mgh 0.1.16

A Collection of Moré-Garbow-Hilstrom https://dl.acm.org/doi/pdf/10.1145/355934.355936
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

use std::f64::consts::E;

pub fn powell_badly_scaled(x: &[f64]) -> f64 {
    let &[x1, x2] = x else {
        panic!("input dimension must be 2");
    };

    // f_1(x) = 10^4 * x1 * x2 - 1
    let f1 = 10000. * x1 * x2 - 1.;

    // f_2(x) = exp(-x1) + exp(-x2) - 1.0001
    let f2 = E.powf(-x1) + E.powf(-x2) - 1.0001;

    f1.powi(2) + f2.powi(2)
}

pub fn init() -> Vec<f64> {
    vec![0., 1.]
}

pub fn min() -> Vec<f64> {
    vec![1.09815933e-5, 9.10614674]
}

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

    #[test]
    fn test_powell_badly_scaled() {
        let x = init();
        let val = powell_badly_scaled(&x);
        assert!(val.is_finite());
    }

    #[test]
    fn test_min() {
        let x = min();
        let val = powell_badly_scaled(&x);
        // not exactly 0.0 because of floating point approximations
        assert!(val < 1e-8);
    }
}