ROL_FreudensteinRoth.hpp

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#ifndef USE_HESSVEC 
#define USE_HESSVEC 1
#endif

#ifndef ROL_FREUDENSTEINROTH_HPP
#define ROL_FREUDENSTEINROTH_HPP

#include "ROL_StdVector.hpp"
#include "ROL_Objective.hpp"

namespace ROL {
namespace ZOO {

  template<class Real>
  class Objective_FreudensteinRoth : public Objective<Real> {

    typedef std::vector<Real> vector;
    typedef Vector<Real>      V;
    typedef StdVector<Real>   SV;

  private:
 
    Teuchos::RCP<const vector> getVector( const V& x ) {
      using Teuchos::dyn_cast;
      return dyn_cast<const SV>(x).getVector();
    }

    Teuchos::RCP<vector> getVector( V& x ) {
      using Teuchos::dyn_cast;
      return dyn_cast<SV>(x).getVector();
    }    

  public:
    Objective_FreudensteinRoth() {}

    Real value( const Vector<Real> &x, Real &tol ) {
      using Teuchos::RCP;

      RCP<const vector> xp = getVector(x);

      Real f1 = -13.0 + (*xp)[0] + ((5.0-(*xp)[1])*(*xp)[1] - 2.0)*(*xp)[1];
      Real f2 = -29.0 + (*xp)[0] + (((*xp)[1]+1.0)*(*xp)[1] - 14.0)*(*xp)[1];

      return f1*f1+f2*f2;
    }

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

      using Teuchos::RCP;
      RCP<const vector> xp = getVector(x);
      RCP<vector> gp = getVector(g);

      Real f1 = -13.0 + (*xp)[0] + ((5.0-(*xp)[1])*(*xp)[1] - 2.0)*(*xp)[1];
      Real f2 = -29.0 + (*xp)[0] + (((*xp)[1]+1.0)*(*xp)[1] - 14.0)*(*xp)[1];

      Real f11 = 1.0;
      Real f12 = 10.0*(*xp)[1] - 3.0*(*xp)[1]*(*xp)[1] - 2.0;
      Real f21 = 1.0;
      Real f22 = 3.0*(*xp)[1]*(*xp)[1] + 2.0*(*xp)[1] - 14.0;

      (*gp)[0] = 2.0*(f11*f1 + f21*f2);
      (*gp)[1] = 2.0*(f12*f1 + f22*f2);
    }
#if USE_HESSVEC
    void hessVec( Vector<Real> &hv, const Vector<Real> &v, const Vector<Real> &x, Real &tol ) {

      using Teuchos::RCP; 
      RCP<const vector> xp = getVector(x);
      RCP<const vector> vp = getVector(v);
      RCP<vector> hvp = getVector(hv);

      Real f1 = -13.0 + (*xp)[0] + ((5.0-(*xp)[1])*(*xp)[1] - 2.0)*(*xp)[1];
      Real f2 = -29.0 + (*xp)[0] + (((*xp)[1]+1.0)*(*xp)[1] - 14.0)*(*xp)[1];

      Real f11 = 1.0;
      Real f12 = 10.0*(*xp)[1] - 3.0*(*xp)[1]*(*xp)[1] - 2.0;
      Real f21 = 1.0;
      Real f22 = 3.0*(*xp)[1]*(*xp)[1] + 2.0*(*xp)[1] - 14.0;

      Real f122 = 10.0 - 6.0*(*xp)[1];
      Real f222 = 6.0*(*xp)[1] + 2.0;

      Real h11 = 2.0*(f11*f11) + 2.0*(f21*f21);
      Real h12 = 2.0*(f12*f11) + 2.0*(f22*f21);
      Real h22 = 2.0*(f122*f1 + f12*f12) + 2.0*(f222*f2 + f22*f22);

      (*hvp)[0] = h11*(*vp)[0] + h12*(*vp)[1];
      (*hvp)[1] = h12*(*vp)[0] + h22*(*vp)[1];
    }
#endif
    void invHessVec( Vector<Real> &hv, const Vector<Real> &v, const Vector<Real> &x, Real &tol ) {

      using Teuchos::RCP;
      RCP<const vector> xp = getVector(x);
      RCP<const vector> vp = getVector(v);
      RCP<vector> hvp = getVector(hv); 

      Real f1 = -13.0 + (*xp)[0] + ((5.0-(*xp)[1])*(*xp)[1] - 2.0)*(*xp)[1];
      Real f2 = -29.0 + (*xp)[0] + (((*xp)[1]+1.0)*(*xp)[1] - 14.0)*(*xp)[1];

      Real f11 = 1.0;
      Real f12 = 10.0*(*xp)[1] - 3.0*(*xp)[1]*(*xp)[1] - 2.0;
      Real f21 = 1.0;
      Real f22 = 3.0*(*xp)[1]*(*xp)[1] + 2.0*(*xp)[1] - 14.0;

      Real f122 = 10.0 - 6.0*(*xp)[1];
      Real f222 = 6.0*(*xp)[1] + 2.0;

      Real h11 = 2.0*(f11*f11) + 2.0*(f21*f21);
      Real h12 = 2.0*(f12*f11) + 2.0*(f22*f21);
      Real h22 = 2.0*(f122*f1 + f12*f12) + 2.0*(f222*f2 + f22*f22);

      (*hvp)[0] = (1.0/(h11*h22-h12*h12))*( h22*(*vp)[0] - h12*(*vp)[1]);
      (*hvp)[1] = (1.0/(h11*h22-h12*h12))*(-h12*(*vp)[0] + h11*(*vp)[1]);
    }
  };

  template<class Real>
  void getFreudensteinRoth( Teuchos::RCP<Objective<Real> > &obj, Vector<Real> &x0, Vector<Real> &x ) {

    typedef std::vector<Real> vector;
    typedef StdVector<Real>   SV;
    using Teuchos::RCP;
    using Teuchos::dyn_cast;

    // Cast Initial Guess and Solution Vectors
    RCP<vector> x0p = dyn_cast<SV>(x0).getVector();
    RCP<vector> xp  = dyn_cast<SV>(x).getVector();

    int n = xp->size();
    // Resize Vectors
    n = 2;
    x0p->resize(n);
    xp->resize(n);
    // Instantiate Objective Function
    obj = Teuchos::rcp( new Objective_FreudensteinRoth<Real> );
    // Get Initial Guess
    (*x0p)[0] =  0.5;
    (*x0p)[1] = -2.0;
    // Get Solution
    (*xp)[0] = 5.0;
    (*xp)[1] = 4.0;
  }


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

#endif