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|
use crate::Float;
use core::{fmt, ops};
#[macro_export]
macro_rules! complex {
($real:expr, $imaginary:expr) => {
$crate::Complex::new($real, $imaginary)
};
}
macro_rules! impl_ops {
($trait:ident, $method:ident, $op:tt) => {
impl<T: Float> ops::$trait for Complex<T> {
type Output = Complex<T>;
fn $method(self, other: Complex<T>) -> Complex<T> {
Complex {
real: self.real $op other.real,
imaginary: self.imaginary $op other.imaginary,
}
}
}
};
($trait:ident, $method:ident, $op:tt, real) => {
impl<T: Float> ops::$trait<T> for Complex<T> {
type Output = Complex<T>;
fn $method(self, other: T) -> Complex<T> {
Complex {
real: self.real $op other,
imaginary: self.imaginary,
}
}
}
};
($trait_assign:ident, $method_assign:ident, $op:tt, assign) => {
impl<T: Float> ops::$trait_assign for Complex<T> {
fn $method_assign(&mut self, other: Complex<T>) {
self.real = self.real $op other.real;
self.imaginary = self.imaginary $op other.imaginary;
}
}
};
($trait_assign:ident, $method_assign:ident, $op:tt, assign_real) => {
impl<T: Float> ops::$trait_assign<T> for Complex<T> {
fn $method_assign(&mut self, other: T) {
self.real = self.real $op other;
}
}
};
}
#[derive(Copy, Clone, PartialOrd, PartialEq)]
pub struct Complex<T: Float> {
pub real: T,
pub imaginary: T,
}
impl<T: Float + fmt::Debug> fmt::Debug for Complex<T> {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
write!(
f,
"Complex {{ real: {:?}, imaginary: {:?} }}",
self.real, self.imaginary
)
}
}
impl<T: Float + fmt::Display> fmt::Display for Complex<T> {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
write!(f, "{} + {}i", self.real, self.imaginary)
}
}
impl<T: Float> ops::Neg for Complex<T> {
type Output = Complex<T>;
fn neg(self) -> Complex<T> {
Complex {
real: -self.real,
imaginary: -self.imaginary,
}
}
}
impl<T: Float> From<T> for Complex<T> {
fn from(real: T) -> Complex<T> {
Complex {
real,
imaginary: T::zero(),
}
}
}
impl<T: Float> Complex<T> {
pub fn new(real: T, imaginary: T) -> Complex<T> {
Complex { real, imaginary }
}
pub fn get_conjugate(&self) -> Complex<T> {
Complex {
real: self.real,
imaginary: -self.imaginary,
}
}
pub fn conjugate(&mut self) {
self.imaginary = -self.imaginary;
}
pub fn phase(&self) -> T {
T::atan2(self.imaginary, self.real)
}
pub fn norm2(&self) -> T {
self.real * self.real + self.imaginary * self.imaginary
}
pub fn abs(&self) -> T {
T::sqrt(self.norm2())
}
}
impl_ops!(Add, add, +);
impl_ops!(Sub, sub, -);
impl<T: Float> ops::Mul for Complex<T> {
type Output = Complex<T>;
fn mul(self, other: Complex<T>) -> Complex<T> {
// (a + bi) * (c + di) = (ac - bd) + (ad + bc)i
Complex {
real: self.real * other.real - self.imaginary * other.imaginary,
imaginary: self.real * other.imaginary + self.imaginary * other.real,
}
}
}
impl<T: Float> ops::Div for Complex<T> {
type Output = Complex<T>;
fn div(self, other: Complex<T>) -> Complex<T> {
// (a + bi) / (c + di) = ((ac + bd) + (bc - ad)i) / (c² + d²)
let denom = other.real * other.real + other.imaginary * other.imaginary;
Complex {
real: (self.real * other.real + self.imaginary * other.imaginary) / denom,
imaginary: (self.imaginary * other.real - self.real * other.imaginary) / denom,
}
}
}
impl_ops!(AddAssign, add_assign, +, assign);
impl_ops!(SubAssign, sub_assign, -, assign);
impl<T: Float> ops::MulAssign for Complex<T> {
fn mul_assign(&mut self, other: Complex<T>) {
let new_real = self.real * other.real - self.imaginary * other.imaginary;
let new_imag = self.real * other.imaginary + self.imaginary * other.real;
self.real = new_real;
self.imaginary = new_imag;
}
}
impl<T: Float> ops::DivAssign for Complex<T> {
fn div_assign(&mut self, other: Complex<T>) {
let denom = other.real * other.real + other.imaginary * other.imaginary;
let new_real = (self.real * other.real + self.imaginary * other.imaginary) / denom;
let new_imag = (self.imaginary * other.real - self.real * other.imaginary) / denom;
self.real = new_real;
self.imaginary = new_imag;
}
}
impl_ops!(Add, add, +, real);
impl_ops!(Sub, sub, -, real);
impl_ops!(Mul, mul, *, real);
impl_ops!(Div, div, /, real);
|
