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use std::num::ParseFloatError;
use std::str::FromStr;
use std::f64::consts::E;
#[derive(Clone, Copy, Default, Debug)]
pub struct Complex {
pub real: f64,
pub imag: f64,
}
impl Complex {
pub fn new(real: f64, imag: f64) -> Self {
Self { real, imag }
}
pub fn div(&mut self, other: &Self) {
let z = other.real * other.real + other.imag * other.imag;
self.real = self.real * other.real + self.imag * other.imag;
self.real /= z;
self.imag = self.imag * other.real - self.real * other.imag;
self.imag /= z;
}
pub fn abs(&self) -> f64 {
(self.real.powi(2) + self.imag.powi(2)).sqrt()
}
pub fn pow(&self, rhs: Self) -> Self {
let r = self.abs();
let x = (self.imag / self.real).atan();
let lnr = r.ln();
let alpha = lnr * rhs.imag + x * rhs.real;
let e_exp = E.powf(lnr * rhs.real - rhs.imag * x);
Complex::new(e_exp * alpha.cos(), e_exp * alpha.sin())
}
pub fn sqrt(&self) -> Self {
self.pow(Complex::new(0.5, 0.0))
}
pub fn cos(&self) -> Self {
let e : Complex = E.into();
let i = Complex::new(0.0, 1.0);
Complex::new(e.pow(&i * self).real, 0.0)
}
pub fn sin(&self) -> Self {
let e : Complex = E.into();
let i = Complex::new(0.0, 1.0);
Complex::new(e.pow(&i * self).imag, 0.0)
}
pub fn tan(&self) -> Self {
self.sin() / self.cos()
}
}
impl std::fmt::Display for Complex {
fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
if self.imag == 0.0 {
write!(f, "{}", self.real)
} else if self.real == 0.0 {
if self.imag == 1.0 {
write!(f, "i")
} else {
write!(f, "{}i", self.imag)
}
} else {
if self.imag == 1.0 {
write!(f, "{} + i", self.real)
} else {
write!(f, "{} + {}i", self.real, self.imag)
}
}
}
}
#[derive(Debug)]
pub struct ComplexParseError;
impl From<ParseFloatError> for ComplexParseError {
fn from(_: ParseFloatError) -> Self {
Self {}
}
}
impl FromStr for Complex {
type Err = ComplexParseError;
fn from_str(s: &str) -> Result<Self, Self::Err> {
let mut c = Complex::default();
let s = s.replace(' ', "");
if s.contains('+') {
let (a, b) = s.split_once('+').unwrap();
if a.contains('i') {
c.imag = a[..a.len() - 1].parse()?;
c.real = b.parse()?;
} else {
c.real = a.parse()?;
c.imag = b[..b.len() - 1].parse()?;
}
} else {
if s.contains('i') {
if s.len() == 1 {
c.imag = 1.0;
} else {
c.imag = s[..s.len() - 1].parse()?;
}
} else {
c.real = s.parse()?;
}
}
Ok(c)
}
}
impl Into<Complex> for f64 {
fn into(self) -> Complex {
Complex::new(self, 0.0)
}
}
impl std::ops::Add for &Complex {
type Output = Complex;
fn add(self, rhs: Self) -> Self::Output {
Complex::new(self.real + rhs.real, self.imag + rhs.imag)
}
}
impl std::ops::Add for Complex {
type Output = Complex;
fn add(self, rhs: Self) -> Self::Output {
&self + &rhs
}
}
impl std::ops::Sub for &Complex {
type Output = Complex;
fn sub(self, rhs: Self) -> Self::Output {
Complex::new(self.real - rhs.real, self.imag - rhs.imag)
}
}
impl std::ops::Sub for Complex {
type Output = Complex;
fn sub(self, rhs: Self) -> Self::Output {
&self - &rhs
}
}
impl std::ops::Mul for &Complex {
type Output = Complex;
fn mul(self, rhs: Self) -> Self::Output {
Complex::new(
self.real * rhs.real - self.imag * rhs.imag,
self.real * rhs.imag + self.imag * rhs.real,
)
}
}
impl std::ops::Mul for Complex {
type Output = Complex;
fn mul(self, rhs: Self) -> Self::Output {
&self * &rhs
}
}
impl std::ops::Div for &Complex {
type Output = Complex;
fn div(self, rhs: Self) -> Self::Output {
let z = rhs.real * rhs.real + rhs.imag * rhs.imag;
Complex::new(
(self.real * rhs.real + self.imag * rhs.imag) / z,
(self.imag * rhs.real - self.real * rhs.imag) / z,
)
}
}
impl std::ops::Div for Complex {
type Output = Complex;
fn div(self, rhs: Self) -> Self::Output {
&self / &rhs
}
}
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