1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
// 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. //! # Himmelblau test function //! //! Defined as //! //! `f(x_1, x_2) = (x_1^2 + x_2 - 11)^2 + (x_1 + x_2^2 - 7)^2` //! //! where `x_i \in [-5, 5]`. //! //! The global minima are at //! * `f(x_1, x_2) = f(3, 2) = 0`. //! * `f(x_1, x_2) = f(-2.805118, 3.131312) = 0`. //! * `f(x_1, x_2) = f(-3.779310, -3.283186) = 0`. //! * `f(x_1, x_2) = f(3.584428, -1.848126) = 0`. use num::{Float, FromPrimitive}; /// Himmelblau test function /// /// Defined as /// /// `f(x_1, x_2) = (x_1^2 + x_2 - 11)^2 + (x_1 + x_2^2 - 7)^2` /// /// where `x_i \in [-5, 5]`. /// /// The global minima are at /// * `f(x_1, x_2) = f(3, 2) = 0`. /// * `f(x_1, x_2) = f(-2.805118, 3.131312) = 0`. /// * `f(x_1, x_2) = f(-3.779310, -3.283186) = 0`. /// * `f(x_1, x_2) = f(3.584428, -1.848126) = 0`. pub fn himmelblau<T: Float + FromPrimitive>(param: &[T]) -> T { assert!(param.len() == 2); let (x1, x2) = (param[0], param[1]); (x1.powi(2) + x2 - T::from_f64(11.0).unwrap()).powi(2) + (x1 + x2.powi(2) - T::from_f64(7.0).unwrap()).powi(2) } mod tests { #[test] fn test_himmelblau_optimum() { assert!((::himmelblau(&[3.0_f32, 2.0_f32])).abs() < ::std::f32::EPSILON); assert!((::himmelblau(&[-2.805118_f32, 3.131312_f32])).abs() < ::std::f32::EPSILON); assert!((::himmelblau(&[-3.779310_f32, -3.283186_f32])).abs() < ::std::f32::EPSILON); assert!((::himmelblau(&[3.584428_f32, -1.848126_f32])).abs() < ::std::f32::EPSILON); // Since I don't know the 64bit location of the minima,the f64 version cannot be reliably // tested without allowing an error several magnitudes larger than EPSILON. // assert!((::himmelblau(&[3.0_f64, 2.0_f64])).abs() < ::std::f64::EPSILON); // assert!((::himmelblau(&[-2.805118_f64, 3.131312_f64])).abs() < ::std::f64::EPSILON); // assert!((::himmelblau(&[-3.779310_f64, -3.283186_f64])).abs() < ::std::f64::EPSILON); // assert!((::himmelblau(&[3.584428_f64, -1.848126_f64])).abs() < ::std::f64::EPSILON); } #[test] #[should_panic] fn test_himmelblau_param_length() { ::himmelblau(&[0.0_f32, -1.0_f32, 0.1_f32]); } }