/**
 * @file maf6_function.hpp
 * @author Satyam Shukla
 *
 * Implementation of the sixth Maf test.
 *
 * 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_MAF_SIX_FUNCTION_HPP
#define ENSMALLEN_PROBLEMS_MAF_SIX_FUNCTION_HPP

namespace ens {
namespace test {

/**
 * The MAF6 function, defined by:
 * \f[
 * theta_M = [theta_i, n - M + 1 <= i <= n]
 * g(x) = \Sigma{i = n - M + 1}^n (x_i - 0.5)^2
 *
 * f_1(x) = 0.5 * cos(theta_1 * pi * 0.5) * cos(theta_2 * pi * 0.5) * ... cos(theta_2 * pi * 0.5) * (1 + g(theta_M))
 * f_2(x) = 0.5 * cos(theta_1 * pi * 0.5) * cos(theta_2 * pi * 0.5) * ... sin(theta_M-1 * pi * 0.5) * (1 + g(theta_M))
 * .
 * .
 * f_M(x) = 0.5 * sin(theta_1 * pi * 0.5) * (1 + g(theta_M))
 * \f]
 *
 * Bounds of the variable space is:
 * 0 <= x_i <= 1 for i = 1,...,n.
 *
 * Where theta_i = 0.5 * (1 + 2 * g(X_M) * x_i) / (1 + g(X_M))
 *
 * This should be optimized to x_i = 0.5 (for all x_i in X_M), at:
 *
 * For more information, please refer to:
 *
 * @code
 * @article{cheng2017benchmark,
 * title={A benchmark test suite for evolutionary many-objective optimization},
 * author={Cheng, Ran and Li, Miqing and Tian, Ye and Zhang, Xingyi and Yang, Shengxiang and Jin, Yaochu and Yao, Xin},
 * journal={Complex \& Intelligent Systems},
 * volume={3},
 * pages={67--81},
 * year={2017},
 * publisher={Springer}
 * }
 * @endcode
 *
 * @tparam MatType Type of matrix to optimize.
 */
template <typename MatType = arma::mat>
class MAF6
{
 private:
  // A fixed no. of Objectives and Variables(|x| = 7, M = 3).
  size_t numObjectives {3};
  size_t numVariables {12};
  size_t I;

 public:
  /**
   * Object Constructor.
   * Initializes the individual objective functions.
   *
   * @param numParetoPoint No. of pareto points in the reference front.
   * @param I The manifold dimension (zero indexed).
   */
  MAF6(size_t I = 2) :
      objectiveF1(0, *this),
      objectiveF2(1, *this),
      objectiveF3(2, *this),
      I(I)
  {/*Nothing to do here.*/}

  //! Get the starting point.
  arma::Col<typename MatType::elem_type> GetInitialPoint()
  {
    // Convenience typedef.
    typedef typename MatType::elem_type ElemType;
    return arma::Col<ElemType>(numVariables, 1, arma::fill::zeros);
  }

  // Get the private variables.

  // Get the number of objectives.
  size_t GetNumObjectives() { return numObjectives; }

  // Get the number of variables.
  size_t GetNumVariables() { return numVariables; }

  // Get the manifold dimension.
  size_t GetI() { return I; }

  /**
   * Set the no. of pareto points.
   *
   * @param I The manifold dimension (0 indexed).
   */
  void SetI(size_t I) { this->I = I; }

  /**
   * Evaluate the G(x) with the given coordinate.
   *
   * @param coords The function coordinates.
   * @return arma::Row<typename MatType::elem_type>
   */
  arma::Row<typename MatType::elem_type> g(const MatType& coords)
  {
    // Convenience typedef.
    typedef typename MatType::elem_type ElemType;

    arma::Row<ElemType> innerSum(size(coords)[1], arma::fill::zeros);

    for (size_t i = numObjectives - 1; i < numVariables; i++)
    {
      innerSum += arma::pow((coords.row(i) - 0.5), 2);
    }

    return innerSum;
  }

  /**
   * Evaluate the objectives with the given coordinate.
   *
   * @param coords The function coordinates.
   * @return arma::Mat<typename MatType::elem_type>
   */
  arma::Mat<typename MatType::elem_type> Evaluate(const MatType& coords)
  {
    // Convenience typedef.
    typedef typename MatType::elem_type ElemType;

    arma::Mat<ElemType> objectives(numObjectives, size(coords)[1]);
    arma::Row<ElemType> G = g(coords);
    arma::Row<ElemType> value = (1.0 + 100 * G);
    arma::Row<ElemType> theta;
    for (size_t i = 0; i < numObjectives - 1; i++)
    {
      if (i < I)
      {
        theta = coords.row(i) * arma::datum::pi * 0.5;
      }
      else
      {
        theta = 0.25 * (1.0  + 2.0 * coords.row(i) % G) / (1.0 + G);
      }
      objectives.row(i) =  value %
          arma::sin(theta);
      value = value % arma::cos(theta);
    }
    objectives.row(numObjectives - 1) = value;
    return objectives;
  }

  // Individual Objective function.
  // Changes based on stop variable provided.
  struct MAF6Objective
  {
    MAF6Objective(size_t stop, MAF6& maf): stop(stop), maf(maf)
    {/* Nothing to do here. */}

    /**
     * Evaluate one objective with the given coordinate.
     *
     * @param coords The function coordinates.
     * @return arma::Col<typename MatType::elem_type>
     */
    typename MatType::elem_type Evaluate(const MatType& coords)
    {
      // Convenience typedef.
      typedef typename MatType::elem_type ElemType;
      ElemType value = 1.0;
      ElemType theta;
      ElemType G = maf.g(coords)[0];
      for (size_t i = 0; i < stop; i++)
      {
        if (i < maf.GetI())
        {
          theta = arma::datum::pi * coords[i] * 0.5;
        }
        else
        {
          theta = 0.25 * (1.0  + 2.0 * coords[i] * G) / (1.0 + G);
        }
        value = value * std::cos(theta);
      }

      if (stop < maf.GetI())
      {
        theta = arma::datum::pi * coords[stop] * 0.5;
      }
      else
      {
        theta = 0.25 * (1.0  + 2.0 * coords[stop] * G) / (1.0 + G);
      }

      if (stop != maf.GetNumObjectives() - 1)
      {
        value = value * std::sin(theta);
      }

      value = value * (1.0 + 100 * G);
      return value;
    }

    MAF6& maf;
    size_t stop;
  };

  // Return back a tuple of objective functions.
  std::tuple<MAF6Objective, MAF6Objective, MAF6Objective> GetObjectives()
  {
    return std::make_tuple(objectiveF1, objectiveF2, objectiveF3);
  }

  MAF6Objective objectiveF1;
  MAF6Objective objectiveF2;
  MAF6Objective objectiveF3;
};

} // namespace test
} // namespace ens

#endif
