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_TestProblem.hpp"
#include "ROL_StdVector.hpp"


namespace ROL {
namespace ZOO {

template<class Real>
class Objective_Zakharov : public Objective<Real> {
private:
    ROL::Ptr<Vector<Real> > k_;  

public:
  
  // Create using a ROL::Vector containing 1,2,3,...,n
  Objective_Zakharov(const ROL::Ptr<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>
class getZakharov : public TestProblem<Real> {
public:
  getZakharov(void) {}

  Ptr<Objective<Real>> getObjective(void) const {
    // Problem dimension
    int n = 10;
    // Instantiate Objective Function
    ROL::Ptr<std::vector<Real> > k_ptr = ROL::makePtr<std::vector<Real>>(n,0.0);
    for ( int i = 0; i < n; i++ ) {
      (*k_ptr)[i] = i+1.0;
    }
    ROL::Ptr<Vector<Real> > k = ROL::makePtr<StdVector<Real>>(k_ptr);
    return ROL::makePtr<Objective_Zakharov<Real>>(k);
  }

  Ptr<Vector<Real>> getInitialGuess(void) const {
    // Problem dimension
    int n = 10;
    // Get Initial Guess
    ROL::Ptr<std::vector<Real> > x0p = ROL::makePtr<std::vector<Real>>(n,3.0);
    return ROL::makePtr<StdVector<Real>>(x0p);
  }

  Ptr<Vector<Real>> getSolution(const int i = 0) const {
    // Problem dimension
    int n = 10;
    // Get Solution
    ROL::Ptr<std::vector<Real> > xp = ROL::makePtr<std::vector<Real>>(n,0.0);
    return ROL::makePtr<StdVector<Real>>(xp);
  }
};


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

#endif