solvr 0.2.0-beta.2

Advanced computing library for real-world problem solving - optimization, differential equations, interpolation, statistics, and more
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
138
139
140
141
142
143
144
145

//! Window function generation algorithms.
//!
//! Pure Rust implementations of window functions as f64 vectors.

use std::f64::consts::PI;

/// Generate Hann window values as f64.
pub fn generate_hann_f64(size: usize) -> Vec<f64> {
    if size == 0 {
        return vec![];
    }
    if size == 1 {
        return vec![1.0];
    }
    let n = size as f64;
    (0..size)
        .map(|i| {
            let x = 2.0 * PI * (i as f64) / n;
            0.5 - 0.5 * x.cos()
        })
        .collect()
}

/// Generate Hamming window values as f64.
pub fn generate_hamming_f64(size: usize) -> Vec<f64> {
    if size == 0 {
        return vec![];
    }
    if size == 1 {
        return vec![1.0];
    }
    let n = size as f64;
    (0..size)
        .map(|i| {
            let x = 2.0 * PI * (i as f64) / n;
            0.54 - 0.46 * x.cos()
        })
        .collect()
}

/// Generate Blackman window values as f64.
pub fn generate_blackman_f64(size: usize) -> Vec<f64> {
    if size == 0 {
        return vec![];
    }
    if size == 1 {
        return vec![1.0];
    }
    let n = size as f64;
    (0..size)
        .map(|i| {
            let x = 2.0 * PI * (i as f64) / n;
            0.42 - 0.5 * x.cos() + 0.08 * (2.0 * x).cos()
        })
        .collect()
}

/// Generate Kaiser window values as f64.
pub fn generate_kaiser_f64(size: usize, beta: f64) -> Vec<f64> {
    if size == 0 {
        return vec![];
    }
    if size == 1 {
        return vec![1.0];
    }

    let n = size as f64;
    let half_n = (n - 1.0) / 2.0;
    let i0_beta = bessel_i0(beta);

    (0..size)
        .map(|i| {
            let x = (i as f64 - half_n) / half_n;
            let arg = beta * (1.0 - x * x).sqrt();
            bessel_i0(arg) / i0_beta
        })
        .collect()
}

/// Modified Bessel function of the first kind, order 0.
///
/// Uses the polynomial approximation from Abramowitz & Stegun.
pub fn bessel_i0(x: f64) -> f64 {
    let ax = x.abs();
    if ax < 3.75 {
        let t = (x / 3.75).powi(2);
        1.0 + t
            * (3.5156229
                + t * (3.0899424
                    + t * (1.2067492 + t * (0.2659732 + t * (0.0360768 + t * 0.0045813)))))
    } else {
        let t = 3.75 / ax;
        let exp_ax = ax.exp();
        (exp_ax / ax.sqrt())
            * (0.39894228
                + t * (0.01328592
                    + t * (0.00225319
                        + t * (-0.00157565
                            + t * (0.00916281
                                + t * (-0.02057706
                                    + t * (0.02635537 + t * (-0.01647633 + t * 0.00392377))))))))
    }
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_hann_window() {
        let window = generate_hann_f64(8);
        assert_eq!(window.len(), 8);
        assert!(window[0].abs() < 1e-10);
        assert!((window[1] - window[7]).abs() < 1e-10);
    }

    #[test]
    fn test_hamming_window() {
        let window = generate_hamming_f64(8);
        assert_eq!(window.len(), 8);
        assert!(window[0] > 0.05);
    }

    #[test]
    fn test_blackman_window() {
        let window = generate_blackman_f64(8);
        assert_eq!(window.len(), 8);
        assert!(window[0].abs() < 1e-10);
    }

    #[test]
    fn test_kaiser_window() {
        let window = generate_kaiser_f64(8, 5.0);
        assert_eq!(window.len(), 8);
        for &w in &window {
            assert!((0.0..=1.0).contains(&w));
        }
    }

    #[test]
    fn test_window_size_edge_cases() {
        assert!(generate_hann_f64(0).is_empty());
        assert_eq!(generate_hann_f64(1), vec![1.0]);
    }
}