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/** \file
    \brief  Contains definitions for Powell's badly scaled function.
    \author Created by D. Ridzal and D. Kouri.
 */

#ifndef USE_HESSVEC 
#define USE_HESSVEC 1
#endif

#ifndef ROL_POWELL_HPP
#define ROL_POWELL_HPP

#include "ROL_ScaledStdVector.hpp"
#include "ROL_Objective.hpp"

namespace ROL {
namespace ZOO {

/** \brief Powell's badly scaled function.
 */
template<class Real>
class Objective_Powell : public Objective<Real> {

public:
  Objective_Powell() {}

  Real value( const Vector<Real> &x, Real &tol ) {
    Teuchos::RCP<const std::vector<Real> > xp
      = Teuchos::dyn_cast<const PrimalScaledStdVector<Real> >(x).getVector();

    Real f1 = 1.e4*(*xp)[0]*(*xp)[1] - 1.0;
    Real f2 = std::exp(-(*xp)[0]) + std::exp(-(*xp)[1]) - 1.0001;

    return f1*f1+f2*f2;
  }

  void gradient( Vector<Real> &g, const Vector<Real> &x, Real &tol ) {
    Teuchos::RCP<std::vector<Real> > gp
      = Teuchos::dyn_cast<DualScaledStdVector<Real> >(g).getVector();
    Teuchos::RCP<const std::vector<Real> > xp
      = Teuchos::dyn_cast<const PrimalScaledStdVector<Real> >(x).getVector();

    Real f1 = 1.e4*(*xp)[0]*(*xp)[1] - 1.0;
    Real f2 = std::exp(-(*xp)[0]) + std::exp(-(*xp)[1]) - 1.0001;

    Real f11 = 1.e4*(*xp)[1];
    Real f12 = 1.e4*(*xp)[0];
    Real f21 = -std::exp(-(*xp)[0]);
    Real f22 = -std::exp(-(*xp)[1]);

    (*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 ) {
    Teuchos::RCP<std::vector<Real> > hvp
      = Teuchos::dyn_cast<DualScaledStdVector<Real> >(hv).getVector();
    Teuchos::RCP<const std::vector<Real> > vp
      = Teuchos::dyn_cast<const PrimalScaledStdVector<Real> >(v).getVector();
    Teuchos::RCP<const std::vector<Real> > xp
      = Teuchos::dyn_cast<const PrimalScaledStdVector<Real> >(x).getVector();

    Real f1 = 1.e4*(*xp)[0]*(*xp)[1] - 1.0;
    Real f2 = std::exp(-(*xp)[0]) + std::exp(-(*xp)[1]) - 1.0001;

    Real f11 = 1.e4*(*xp)[1];
    Real f12 = 1.e4*(*xp)[0];
    Real f21 = -std::exp(-(*xp)[0]);
    Real f22 = -std::exp(-(*xp)[1]);

    Real f111 = 0.0;
    Real f112 = 1.e4;
    Real f121 = 1.e4;
    Real f122 = 0.0;
    Real f211 = std::exp(-(*xp)[0]);
    Real f212 = 0.0;
    Real f221 = 0.0;
    Real f222 = std::exp(-(*xp)[1]);

    Real h11 = 2.0*(f111*f1 + f11*f11) + 2.0*(f211*f2 + f21*f21);
    Real h12 = 2.0*(f112*f1 + f11*f12) + 2.0*(f212*f2 + f21*f22);
    Real h21 = 2.0*(f121*f1 + f21*f11) + 2.0*(f221*f2 + 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] = h21*(*vp)[0] + h22*(*vp)[1];
  }
#endif
  void invHessVec( Vector<Real> &hv, const Vector<Real> &v, const Vector<Real> &x, Real &tol ) {
    Teuchos::RCP<std::vector<Real> > hvp
      = Teuchos::dyn_cast<PrimalScaledStdVector<Real> >(hv).getVector();
    Teuchos::RCP<const std::vector<Real> > vp
      = Teuchos::dyn_cast<const DualScaledStdVector<Real> >(v).getVector();
    Teuchos::RCP<const std::vector<Real> > xp
      = Teuchos::dyn_cast<const PrimalScaledStdVector<Real> >(x).getVector();

    Real f1 = 1.e4*(*xp)[0]*(*xp)[1] - 1.0;
    Real f2 = std::exp(-(*xp)[0]) + std::exp(-(*xp)[1]) - 1.0001;

    Real f11 = 1.e4*(*xp)[1];
    Real f12 = 1.e4*(*xp)[0];
    Real f21 = -std::exp(-(*xp)[0]);
    Real f22 = -std::exp(-(*xp)[1]);

    Real f111 = 0.0;
    Real f112 = 1.e4;
    Real f121 = 1.e4;
    Real f122 = 0.0;
    Real f211 = std::exp(-(*xp)[0]);
    Real f212 = 0.0;
    Real f221 = 0.0;
    Real f222 = std::exp(-(*xp)[1]);

    Real h11 = 2.0*(f111*f1 + f11*f11) + 2.0*(f211*f2 + f21*f21);
    Real h12 = 2.0*(f112*f1 + f11*f12) + 2.0*(f212*f2 + f21*f22);
    Real h21 = 2.0*(f121*f1 + f21*f11) + 2.0*(f221*f2 + f22*f21);
    Real h22 = 2.0*(f122*f1 + f12*f12) + 2.0*(f222*f2 + f22*f22);

    (*hvp)[0] = (1.0/(h11*h22-h12*h21))*( h22*(*vp)[0] - h21*(*vp)[1]);
    (*hvp)[1] = (1.0/(h11*h22-h12*h21))*(-h12*(*vp)[0] + h11*(*vp)[1]);
  }
};

template<class Real>
void getPowell( Teuchos::RCP<Objective<Real> > &obj,
                Teuchos::RCP<Vector<Real> >    &x0,
                Teuchos::RCP<Vector<Real> >    &x ) {
  // Problem dimension
  int n = 2;

  // Get problem scaling
  Teuchos::RCP<std::vector<Real> > scale = Teuchos::rcp(new std::vector<Real>(n,0.0));
  (*scale)[0] = 1.e10; (*scale)[1] = 1.e-2;

  // Get Initial Guess
  Teuchos::RCP<std::vector<Real> > x0p = Teuchos::rcp(new std::vector<Real>(n,0.0));
  (*x0p)[0] = 0.0; (*x0p)[1] = 1.0;
  x0 = Teuchos::rcp(new PrimalScaledStdVector<Real>(x0p,scale));

  // Get Solution: (*xp)[0] = 1.0981770261368074e-05;
  Teuchos::RCP<std::vector<Real> > xp = Teuchos::rcp(new std::vector<Real>(n,0.0));
  (*xp)[0] = 1.098e-05; (*xp)[1] = 9.106;
  x = Teuchos::rcp(new PrimalScaledStdVector<Real>(xp,scale));

  // Instantiate Objective Function
  obj = Teuchos::rcp(new Objective_Powell<Real>);
}

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

#endif
