ROL::HouseholderReflector< Real > Class Template Reference

Provides the interface to create a Householder reflector operator, that when applied to a vector x, produces a vector parallel to y. More...

#include <ROL_HouseholderReflector.hpp>

Inheritance diagram for ROL::HouseholderReflector< Real >:

Public Member Functions
	HouseholderReflector (const ROL::Ptr< const Vector< Real > > &x, const ROL::Ptr< const Vector< Real > > &y)
	HouseholderReflector (const ROL::Ptr< const Vector< Real > > &x, const ROL::Ptr< const Vector< Real > > &y, ROL::Ptr< Vector< Real > > &scratch)
	HouseholderReflector (const ROL::Ptr< const Vector< Real > > &x)
	HouseholderReflector (const ROL::Ptr< const Vector< Real > > &x, ROL::Ptr< Vector< Real > > &scratch)
void	apply (Vector< Real > &Hv, const Vector< Real > &v, Real &tol) const
	Apply linear operator. More...
void	applyInverse (Vector< Real > &Hv, const Vector< Real > &v, Real &tol) const
	Apply inverse of linear operator. More...
Public Member Functions inherited from ROL::LinearOperator< Real >
virtual	~LinearOperator ()
virtual void	update (const Vector< Real > &x, bool flag=true, int iter=-1)
	Update linear operator. More...
virtual void	applyAdjoint (Vector< Real > &Hv, const Vector< Real > &v, Real &tol) const
	Apply adjoint of linear operator. More...
virtual void	applyAdjointInverse (Vector< Real > &Hv, const Vector< Real > &v, Real &tol) const
	Apply adjoint of the inverse linear operator. More...

Private Types
typedef Vector< Real >	V

Private Attributes
const ROL::Ptr< const V >	x_
const ROL::Ptr< const V >	y_
ROL::Ptr< V >	u_

Detailed Description

template<class Real>
class ROL::HouseholderReflector< Real >

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

\[ Hv = (I-2u\otimes u) x = \frac{||x||}{||y||} y \]

where

\[ \hat u = x + \sign(\langle x,u\rangle)\frac{||x||}{||y||}y,\quad u = \frac{\hat u}{||\hat u||} \]

If y is not specified, it is taken to be the first canonical vector

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Definition at line 41 of file ROL_HouseholderReflector.hpp.

Member Typedef Documentation

template<class Real>

typedef Vector<Real> ROL::HouseholderReflector< Real >::V

private

Definition at line 43 of file ROL_HouseholderReflector.hpp.

Constructor & Destructor Documentation

template<class Real>

ROL::HouseholderReflector< Real >::HouseholderReflector ( const ROL::Ptr< const Vector< Real > > &  x, const ROL::Ptr< const Vector< Real > > &  y  )

inline

Definition at line 54 of file ROL_HouseholderReflector.hpp.

template<class Real>

ROL::HouseholderReflector< Real >::HouseholderReflector ( const ROL::Ptr< const Vector< Real > > &  x, const ROL::Ptr< const Vector< Real > > &  y, ROL::Ptr< Vector< Real > > &  scratch  )

inline

Definition at line 58 of file ROL_HouseholderReflector.hpp.

template<class Real>

ROL::HouseholderReflector< Real >::HouseholderReflector ( const ROL::Ptr< const Vector< Real > > &  x )

inline

Definition at line 62 of file ROL_HouseholderReflector.hpp.

template<class Real>

ROL::HouseholderReflector< Real >::HouseholderReflector ( const ROL::Ptr< const Vector< Real > > &  x, ROL::Ptr< Vector< Real > > &  scratch  )

inline

Definition at line 64 of file ROL_HouseholderReflector.hpp.

Member Function Documentation

template<class Real>

void ROL::HouseholderReflector< Real >::apply ( Vector< Real > &  Hv, const Vector< Real > &  v, Real &  tol  ) const

inlinevirtual

Apply linear operator.

This function applies the linear operator to a vector.

Parameters

[out]	Hv	is the output vector.
[in]	v	is the input vector.
[in]	tol	is a tolerance for inexact linear operator application.

Implements ROL::LinearOperator< Real >.

Definition at line 69 of file ROL_HouseholderReflector.hpp.

References ROL::Vector< Real >::axpy(), ROL::Vector< Real >::set(), ROL::HouseholderReflector< Real >::u_, ROL::HouseholderReflector< Real >::x_, and ROL::HouseholderReflector< Real >::y_.

Referenced by ROL::HouseholderReflector< Real >::applyInverse(), and main().

template<class Real>

void ROL::HouseholderReflector< Real >::applyInverse ( Vector< Real > &  Hv, const Vector< Real > &  v, Real &  tol  ) const

inlinevirtual

Apply inverse of linear operator.

This function applies the inverse of linear operator to a vector.

Parameters

[out]	Hv	is the output vector.
[in]	v	is the input vector.
[in]	tol	is a tolerance for inexact linear operator application.

Reimplemented from ROL::LinearOperator< Real >.

Definition at line 87 of file ROL_HouseholderReflector.hpp.

References ROL::HouseholderReflector< Real >::apply().

Member Data Documentation

template<class Real>

const ROL::Ptr<const V> ROL::HouseholderReflector< Real >::x_

private

Definition at line 47 of file ROL_HouseholderReflector.hpp.

Referenced by ROL::HouseholderReflector< Real >::apply().

template<class Real>

const ROL::Ptr<const V> ROL::HouseholderReflector< Real >::y_

private

Definition at line 48 of file ROL_HouseholderReflector.hpp.

Referenced by ROL::HouseholderReflector< Real >::apply().

template<class Real>

ROL::Ptr<V> ROL::HouseholderReflector< Real >::u_

private

Definition at line 50 of file ROL_HouseholderReflector.hpp.

Referenced by ROL::HouseholderReflector< Real >::apply().

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The documentation for this class was generated from the following file:

• ROL_HouseholderReflector.hpp