Schaffer2.hh

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/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\
 * Copyright (c) 2025, Davide Stocco, Mattia Piazza and Enrico Bertolazzi.                       *
 *                                                                                               *
 * The Optimist project is distributed under the BSD 2-Clause License.                           *
 *                                                                                               *
 * Davide Stocco                          Mattia Piazza                        Enrico Bertolazzi *
 * University of Trento               University of Trento                  University of Trento *
 * davide.stocco@unitn.it            mattia.piazza@unitn.it           enrico.bertolazzi@unitn.it *
\* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
 
#pragma once
 
#ifndef OPTIMIST_TESTSET_SCHAFFER2_HH
#define OPTIMIST_TESTSET_SCHAFFER2_HH
 
#include "Optimist/TestSet.hh"
 
namespace Optimist
{
 
  namespace TestSet
  {

    template <typename Real>
    class Schaffer2 : public Function<Real, 2, 1, Schaffer2<Real>>
    {
    public:
      using Vector    = typename Function<Real, 2, 1, Schaffer2<Real>>::Vector;
      using RowVector = typename Function<Real, 2, 1, Schaffer2<Real>>::RowVector;
      using Matrix    = typename Function<Real, 2, 1, Schaffer2<Real>>::Matrix;
 
      OPTIMIST_BASIC_CONSTANTS(Real) 
 
      
      Schaffer2()
      {
        this->m_solutions.emplace_back(0.0, 0.0);
        for (Real x{-100}; x < 100 + EPSILON; x += 100/25.0) {
          for (Real y{-100}; y < 100 + EPSILON; y += 100/25.0) {
            this->m_guesses.emplace_back(x, y);
          }
        }
      }

      std::string name_impl() const {return "Schaffer2";}

      void evaluate_impl(const Vector & x, Real & out) const
      {
        Real xx_0{x(0)*x(0)};
        Real xx_1{x(1)*x(1)};
        Real xx_0_m_xx_1{xx_0 - xx_1};
        Real xx_0_p_xx_1{xx_0 + xx_1};
        out = 0.5 + (std::sin(xx_0_m_xx_1)*std::sin(xx_0_m_xx_1) - 0.5) /
          ((1.0 + 0.001*(xx_0_p_xx_1))*(1.0 + 0.001*(xx_0_p_xx_1)));
      }

      void first_derivative_impl(const Vector & x, RowVector & out) const
      {
        Real xx_0{x(0)*x(0)};
        Real xx_1{x(1)*x(1)};
        Real xx_0_m_xx_1{xx_0 - xx_1};
        Real xx_0_p_xx_1{xx_0 + xx_1};
        Real tmp{1.0 + 0.001*(xx_0_p_xx_1)};
        Real tmp2{tmp*tmp}, tmp3{tmp2*tmp};
        out(0) = 2.0*x(0)*std::sin(xx_0_m_xx_1) / tmp2 -
          2.0*0.001*x(0)*std::cos(xx_0_m_xx_1) / tmp3;
        out(1) = -2.0*x(1)*std::sin(xx_0_m_xx_1) / tmp2 +
          2.0*0.001*x(1)*std::cos(xx_0_m_xx_1) / tmp3;
      }

      void second_derivative_impl(const Vector & x, Matrix & out) const
      {
        Real xx_0{x(0)*x(0)};
        Real xx_1{x(1)*x(1)};
        Real xx_0_m_xx_1{xx_0 - xx_1};
        Real xx_0_p_xx_1{xx_0 + xx_1};
        Real tmp{1.0 + 0.001*(xx_0_p_xx_1)};
        Real tmp2{tmp*tmp}, tmp3{tmp2*tmp}, tmp4{tmp2*tmp2};
        out(0, 0) = 2.0*std::sin(xx_0_m_xx_1) / tmp2 -
          4.0*x(0)*x(0)*std::sin(xx_0_m_xx_1) / tmp3 +
          6.0*0.001*x(0)*x(0)*std::cos(xx_0_m_xx_1) / tmp4;
        out(0, 1) = -2.0*x(0)*x(1)*std::sin(xx_0_m_xx_1) / tmp3 +
          6.0*0.001*x(0)*x(1)*std::cos(xx_0_m_xx_1) / tmp4;
        out(1, 0) = out(0, 1);
        out(1, 1) = 2.0*std::sin(xx_0_m_xx_1) / tmp2 -
          4.0*x(1)*x(1)*std::sin(xx_0_m_xx_1) / tmp3 +
          6.0*0.001*x(1)*x(1)*std::cos(xx_0_m_xx_1) / tmp4;
      }
 
    }; // class Schaffer2
 
  } // namespace TestSet
 
} // namespace Optimist
 
#endif // OPTIMIST_TESTSET_SCHAFFER2_HH