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/*
* Copyright Nick Thompson, 2024
* Use, modification and distribution are subject to the
* Boost Software License, Version 1.0. (See accompanying file
* LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
*/
#ifndef TEST_FUNCTIONS_FOR_OPTIMIZATION_HPP
#define TEST_FUNCTIONS_FOR_OPTIMIZATION_HPP
#include <boost/math/constants/constants.hpp>
#include <array>
#include <vector>
// Taken from: https://en.wikipedia.org/wiki/Test_functions_for_optimization
template <typename Real> Real ackley(std::array<Real, 2> const &v) {
using std::sqrt;
using std::cos;
using std::exp;
using boost::math::constants::two_pi;
using boost::math::constants::e;
Real x = v[0];
Real y = v[1];
Real arg1 = -sqrt((x * x + y * y) / 2) / 5;
Real arg2 = cos(two_pi<Real>() * x) + cos(two_pi<Real>() * y);
return -20 * exp(arg1) - exp(arg2 / 2) + 20 + e<Real>();
}
template <typename Real> auto rosenbrock_saddle(std::array<Real, 2> const &v) -> Real {
Real x { v[0] };
Real y { v[1] };
return static_cast<Real>(100 * (x * x - y) * (x * x - y) + (1 - x) * (1 - x));
}
template <class Real> Real rastrigin(std::vector<Real> const &v) {
using std::cos;
using boost::math::constants::two_pi;
auto A = static_cast<Real>(10);
auto y = static_cast<Real>(10 * v.size());
for (auto x : v) {
y += x * x - A * cos(two_pi<Real>() * x);
}
return y;
}
// Useful for testing return-type != scalar argument type,
// and robustness to NaNs:
double sphere(std::vector<float> const &v) {
double r = 0.0;
for (auto x : v) {
double x_ = static_cast<double>(x);
r += x_ * x_;
}
if (r >= 1) {
return std::numeric_limits<double>::quiet_NaN();
}
return r;
}
template<typename Real>
Real three_hump_camel(std::array<Real, 2> const & v) {
Real x = v[0];
Real y = v[1];
auto xsq = x*x;
return 2*xsq - (1 + Real(1)/Real(20))*xsq*xsq + xsq*xsq*xsq/6 + x*y + y*y;
}
// Minima occurs at (3, 1/2) with value 0:
template<typename Real>
Real beale(std::array<Real, 2> const & v) {
Real x = v[0];
Real y = v[1];
Real t1 = Real(3)/Real(2) -x + x*y;
Real t2 = Real(9)/Real(4) -x + x*y*y;
Real t3 = Real(21)/Real(8) -x + x*y*y*y;
return t1*t1 + t2*t2 + t3*t3;
}
#endif
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