1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
|
use std::ops::{Add, Sub, Mul, Div, Neg};
use ::num_traits::{Trig, Pow, ArithmeticOps, SignedArithmeticOps};
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub struct Complex<T> {
pub real: T,
pub 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: SignedArithmeticOps {
pub fn conjugate(self) -> Complex<T> {
Complex::new(self.real, -self.imag)
}
}
impl<T> Complex<T> where T: Pow + ArithmeticOps + Copy {
pub fn magnitude(self) -> T {
(self.real.pow(2) + self.imag.pow(2)).sqrt()
}
}
impl<T> Complex<T> where T: Trig {
pub fn angle(self) -> T {
self.imag.atan2(self.real)
}
}
impl<T> Complex<T> where T: Trig + Pow + ArithmeticOps + Copy {
/// ```
/// use worthe_signals::complex::Complex;
/// use std::f32;
///
/// 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);
/// ```
pub fn from_polar(r: T, theta: T) -> Complex<T> {
let real = r*theta.cos();
let imag = r*theta.sin();
Complex::new(real, imag)
}
pub fn to_polar(self) -> (T, T) {
(self.magnitude(), self.angle())
}
}
impl<T> Add for Complex<T> where T: ArithmeticOps + Copy {
type Output = Complex<T>;
/// ```
/// use worthe_signals::complex::Complex;
/// let a = Complex::new(1, 5);
/// let b = Complex::new(-3, 2);
/// assert_eq!(a+b, Complex::new(-2, 7));
/// ```
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: ArithmeticOps + Copy {
type Output = Complex<T>;
/// ```
/// use worthe_signals::complex::Complex;
/// let a = Complex::new(1, 5);
/// let b = Complex::new(-3, 2);
/// assert_eq!(a-b, Complex::new(4, 3));
/// ```
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: ArithmeticOps + Copy {
type Output = Complex<T>;
/// ```
/// use worthe_signals::complex::Complex;
/// let a = Complex::new(3, 4);
/// let b = Complex::new(2, 3);
/// assert_eq!(a*b, Complex::new(-6, 17));
/// ```
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: SignedArithmeticOps + Copy {
type Output = Complex<T>;
/// ```
/// use worthe_signals::complex::Complex;
/// let a = Complex::new(6, 8);
/// let b = Complex::new(3, 4);
/// assert_eq!(a/b, Complex::new(2, 0));
/// ```
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)
}
}
impl<T> Neg for Complex<T> where T: SignedArithmeticOps + Copy {
type Output = Complex<T>;
/// ```
/// use worthe_signals::complex::Complex;
/// let a = Complex::new(6, 8);
/// assert_eq!(-a, Complex::new(0, 0)-a);
/// ```
fn neg(self) -> Self {
Complex::new(-self.real, -self.imag)
}
}
#[cfg(test)]
mod tests {
use super::*;
use std::i32;
quickcheck! {
fn add_zero(real: i32, imag: i32) -> bool {
let com = Complex::new(real, imag);
let zero = Complex::new(0, 0);
com == com + zero
}
fn sub_zero(real: i32, imag: i32) -> bool {
let com = Complex::new(real, imag);
let zero = Complex::new(0, 0);
com == com - zero
}
fn times_zero(real: i32, imag: i32) -> bool {
let com = Complex::new(real, imag);
let zero = Complex::new(0, 0);
zero == com * zero
}
fn times_one(real: i32, imag: i32) -> bool {
let com = Complex::new(real, imag);
let one = Complex::new(1, 0);
com == com * one
}
fn double(real: i32, imag: i32) -> bool {
let com = Complex::new(real, imag);
com+com == com*Complex::new(2, 0)
}
fn additive_inverse(real1: i32, imag1: i32, real2: i32, imag2: i32) -> bool {
let com1 = Complex::new(real1, imag1);
let com2 = Complex::new(real2, imag2);
com1 == (com1+com2)-com2
}
fn multiplicative_inverse(real1: i32, imag1: i32, real2: i32, imag2: i32) -> bool {
let com1 = Complex::new(real1, imag1);
let com2 = Complex::new(real2, imag2);
com1 == (com1*com2)/com2
}
fn commutative_addition(real1: i32, imag1: i32, real2: i32, imag2: i32) -> bool {
let com1 = Complex::new(real1, imag1);
let com2 = Complex::new(real2, imag2);
com1 + com2 == com2 + com1
}
}
}
|
