Axect/Peroxide: Rust numeric library with R, MATLAB & Python syntax

原作者: [db:作者] 来自: 网络收藏邀请

开源软件名称（OpenSource Name）：

Axect/Peroxide

开源软件地址(OpenSource Url)：

https://github.com/Axect/Peroxide

开源编程语言(OpenSource Language)：

Rust 99.9%

开源软件介绍(OpenSource Introduction)：

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)
- Cholesky Decomposition (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
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
- Splines
  - Cubic Spline
  - Cubic Hermite Spline
    - Estimate slope via Akima
    - Estimate slope via Quadratic interpolation
- 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
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)

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 0.30.11

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 or Cholesky Decomposition 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.
  - 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
  - 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 : Cubic spline & Cubic Hermite 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
  - mod.rs
  - dist.rs : Probability distributions
  - ops.rs : Some probabilistic operations
  - rand.rs : Wrapper for rand crate
  - stat.rs : 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