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/** \file
    \brief  Contains definitions for W. Hock and K. Schittkowski 2nd test function.
    \author Created by D. Ridzal and D. Kouri.
 */

#ifndef USE_HESSVEC 
#define USE_HESSVEC 1
#endif

#ifndef ROL_HS2_HPP
#define ROL_HS2_HPP

#include "ROL_StdVector.hpp"
#include "ROL_Objective.hpp"
#include "ROL_BoundConstraint.hpp"
#include "ROL_Types.hpp"

namespace ROL {
namespace ZOO {

  /** \brief W. Hock and K. Schittkowski 2nd test function.
   */
  template<class Real>
  class Objective_HS2 : 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_HS2(void) {}

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

      using Teuchos::RCP;
      RCP<const vector> ex = getVector(x); 
      return 100.0 * std::pow((*ex)[1] - std::pow((*ex)[0],2.0),2.0) + std::pow(1.0-(*ex)[0],2.0);
    }

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

      using Teuchos::RCP;
      RCP<const vector> ex = getVector(x);
      RCP<vector> eg = getVector(g);
      (*eg)[0] = -400.0 * ((*ex)[1] - std::pow((*ex)[0],2.0)) * (*ex)[0] - 2.0 * (1.0-(*ex)[0]);
      (*eg)[1] =  200.0 * ((*ex)[1] - std::pow((*ex)[0],2.0)); 
    }
#if USE_HESSVEC
    void hessVec( Vector<Real> &hv, const Vector<Real> &v, const Vector<Real> &x, Real &tol ) {

      using Teuchos::RCP;
      RCP<const vector> ex = getVector(x);
      RCP<const vector> ev = getVector(v);
      RCP<vector> ehv = getVector(hv);
 
      Real h11 = -400.0 * (*ex)[1] + 1200.0 * std::pow((*ex)[0],2.0) + 2.0; 
      Real h22 =  200.0;
      Real h12 = -400.0 * (*ex)[0];
      Real h21 = -400.0 * (*ex)[0];

      Real alpha = 1.0;

      (*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 ) {
 
      using Teuchos::RCP;
      RCP<const vector> ex = getVector(x);
      RCP<const vector> ev = getVector(v);
      RCP< vector> ehv = getVector(hv);
     
      Real h11 = -400.0 * (*ex)[1] + 1200.0 * std::pow((*ex)[0],2.0) + 2.0; 
      Real h22 =  200.0;
      Real h12 = -400.0 * (*ex)[0];
      Real h21 = -400.0 * (*ex)[0];
  
      (*ehv)[0] = 1.0/(h11*h22 - h12*h21) * (h22 * (*ev)[0] - h12 * (*ev)[1]);
      (*ehv)[1] = 1.0/(h11*h22 - h12*h21) * (-h21 * (*ev)[0] + h11 * (*ev)[1]);
    }
  };

template<class Real>
void getHS2( Teuchos::RCP<Objective<Real> >       &obj,
             Teuchos::RCP<BoundConstraint<Real> > &con, 
             Teuchos::RCP<Vector<Real> >          &x0,
             Teuchos::RCP<Vector<Real> >          &x ) {
  // Problem dimension
  int n = 2;

  // Get Initial Guess
  Teuchos::RCP<std::vector<Real> > x0p = Teuchos::rcp(new std::vector<Real>(n,0.0));
  (*x0p)[0] = -2.0; (*x0p)[1] = 1.0;
  x0 = Teuchos::rcp(new StdVector<Real>(x0p));

  // Get Solution
  Teuchos::RCP<std::vector<Real> > xp = Teuchos::rcp(new 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;
  x = Teuchos::rcp(new StdVector<Real>(xp));

  // Instantiate Objective Function
  obj = Teuchos::rcp(new Objective_HS2<Real>);

  // Instantiate BoundConstraint
  Teuchos::RCP<std::vector<Real> > lp = Teuchos::rcp(new std::vector<Real>(n,0.0));
  (*lp)[0] = ROL_NINF; (*lp)[1] = 1.5;
  Teuchos::RCP<Vector<Real> > l = Teuchos::rcp( new StdVector<Real>(lp) );
  Teuchos::RCP<std::vector<Real> > up = Teuchos::rcp(new std::vector<Real>(n,0.0));
  (*up)[0] = ROL_INF; (*up)[1] = ROL_INF; 
  Teuchos::RCP<Vector<Real> > u = Teuchos::rcp( new StdVector<Real>(up) );
  con = Teuchos::rcp(new BoundConstraint<Real>(l,u));
}

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

#endif
