RVL::LinearOp

RVL::LinearOp< Scalar > Class Template Reference

Principal RVL interface for Linear Operators. More...

#include <linop_base.hh>

Inheritance diagram for RVL::LinearOp< Scalar >:


Public Member Functions
	LinearOp ()
	LinearOp (const LinearOp< Scalar > &Op)
virtual	~LinearOp ()
void	applyOp (Vector< Scalar > const &x, Vector< Scalar > &y) const
	This function assigns to the value .
void	applyAdjOp (Vector< Scalar > const &x, Vector< Scalar > &y) const
	This function assigns to the value .
virtual void	applyPlusOp (Vector< Scalar > const &x, Vector< Scalar > &y) const
	Apply and increment, like axpy: $y = \alpha A x + y$ .
virtual void	applyPlusAdjOp (Vector< Scalar > const &x, Vector< Scalar > &y) const
	Apply and increment, like axpy: $y = \alpha A^T x + y$ .
virtual void	applyOp (Scalar alpha, Vector< Scalar > const &x, Scalar beta, Vector< Scalar > &y) const
	Apply and linear combination: $y = \alpha A x + \beta y$ .
virtual void	applyAdjOp (Scalar alpha, Vector< Scalar > const &x, Scalar beta, Vector< Scalar > &y) const
	Adjoint apply and linear combination: $y = \alpha A^* x + \beta y$ .
Protected Member Functions
void *	operator new (size_t size)
	operator new - not available to general public, but available to children who will use it to define a clone method, for example
virtual void	applyAdj (const Vector< Scalar > &x, Vector< Scalar > &y) const =0
	Evaluation of adjoint linear operator on constant input vector x, output written on mutable vector y.
void	applyDeriv (const Vector< Scalar > &, const Vector< Scalar > &dx, Vector< Scalar > &dy) const
	implemented derivative method - a linear operator is its own derivative.
void	applyAdjDeriv (const Vector< Scalar > &, const Vector< Scalar > &dy, Vector< Scalar > &dx) const
	similar to applyDeriv.
void	applyDeriv2 (const Vector< Scalar > &, const Vector< Scalar > &, const Vector< Scalar > &, Vector< Scalar > &dy) const
	implemented deriv2 method - deriv2 of a linear operator is zero.
void	applyAdjDeriv2 (const Vector< Scalar > &, const Vector< Scalar > &, const Vector< Scalar > &, Vector< Scalar > &dx1) const
	similar to applyDeriv

Detailed Description

template<class Scalar>
class RVL::LinearOp< Scalar >

Principal RVL interface for Linear Operators.

Since linear operators in Hilbert space have well-defined adjoints, this class really defines a pair of operators, adjoint to each other.

The abstract public interface consists of

getDomain, getRange: statements of domain and range
applyOp, applyAdjOp: application of the operator and its adjoint
getDomain() method returns a const refer ence to the RVL::Space representing the domain; getRange() does likewise for the range. These are pure virtual methods, so will need to be implemented in instantiable derived classes. Typical implementations of getDomain and getRange will expose references to const Space data members.
The applyOp() method accepts a const RVL::Vector argument representing the input vector, and a mutable RVL::Vector argument representing the ouput. The input must be a member of the domain, and the output a member of the range, and these conditions are checked in the method body using RVL::Space::operator=, RVL::Vector::getSpace, and the getDomain and getRange methods of this class. Similarly the applyAdjOp method implements application of the adjoint, and sanity-checks its arguments as well. Note that both applyOp and applyAdjOp are implemented, and may not be overridden in child classes.
The applyOp and applyAdjOp methods delegate the computations inherent in the action of the linear operator and its adjoint to two pure virtual protected methods, apply and applyAdj, which accept the same arguments. The subclass writer will thus need to implement apply and applyAdj. This device permits the sanity tests for membership in domain and range to be hard-coded in applyOp and applyAdjOp, relieving the subclass writer of the necessity to test the dimensional and other conditions implicit in membership.
A protected pure virtual copy constructor (clone) must also be supplied; a typical implementation delegates to the copy constructor of the subclass.
In summary, the subclass writer must implement three protected methods:
- clone: usually calls copy constructor
- apply: code for action of operator, can assume membership of input and output in domain and range without further tests
- applyAdj: code for adjoint action of operator, can assume membership of input and output in domain and range without further tests
and two public methods (usually by returning reference member data):
- getDomain: returns const reference to domain RVL::Space
- getRange: returns const reference to range RVL::Space
A unit test for validity of the adjoint relationship is supplied as part of RVL, in the form of a standalone function (AdjointTest). It is HIGHLY RECOMMENDED that every concrete LinearOp implementation be subjected to this test.

Definition at line 123 of file linop_base.hh.

Constructor & Destructor Documentation

template<class Scalar>

RVL::LinearOp< Scalar >::LinearOp ( )

Definition at line 182 of file linop_base.hh.

template<class Scalar>

RVL::LinearOp< Scalar >::LinearOp ( const LinearOp< Scalar > & Op )

Definition at line 183 of file linop_base.hh.

template<class Scalar>

virtual RVL::LinearOp< Scalar >::~LinearOp ( ) [virtual]

Definition at line 184 of file linop_base.hh.

Member Function Documentation

template<class Scalar>

void* RVL::LinearOp< Scalar >::operator new ( size_t size ) [protected]

operator new - not available to general public, but available to children who will use it to define a clone method, for example

Version 1.0: user control, for the bold. "There are old sailors, and there are bold sailors, but there are no old, bold sailors."

Reimplemented from RVL::Operator< Scalar >.

Definition at line 137 of file linop_base.hh.

template<class Scalar>

virtual void RVL::LinearOp< Scalar >::applyAdj	(	const Vector< Scalar > &	x,
		Vector< Scalar > &	y
	)			const `[protected, pure virtual]`

Evaluation of adjoint linear operator on constant input vector x, output written on mutable vector y.

Accessed only through public applyOp method, so creator of subclasses may assume that input is in domain, output is in range

Implemented in RVL::BlockLinearOp< Scalar >, RVL::BlockLinearOpBlock< Scalar >, RVL::ColumnLinearOp< Scalar >, RVL::CompLinearOp< Scalar >, RVL::LinearOpFO< Scalar >, RVL::AdjLinearOp< Scalar >, RVL::NormalLinearOp< Scalar >, RVL::ScaleOpFwd< Scalar >, RVL::ScaleOpInv< Scalar >, RVL::LinCombLinearOp< Scalar >, RVL::LinearBilinearOp< Scalar >, RVL::LinearRestrictOp< Scalar >, RVL::DerivEvaluation< Scalar >, and RVL::PartialDerivEvaluation< Scalar >.

Referenced by RVL::LinearOp< Scalar >::applyAdjDeriv(), and RVL::LinearOp< Scalar >::applyAdjOp().

template<class Scalar>

void RVL::LinearOp< Scalar >::applyDeriv	(	const Vector< Scalar > &	,
		const Vector< Scalar > &	dx,
		Vector< Scalar > &	dy
	)			const `[protected, virtual]`

implemented derivative method - a linear operator is its own derivative.

First arg: position, of which result is independent.

Implements RVL::Operator< Scalar >.

Definition at line 156 of file linop_base.hh.

References RVL::Operator< Scalar >::apply().

template<class Scalar>

void RVL::LinearOp< Scalar >::applyAdjDeriv	(	const Vector< Scalar > &	,
		const Vector< Scalar > &	dy,
		Vector< Scalar > &	dx
	)			const `[protected, virtual]`

similar to applyDeriv.

First arg: position, of which result is independent.

Implements RVL::Operator< Scalar >.

Definition at line 161 of file linop_base.hh.

References RVL::LinearOp< Scalar >::applyAdj().

template<class Scalar>

void RVL::LinearOp< Scalar >::applyDeriv2	(	const Vector< Scalar > &	,
		const Vector< Scalar > &	,
		const Vector< Scalar > &	,
		Vector< Scalar > &	dy
	)			const `[protected, virtual]`

implemented deriv2 method - deriv2 of a linear operator is zero.

First three args: position, two perturbation vectors in domain - result is independent of these.

Reimplemented from RVL::Operator< Scalar >.

Definition at line 169 of file linop_base.hh.

References RVL::Vector< Scalar >::zero().

template<class Scalar>

void RVL::LinearOp< Scalar >::applyAdjDeriv2	(	const Vector< Scalar > &	,
		const Vector< Scalar > &	,
		const Vector< Scalar > &	,
		Vector< Scalar > &	dx1
	)			const `[protected, virtual]`

similar to applyDeriv

Reimplemented from RVL::Operator< Scalar >.

Definition at line 175 of file linop_base.hh.

References RVL::Vector< Scalar >::zero().

template<class Scalar>

void RVL::LinearOp< Scalar >::applyOp	(	Vector< Scalar > const &	x,
		Vector< Scalar > &	y
	)			const

This function assigns to $ y $ the value $ A x$ .

Output vector y may not be aliased with input vector x. Applies standard sanity test, then delegates to protected apply method.

Definition at line 193 of file linop_base.hh.

References RVL::Operator< Scalar >::apply(), RVL::Operator< Scalar >::getDomain(), RVL::Operator< Scalar >::getRange(), RVL::Vector< Scalar >::getSpace(), and RVL::Writeable::write().

Referenced by RVL::AdjointTest(), RVL::CompLinearOp< Scalar >::apply(), RVL::ScaleOpFwd< Scalar >::applyAdj(), RVL::NormalLinearOp< Scalar >::applyAdj(), RVL::LinearOp< Scalar >::applyOp(), and RVL::LinearOp< Scalar >::applyPlusOp().

template<class Scalar>

void RVL::LinearOp< Scalar >::applyAdjOp	(	Vector< Scalar > const &	x,
		Vector< Scalar > &	y
	)			const

This function assigns to $ y $ the value $ A^* x$ .

Output vector y may not be aliased with input vector x. Applies standard sanity test, then delegates to protected applyAdj method.

Definition at line 252 of file linop_base.hh.

References RVL::LinearOp< Scalar >::applyAdj(), RVL::Operator< Scalar >::getDomain(), RVL::Operator< Scalar >::getRange(), RVL::Vector< Scalar >::getSpace(), and RVL::Writeable::write().

Referenced by RVL::AdjointTest(), RVL::CompLinearOp< Scalar >::applyAdj(), RVL::LinearOp< Scalar >::applyAdjOp(), and RVL::LinearOp< Scalar >::applyPlusAdjOp().

template<class Scalar>

virtual void RVL::LinearOp< Scalar >::applyPlusOp	(	Vector< Scalar > const &	x,
		Vector< Scalar > &	y
	)			const `[virtual]`

Apply and increment, like axpy: $y = \alpha A x + y$ .

Obvious default implementation provided for convenience, can be overridden to fuse loops for efficiency, if desired. Output vector y may not be aliased with input vector x.

Definition at line 310 of file linop_base.hh.

References RVL::LinearOp< Scalar >::applyOp(), and RVL::Vector< Scalar >::linComb().

template<class Scalar>

virtual void RVL::LinearOp< Scalar >::applyPlusAdjOp	(	Vector< Scalar > const &	x,
		Vector< Scalar > &	y
	)			const `[virtual]`

Apply and increment, like axpy: $y = \alpha A^T x + y$ .

Obvious default implementation provided for convenience, can be overridden to fuse loops for efficiency, if desired. Output vector y may not be aliased with input vector x.

Definition at line 328 of file linop_base.hh.

References RVL::LinearOp< Scalar >::applyAdjOp(), and RVL::Vector< Scalar >::linComb().

template<class Scalar>

virtual void RVL::LinearOp< Scalar >::applyOp	(	Scalar	alpha,
		Vector< Scalar > const &	x,
		Scalar	beta,
		Vector< Scalar > &	y
	)			const `[virtual]`

Apply and linear combination: $y = \alpha A x + \beta y$ .

Obvious default implementation provided for convenience, can be overridden to fuse loops for efficiency, if desired. Output vector y may not be aliased with input vector x.

Definition at line 346 of file linop_base.hh.

References RVL::LinearOp< Scalar >::applyOp(), and RVL::Vector< Scalar >::linComb().

template<class Scalar>

virtual void RVL::LinearOp< Scalar >::applyAdjOp	(	Scalar	alpha,
		Vector< Scalar > const &	x,
		Scalar	beta,
		Vector< Scalar > &	y
	)			const `[virtual]`

Adjoint apply and linear combination: $y = \alpha A^* x + \beta y$ .

Obvious default implementation provided for convenience, can be overridden to fuse loops for efficiency, if desired. Output vector y may not be aliased with input vector x.

Definition at line 365 of file linop_base.hh.

References RVL::LinearOp< Scalar >::applyAdjOp(), and RVL::Vector< Scalar >::linComb().

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

linop_base.hh

Generated on 5 Jan 2017 for RVL by

1.4.7

RVL::LinearOp< Scalar > Class Template Reference

Public Member Functions

Protected Member Functions

Detailed Description

template<class Scalar> class RVL::LinearOp< Scalar >

Constructor & Destructor Documentation

Member Function Documentation

template<class Scalar>
class RVL::LinearOp< Scalar >