ROL_Zakharov.hpp

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#ifndef USE_HESSVEC 
#define USE_HESSVEC 1
#endif

#ifndef ROL_ZAKHAROV_HPP
#define ROL_ZAKHAROV_HPP

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


namespace ROL {
namespace ZOO {

  template<class Real>
  class Objective_Zakharov : public Objective<Real> {
  private:
      Teuchos::RCP<Vector<Real> > k_;  

  public:
    
    // Create using a ROL::Vector containing 1,2,3,...,n
    Objective_Zakharov(const Teuchos::RCP<Vector<Real> > k) : k_(k) {}

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

        Real xdotx = x.dot(x); 
        Real kdotx = x.dot(*k_); 

        Real val = xdotx + pow(kdotx,2)/4.0 + pow(kdotx,4)/16.0;

        return val;
    }

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

        Real kdotx = x.dot(*k_);
        Real coeff = 0.25*(2.0*kdotx+pow(kdotx,3.0));

        g.set(x);
        g.scale(2.0);
        g.axpy(coeff,*k_);
    }

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

        Real kdotd = d.dot(*k_);
        Real kdotx = x.dot(*k_);
        Real xdotd = x.dot(d);
        
        Real coeff = 0.25*(2.0*kdotx+pow(kdotx,3.0));

        Real deriv = 2*xdotd + coeff*kdotd;
 
        return deriv;

    }

#if USE_HESSVEC
    void hessVec( Vector<Real> &hv, const Vector<Real> &v, const Vector<Real> &x, Real &tol ) {

        Real kdotx = x.dot(*k_);
        Real kdotv = v.dot(*k_);
        Real coeff = 0.25*(2.0+3.0*pow(kdotx,2.0))*kdotv;

        hv.set(v);
        hv.scale(2.0);
        hv.axpy(coeff,*k_);
    }
#endif
    void invHessVec( Vector<Real> &ihv, const Vector<Real> &v, const Vector<Real> &x, Real &tol ) {
    
        Real kdotv = v.dot(*k_);
        Real kdotx = x.dot(*k_);
        Real kdotk = (*k_).dot(*k_);
        Real coeff = -kdotv/(2.0*kdotk+16.0/(2.0+3.0*pow(kdotx,2.0)));
        
        ihv.set(v);
        ihv.scale(0.5);
        ihv.axpy(coeff,*k_); 
    }
};



template<class Real>
void getZakharov( Teuchos::RCP<Objective<Real> > &obj, Vector<Real> &x0, Vector<Real> &x ) {
  
    using Teuchos::RCP;
    using Teuchos::rcp;
    using Teuchos::dyn_cast; 

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

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

    uint n = xp->size();
    // Resize Vectors
    n = 10;

    RCP<vector> k_rcp = rcp(new vector(n,0));
    for(uint i=0;i<n;++i) {
        (*k_rcp)[i] = i+1.0;    
    }    
    RCP<V> k = rcp(new SV(k_rcp));
    x0p->resize(n);
    xp->resize(n);
    // Instantiate Objective Function
    obj = rcp( new Objective_Zakharov<Real>(k) );
    // Get Initial Guess
    (*x0p)[0] =  3.0;
    (*x0p)[1] =  3.0;
    // Get Solution
    (*xp)[0] = 0.0;
    (*xp)[1] = 0.0;
  }


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

#endif