/**
 * @file levy_function_n13_impl.hpp
 * @author Suryoday Basak
 *
 * Implementation of the Levy function N.13.
 *
 * ensmallen is free software; you may redistribute it and/or modify it under
 * the terms of the 3-clause BSD license.  You should have received a copy of
 * the 3-clause BSD license along with ensmallen.  If not, see
 * http://www.opensource.org/licenses/BSD-3-Clause for more information.
 */
#ifndef ENSMALLEN_PROBLEMS_LEVY_FUNCTION_N13_IMPL_HPP
#define ENSMALLEN_PROBLEMS_LEVY_FUNCTION_N13_IMPL_HPP

// In case it hasn't been included yet.
#include "levy_function_n13.hpp"

namespace ens {
namespace test {

inline LevyFunctionN13::LevyFunctionN13() { /* Nothing to do here */ }

inline void LevyFunctionN13::Shuffle() { /* Nothing to do here */ }

template<typename MatType>
typename MatType::elem_type LevyFunctionN13::Evaluate(
    const MatType& coordinates,
    const size_t /* begin */,
    const size_t /* batchSize */) const
{
  // Convenience typedef.
  typedef typename MatType::elem_type ElemType;

  // For convenience; we assume these temporaries will be optimized out.
  const ElemType x1 = coordinates(0);
  const ElemType x2 = coordinates(1);

  const ElemType objective =
      std::pow(std::sin(3 * arma::Datum<ElemType>::pi * x1), ElemType(2)) +
      (std::pow(x1 - 1, ElemType(2)) * (1 + std::pow(
          std::sin(3 * arma::Datum<ElemType>::pi * x2), ElemType(2)))) +
      (std::pow(x2 - 1, ElemType(2)) * (1 + std::pow(
          std::sin(2 * arma::Datum<ElemType>::pi * x2), ElemType(2))));

  return objective;
}

template<typename MatType>
typename MatType::elem_type LevyFunctionN13::Evaluate(
    const MatType& coordinates) const
{
  return Evaluate(coordinates, 0, NumFunctions());
}

template<typename MatType, typename GradType>
inline void LevyFunctionN13::Gradient(const MatType& coordinates,
                                      const size_t /* begin */,
                                      GradType& gradient,
                                      const size_t /* batchSize */) const
{
  // Convenience typedef.
  typedef typename MatType::elem_type ElemType;

  // For convenience; we assume these temporaries will be optimized out.
  const ElemType x1 = coordinates(0);
  const ElemType x2 = coordinates(1);
  gradient.set_size(2, 1);

  gradient(0) = (2 * x1 - 2) *
      (std::pow(std::sin(3 * arma::Datum<ElemType>::pi * x2), ElemType(2)) +
      1) + 6 * arma::Datum<ElemType>::pi *
      std::sin(3 * arma::Datum<ElemType>::pi * x1) *
      std::cos(3 * arma::Datum<ElemType>::pi * x1);

  gradient(1) = 6 * arma::Datum<ElemType>::pi * std::pow(x1 - 1, ElemType(2)) *
      std::sin(3 * arma::Datum<ElemType>::pi * x2) *
      std::cos(3 * arma::Datum<ElemType>::pi * x2) +
      4 * arma::Datum<ElemType>::pi * std::pow(x2 - 1, ElemType(2)) *
      std::sin(2 * arma::Datum<ElemType>::pi * x2) *
      std::cos(2 * arma::Datum<ElemType>::pi * x2) + (2 * x2 - 2) *
      (std::pow(std::sin(2 * arma::Datum<ElemType>::pi * x2), ElemType(2)) + 1);
}

template<typename MatType, typename GradType>
inline void LevyFunctionN13::Gradient(const MatType& coordinates,
                                      GradType& gradient)
{
  Gradient(coordinates, 0, gradient, 1);
}

} // namespace test
} // namespace ens

#endif
