math_audio_test_functions/functions/
qing.rs

1//! Qing test function
2
3use ndarray::Array1;
4
5/// Qing function - separable multimodal function
6/// Global minimum: f(x) = 0 at x = (±√i, ±√2, ..., ±√n)
7/// Bounds: x_i in [-500, 500]
8pub fn qing(x: &Array1<f64>) -> f64 {
9    x.iter()
10        .enumerate()
11        .map(|(i, &xi)| (xi.powi(2) - (i + 1) as f64).powi(2))
12        .sum()
13}
14#[cfg(test)]
15mod tests {
16    use super::*;
17
18    #[test]
19    fn test_qing_known_properties() {
20        // Test some properties of the Qing function
21        use ndarray::Array1;
22
23        // Test the known global optima
24        let x_pos = Array1::from(vec![1.0, (2.0_f64).sqrt()]);
25        let f_pos = qing(&x_pos);
26        assert!(
27            f_pos.abs() < 1e-10,
28            "Positive global optimum value not as expected: {}",
29            f_pos
30        );
31
32        let x_neg = Array1::from(vec![-1.0, -(2.0_f64).sqrt()]);
33        let f_neg = qing(&x_neg);
34        assert!(
35            f_neg.abs() < 1e-10,
36            "Negative global optimum value not as expected: {}",
37            f_neg
38        );
39
40        // Test that function is always non-negative (sum of squares)
41        let test_points = vec![
42            vec![0.0, 0.0],
43            vec![10.0, 10.0],
44            vec![-50.0, 30.0],
45            vec![100.0, -200.0],
46        ];
47
48        for point in test_points {
49            let x = Array1::from(point.clone());
50            let f = qing(&x);
51
52            assert!(
53                f >= 0.0,
54                "Function should be non-negative at {:?}: {}",
55                point,
56                f
57            );
58            assert!(
59                f.is_finite(),
60                "Function should be finite at {:?}: {}",
61                point,
62                f
63            );
64        }
65
66        // Test boundary behavior
67        let x_boundary = Array1::from(vec![500.0, -500.0]);
68        let f_boundary = qing(&x_boundary);
69        assert!(
70            f_boundary >= 0.0,
71            "Function at boundary should be non-negative"
72        );
73        assert!(
74            f_boundary.is_finite(),
75            "Function at boundary should be finite"
76        );
77    }
78}
math_audio_test_functions/functions/qing.rs

math_audio_test_functions/functions/
qing.rs
