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 jennrich_and_sampson(x: &[f64], m: usize) -> f64 {
    let &[x1, x2] = x else {
        panic!("input dimension must be 2");
    };
    if m < 2 { // Image says m=10 usually, but formula valid for m >= 2
         panic!("number of auxiliary function must be at least 2");
    }
    let mut res = 0.0;

    for i in 1..=m {
         // f_i(x) = 2 + 2i - (exp(i * x1) + exp(i * x2))
         let fi = 2.0 + 2.0 * i as f64 - (E.powf(i as f64 * x1) + E.powf(i as f64 * x2));
         res += fi.powi(2);
    }
    res
}

pub fn init() -> Vec<f64> {
    vec![0.3, 0.4]
}

pub fn min() -> Vec<f64> {
    vec![0.2578, 0.2578]
}

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

    #[test]
    fn test_jennrich_and_sampson() {
        let x = init();
        let val = jennrich_and_sampson(&x, 10);
        assert!(val.is_finite());
    }

    #[test]
    fn test_min() {
        let x = min();
        let val = jennrich_and_sampson(&x, 10);
        // around 124.362
        assert!((val - 124.362).abs() < 1e-1);
    }
}