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// Copyright 2018 Stefan Kroboth // // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or // http://apache.org/licenses/LICENSE-2.0> or the MIT license <LICENSE-MIT or // http://opensource.org/licenses/MIT>, at your option. This file may not be // copied, modified, or distributed except according to those terms. //! # Rastrigin test function //! //! Defined as //! //! `f(x_1, x_2, ..., x_n) = a * n + \sum_{i=1}^{n} \left[ x_i^2 - a * cos(2 * pi * x_i) \right]` //! //! where `x_i \in [-5.12, 5.12]` and `a = 10` //! //! The global minimum is at `f(x_1, x_2, ..., x_n) = f(0, 0, ..., 0) = 0`. use num::{Float, FromPrimitive}; use std::f64::consts::PI; use std::iter::Sum; /// Rastrigin test function /// /// Defined as /// /// `f(x_1, x_2, ..., x_n) = a * n + \sum_{i=1}^{n} \left[ x_i^2 - a * cos(2 * pi * x_i) \right]` /// /// where `x_i \in [-5.12, 5.12]` and `a = 10` /// /// The global minimum is at `f(x_1, x_2, ..., x_n) = f(0, 0, ..., 0) = 0`. pub fn rastrigin<T: Float + FromPrimitive + Sum>(param: &[T]) -> T { rastrigin_a(param, T::from_f64(10.0).unwrap()) } /// Rastrigin test function /// /// The same as `rastrigin`; however, it allows to set the parameter a. pub fn rastrigin_a<T: Float + FromPrimitive + Sum>(param: &[T], a: T) -> T { a * T::from_usize(param.len()).unwrap() + param .iter() .map(|&x| x.powi(2) - a * (T::from_f64(2.0 * PI).unwrap() * x).cos()) .sum() } mod tests { // use super::{rastrigin, rastrigin_a}; // use std; #[test] fn test_rastrigin_optimum() { assert!(::rastrigin(&[0.0_f32, 0.0_f32]).abs() < ::std::f32::EPSILON); assert!(::rastrigin(&[0.0_f64, 0.0_f64]).abs() < ::std::f64::EPSILON); } #[test] fn test_parameter_a() { assert!( ::rastrigin(&[0.0_f32, 0.0_f32]).abs() == ::rastrigin_a(&[0.0_f32, 0.0_f32], 10.0).abs() ); } }