/*
 * 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>

/* simple n-d quadratic function */
template<typename RealType>
RealType
quadratic(std::vector<RealType>& x)
{
  RealType res{ 0.0 };
  for (auto& item : x) {
    res += item * item;
  }
  return res;
}

template<typename RealType>
RealType
quadratic_high_cond_2D(std::vector<RealType>& x)
{
  return 1000 * x[0] * x[0] + x[1] * x[1];
}

// Taken from: https://en.wikipedia.org/wiki/Test_functions_for_optimization
template<typename Real>
Real
ackley(std::array<Real, 2> const& v)
{
  using boost::math::constants::e;
  using boost::math::constants::two_pi;
  using std::cos;
  using std::exp;
  using std::sqrt;
  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 boost::math::constants::two_pi;
  using std::cos;
  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