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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. //! # Beale test function //! //! Defined as //! //! `f(x_1, x_2) = (1.5 - x_1 + x_1 * x_2)^2 + (2.25 - x_1 + x_1 * x_2^2)^2 + //! (2.625 - x_1 + x1 * x_2^3)^2` //! //! where `x_i \in [-4.5, 4.5]`. //! //! The global minimum is at `f(x_1, x_2) = f(3, 0.5) = 0`. use num::{Float, FromPrimitive}; /// Beale test function /// /// Defined as /// /// `f(x_1, x_2) = (1.5 - x_1 + x_1 * x_2)^2 + (2.25 - x_1 + x_1 * x_2^2)^2 + /// (2.625 - x_1 + x1 * x_2^3)^2` /// /// where `x_i \in [-4.5, 4.5]`. /// /// The global minimum is at `f(x_1, x_2) = f(3, 0.5) = 0`. pub fn beale<T: Float + FromPrimitive>(param: &[T]) -> T { assert!(param.len() == 2); let (x1, x2) = (param[0], param[1]); (T::from_f64(1.5).unwrap() - x1 + x1 * x2).powi(2) + (T::from_f64(2.25).unwrap() - x1 + x1 * (x2.powi(2))).powi(2) + (T::from_f64(2.625).unwrap() - x1 + x1 * (x2.powi(3))).powi(2) } mod tests { #[test] fn test_beale_optimum() { assert!(::beale(&[3.0_f32, 0.5_f32]).abs() < ::std::f32::EPSILON); assert!(::beale(&[3.0_f64, 0.5_f64]).abs() < ::std::f64::EPSILON); } #[test] #[should_panic] fn test_beale_param_length() { ::beale(&[0.0_f32, -1.0_f32, 0.1_f32]); } }