# Peroxide
[](https://crates.io/crates/peroxide)
[](https://docs.rs/peroxide/)
[](https://travis-ci.org/Axect/Peroxide)
Rust numeric library with R Syntax.
## Latest README version
Corresponds with `0.6.0`.
## Install
* Add next line to your `cargo.toml`
```toml
peroxide = "0.6"
```
## Usage
### Initial Import
```rust
extern crate peroxide;
use peroxide::*;
```
### Vec\<f64\> Declaration
```R
# R
a = c(1,2,3,4)
b = seq(1,5,2) # (=c(1,3,5))
```
```rust
// Peroxide
extern crate peroxide;
use peroxide::*;
fn main() {
let a = c!(1,2,3,4);
let b = seq!(1,5,2); // (=c!(1,3,5))
}
```
### Matrix Declaration
```R
# R
a = matrix(1:4, 2, 2, T)
```
```rust
// Peroxide (All belows are same)
extern crate peroxide;
use peroxide::*;
fn main() {
// matrix function
let a = matrix(vec![1,2,3,4], 2, 2, Row);
let b = matrix(c!(1,2,3,4), 2, 2, Row);
let c = matrix(seq!(1,4,1), 2, 2, Row);
// matrix macro (More convenient)
let d = matrix!(1;4;1, 2, 2, Row);
}
```
### Print
```R
# R
a = matrix(1:4, 2, 2, T)
print(a)
# [,1] [,2]
# [1,] 1 2
# [2,] 3 4
```
```rust
// Peroxide
extern crate peroxide;
use peroxide::*;
fn main() {
let a = matrix!(1;4;1, 2, 2, Row);
println!("{}", a);
// Or
a.print();
}
// c[0] c[1]
// r[0] 1 2
// r[1] 3 4
```
### Concatenate
**1. Vector + Vector => Vector**
```R
# R
a = c(1,2,3)
b = c(4,5,6)
c = c(a, b)
print(c) # c(1,2,3,4,5,6)
```
```rust
// Peroxide
extern crate peroxide;
use peroxide::*;
fn main() {
let a = c!(1,2,3);
let b = c!(4,5,6);
let c = c!(a; b); // Must use semi-colon btw vectors
c.print();
}
```
**2. Matrix + Matrix => Matrix**
```R
# R
# cbind
a = matrix(1:4, 2, 2, F)
b = matrix(c(5,6), 2, 1, F)
c = cbind(a, b)
print(c)
# [,1] [,2] [,3]
#[1,] 1 3 5
#[2,] 2 4 6
# rbind
a = matrix(1:4, 2, 2, T)
b = matrix(c(5,6), 1, 2, T)
c = rbind(a,b)
print(c)
# [,1] [,2]
#[1,] 1 2
#[2,] 3 4
#[3,] 5 6
```
```rust
// Peroxide
extern crate peroxide;
use peroxide::*;
fn main() {
// cbind
let a = matrix!(1;4;1, 2, 2, Col);
let b = matrix(c!(5,6), 2, 1, Col);
let c = cbind!(a, b);
c.print();
// c[0] c[1] c[2]
// r[0] 1 3 5
// r[1] 2 4 6
// rbind
let d = matrix!(1;4;1, 2, 2, Row);
let e = matrix(c!(5,6),1, 2, Row);
let f = rbind!(a, b);
f.print();
// c[0] c[1]
// r[0] 1 2
// r[1] 3 4
// r[2] 5 6
}
```
### Matrix operation
* If you want to do multiple operations on same matrix, then you should use `clone` because Rust `std::ops` consume value.
```R
# R
a = matrix(1:4, 2, 2, T)
b = matrix(1:4, 2, 2, F)
print(a + b)
print(a - b)
print(a * b)
print(a %*% b)
```
```rust
// Peroxide
extern crate peroxide;
use peroxide::*;
fn main() {
let a = matrix!(1;4;1, 2, 2, Row);
let b = matrix!(1;4;1, 2, 2, Col);
println!("{}", a.clone() + b.clone());
println!("{}", a.clone() - b.clone());
println!("{}", a.clone() * b.clone()); // Element-wise multiplication
println!("{}", a % b); // Matrix multiplication
// Consume -> You can't use a,b anymore.
}
```
### LU Decomposition
* Peroxide uses complete pivoting LU decomposition. - Very stable.
* Also there are lots of error handling for LU, so, you should use `Option`
```rust
// Peroxide
extern crate peroxide;
use peroxide::*;
fn main() {
let a = matrix(c!(1,2,3,4), 2, 2, Row);
let pqlu = a.lu().unwrap(); // for singular matrix, returns None
let (p,q,l,u) = (pqlu.p, pqlu.q, pqlu.l, pqlu.u);
assert_eq!(p, vec![(0,1)]); // swap 0 & 1 (Row)
assert_eq!(q, vec![(0,1)]); // swap 0 & 1 (Col)
assert_eq!(l, matrix(c!(1,0,0.5,1),2,2,Row));
assert_eq!(u, matrix(c!(4,3,0,-0.5),2,2,Row));
}
```
### Determinant
* Determinant is implemented using by LU decomposition (O(n^3))
```rust
// Peroxide
extern crate peroxide;
use peroxide::*;
fn main() {
let a = matrix(c!(1,2,3,4), 2, 2, Row);
assert_eq!(a.det(), -2f64);
}
```
### Inverse
* Inverse is also implemented using by LU decomposition
* To handle singularity, output type is `Option<Matrix>`
* To obtain inverse, you should use `unwrap` or pattern matching
```rust
// Peroxide
extern crate peroxide;
use peroxide::*;
fn main() {
// Non-singular
let a = matrix!(1;4;1, 2, 2, Row);
assert_eq!(a.inv().unwrap(), matrix(c!(-2,1,1.5,-0.5),2,2,Row));
// Singular
let b = matrix!(1;9;1, 3, 3, Row);
assert_eq!(b.inv(), None);
}
```
### Extract Column or Row
```R
# R
a = matrix(1:4, 2, 2, T)
print(a[,1])
print(a[,2])
print(a[1,])
print(a[2,])
```
```rust
//Peroxide
extern crate peroxide;
use peroxide::*;
fn main() {
let a = matrix!(1;4;1, 2, 2, Row);
a.col(0).print();
a.col(1).print();
a.row(0).print();
a.row(1).print();
}
```
### Functional Programming
```rust
// Peroxide
extern crate peroxide;
use peroxide::*;
fn main() {
let a = matrix!(1;4;1, 2, 2, Row);
println!("{}", a.fmap(|x| x + 1.0));
println!("{}", a.fmap(|x| x - 1.0));
println!("{}", a.fmap(|x| x * 2.0));
}
// Results
//
// c[0] c[1]
// r[0] 2 3
// r[1] 4 5
//
// c[0] c[1]
// r[0] 0 1
// r[1] 2 3
//
// c[0] c[1]
// r[0] 2 4
// r[1] 6 8
```
### Write to CSV
You can write matrix to csv by two ways.
```rust
// Peroxide
extern crate peroxide;
use peroxide::*;
use std::process; // for error handling
fn main() {
// 1. Just write
let a = matrix!(1;4;1, 2, 2, Row);
a.write("test.csv"); // It will save a to test.csv
// 2. Error Handling
let b = matrix!(1;4;1, 2, 2, Row);
if let Err(err) = b.write("test.csv") {
println!("{}", err);
process::exit(1);
}
}
```
### Read from CSV
You can read matrix with error handling
```rust
// Peroxide
extern crate peroxide;
use peroxide::*;
use std::process;
fn main() {
let m = read("test.csv", false); // no header
// Error handling
match m {
Ok(mat) => println!("{}", mat),
Err(err) => {
println!("{}", err);
process::exit(1);
}
}
// Just write
let n = read("test.csv", false).unwrap(); // no header
println!("{}", n);
}
```
### Statistics
* `mean` - Mean
* `var` - Variance
* `sd` - Standard Deviation
* `cov` - Covariance
* `cor` - Pearson's Coefficient
```r
# R
# Vector Stats
a <- c(1,2,3)
b <- c(3,2,1)
print(mean(a))
print(var(a))
print(sd(a))
print(cov(a, b))
print(cor(a, b))
# Matrix Stats
m <- matrix(c(1,2,3,3,2,1), 3, 2, F)
print(cov(m))
```
```rust
// Peroxide
extern crate peroxide;
use peroxide::*;
fn main() {
// Vector Stats
let a = c!(1,2,3);
let b = c!(3,2,1);
println!("{}",a.mean());
println!("{}",a.var());
println!("{}",a.sd());
println!("{}",cov(&a, &b)); // Should borrow! - Not consume value
println!("{}",cor(&a, &b));
// Matrix Stats
let m = matrix(c!(1,2,3,3,2,1), 3, 2, Col);
println!("{}",m.cov());
}
```
### Linear Regression
* `lm(x, y)`
```r
# R
a <- c(1,2,3,4,5)
b <- a + rnorm(5)
lm(b ~ a)
#Call:
#lm(formula = b ~ a)
#
#Coefficients:
#(Intercept) a
# 0.5076 0.8305
```
```rust
//Peroxide
extern crate peroxide;
use peroxide::*;
fn main() {
let a = c!(1,2,3,4,5).to_matrix();
let b = a.clone() + Normal::new(0,1).sample(5).to_matrix();
lm!(b ~ a).print();
// c[0]
// r[0] 0.7219
// r[1] 0.8058
}
```
### Random
Current available distribution
* Uniform (Wrap `rand` crate)
* Normal (Using ziggurat algorithm)
```rust
// Peroxide
extern crate peroxide;
use peroxide::*;
fn main() {
// Uniform unsigned integers
let v_u32 = Uniform::new(1u32, 11);
v_u32.sample(10).print();
// Uniform 64bit float numbers
let v_f64 = Uniform::new(1f64, 11f64);
v_f64.sample(10).print();
// Normal distribution with mean 0, sd 1
let v_n = Normal::new(0, 1);
println!("{}", v_n.sample(1000).mean()); // almost 0
println!("{}", v_n.sample(1000).sd()); // almost 1
}
```
### Polynomial
```rust
// Peroxide
extern crate peroxide;
use peroxide::*;
fn main() {
// Declare polynomial
let a = poly(c!(1,3,2));
a.print(); // x^2 + 3x + 2
a.eval(1); // Evaluate when x = 1 -> 6.0
let b = poly(c!(1,2,3,4)); // x^3 + 2x^2 + 3x + 4
(a.clone() + b.clone()).print(); // x^3 + 3x^2 + 6x + 6
(a.clone() - b.clone()).print(); // -x^3 - x^2 - 2
(a.clone() * b.clone()).print(); // x^5 + 5x^4 + 11x^3 + 17x^2 + 18x + 8
let c = poly(c!(1, -1));
c.print(); // x - 1
c.pow(2).print(); // x^2 - 2x + 1
}
```
### Interpolation (Beta)
* Lagrange polynomial interpolation
* Chebyshev nodes
```rust
// Peroxide
extern crate peroxide;
use peroxide::*;
fn main() {
let a = c!(-1, 0, 1);
let b = c!(1, 0, 1);
let l = lagrange_polynomial(a, b);
l.print(); // x^2
}
```
### Spline (Beta)
* Natural cubic spline
```rust
// Peroxide
extern crate peroxide;
use peroxide::*;
fn main() {
let x = c!(0.9, 1.3, 1.9, 2.1);
let y = c!(1.3, 1.5, 1.85, 2.1);
let s = cubic_spline(x, y);
for i in 0 .. s.len() {
s[i].print();
}
// -0.2347x^3 + 0.6338x^2 - 0.0329x + 0.9873
// 0.9096x^3 - 3.8292x^2 + 5.7691x - 1.5268
// -2.2594x^3 + 14.2342x^2 - 28.5513x + 20.2094
}
```
### MATLAB like macro
* `zeros` - zero vector or matrix
* `eye` - identity matrix
* `rand` - random matrix (range from 0 to 1)
## Version Info
To see [Release.md](./RELEASES.md)