HCL_LinearOp

class HCL_LinearOp_d : public HCL_Base

HCL_LinearOp_d is the base class for all linear operators

Inheritance:

Public Methods

Inherited from HCL_Base:

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

Documentation

HCL_LinearOp_d is the base class for all linear operators. This class represents a linear operator mapping one vector space to another. The primary methods are:
Domain Returns a reference to the domain of the operator. This is used primarily for error-checking.
Range Returns a reference to the range of the operator. This is used primarily for error-checking.
Image Computes the action of the operator on a vector. Here is an example illustrating the use of Domain, Range, and Image:
   void fcn( HCL_LinearOp_d & L,HCL_Vector_d & x,HCL_Vector_d & y )
   {
      if( x.Space() != L.Domain() || y.Space() != L.Range() )
         // Error condition
      .
      .
      .
      L.Image( x,y ); // y <-- Lx
      .
      .
      .
   }
ImageAdd Computes or , where a and b are scalars.
AdjImage Computes the action of the adjoint of the operator on a vector. This method is used as follows:
      L.AdjImage( y,x ); // x <-- L'y
The method is implemented as an error in this base class. In a derived class, this method must be implemented to behave as advertised if the operator will be used by algorithms which require the adjoint. If the operator is not intended to be used by such algorithms, then this method need not be over-ridden.
AdjImageAdd Analogous to ImageAdd, but for the adjoint.
InvImage Computes the action of the inverse of the operator on a vector. This method is used as follows:
      L.InvImage( y,x ); // x <-- L^{-1}y
The method is implemented as an error in this base class. In a derived class, this method must be implemented to behave as advertised if the operator will be used by algorithms which require the inverse. If the operator is not intended to be used by such algorithms, then this method need not be over-ridden.
InvImageAdd Analogous to ImageAdd, but for the inverse.
InvAdjImage Computes the action of the inverse of the adjoint on a vector. The method is implemented as an error in this base class. In a derived class, this method must be implemented to behave as advertised if the operator will be used by algorithms which require the inverse of the adjoint. If the operator is not intended to be used by such algorithms, then this method need not be over-ridden.
InvAdjImageAdd Analogous to ImageAdd, but for the inverse of the adjoint.
CheckAdj tests that the operator and its adjoint satisfy the "adjointness" relationship.
NormalImage Computes the action of the normal operator on a vector. This method is used as follows:
      L.NormalImage( x,z ); // z <-- L'Ly
The method is implemented in this base class to call the Image method followed by the AdjImage method. In a derived class, this method can be reimplemented if there is a more efficient way to compute the normal operator.
NormalImageAdd Analogous to ImageAdd, but for the normal operator.
CheckNormal tests that the Image, AdjImage, and NormalImage methods are consistent.
Note that this class makes no assumption about the representation of the operator. Examples include operators defined by dense or sparse matrices and solution operators of (linear) PDEs defined by simulations.

virtual HCL_VectorSpace_d& Domain() const

Domain space access. Returns a reference to the domain of the operator, which is an HCL_VectorSpace_d. Pure virtual: must be implemented in any derived instantiable class.

virtual HCL_VectorSpace_d& Range() const

Range space access. Returns a reference to the range of the operator, which is an HCL_VectorSpace_d. Pure virtual: must be implemented in any derived instantiable class.

virtual void Image( const HCL_Vector_d & x, HCL_Vector_d & y ) const

Image computes the action of the operator on x, giving y. Pure virtual: must be implemented in any derived instantiable class.

virtual void AdjImage( const HCL_Vector_d & y, HCL_Vector_d & x ) const

AdjImage computes the action of the adjoint on y, giving x. This method is implemented in the base class to return an error message. To obtain a working AdjImage in any derived instantiable class, you must override this default.

int CheckAdj(int Display = 1, double tol = 1000 )

CheckAdj tests that the operator and its adjoint satisfy the "adjointness" relationship. The return value is 1 if an error is detected, zero otherwise. The first input is a display flag; zero means no display, 1 means display a message only if there is an error, and 2 means displays the results of the test, whether there is an error or not. The second input sets the tolerance for the floating-point tests; an error is reported if two results which ought to be equal differ by a relative amount greater than tol times machine epsilon. This method is implemented in this class.

virtual void NormalImage( const HCL_Vector_d & x, HCL_Vector_d & z ) const

NormalImage computes the action of the normal on x, giving z. This method is given a default implementation in this class. Custom implementations may be more efficient than the default.

int CheckNormal( int display = 1, double tol = 100 )

CheckNormal tests that the normal operator N is really defined by N = A'A. The return value is 1 if an error is detected, zero otherwise. The first input is a display flag; zero means no display, 1 means display a message only if there is an error, and 2 means displays the results of the test, whether there is an error or not. The second input sets the tolerance for the floating-point tests; an error is reported if two results which ought to be equal differ by a relative amount greater than tol times machine epsilon. This method is implemented in this class.

virtual void InvImage(const HCL_Vector_d & y, HCL_Vector_d & x) const

InvImage computes the action of the inverse on y, giving x. This method is implemented in the base class to return an error message. To obtain a working InvImage in any derived instantiable class, you must override this default.

virtual void InvAdjImage(const HCL_Vector_d & x, HCL_Vector_d & y) const

InvAdjImage computes the action of the inverse adjoint on x, giving y. This method is implemented in the base class to return an error message. To obtain a working InvAdjImage in any derived instantiable class, you must override this default.

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

ImageAdd implements

. This provides for efficiency in creating linear combinations of the operator output and another vector. An efficient implementation will avoid temporary storage of intermediate results, as well as multiple passes through the data. The scalars default to 1.0; if left at their default values, no multiplies are actually performed. For convenience we provide a default (inefficient) implementation: efficient implementations for concrete operators will override this.

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

AdjImageAdd implements

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

NormalImageAdd implements

. This provides for efficiency in creating linear combinations of the operator output and another vector, as frequently occurs in iterative algorithms. An efficient implementation will avoid temporary storage of intermediate results, as well as multiple passes through the data. The scalars default to 1.0; if left at their default values, no multiplies are actually performed. For convenience we provide a default (inefficient) implementation: efficient implementations for concrete operators will override this.

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

InvImageAdd implements

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

InvAdjImageAdd implements

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

ImageAdd implements

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

AdjImageAdd implements

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

NormalImageAdd implements

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

InvImageAdd implements

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

InvAdjImageAdd implements

Direct child classes:: HCL_lmbfgsOp1_d
HCL_ZeroLinearOp_d
HCL_ScaleLinearOp_d
HCL_DiagScaleLinearOp_d
HCL_LinCombLinearOp_d
HCL_CompLinearOp_d
HCL_DiagBlockLinearOp_d
HCL_BlockLinearOp_d
HCL_BigMFcnlHessian_d
HCL_Normal_d
HCL_InvLinearOp_d
HCL_Adjoint_d
HCL_OpDefaultPartialDeriv_d
HCL_OpDefaultDeriv_d
HCL_FunctionalDefaultHessianBlock_d
HCL_FunctionalDefaultHessian_d
HCL_RestrictedBiLinearOp_d
HCL_UpperTriangularMatOp_d
HCL_SymSparseRCSMatOp_d
HCL_SymMatOp_d
HCL_SparseRCSMatOp_d
HCL_LowerTriangularMatOp_d
HCL_GeneralMatOp_d
HCL_TRSSOp_d

alphabetic index hierarchy of classes

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virtual HCL_VectorSpace_d&	Domain () const Domain space access
virtual HCL_VectorSpace_d&	Range () const Range space access
virtual void	Image ( const HCL_Vector_d & x, HCL_Vector_d & y ) const Image computes the action of the operator on x, giving y
virtual void	AdjImage ( const HCL_Vector_d & y, HCL_Vector_d & x ) const AdjImage computes the action of the adjoint on y, giving x
int	CheckAdj (int Display = 1, double tol = 1000 ) CheckAdj tests that the operator and its adjoint satisfy the "adjointness" relationship
virtual void	NormalImage ( const HCL_Vector_d & x, HCL_Vector_d & z ) const NormalImage computes the action of the normal on x, giving z
int	CheckNormal ( int display = 1, double tol = 100 ) CheckNormal tests that the normal operator N is really defined by N = A'A
virtual void	InvImage (const HCL_Vector_d & y, HCL_Vector_d & x) const InvImage computes the action of the inverse on y, giving x
virtual void	InvAdjImage (const HCL_Vector_d & x, HCL_Vector_d & y) const InvAdjImage computes the action of the inverse adjoint on x, giving y
virtual void	ImageAdd (const HCL_Vector_d & x, const HCL_Vector_d & z, HCL_Vector_d & y, double a=1.0, double b=1.0) const ImageAdd implements
virtual void	AdjImageAdd (const HCL_Vector_d & x, const HCL_Vector_d & z, HCL_Vector_d & y, double a=1.0, double b=1.0) const AdjImageAdd implements
virtual void	NormalImageAdd (const HCL_Vector_d & x, const HCL_Vector_d & z, HCL_Vector_d & y, double a=1.0, double b=1.0) const NormalImageAdd implements
virtual void	InvImageAdd (const HCL_Vector_d & x, const HCL_Vector_d & z, HCL_Vector_d & y, double a=1.0, double b=1.0) const InvImageAdd implements
virtual void	InvAdjImageAdd (const HCL_Vector_d & x, const HCL_Vector_d & z, HCL_Vector_d & y, double a=1.0, double b=1.0) const InvAdjImageAdd implements
virtual void	ImageAdd (const HCL_Vector_d & x, HCL_Vector_d & y, double a=1.0, double b=1.0) const ImageAdd implements
virtual void	AdjImageAdd (const HCL_Vector_d & x, HCL_Vector_d & y, double a=1.0, double b=1.0) const AdjImageAdd implements
virtual void	NormalImageAdd (const HCL_Vector_d & x, HCL_Vector_d & y, double a=1.0, double b=1.0) const NormalImageAdd implements
virtual void	InvImageAdd (const HCL_Vector_d & x, HCL_Vector_d & y, double a=1.0, double b=1.0) const InvImageAdd implements
virtual void	InvAdjImageAdd (const HCL_Vector_d & x, HCL_Vector_d & y, double a=1.0, double b=1.0) const InvAdjImageAdd implements

class HCL_LinearOp_d : public HCL_Base

Inheritance:

Public Methods

Inherited from HCL_Base:

Public Methods

Documentation