ew_testfunc/
lib.rs

1//! The module with functions to test optimization algorithms.
2
3use num::Float;
4
5
6/// Paraboloid.
7///
8/// y = (x0 - 1)^2 + (x1 - 2)^2 + (x2 - 3)^2 ... (xn - n)^2
9/// The min val is 0.0 for point (1.0, 2.0, 3.0, ... n).
10///
11/// ```
12/// use ew_testfunc::paraboloid;
13///
14/// let x = vec![1.0, 2.0, 3.0, 4.0, 5.0];
15/// let value = paraboloid(&x);
16///
17/// assert!(value < 1e-5);
18/// assert!(value >= 0.0);
19/// ```
20pub fn paraboloid<G: Float>(x: &Vec<G>) -> f64 {
21    let mut result = G::from(0.0).unwrap();
22    for (n, val) in x.iter().enumerate() {
23        result = result + (*val - (G::from(n).unwrap() + G::from(1.0).unwrap())).powi(2);
24    }
25
26    result.to_f64().unwrap()
27}
28
29/// The Schwefel function
30///
31/// # Parameters
32/// Any x lies in [-500.0; 500.0]. 
33/// For any x lies in [-500.0; 500.0] global minimum located in x' = (420.9687, 420.9687, ...).
34/// f(x') = 0.
35///
36/// ```
37/// use ew_testfunc::schwefel;
38///
39/// let x = vec![420.9687, 420.9687, 420.9687, 420.9687];
40/// let value = schwefel(&x);
41/// assert!(value.abs() < 1e-4);
42/// ```
43pub fn schwefel<G: Float>(x: &Vec<G>) -> f64 {
44    let result = G::from(418.9829).unwrap() * G::from(x.len()).unwrap() - x.iter().fold(G::zero(), |acc, &xi| acc + xi * xi.abs().sqrt().sin());
45
46    result.to_f64().unwrap()
47}
48
49/// The Rastrigin function
50///
51/// # Parameters
52/// Global minimum is x' = (0, 0, ...) for xn in (-5.12; +5.12)
53/// f(x') = 0
54///
55/// ```
56/// use ew_testfunc::rastrigin;
57///
58/// let x = vec![0.0_f32, 0.0_f32, 0.0_f32, 0.0_f32, 0.0_f32, 0.0_f32];
59/// let value = rastrigin(&x);
60/// assert!(value.abs() < 1e-7);
61/// ```
62pub fn rastrigin<G: Float>(x: &Vec<G>) -> f64 {
63    let a = G::from(10.0_f64).unwrap();
64    let pi = G::from(3.14159265358979_f64).unwrap();
65    let result = a * G::from(x.len()).unwrap() +
66        x.iter().fold(G::zero(), |acc, &xi| acc + xi * xi - a * (G::from(2).unwrap() * pi * xi).cos());
67
68    result.to_f64().unwrap()
69}
70
71/// The Rosenbrock function
72///
73/// # Parameters
74/// Global minimum is x' = (1, 1, ...) for xn in (-inf; +inf)
75/// f(x') = 0
76///
77/// ```
78/// use ew_testfunc::rosenbrock;
79///
80/// let x = vec![1.0_f32, 1.0_f32, 1.0_f32, 1.0_f32, 1.0_f32, 1.0_f32];
81/// let value = rosenbrock(&x);
82/// assert!(value.abs() < 1e-7);
83/// ```
84pub fn rosenbrock<G: Float>(x: &Vec<G>) -> f64 {
85    let mut sum = G::from(0.0).unwrap();
86    for n in 0..x.len() - 1 {
87        sum = sum + G::from(100.0).unwrap() * ((x[n + 1] - x[n] * x[n]).powi(2)) + (G::from(1.0).unwrap() - x[n]).powi(2);
88    }
89
90    sum.to_f64().unwrap()
91}
ew_testfunc/lib.rs

ew_testfunc/
lib.rs
