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// Rapid Optimization Library (ROL) Package
// Copyright (2014) Sandia Corporation
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#ifndef ROL_HOUSEHOLDERREFLECTOR_H
#define ROL_HOUSEHOLDERREFLECTOR_H
#include "ROL_LinearOperator.hpp"
/** @ingroup func_group
\class ROL::HouseholderReflector
\brief Provides the interface to create a Householder reflector
operator, that when applied to a vector x, produces a
vector parallel to y
Forms the linear operator H such that
\f[
Hv = (I-2u\otimes u) x = \frac{||x||}{||y||} y
\f]
where
\f[
\hat u = x + \sign(\langle x,u\rangle)\frac{||x||}{||y||}y,\quad u = \frac{\hat u}{||\hat u||}
\f]
If y is not specified, it is taken to be the first canonical vector
---
*/
namespace ROL {
template <class Real>
class HouseholderReflector : public LinearOperator<Real> {
typedef Vector<Real> V;
private:
const Teuchos::RCP<const V> x_;
const Teuchos::RCP<const V> y_;
Teuchos::RCP<V> u_;
public:
HouseholderReflector( const Teuchos::RCP<const Vector<Real> > &x,
const Teuchos::RCP<const Vector<Real> > &y) : x_(x), y_(y), u_(x->clone()) {}
HouseholderReflector( const Teuchos::RCP<const Vector<Real> > &x,
const Teuchos::RCP<const Vector<Real> > &y,
Teuchos::RCP<Vector<Real> > &scratch ) : x_(x), y_(y), u_(scratch) {}
HouseholderReflector( const Teuchos::RCP<const Vector<Real> > &x ) : x_(x), y_(x->basis(0)), u_(x->clone()) {}
HouseholderReflector( const Teuchos::RCP<const Vector<Real> > &x,
Teuchos::RCP<Vector<Real> > &scratch ) : x_(x), y_(x->basis(0)), u_(scratch) {}
void apply( Vector<Real> &Hv, const Vector<Real> &v, Real &tol ) const {
Real xdoty = x_->dot(*y_);
Real xnorm = x_->norm();
Real ynorm = y_->norm();
Real sgn = xdoty/std::abs(xdoty);
Real alpha = sgn*xnorm/ynorm;
u_->set(*x_);
u_->axpy(alpha,*y_);
Real beta = -2.0*u_->dot(v)/u_->dot(*u_);
Hv.set(v);
Hv.axpy(beta,*u_);
}
void applyInverse( Vector<Real> &Hv, const Vector<Real> &v, Real &tol ) const {
apply(Hv,v,tol);
}
}; // class HouseholderReflector
} // namespace ROL
#endif // ROL_HOUSEHOLDERREFLECTOR_H
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