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> {
private:
  using Secant<Real>::state_;
 
public:
  lBFGS(int M, bool useDefaultScaling = true, Real Bscaling = Real(1))
    : Secant<Real>(M,useDefaultScaling,Bscaling) {}
 
  // Apply lBFGS Approximate Inverse Hessian
  void applyH( Vector<Real> &Hv, const Vector<Real> &v ) const {
    const 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
    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  = Hv.apply(*state_->gradDiff[i]);
      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 {
    const Real one(1);
 
    // Apply initial Hessian approximation to v
    Secant<Real>::applyB0(Bv,v);
 
    std::vector<Ptr<Vector<Real>>> a(state_->current+1);
    std::vector<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 = v.apply(*b[i]);
      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());
        bs = (state_->iterDiff[i])->apply(*b[j]);
        a[i]->axpy(bs,*b[j]);
        //as = (state_->iterDiff[i])->dot(a[j]->dual());
        as = (state_->iterDiff[i])->apply(*a[j]);
        a[i]->axpy(-as,*a[j]);
      }
      //as = (state_->iterDiff[i])->dot(a[i]->dual());
      as = (state_->iterDiff[i])->apply(*a[i]);
      a[i]->scale(one/sqrt(as));
      //av = v.dot(a[i]->dual());
      av = v.apply(*a[i]);
      Bv.axpy(-av,*a[i]);
    }
  }
};
 
}
 
#endif