ROL_lBFGS.hpp

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#ifndef ROL_LBFGS_H
#define ROL_LBFGS_H

#include "ROL_Secant.hpp"

namespace ROL {

template<class Real>
class lBFGS : public Secant<Real> {
public:
  lBFGS(int M) : Secant<Real>(M) {}

  // Apply lBFGS Approximate Inverse Hessian
  void applyH( Vector<Real> &Hv, const Vector<Real> &v ) const {
    // Get Generic Secant State
    const ROL::Ptr<SecantState<Real> >& state = Secant<Real>::get_state();
    Real zero(0);

    Hv.set(v.dual());
    std::vector<Real> alpha(state->current+1,zero);
    for (int i = state->current; i>=0; i--) {
      alpha[i]  = state->iterDiff[i]->dot(Hv);
      alpha[i] /= state->product[i];
      Hv.axpy(-alpha[i],(state->gradDiff[i])->dual());
    }

    // Apply initial inverse Hessian approximation to v
    ROL::Ptr<Vector<Real> > tmp = Hv.clone();
    Secant<Real>::applyH0(*tmp,Hv.dual());
    Hv.set(*tmp);

    Real beta(0);
    for (int i = 0; i <= state->current; i++) {
      beta  = Hv.dot((state->gradDiff[i])->dual());
      beta /= state->product[i];
      Hv.axpy((alpha[i]-beta),*(state->iterDiff[i]));
    }
  }

  // Apply lBFGS Approximate Hessian
  void applyB( Vector<Real> &Bv, const Vector<Real> &v ) const {
    // Get Generic Secant State
    const ROL::Ptr<SecantState<Real> >& state = Secant<Real>::get_state();
    Real one(1);

    // Apply initial Hessian approximation to v
    Secant<Real>::applyB0(Bv,v);

    std::vector<ROL::Ptr<Vector<Real> > > a(state->current+1);
    std::vector<ROL::Ptr<Vector<Real> > > b(state->current+1);
    Real bv(0), av(0), bs(0), as(0);
    for (int i = 0; i <= state->current; i++) {
      b[i] = Bv.clone();
      b[i]->set(*(state->gradDiff[i]));
      b[i]->scale(one/sqrt(state->product[i]));
      bv = v.dot(b[i]->dual());
      Bv.axpy(bv,*b[i]);

      a[i] = Bv.clone();
      Secant<Real>::applyB0(*a[i],*(state->iterDiff[i]));

      for (int j = 0; j < i; j++) {
        bs = (state->iterDiff[i])->dot(b[j]->dual());
        a[i]->axpy(bs,*b[j]);
        as = (state->iterDiff[i])->dot(a[j]->dual());
        a[i]->axpy(-as,*a[j]);
      }
      as = (state->iterDiff[i])->dot(a[i]->dual());
      a[i]->scale(one/sqrt(as));
      av = v.dot(a[i]->dual());
      Bv.axpy(-av,*a[i]);
    }
  }
};

}

#endif