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// Copyright 2018 Stefan Kroboth
//
// copied, modified, or distributed except according to those terms.

//! # Ackley test function
//!
//! Defined as
//!
//! f(x_1, x_2, ..., x_n) = - a * exp( -b \sqrt{\frac{1}{d}\sum_{i=1}^n x_i^2 ) -
//! exp( \frac{1}{d} cos(c * x_i) ) + a + exp(1)
//!
//! where x_i \in [-32.768, 32.768] and usually a = 10, b = 0.2 and c = 2*pi
//!
//! 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;

/// Ackley test function
///
/// Defined as
///
/// f(x_1, x_2, ..., x_n) = - a * exp( -b \sqrt{\frac{1}{d}\sum_{i=1}^n x_i^2 ) -
/// exp( \frac{1}{d} cos(c * x_i) ) + a + exp(1)
///
/// where x_i \in [-32.768, 32.768] and usually a = 10, b = 0.2 and c = 2*pi
///
/// The global minimum is at f(x_1, x_2, ..., x_n) = f(0, 0, ..., 0) = 0.
pub fn ackley<T: Float + FromPrimitive + Sum>(param: &[T]) -> T {
ackley_param(
param,
T::from_f64(20.0).unwrap(),
T::from_f64(0.2).unwrap(),
T::from_f64(2.0 * PI).unwrap(),
)
}

/// Ackley test function
///
/// The same as ackley; however, it allows to set the parameters a, b and c.
pub fn ackley_param<T: Float + FromPrimitive + Sum>(param: &[T], a: T, b: T, c: T) -> T {
let num1 = T::from_f64(1.0).unwrap();
let n = T::from_usize(param.len()).unwrap();
-a * (-b * ((num1 / n) * param.iter().map(|x| x.powi(2)).sum()).sqrt()).exp()
- ((num1 / n) * param.iter().map(|x| (c * *x).cos()).sum()).exp() + a + num1.exp()
}

mod tests {

#[test]
fn test_ackley_optimum() {
// There seem to be numerical problems which is why the epsilons are multiplied with a
// factor. Not sure if this is acceptable...
assert!(::ackley(&[0.0_f32, 0.0_f32, 0.0_f32]).abs() < ::std::f32::EPSILON * 10_f32);
assert!(::ackley(&[0.0_f64, 0.0_f64, 0.0_f64]).abs() < ::std::f64::EPSILON * 3_f64);
}

#[test]
fn test_parameters() {
assert!(
::ackley(&[0.0_f64, 0.0_f64, 0.0_f64]).abs()
== ::ackley_param(
&[0.0_f64, 0.0_f64, 0.0_f64],
20.0,
0.2,
2.0 * ::std::f64::consts::PI
).abs()
);
}
}