EllipticParaboloid.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_COST_FUNCTION_ELLIPTIC_PARABOLOID_HH
#define OPTIMIST_COST_FUNCTION_ELLIPTIC_PARABOLOID_HH
 
#include "Optimist/TestSet.hh"
#include "Optimist/Function/CostFunction.hh"
 
namespace Optimist
{
 
  namespace TestSet
  {

    template <typename Real>
    class EllipticParaboloid : public CostFunction<Real, 2, EllipticParaboloid<Real>>
    {
      Real m_a{1.0}; 
      Real m_b{1.0}; 
 
    public:
      OPTIMIST_BASIC_CONSTANTS(Real) 
 
      using Vector    = typename CostFunction<Real, 2, EllipticParaboloid<Real>>::Vector;
      using RowVector = typename CostFunction<Real, 2, EllipticParaboloid<Real>>::RowVector;
      using Matrix    = typename CostFunction<Real, 2, EllipticParaboloid<Real>>::Matrix;

      EllipticParaboloid()
      {
        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 "EllipticParaboloid";}

      void evaluate_impl(const Vector & x, Real & out) const
      {
        out = this->m_a*x(0)*x(0) + this->m_b*x(1)*x(1);
      }

      void first_derivative_impl(const Vector & x, RowVector & out) const
      {
        out(0) = 2.0*this->m_a*x(0);
        out(1) = 2.0*this->m_b*x(1);
      }

      void second_derivative_impl(const Vector & /*x*/, Matrix & out) const
      {
        out(0, 0) = 2.0*this->m_a;
        out(0, 1) = 0.0;
        out(1, 0) = 0.0;
        out(1, 1) = 2.0*this->m_b;
      }
 
    }; // class EllipticParaboloid
 
  } // namespace TestSet
 
} // namespace Optimist
 
#endif // OPTIMIST_COST_FUNCTION_ELLIPTIC_PARABOLOID_HH