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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. //! # Cross-in-tray test function //! //! Defined as //! //! `f(x_1, x_2) = -0.0001 * ( | sin(x_1)*sin(x_2)*exp(| 100 - //! \sqrt{x_1^2+_2^2) / pi |) | + 1)^0.1` //! //! where `x_i \in [-10, 10]`. //! //! The global minima are at //! * `f(x_1, x_2) = f(1.34941, 1.34941) = -2.06261`. //! * `f(x_1, x_2) = f(1.34941, -1.34941) = -2.06261`. //! * `f(x_1, x_2) = f(-1.34941, 1.34941) = -2.06261`. //! * `f(x_1, x_2) = f(-1.34941, -1.34941) = -2.06261`. use std::f64::consts::PI; /// Cross-in-tray test function /// /// Defined as /// /// `f(x_1, x_2) = -0.0001 * ( | sin(x_1)*sin(x_2)*exp(| 100 - /// \sqrt{x_1^2+_2^2) / pi |) | + 1)^0.1` /// /// where `x_i \in [-10, 10]`. /// /// The global minima are at /// * `f(x_1, x_2) = f(1.34941, 1.34941) = -2.06261`. /// * `f(x_1, x_2) = f(1.34941, -1.34941) = -2.06261`. /// * `f(x_1, x_2) = f(-1.34941, 1.34941) = -2.06261`. /// * `f(x_1, x_2) = f(-1.34941, -1.34941) = -2.06261`. pub fn cross_in_tray(param: &[f64]) -> f64 { assert!(param.len() == 2); let (x1, x2) = (param[0], param[1]); // let pi = T::from_f64(PI).unwrap(); // T::from_f64(-0.0001).unwrap() // * ((x1.sin() * x2.sin() // * (T::from_f64(100.0).unwrap() - (x1.powi(2) + x2.powi(2)).sqrt() / pi) // .abs() // .exp()) // .abs() + T::from_f64(1.0).unwrap()) // .powf(T::from_f64(0.1).unwrap()) -0.0001 * ((x1.sin() * x2.sin() * (100.0 - (x1.powi(2) + x2.powi(2)).sqrt() / PI).abs().exp()).abs() + 1.0) .powf(0.1) } mod tests { #[test] fn test_cross_in_tray_optimum() { // This isnt exactly a great way to test this. The function can only be computed with the // use of f64; however, I only have the minimum points available in f32, which is why I use // the f32 EPSILONs. assert!( (::cross_in_tray(&[1.34941_f64, 1.34941_f64]) + 2.062611870).abs() < ::std::f32::EPSILON.into() ); assert!( (::cross_in_tray(&[1.34941_f64, -1.34941_f64]) + 2.062611870).abs() < ::std::f32::EPSILON.into() ); assert!( (::cross_in_tray(&[-1.34941_f64, 1.34941_f64]) + 2.062611870).abs() < ::std::f32::EPSILON.into() ); assert!( (::cross_in_tray(&[-1.34941_f64, -1.34941_f64]) + 2.062611870).abs() < ::std::f32::EPSILON.into() ); } #[test] #[should_panic] fn test_cross_in_tray_param_length() { ::cross_in_tray(&[0.0, -1.0, 0.1]); } }