ROL_HS38.hpp

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#ifndef USE_HESSVEC 
#define USE_HESSVEC 1
#endif

#ifndef ROL_HS38_HPP
#define ROL_HS38_HPP

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

namespace ROL {
namespace ZOO {

  template<class Real>
  class Objective_HS38 : 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_HS38(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) + 
              90.0 * std::pow((*ex)[3] - std::pow((*ex)[2],2.0),2.0) + std::pow(1.0-(*ex)[2],2.0) +
              10.1 * (std::pow((*ex)[1] - 1.0,2.0) + std::pow((*ex)[3]-1.0,2.0)) + 
              19.8 * ((*ex)[1] - 1.0) * ((*ex)[3] - 1.0);
    }

    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] = -4.0 * 100.0 * ((*ex)[1] - std::pow((*ex)[0],2.0)) * (*ex)[0] - 2.0 * (1.0-(*ex)[0]);
      (*eg)[1] = 2.0 * 100.0 * ((*ex)[1] - std::pow((*ex)[0],2.0)) + 
                 2.0 * 10.1 * ((*ex)[1] - 1.0) + 19.8*((*ex)[3] - 1.0); 
      (*eg)[2] = -4.0 * 90.0 * ((*ex)[3] - std::pow((*ex)[2],2.0)) * (*ex)[2] - 2.0 * (1.0-(*ex)[2]);
      (*eg)[3] = 2.0 * 90.0 * ((*ex)[3] - std::pow((*ex)[2],2.0)) + 
                 2.0 * 10.1 * ((*ex)[3] - 1.0) + 19.8*((*ex)[1] - 1.0); 
    }
#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 = -4.0 * 100.0 * (*ex)[1] + 12.0 * 100.0 * std::pow((*ex)[0],2.0) + 2.0; 
      Real h12 = -4.0 * 100.0 * (*ex)[0];
      Real h13 = 0.0;
      Real h14 = 0.0;
      Real h21 = -4.0 * 100.0 * (*ex)[0];
      Real h22 = 2.0 * 100.0 + 2.0 * 10.1;
      Real h23 = 0.0;
      Real h24 = 19.8;
      Real h31 = 0.0;
      Real h32 = 0.0;
      Real h33 = -4.0 * 90.0 * (*ex)[3] + 12.0 * 90.0 * std::pow((*ex)[2],2.0) + 2.0; 
      Real h34 = -4.0 * 90.0 * (*ex)[2];
      Real h41 = 0.0;
      Real h42 = 19.8;
      Real h43 = -4.0 * 90.0 * (*ex)[2];
      Real h44 = 2.0 * 90.0 + 2.0 * 10.1;

      (*ehv)[0] = h11 * (*ev)[0] + h12 * (*ev)[1] + h13 * (*ev)[2] + h14 * (*ev)[3];
      (*ehv)[1] = h21 * (*ev)[0] + h22 * (*ev)[1] + h23 * (*ev)[2] + h24 * (*ev)[3];
      (*ehv)[2] = h31 * (*ev)[0] + h32 * (*ev)[1] + h33 * (*ev)[2] + h34 * (*ev)[3];
      (*ehv)[3] = h41 * (*ev)[0] + h42 * (*ev)[1] + h43 * (*ev)[2] + h44 * (*ev)[3];
    } 
#endif
  };

  template<class Real>
  void getHS38( Teuchos::RCP<Objective<Real> > &obj, Teuchos::RCP<BoundConstraint<Real> > &con, 
                Vector<Real> &x0, Vector<Real> &x ) {

    typedef std::vector<Real> vector;
    typedef Vector<Real>      V;
    typedef StdVector<Real>   SV;
    using Teuchos::RCP;
    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 = 4;
    x0p->resize(n);
    xp->resize(n);
    // Instantiate Objective Function
    obj = rcp( new Objective_HS38<Real> );

    // Instantiate BoundConstraint

    RCP<vector> l_rcp = rcp( new vector(n,-10.0) );
    RCP<vector> u_rcp = rcp( new vector(n, 10.0) );

    RCP<V> l = rcp( new SV(l_rcp) );
    RCP<V> u = rcp( new SV(u_rcp) );

    con = rcp( new BoundConstraint<Real>(l,u) );

    // Get Initial Guess
    (*x0p)[0] = -3.0;
    (*x0p)[1] = -1.0;
    (*x0p)[2] = -3.0;
    (*x0p)[3] = -1.0;
    // Get Solution
    (*xp)[0] = 1.0;
    (*xp)[1] = 1.0;
    (*xp)[2] = 1.0;
    (*xp)[3] = 1.0;
  }


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

#endif