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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. //! # Sphere function //! //! Defined as //! //! `f(x) = \sum_{i=1}^n x_i^2` //! //! where `x_i \in (-\infty, \infty)` //! //! The minimum is at `f(x_1, x_2, ..., x_n) = f(0, 0, ..., 0) = 0`. use num::{Float, FromPrimitive}; use std::iter::Sum; /// Sphere test function /// /// Defined as /// /// `f(x_1, x_2, ..., x_n) = \sum_{i=1}^n x_i^2 /// /// where `x_i \in (-\infty, \infty)` and `n > 0`. /// /// The global minimum is at `f(x_1, x_2, ..., x_n) = f(0, 0, ..., 0) = 0`. pub fn sphere<T: Float + FromPrimitive + Sum>(param: &[T]) -> T { param.iter().map(|x| x.powi(2)).sum() } /// Derivative of sphere test function /// /// Defined as /// /// `f(x_1, x_2, ..., x_n) = (2 * x_1, 2 * x_2, ... 2 * x_n)` /// /// where `x_i \in (-\infty, \infty)` and `n > 0`. pub fn sphere_derivative<T: Float + FromPrimitive>(param: &[T]) -> Vec<T> { let num2 = T::from_f64(2.0).unwrap(); param.iter().map(|x| num2 * *x).collect() } #[cfg(test)] mod tests { use super::*; use std; #[test] fn test_sphere_optimum() { assert!(sphere(&[0.0_f32, 0.0_f32]).abs() < std::f32::EPSILON); assert!(sphere(&[0.0_f64, 0.0_f64]).abs() < std::f64::EPSILON); } }