argmin_testfunctions 0.1.1

Test functions for optimization algorithms
Documentation 
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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.

//! # Schaffer test function No. 2
//!
//! Defined as
//!
//! `f(x_1, x_2) = 0.5 + (sin^2(x_1^2 - x_2^2) - 0.5) / (1 + 0.001*(x_1^2 + x_2^2))^2`
//!
//! where `x_i \in [-100, 100]`.
//!
//! The global minimum is at `f(x_1, x_2) = f(0, 0) = 0`.
//!
//! # Schaffer test function No. 4
//!
//! Defined as
//!
//! `f(x_1, x_2) = 0.5 + (cos(sin(abs(x_1^2 - x_2^2)))^2 - 0.5) / (1 + 0.001*(x_1^2 + x_2^2))^2`
//!
//! where `x_i \in [-100, 100]`.
//!
//! The global minimum is at `f(x_1, x_2) = f(0, 1.25313) = 0.291992`.

use num::{Float, FromPrimitive};

/// Schaffer test function No. 2
///
/// Defined as
///
/// `f(x_1, x_2) = 0.5 + (sin^2(x_1^2 - x_2^2) - 0.5) / (1 + 0.001*(x_1^2 + x_2^2))^2`
///
/// where `x_i \in [-100, 100]`.
///
/// The global minimum is at `f(x_1, x_2) = f(0, 0) = 0`.
pub fn schaffer_n2<T: Float + FromPrimitive>(param: &[T]) -> T {
    let plen = param.len();
    assert!(plen == 2);
    let (x1, x2) = (param[0], param[1]);
    let n05 = T::from_f64(0.5).unwrap();
    let n1 = T::from_f64(1.0).unwrap();
    let n0001 = T::from_f64(0.0001).unwrap();
    n05 + ((x1.powi(2) - x2.powi(2)).sin().powi(2) - n05)
        / (n1 + n0001 * (x1.powi(2) + x2.powi(2))).powi(2)
}

/// Schaffer test function No. 4
///
/// Defined as
///
/// `f(x_1, x_2) = 0.5 + (cos(sin(abs(x_1^2 - x_2^2)))^2 - 0.5) / (1 + 0.001*(x_1^2 + x_2^2))^2`
///
/// where `x_i \in [-100, 100]`.
///
/// The global minimum is at `f(x_1, x_2) = f(0, 1.25313) = 0.291992`.
pub fn schaffer_n4<T: Float + FromPrimitive>(param: &[T]) -> T {
    let plen = param.len();
    assert!(plen == 2);
    let (x1, x2) = (param[0], param[1]);
    let n05 = T::from_f64(0.5).unwrap();
    let n1 = T::from_f64(1.0).unwrap();
    let n0001 = T::from_f64(0.0001).unwrap();
    n05 + ((x1.powi(2) - x2.powi(2)).abs().sin().cos().powi(2) - n05)
        / (n1 + n0001 * (x1.powi(2) + x2.powi(2))).powi(2)
}

mod tests {
    #[test]
    fn test_schaffer_n2_optimum() {
        assert!((::schaffer_n2(&[0_f32, 0_f32])).abs() < ::std::f32::EPSILON);
        assert!((::schaffer_n2(&[0_f64, 0_f64])).abs() < ::std::f64::EPSILON);
    }

    #[test]
    fn test_schaffer_n4_optimum() {
        assert!((::schaffer_n4(&[0_f32, 1.25313_f32]) - 0.291992).abs() < ::std::f32::EPSILON);
    }

    #[test]
    #[should_panic]
    fn test_schaffer_n2_param_length() {
        ::schaffer_n2(&[0.0_f32, 0.0_f32, 0.0_f32]);
    }

    #[test]
    #[should_panic]
    fn test_schaffer_n4_param_length() {
        ::schaffer_n4(&[0.0_f32, 0.0_f32, 0.0_f32]);
    }
}