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use std::ops::{Add, Sub, Mul, Div, Neg};
use ::num_traits::{Trig, Pow};
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub struct Complex<T> {
real: T,
imag: T
}
impl<T> Complex<T> {
pub fn new(real: T, imag: T) -> Complex<T> {
Complex{real: real, imag: imag}
}
}
impl<T> Complex<T> where T: Neg<Output=T> {
pub fn conjugate(self) -> Complex<T> {
Complex::new(self.real, -self.imag)
}
}
impl<T> Complex<T> where T: Trig + Mul<Output=T> + Copy {
pub fn from_polar(r: T, theta: T) -> Complex<T> {
let real = r*theta.cos();
let imag = r*theta.sin();
Complex::new(real, imag)
}
}
impl<T> Complex<T> where T: Pow + Add<Output=T> + Copy {
pub fn magnitude(self) -> T {
(self.real.pow(2) + self.imag.pow(2)).sqrt()
}
}
impl<T> Complex<T> where T: Trig + Copy {
pub fn angle(self) -> T {
self.imag.atan2(self.real)
}
}
impl<T> Complex<T> where T: Trig + Pow + Add<Output=T> + Copy {
pub fn to_polar(self) -> (T, T) {
(self.magnitude(), self.angle())
}
}
impl<T> Add for Complex<T> where T: Add<Output=T> + Copy {
type Output = Complex<T>;
fn add(self, other: Self) -> Self {
let real = self.real + other.real;
let imag = self.imag + other.imag;
Complex::new(real, imag)
}
}
impl<T> Sub for Complex<T> where T: Sub<Output=T> + Copy {
type Output = Complex<T>;
fn sub(self, other: Self) -> Self {
let real = self.real - other.real;
let imag = self.imag - other.imag;
Complex::new(real, imag)
}
}
impl<T> Mul for Complex<T> where T: Add<Output=T> + Mul<Output=T> + Sub<Output=T> + Copy {
type Output = Complex<T>;
fn mul(self, other: Self) -> Self {
let real = (self.real * other.real) - (self.imag * other.imag);
let imag = (self.real * other.imag) + (self.imag * other.real);
Complex::new(real, imag)
}
}
impl<T> Div for Complex<T> where T: Add<Output=T> + Mul<Output=T> + Sub<Output=T> + Div<Output=T> + Neg<Output=T> + Copy {
type Output = Complex<T>;
fn div(self, other: Self) -> Self {
// multiply numerator and denominator by denominator's complex
// conjugate, to give a pure real denominator.
let other_conj = other.conjugate();
let num = self * other_conj;
let denom = (other * other_conj).real;
let real = num.real / denom;
let imag = num.imag / denom;
Complex::new(real, imag)
}
}
#[cfg(test)]
mod tests {
use super::*;
use std::f32;
#[test]
fn addition() {
let a = Complex::new(1, 5);
let b = Complex::new(-3, 2);
assert_eq!(a+b, Complex::new(-2, 7));
}
#[test]
fn subtraction() {
let a = Complex::new(1, 5);
let b = Complex::new(-3, 2);
assert_eq!(a-b, Complex::new(4, 3));
}
#[test]
fn multiplication() {
let a = Complex::new(3, 4);
let b = Complex::new(2, 3);
assert_eq!(a*b, Complex::new(-6, 17));
}
#[test]
fn division() {
let a = Complex::new(6, 8);
let b = Complex::new(3, 4);
assert_eq!(a/b, Complex::new(2, 0));
}
#[test]
fn from_polar() {
let right = Complex::from_polar(1.0 as f32, 0.0 as f32);
assert!((right.real-1.0).abs() < f32::EPSILON);
assert!((right.imag-0.0).abs() < f32::EPSILON);
let up = Complex::from_polar(1.0 as f32, f32::consts::PI/2.0);
assert!((up.real-0.0).abs() < f32::EPSILON/2.0);
assert!((up.imag-1.0).abs() < f32::EPSILON/2.0);
let left = Complex::from_polar(1.0 as f32, f32::consts::PI);
assert!((left.real+1.0).abs() < f32::EPSILON);
assert!((left.imag-0.0).abs() < f32::EPSILON);
let down = Complex::from_polar(1.0 as f32, f32::consts::PI*3.0/2.0);
assert!((down.real-0.0).abs() < f32::EPSILON);
assert!((down.imag+1.0).abs() < f32::EPSILON);
//not sure why the error here is more than epsilon. My guess
// is that it's the 2.0*PI, meaning that the value for PI has
// twice the normal error.
let rev = Complex::from_polar(1.0 as f32, f32::consts::PI*2.0);
assert!((rev.real-1.0).abs() < f32::EPSILON*2.0);
assert!((rev.imag-0.0).abs() < f32::EPSILON*2.0);
}
}
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