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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);
    }
}