HCL_EvaluateOp

class HCL_EvaluateOp_d : public HCL_Base

This class represents an "evaluation" object that will be created by an HCL_Op_d object to represent the image and derivatives of the operator at a point

Inheritance:

Public Methods
Protected Methods

Inherited from HCL_Base:

Public Methods
void IncCount() const
void DecCount() const
int Count() const
virtual ostream& Write(ostream &) const

Documentation

This class represents an "evaluation" object that will be created by an HCL_Op_d object to represent the image and derivatives of the operator at a point. Thus, if is a nonlinear operator and is a vector in the domain, then the evaluation object represents the triple The purpose of having an evaluation object is to deal with the common situation in which the operator image and derivatives share some intermediate calculations. A typical implementation of such an operator involves defining an evaluation object whose constructor performs these intermediate calculations. The Image method then completes the computation of the operator image, while the Deriv and SecondDeriv methods complete the calculation of the derivatives.
The operator image and derivatives should then be accessed through the ImageRef, DerivRef, and SecondDerivRef methods. These are methods implemented in the base class (i.e. they do not need to be redefined in a derived class). The ImageRef method invokes Image to get the image and returns a reference to it. On subsequent calls, ImageRef merely references the stored value. The other "reference" methods work in a similar fashion.
Here is a summary of the primary methods of this class:

Domain Returns a reference to the domain of the underlying operator.
Range Returns a reference to the range of the underlying operator.
Image Computes the image of the operator at the point at which this object was created. Must be implemented by the creator of a concrete class.
ImageRef Calls Image, if necessary, to compute the operator image, saves it, and returns it. Implemented in the base class.
ImageAdd Adds the image of the operator to the output (as opposed to Image, which overwrites the output with the image).
Deriv Computes the derivative of the operator, at the point at which this object was created, as an HCL_LinearOp_d. Must be implemented by the creator of a concrete class.
DerivRef Calls Deriv, if necessary, to compute the derivatives, saves it, and returns a reference to it. Implemented in the base class.
SecondDeriv Computes the second derivative of the operator, at the point at which this object was created, as a HCL_BiLinearOp_d. Must be implemented by the creator of a concrete class.
SecondDerivRef Calls SecondDeriv, if necessary, to compute the second derivative, saves it, and returns a reference to it. Implemented in the base class.
In addition to the above methods, HCL_EvaluateOp_d has a number of protected virtual functions that allow the user to avoid writing distinct derivative classes if desired. If these methods, which include DerivImage, SecondDerivImage, and others, are over-ridden in a derived class, then the default Deriv and SecondDeriv methods can be used, which create instances of HCL_OpDefaultDeriv_d and HCL_OpDefaultSecondDeriv_d.
See the following report for more details and concrete examples.
"Implementing operators in HCL", Technical Report 99-22, Department of Computational and Applied Mathematics, Rice University, Houston, TX 77251-1892.
downloadable from the HCL home page.

virtual void DerivImage( const HCL_Vector_d & dx, HCL_Vector_d & dy ) const

DerivImage computes the image of the derivative on dx, yielding dy. Default implementation returns an error message and exits. To use the default Deriv method in a derived class, you must override the default implementation of this method with one that actually implements the derivative. In that case the linear operator (HCL_LinearOp_d) returned by Deriv will be an instance of HCL_OpDefaultDeriv_d.

virtual void DerivAdjImage( const HCL_Vector_d & dy, HCL_Vector_d & dx ) const

DerivAdjImage computes the image of the adjoint of the derivative on dy, yielding dx. Default implementation returns an error message and exits. To use the default Deriv method in a derived class, you must override the default implementation of this method with one that actually implements the derivative. In that case the linear operator (HCL_LinearOp_d) returned by Deriv will be an instance of HCL_OpDefaultDeriv_d.

virtual void DerivInvImage( const HCL_Vector_d & dy, HCL_Vector_d & dx ) const

DerivInvImage computes the image of the inverse of the derivative on dy, yielding dx. Default implementation returns an error message and exits. To use the default Deriv method in a derived class, you must override the default implementation of this method with one that actually implements the derivative. In that case the linear operator (HCL_LinearOp_d) returned by Deriv will be an instance of HCL_OpDefaultDeriv_d.

virtual void DerivInvAdjImage( const HCL_Vector_d & dx, HCL_Vector_d & dy ) const

DerivInvAdjImage computes the image of the inverse of the adjoint of the derivative on dx, yielding dy. Default implementation returns an error message and exits. To use the default Deriv method in a derived class, you must override the default implementation of this method with one that actually implements the derivative. In that case the linear operator ( HCL_LinearOp_d) returned by Deriv will be an instance of HCL_OpDefaultDeriv_d.

virtual void SecondDerivImage( const HCL_Vector_d & dx1, const HCL_Vector_d & dx2, HCL_Vector_d & dy ) const

SecondDerivImage computes the image of the second derivative on dx1 and dx2, yielding dy. Default implementation returns an error message and exits. To use the default SecondDeriv method in a derived class, you must override the default implementation of this method with one that actually implements the derivative. In that case the bilinear operator (HCL_BiLinearOp_d) returned by SeondDeriv will be an instance of HCL_OpDefaultDeriv_d.

virtual void SecondDerivPartialAdjImage(const HCL_Vector_d & dx1, const HCL_Vector_d & dy, HCL_Vector_d & dx2 ) const

SecondDerivPartialAdjImage computes the image of the so-called "partial adjoint" of the second derivative (which is a bilinear operator) on dx1 and dy, yielding dx2. See the documentation for HCL_BiLinearOp_d for more details about bilinear operators and partial adjoints. Note that since the second derivative of a (sufficiently smooth) operator is symmetric, there is no ambiguity about which partial adjoint is intended. Default implementation returns an error message and exits. To use the default SecondDeriv method in a derived class, you must override the default implementation of this method with one that actually implements the derivative. In that case the bilinear operator (HCL_BiLinearOp_d) returned by SeondDeriv will be an instance of HCL_OpDefaultDeriv_d.

virtual HCL_VectorSpace_d& Domain() const

Domain returns a reference to the domain of the underlying operator. Pure virtual: must be implemented in any derived instantiable class.

virtual HCL_VectorSpace_d& Range() const

Range returns a reference to the range of the underlying operator. Pure virtual: must be implemented in any derived instantiable class.

virtual void Image( HCL_Vector_d & y ) const

Image computes the image of the operator and assigns it to y. Pure virtual: must be implemented in any derived instantiable class.

virtual void ImageAdd( HCL_Vector_d & y, double a=1.0, double b=1.0 ) const

ImageAdd computes

. This method is given a default implementation in the base class, and need not be re-implemented in a derived class unless it is desired to obtain the gain in efficiency from "loop-fusion". Note that the scalars a and b are optional and default to 1.0.

virtual void ImageAdd( const HCL_Vector_d & z, HCL_Vector_d & y, double a=1.0, double b=1.0 ) const

ImageAdd computes

virtual const HCL_Vector_d& ImageRef() const

ImageRef returns a reference to the image of the operator at this point. The user has a choice of calling Image, in which case the storage for the result is managed by the calling routine, or calling ImageRef, in which the Evaluation object manages the storage. This method is implemented in this class.

virtual HCL_LinearOp_d* Deriv() const

Deriv computes the derivative of the operator. Note that this method constructs an HCL_LinearOp_d, which the calling program is responsible for deleting with HCL_delete. The default implementation requires that default implementations of DerivImage and related methods be overridden with code that really does the job - see documentation on these classes, above.

virtual const HCL_LinearOp_d& DerivRef() const

DerivRef returns a reference to the derivative at this point. The programmer has a choice of calling Deriv, in which case the calling routine is responsible for managing the storage, or calling DerivRef, in which case the Evaluation object does. This method is implemented in this class.

virtual HCL_BiLinearOp_d* SecondDeriv() const

SecondDeriv computes the second derivative of the operator. The second derivative is a bilinear operator which knows how to compute all relevant adjoints. The default implementation requires that default implementations of SecondDerivImage and related methods be overridden with code that really does the job - see documentation on these classes, above.

virtual const HCL_BiLinearOp_d& SecondDerivRef() const

SecondDerivRef returns a reference to the second derivative at this point. The programmer has a choice of calling SecondDeriv, in which case the calling routine is responsible for managing the storage, or calling SecondDerivRef, in which case the Evaluation object does. This method is implemented in this class.

Direct child classes:: HCL_EvalLNLOp_d
HCL_EvalOpProductDomain_d
HCL_OpDefaultEval_d

alphabetic index hierarchy of classes

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(c)opyright by Malte Zöckler, Roland Wunderling
contact: doc++@zib.de

virtual HCL_VectorSpace_d&	Domain () const Domain returns a reference to the domain of the underlying operator
virtual HCL_VectorSpace_d&	Range () const Range returns a reference to the range of the underlying operator
virtual void	Image ( HCL_Vector_d & y ) const Image computes the image of the operator and assigns it to y
virtual void	ImageAdd ( HCL_Vector_d & y, double a=1.0, double b=1.0 ) const ImageAdd computes
virtual void	ImageAdd ( const HCL_Vector_d & z, HCL_Vector_d & y, double a=1.0, double b=1.0 ) const ImageAdd computes
virtual const HCL_Vector_d&	ImageRef () const ImageRef returns a reference to the image of the operator at this point
virtual HCL_LinearOp_d*	Deriv () const Deriv computes the derivative of the operator
virtual const HCL_LinearOp_d&	DerivRef () const DerivRef returns a reference to the derivative at this point
virtual HCL_BiLinearOp_d*	SecondDeriv () const SecondDeriv computes the second derivative of the operator
virtual const HCL_BiLinearOp_d&	SecondDerivRef () const SecondDerivRef returns a reference to the second derivative at this point

virtual void	DerivImage ( const HCL_Vector_d & dx, HCL_Vector_d & dy ) const DerivImage computes the image of the derivative on dx, yielding dy
virtual void	DerivAdjImage ( const HCL_Vector_d & dy, HCL_Vector_d & dx ) const DerivAdjImage computes the image of the adjoint of the derivative on dy, yielding dx
virtual void	DerivInvImage ( const HCL_Vector_d & dy, HCL_Vector_d & dx ) const DerivInvImage computes the image of the inverse of the derivative on dy, yielding dx
virtual void	DerivInvAdjImage ( const HCL_Vector_d & dx, HCL_Vector_d & dy ) const DerivInvAdjImage computes the image of the inverse of the adjoint of the derivative on dx, yielding dy
virtual void	SecondDerivImage ( const HCL_Vector_d & dx1, const HCL_Vector_d & dx2, HCL_Vector_d & dy ) const SecondDerivImage computes the image of the second derivative on dx1 and dx2, yielding dy
virtual void	SecondDerivPartialAdjImage (const HCL_Vector_d & dx1, const HCL_Vector_d & dy, HCL_Vector_d & dx2 ) const SecondDerivPartialAdjImage computes the image of the so-called "partial adjoint" of the second derivative (which is a bilinear operator) on dx1 and dy, yielding dx2

class HCL_EvaluateOp_d : public HCL_Base

Inheritance:

Public Methods

Protected Methods

Inherited from HCL_Base:

Public Methods

Documentation