/**
 * @file levy_function_n13.hpp
 * @author Suryoday Basak
 *
 * Definition 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_HPP
#define ENSMALLEN_PROBLEMS_LEVY_FUNCTION_N13_HPP

namespace ens {
namespace test {

/**
 * The Levy function N.13, defined by
 *
 * \f[
 * f(x_1, x_2) = sin(3 * pi * x_1)^2 + (x_1 - 1)^2 *
 *               (1 + (sin(3 * pi * x_2)^2)) +
 *               (x_2 - 1)^2 * (1 + sin(2 * pi * x_2)^2)
 * \f]
 * This should optimize to f(x_1, x_2) = 0, at x = [1, 1].
 *
 * For more information, please refer to:
 *
 * @code
 * @misc{LevyFunction,
 *   URL = {http://www.sfu.ca/~ssurjano/levy13.html},
 * }
 * @endcode
 */
class LevyFunctionN13
{
 public:
  //! Initialize the LevyFunctionN13 object.
  LevyFunctionN13();

  /**
   * Shuffle the order of function visitation. This may be called by the
   * optimizer.
   */
  void Shuffle();

  //! Return 1 (the number of functions).
  size_t NumFunctions() const { return 1; }

  /**
   * Evaluate a function for a particular batch-size.
   *
   * @param coordinates The function coordinates.
   * @param begin The first function.
   * @param batchSize Number of points to process.
   */
  template<typename MatType>
  typename MatType::elem_type Evaluate(const MatType& coordinates,
                                       const size_t begin,
                                       const size_t batchSize) const;

  /**
   * Evaluate a function with the given coordinates.
   *
   * @param coordinates The function coordinates.
   */
  template<typename MatType>
  typename MatType::elem_type Evaluate(const MatType& coordinates) const;

  /**
   * Evaluate the gradient of a function for a particular batch-size.
   *
   * @param coordinates The function coordinates.
   * @param begin The first function.
   * @param gradient The function gradient.
   * @param batchSize Number of points to process.
   */
  template<typename MatType, typename GradType>
  void Gradient(const MatType& coordinates,
                const size_t begin,
                GradType& gradient,
                const size_t batchSize) const;

  /**
   * Evaluate the gradient of a function with the given coordinates.
   *
   * @param coordinates The function coordinates.
   * @param gradient The function gradient.
   */
  template<typename MatType, typename GradType>
  void Gradient(const MatType& coordinates, GradType& gradient);

  // Note: GetInitialPoint(), GetFinalPoint(), and GetFinalObjective() are not
  // required for using ensmallen to optimize this function!  They are
  // specifically used as a convenience just for ensmallen's testing
  // infrastructure.

  //! Get the starting point.
  template<typename MatType = arma::mat>
  MatType GetInitialPoint() const { return MatType("0.9; 1.1"); }

  //! Get the final point.
  template<typename MatType = arma::mat>
  MatType GetFinalPoint() const { return MatType("1.0; 1.0"); }

  //! Get the final objective.
  double GetFinalObjective() const { return 0.0; }
};

} // namespace test
} // namespace ens

// Include implementation.
#include "levy_function_n13_impl.hpp"

#endif // ENSMALLEN_PROBLEMS_LEVY_FUNCTION_N13_HPP
