mgh 0.1.16

A Collection of Moré-Garbow-Hilstrom https://dl.acm.org/doi/pdf/10.1145/355934.355936
Documentation 
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use std::f64::consts::E;

pub fn brown_and_dennis(x: &[f64], m: usize) -> f64 {
    let &[x1, x2, x3, x4] = x else {
        panic!("input dimension must be 4");
    };

    if m < x.len() {
        panic!("number of auxiliary function must be at least n");
    }
    let mut res = 0.;

    for i in 1..(m + 1) {
        // t_i = i / 5
        let t = (i as f64) / 5.;

        // f_i(x) = (x_1 + t_i x_2 - e^t_i)^2 + (x_3 + x_4 sin(t_i) - cos(t_i))^2
        let f = (x1 + t * x2 - E.powf(t)).powi(2) + (x3 + x4 * t.sin() - t.cos()).powi(2);
        res += f.powi(2);
    }
    res
}

pub fn init() -> Vec<f64> {
    vec![25., 5., -5., -1.]
}

pub fn min() -> Vec<f64> {
    vec![-11.59444, 13.20363, -0.4034395, 0.2367788]
}

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

    #[test]
    fn test_brown_and_dennis() {
        let x = init();
        let val = brown_and_dennis(&x, 20);
        assert!(val.is_finite());
    }

    #[test]
    fn test_global_minimum() {
        let x = min();
        let val = brown_and_dennis(&x, 20);
        assert!((val - 85822.2).abs() < 1e-1);
    }
}