ROL_HS2.hpp

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#ifndef USE_HESSVEC 
#define USE_HESSVEC 1
#endif

#ifndef ROL_HS2_HPP
#define ROL_HS2_HPP

#include "ROL_StdVector.hpp"
#include "ROL_TestProblem.hpp"
#include "ROL_Bounds.hpp"
#include "ROL_Types.hpp"

namespace ROL {
namespace ZOO {

  template<class Real>
  class Objective_HS2 : public Objective<Real> {
 
    typedef std::vector<Real> vector;
    typedef Vector<Real>      V;
    typedef StdVector<Real>   SV;

  private:
    
    Ptr<const vector> getVector( const V& x ) {
      
      return dynamic_cast<const SV&>(x).getVector(); 
    }

    Ptr<vector> getVector( V& x ) {
      
      return dynamic_cast<SV&>(x).getVector();
    }

  public:
    Objective_HS2(void) {}

    Real value( const Vector<Real> &x, Real &tol ) {

      
      Ptr<const vector> ex = getVector(x); 
      return static_cast<Real>(100) * std::pow((*ex)[1] - std::pow((*ex)[0],2),2)
           + std::pow(static_cast<Real>(1)-(*ex)[0],2);
    }

    void gradient( Vector<Real> &g, const Vector<Real> &x, Real &tol ) {

      
      Ptr<const vector> ex = getVector(x);
      Ptr<vector> eg = getVector(g);
      (*eg)[0] = static_cast<Real>(-400) * ((*ex)[1] - std::pow((*ex)[0],2))
               * (*ex)[0] - static_cast<Real>(2) * (static_cast<Real>(1)-(*ex)[0]);
      (*eg)[1] = static_cast<Real>(200) * ((*ex)[1] - std::pow((*ex)[0],2)); 
    }
#if USE_HESSVEC
    void hessVec( Vector<Real> &hv, const Vector<Real> &v, const Vector<Real> &x, Real &tol ) {

      
      Ptr<const vector> ex = getVector(x);
      Ptr<const vector> ev = getVector(v);
      Ptr<vector> ehv = getVector(hv);
 
      Real h11 = static_cast<Real>(-400) * (*ex)[1]
               + static_cast<Real>(1200) * std::pow((*ex)[0],2)
               + static_cast<Real>(2); 
      Real h22 = static_cast<Real>(200);
      Real h12 = static_cast<Real>(-400) * (*ex)[0];
      Real h21 = static_cast<Real>(-400) * (*ex)[0];

      Real alpha(0);

      (*ehv)[0] = (h11+alpha) * (*ev)[0] + h12 * (*ev)[1];
      (*ehv)[1] = h21 * (*ev)[0] + (h22+alpha) * (*ev)[1];
    } 
#endif
    void invHessVec( Vector<Real> &hv, const Vector<Real> &v, const Vector<Real> &x, Real &tol ) {
 
      
      Ptr<const vector> ex = getVector(x);
      Ptr<const vector> ev = getVector(v);
      Ptr< vector> ehv = getVector(hv);
     
      Real h11 = static_cast<Real>(-400) * (*ex)[1]
               + static_cast<Real>(1200) * std::pow((*ex)[0],2)
               + static_cast<Real>(2); 
      Real h22 = static_cast<Real>(200);
      Real h12 = static_cast<Real>(-400) * (*ex)[0];
      Real h21 = static_cast<Real>(-400) * (*ex)[0];
  
      (*ehv)[0] = static_cast<Real>(1)/(h11*h22 - h12*h21)
                * (h22 * (*ev)[0] - h12 * (*ev)[1]);
      (*ehv)[1] = static_cast<Real>(1)/(h11*h22 - h12*h21)
                * (-h21 * (*ev)[0] + h11 * (*ev)[1]);
    }
  };

template<class Real>
class getHS2 : public TestProblem<Real> {
public:
  getHS2(void) {}

  Ptr<Objective<Real>> getObjective(void) const {
    // Instantiate Objective Function
    return makePtr<Objective_HS2<Real>>();
  }

  Ptr<Vector<Real>> getInitialGuess(void) const {
    // Problem dimension
    int n = 2;
    // Get Initial Guess
    Ptr<std::vector<Real> > x0p = makePtr<std::vector<Real>>(n,0.0);
    (*x0p)[0] = -2.0; (*x0p)[1] = 1.0;
    return makePtr<StdVector<Real>>(x0p);
  }

  Ptr<Vector<Real>> getSolution(const int i = 0) const {
    // Problem dimension
    int n = 2;
    // Get Solution
    Ptr<std::vector<Real> > xp = makePtr<std::vector<Real>>(n,0.0);
    Real a = std::sqrt(598.0/1200.0);
    Real b = 400.0 * std::pow(a,3.0);
    (*xp)[0] = 2.0*a*std::cos(1.0/3.0 * std::acos(1.0/b));
    (*xp)[1] = 1.5;
    return makePtr<StdVector<Real>>(xp);
  }

  Ptr<BoundConstraint<Real>> getBoundConstraint(void) const {
    // Problem dimension
    int n = 2;
    // Instantiate BoundConstraint
    Ptr<std::vector<Real> > lp = makePtr<std::vector<Real>>(n,0.0);
    (*lp)[0] = ROL_NINF<Real>(); (*lp)[1] = 1.5;
    Ptr<Vector<Real> > l = makePtr<StdVector<Real>>(lp);
    Ptr<std::vector<Real> > up = makePtr<std::vector<Real>>(n,0.0);
    (*up)[0] = ROL_INF<Real>(); (*up)[1] = ROL_INF<Real>(); 
    Ptr<Vector<Real> > u = makePtr<StdVector<Real>>(up);
    return makePtr<Bounds<Real>>(l,u);
  }
};

} // End ZOO Namespace
} // End ROL Namespace

#endif