ROL_DynamicTrackingObjective.hpp

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#pragma once
#ifndef ROL_DYNAMICTRACKINGOBJECTIVE_HPP
#define ROL_DYNAMICTRACKINGOBJECTIVE_HPP

#include "ROL_DynamicObjective.hpp"
#include "ROL_VectorWorkspace.hpp"


namespace ROL {

template<typename Real>
class DynamicTrackingObjective : public DynamicObjective<Real> {
public:

  using V         = Vector<Real>;
  using TS        = TimeStamp<Real>;
  using size_type = typename PartitionedVector<Real>::size_type;  

private:

  Ptr<PartitionedVector<Real>>  target_;

  size_type             Nt_;     // Number of time steps
  Real                  alpha_;  // Regularization parameter

  mutable VectorWorkspace<Real> workspace_;

public:

  DynamicTrackingObjective( const Ptr<PartitionedVector<Real>>& target, Real alpha=0.0 ) : 
    target_(target), Nt_(target_->numVectors()), alpha_(alpha) {}
  
  virtual ~DynamicTrackingObjective() {}  

  virtual Real value( const V& uo, const V& un, 
                      const V& z, const TS& timeStamp ) const override {
    Real dt = timeStamp.t.at(1)-timeStamp.t.at(0);

    size_type k = timeStamp.k;     

    auto udiff = workspace_.copy(un);
    auto utarg = target_->get(k);

    udiff->axpy(-1.0, *utarg);

    Real result = 0.5*dt*( 0.5*udiff->dot(*udiff) + alpha_*z.dot(z) );
    
    if( k>0 ) {
      utarg = target_->get(k-1);
      udiff->set(uo);
      udiff->axpy(-1.0,*utarg);
      result += 0.25*dt*(udiff->dot(*udiff));
    }
    return result;
  }

  //----------------------------------------------------------------------------
  // Gradient Terms
  virtual void gradient_uo( V& g, const V& uo, const V& un, 
                            const V& z, const TS& timeStamp ) const override {
    Real dt = timeStamp.t.at(1)-timeStamp.t.at(0);
    if( timeStamp.k>0 ) {
      g.set(uo);
      g.axpy(-1.0, *(target_->get(timeStamp.k-1)) );
      g.scale(0.5*dt);
    }
    else g.zero();
  }

  virtual void gradient_un( V& g, const V& uo, const V& un, 
                            const V& z, const TS& timeStamp ) const override {
    Real dt = timeStamp.t.at(1)-timeStamp.t.at(0);
    g.set(un);
    g.axpy(-1.0, *(target_->get(timeStamp.k)) );
    g.scale(0.5*dt);
  }

  virtual void gradient_z( V& g, const V& uo, const V& un, 
                           const V& z, const TS& timeStamp ) const override {
    Real dt = timeStamp.t.at(1)-timeStamp.t.at(0);
    g.set(z);
    g.scale(dt*alpha_);
  }

  //----------------------------------------------------------------------------
  // Hessian-Vector product terms
  virtual void hessVec_uo_uo( V& hv, const V& v, const V& uo, const V& un, 
                              const V& z, const TS& timeStamp ) const override {
    Real dt = timeStamp.t.at(1)-timeStamp.t.at(0);
    if( timeStamp.k>0 ) {
      hv.set(v);
      hv.scale(dt/2.0);
    }
    else hv.zero();
  }

  virtual void hessVec_uo_un( V& hv, const V& v, const V& uo, const V& un, 
                              const V& z, const TS& timeStamp ) const override { 
    hv.zero(); 
  }

  virtual void hessVec_uo_z( V& hv, const V& v, const V& uo, const V& un, 
                             const V& z, const TS& timeStamp ) const override { 
    hv.zero(); 
  }

  virtual void hessVec_un_uo( V& hv, const V& v, const V& uo, const V& un, 
                              const V& z, const TS& timeStamp ) const override {
    hv.zero();
  }

  virtual void hessVec_un_un( V& hv, const V& v, const V& uo, const V& un, 
                              const V& z, const TS& timeStamp ) const override {
    Real dt = timeStamp.t.at(1)-timeStamp.t.at(0);
    hv.set(v);
    hv.scale(dt/2.0);
  }

  virtual void hessVec_un_z( V& hv, const V& v, const V& uo, const V& un, 
                             const V& z, const TS& timeStamp ) const override {
    hv.zero();
  }

  virtual void hessVec_z_uo( V& hv, const V& v, const V& uo, const V& un, 
                              const V& z, const TS& timeStamp ) const override {
    hv.zero();
  }

  virtual void hessVec_z_un( V& hv, const V& v, const V& uo, const V& un, 
                              const V& z, const TS& timeStamp ) const override {
    hv.zero();
  }

  virtual void hessVec_z_z( V& hv, const V& v, const V& uo, const V& un, 
                             const V& z, const TS& timeStamp ) const override {
    Real dt = timeStamp.t.at(1)-timeStamp.t.at(0);
    hv.set(v);
    hv.scale(alpha_*dt);
  }

}; // DynamicTrackingObjective


template<typename Real>
inline Ptr<DynamicObjective<Real>> 
make_DynamicTrackingObjective( const Ptr<PartitionedVector<Real>>& target, Real alpha=0.0 ) {
  Ptr<DynamicObjective<Real>> obj = makePtr<DynamicTrackingObjective<Real>>(target,alpha);
  return obj;
}

} // namespace ROL

#endif  // ROL_DYNAMICTRACKINGOBJECTIVE_HPP