deep_causality_num 0.3.2

Number utils for for deep_causality crate.
Documentation 
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

/*
 * SPDX-License-Identifier: MIT
 * Copyright (c) 2023 - 2026. The DeepCausality Authors and Contributors. All Rights Reserved.
 */
use crate::{Complex, DivisionAlgebra, One, RealField, Zero};

impl<T: RealField> Complex<T> {
    /// Computes the norm (magnitude or absolute value) of the complex number.
    #[inline]
    pub fn norm(&self) -> T {
        self.norm_sqr().sqrt()
    }

    /// Computes the argument (phase angle) of the complex number in radians.
    #[inline]
    pub fn arg(&self) -> T {
        self.im.atan2(self.re)
    }

    /// Raises to an integer power.
    #[inline]
    pub fn powi(&self, n: i32) -> Self {
        if n == 0 {
            return Self::one();
        }
        let mut res = Self::one();
        let mut base = *self;
        let mut n_abs = n.abs();

        while n_abs > 0 {
            if n_abs % 2 == 1 {
                res *= base;
            }
            base = base * base;
            n_abs /= 2;
        }

        if n < 0 { res._inverse_impl() } else { res }
    }

    /// Raises a to a real (scalar) power.
    #[inline]
    pub fn powf(&self, n: T) -> Self {
        // (r * (cos(t) + i*sin(t)))^n = r^n * (cos(n*t) + i*sin(n*t))
        let r_pow_n = self.norm().powf(n);
        let n_theta = self.arg() * n;
        Self::new(r_pow_n * n_theta.cos(), r_pow_n * n_theta.sin())
    }

    /// Raises to a complex power.
    #[inline]
    pub fn powc(&self, n: Self) -> Self {
        // z^w = exp(w * ln(z))
        (n * self.ln()).exp()
    }

    /// Computes the principal square root of a complex number.
    #[inline]
    pub fn sqrt(self) -> Self {
        if self.is_zero() {
            return Self::zero();
        }
        let norm = self.norm();
        let half = T::one() / (T::one() + T::one());
        let re_sqrt = ((norm + self.re) * half).sqrt();
        let im_sqrt = ((norm - self.re) * half).sqrt();

        if self.im >= T::zero() {
            Self::new(re_sqrt, im_sqrt)
        } else {
            Self::new(re_sqrt, -im_sqrt)
        }
    }

    /// Computes `e^(self)`, where `e` is the base of the natural logarithm.
    #[inline]
    pub fn exp(self) -> Self {
        // e^(a + bi) = e^a * (cos(b) + i * sin(b))
        let exp_re = self.re.exp();
        Self::new(exp_re * self.im.cos(), exp_re * self.im.sin())
    }

    /// Computes the natural logarithm of a complex number.
    #[inline]
    pub fn ln(self) -> Self {
        // ln(z) = ln(|z|) + i * arg(z)
        Self::new(self.norm().ln(), self.arg())
    }

    /// Computes the sine of a complex number.
    #[inline]
    pub fn sin(self) -> Self {
        Self::new(
            self.re.sin() * self.im.cosh(),
            self.re.cos() * self.im.sinh(),
        )
    }

    /// Computes the cosine of a complex number.
    #[inline]
    pub fn cos(self) -> Self {
        Self::new(
            self.re.cos() * self.im.cosh(),
            -self.re.sin() * self.im.sinh(),
        )
    }

    /// Computes the tangent of a complex number.
    #[inline]
    pub fn tan(self) -> Self {
        self.sin() / self.cos()
    }

    /// Computes the hyperbolic sine of a complex number.
    #[inline]
    pub fn sinh(self) -> Self {
        Self::new(
            self.re.sinh() * self.im.cos(),
            self.re.cosh() * self.im.sin(),
        )
    }

    /// Computes the hyperbolic cosine of a complex number.
    #[inline]
    pub fn cosh(self) -> Self {
        Self::new(
            self.re.cosh() * self.im.cos(),
            self.re.sinh() * self.im.sin(),
        )
    }

    /// Computes the hyperbolic tangent of a complex number.
    #[inline]
    pub fn tanh(self) -> Self {
        self.sinh() / self.cosh()
    }
}