-linear regression
- root.rs : Root finding
- spline.rs : Natural 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 of`puruspe`

)- mod.rs
- function.rs : Special functions

**statistics**: Statistical Tools**structure**: Fundamental data structures- ad.rs : Automatic Differentation
- dataframe.rs : Dataframe
- matrix.rs : Matrix
- mod.rs
- polynomial.rs : Polynomial
- sparse.rs : For sparse structure (
*Beta*) - vector.rs : Extra tools for
`Vec<f64>`

**traits**- fp.rs : Functional programming toolbox
- general.rs : General algorithms
- math.rs : Mathematics
- mod.rs
- 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
- mod.rs
- non_macro.rs : Primordial version of macros
- plot.rs : To draw plot (using
`pyo3`

) - 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

- lib.rs :

## Documentation

## Example

## Version Info

To see RELEASES.md

## Contributes Guide

See CONTRIBUTES.md

## TODO

To see TODO.md