Schaffer2.hh

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

    template <typename Vector>
      requires TypeTrait<Vector>::IsEigen && (!TypeTrait<Vector>::IsFixed ||
                                              TypeTrait<Vector>::Dimension == 2)
    class Schaffer2
        : public Function<Vector, typename Vector::Scalar, Schaffer2<Vector>> {
     public:
      using VectorTrait = TypeTrait<Vector>;
      using Scalar      = typename Vector::Scalar;
      using typename Function<Vector,
                              typename Vector::Scalar,
                              Schaffer2<Vector>>::FirstDerivative;
      using typename Function<Vector,
                              typename Vector::Scalar,
                              Schaffer2<Vector>>::SecondDerivative;
 
      OPTIMIST_BASIC_CONSTANTS(Scalar)
 
      
      Schaffer2() {
        this->m_solutions.resize(1);
        this->m_guesses.resize(2);
        this->m_solutions.resize(1);
        this->m_guesses.resize(2);
        if constexpr (VectorTrait::IsFixed) {
          this->m_solutions[0] << 0.0, 0.0;
          this->m_guesses[0] << -10, -10;
          this->m_guesses[1] << 10, 10;
        } else if constexpr (!VectorTrait::IsSparse) {
          this->m_solutions[0].resize(2);
          this->m_solutions[0] << 0.0, 0.0;
          this->m_guesses[0].resize(2);
          this->m_guesses[0] << -10, -10;
          this->m_guesses[1].resize(2);
          this->m_guesses[1] << 10, 10;
        } else if constexpr (VectorTrait::IsSparse) {
          this->m_solutions[0].resize(2);
          this->m_solutions[0].reserve(2);
          this->m_solutions[0].coeffRef(0) = 0.0;
          this->m_solutions[0].coeffRef(1) = 0.0;
          this->m_guesses[0].resize(2);
          this->m_guesses[0].reserve(2);
          this->m_guesses[0].coeffRef(0) = -10;
          this->m_guesses[0].coeffRef(1) = -10;
          this->m_guesses[1].resize(2);
          this->m_guesses[1].reserve(2);
          this->m_guesses[1].coeffRef(0) = 10;
          this->m_guesses[1].coeffRef(1) = 10;
        }
      }

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

      bool evaluate_impl(const Vector &x, Scalar &out) const {
        Scalar xx_0, xx_1;
        if constexpr (VectorTrait::IsSparse) {
          xx_0 = x.coeff(0) * x.coeff(0);
          xx_1 = x.coeff(1) * x.coeff(1);
        } else {
          xx_0 = x(0) * x(0);
          xx_1 = x(1) * x(1);
        }
        Scalar xx_0_m_xx_1{xx_0 - xx_1};
        Scalar 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)));
        return std::isfinite(out);
      }

      bool first_derivative_impl(const Vector &x, FirstDerivative &out) const {
        Scalar xx_0, xx_1;
        if constexpr (VectorTrait::IsSparse) {
          xx_0 = x.coeff(0) * x.coeff(0);
          xx_1 = x.coeff(1) * x.coeff(1);
        } else {
          xx_0 = x(0) * x(0);
          xx_1 = x(1) * x(1);
        }
        Scalar xx_0_m_xx_1{xx_0 - xx_1};
        Scalar xx_0_p_xx_1{xx_0 + xx_1};
        Scalar tmp{static_cast<Scalar>(1.0) +
                   static_cast<Scalar>(0.001) * xx_0_p_xx_1};
        Scalar tmp2{tmp * tmp}, tmp3{tmp2 * tmp};
        if constexpr (VectorTrait::IsFixed) {
          out << 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,
              -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;
        } else if constexpr (VectorTrait::IsDynamic) {
          out.resize(2);
          out << 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,
              -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;
        } else if constexpr (VectorTrait::IsSparse) {
          out.resize(2);
          out.reserve(2);
          out.coeffRef(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.coeffRef(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;
        }
 
        return out.allFinite();
      }

      bool second_derivative_impl(const Vector &x,
                                  SecondDerivative &out) const {
        Scalar xx_0, xx_1;
        if constexpr (VectorTrait::IsSparse) {
          xx_0 = x.coeff(0) * x.coeff(0);
          xx_1 = x.coeff(1) * x.coeff(1);
        } else {
          xx_0 = x(0) * x(0);
          xx_1 = x(1) * x(1);
        }
        Scalar xx_0_m_xx_1{xx_0 - xx_1};
        Scalar xx_0_p_xx_1{xx_0 + xx_1};
        Scalar tmp{static_cast<Scalar>(1.0) +
                   static_cast<Scalar>(0.001) * (xx_0_p_xx_1)};
        Scalar tmp2{tmp * tmp}, tmp3{tmp2 * tmp}, tmp4{tmp2 * tmp2};
        if constexpr (VectorTrait::IsFixed) {
          out.resize(2, 2);
          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;
        } else if constexpr (VectorTrait::IsDynamic) {
          out.resize(2, 2);
          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;
        } else if constexpr (VectorTrait::IsSparse) {
          out.resize(2, 2);
          out.reserve(4);
          out.coeffRef(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.coeffRef(0, 1) =
              -2.0 * x.coeff(0) * x.coeff(1) * std::sin(xx_0_m_xx_1) / tmp3 +
              6.0 * 0.001 * x.coeff(0) * x.coeff(1) * std::cos(xx_0_m_xx_1) /
                  tmp4;
          out.coeffRef(1, 0) = out.coeff(0, 1);
          out.coeffRef(1, 1) =
              2.0 * std::sin(xx_0_m_xx_1) / tmp2 -
              4.0 * x.coeff(1) * x.coeff(1) * std::sin(xx_0_m_xx_1) / tmp3 +
              6.0 * 0.001 * x.coeff(1) * x.coeff(1) * std::cos(xx_0_m_xx_1) /
                  tmp4;
        }
 
        return out.allFinite();
      }
 
    };  // class Schaffer2
 
  }  // namespace TestSet
 
}  // namespace Optimist
 
#endif  // OPTIMIST_TESTSET_SCHAFFER2_HH