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_Objective.hpp"
#include "ROL_BoundConstraint.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:
    
    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, 
                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 = 2;
    x0p->resize(n);
    xp->resize(n);
    // Instantiate Objective Function
    obj = rcp( new Objective_HS2<Real> );

    // Instantiate BoundConstraint
    RCP<vector> l_rcp = rcp( new vector(n,0.0) );      
    RCP<vector> u_rcp = rcp( new vector(n,0.0) );

    (*l_rcp)[0] = -0.1*ROL_OVERFLOW;
    (*l_rcp)[1] =  1.5;
    (*u_rcp)[0] =  0.1*ROL_OVERFLOW;
    (*u_rcp)[1] =  0.1*ROL_OVERFLOW; 

    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] =  -2.0;
    (*x0p)[1] =  1.0;
    // Get Solution
    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;
  }


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

#endif