/**
 * @file dtlz1_function.hpp
 * @author Satyam Shukla
 *
 * Implementation of the first DTLZ(Deb, Thiele, Laumanns, and Zitzler) 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_DTLZ_ONE_FUNCTION_HPP
#define ENSMALLEN_PROBLEMS_DTLZ_ONE_FUNCTION_HPP

#include "../../moead/weight_init_policies/uniform_init.hpp"

namespace ens {
namespace test {

/**
 * The DTLZ1 function, defined by:
 * \f[
 * x_M = [x_i, n - M + 1 <= i <= n]
 * g(x) = 100 * [|x_M| + \Sigma{i = n - M + 1}^n (x_i - 0.5)^2 - cos(20 * pi * 
 *   (x_i - 0.5))]
 * 
 * f_1(x) = 0.5 * x_1 * x_2 * ... x_M-1 * (1 + g(x_M)) 
 * f_2(x) = 0.5 * x_1 * x_2 * ... (1 - x_M-1) * (1 + g(x_M))
 * .
 * .
 * f_M(x) = 0.5 * (1 - x_1) * (1 + g(x_M))
 * \f]
 *
 * Bounds of the variable space is:
 * 0 <= x_i <= 1 for i = 1,...,n.
 *
 * This should be optimized to x_i = 0.5 (for all x_i in x_M), at:
 * the objective function values lie on the linear hyper-plane: 
 * \Sigma { m = 1}^M f_m* =0.5.
 *
 * For more information, please refer to:
 *
 * @code
 * @incollection{deb2005scalable,
 * title={Scalable test problems for evolutionary multiobjective optimization},
 * author={Deb, Kalyanmoy and Thiele, Lothar and Laumanns, Marco and Zitzler, Eckart},
 * booktitle={Evolutionary multiobjective optimization: theoretical advances and applications},
 * pages={105--145},
 * year={2005},
 * publisher={Springer}
 * }
 * @endcode
 *
 * @tparam MatType Type of matrix to optimize.
 */
  template <typename MatType = arma::mat>
  class DTLZ1
  {
    private:

    // A fixed no. of Objectives and Variables(|x| = 7, M = 3).
    size_t numObjectives {3};
    size_t numVariables {7};
    size_t numParetoPoints;

    public:

      /**
       * Object Constructor.
       * Initializes the individual objective functions.
       *
       * @param numParetoPoint No. of pareto points in the reference front.
       */
      DTLZ1 (size_t numParetoPoint = 136) :
        numParetoPoints(numParetoPoint),
        objectiveF1(0, *this),
        objectiveF2(1, *this),
        objectiveF3(2, *this)
      {/* Nothing to do here */}

      // Get the private variables.
      
      // Get the number of objectives.
      size_t GetNumObjectives()
      { return this -> numObjectives; }

      // Get the number of Variables.
      size_t GetNumVariables()
      { return this -> numVariables; }

      /**
      * Set the no. of pareto points.
      *
      * @param numParetoPoint No. of pareto points in the reference front.
      */
      void SetNumParetoPoint (size_t numParetoPoint)
      { this -> numParetoPoints = numParetoPoint; }

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

      /**
      * 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)
      {
        size_t k = numVariables - numObjectives + 1;

        // 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) - 
              arma::cos(20 * arma::datum::pi * (coords.row(i) - 0.5)); 
        } 
        
        return 100 * (k + 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 = 0.5 * (1. + G);
        for (size_t i = 0; i < numObjectives - 1; i++)
        {
          objectives.row(i) =  value % (1.0 - coords.row(i));
          value = value % coords.row(i);
        }
        objectives.row(numObjectives - 1) = value;
        return objectives;    
      }
      
      // Individual Objective function.
      // Changes based on stop variable provided. 
      struct DTLZObjective
      {
        DTLZObjective(size_t stop, DTLZ1<MatType>& dtlz) : stop(stop), dtlz(dtlz)
        {/* 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 = 0.5;
          for (size_t i = 0; i < stop; i++)
          {
            value = value * coords[i];
          }

          if(stop != dtlz.numObjectives - 1)
          {
            value = value * (1. - coords[stop]);
          }
          else
          {
            value = value * coords[stop];
          }

          value = value * (1. + dtlz.g(coords)[0]);
          return value; 
        }        

        DTLZ1& dtlz;
        size_t stop;
      };

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

      //! Get the Reference Front.
      //! Front. The implementation has been taken from pymoo.
      arma::mat GetReferenceFront()
      {
        Uniform refGenerator;
        return 0.5 * refGenerator.Generate<arma::mat>(3, numParetoPoints, 0);
      }

    DTLZObjective objectiveF1;
    DTLZObjective objectiveF2;
    DTLZObjective objectiveF3;
  };
  } //namespace test
  } //namespace ens

#endif
