describes an inverse linear mapping X->Y More...

#include <linear_operator_inverse.h>

Inheritance diagram for ug::ILinearOperatorInverse< X, Y >:

Public Types
typedef Y	codomain_function_type
	Range space.

typedef X	domain_function_type
	Domain space.

Public Types inherited from ug::ILinearIterator< X, Y >
typedef Y	codomain_function_type
	Range space.

typedef X	domain_function_type
	Domain space.

Public Member Functions
virtual bool	apply (Y &u, const X &f)=0
	applies inverse operator, i.e. returns u = A^{-1} f

virtual bool	apply_return_defect (Y &u, X &f)=0
	applies inverse operator, i.e. returns u = A^{-1} f and returns defect d := f - A*u

virtual bool	apply_update_defect (Y &u, X &f)
	compute new correction c = Bd and update defect d := d - Ac

virtual SmartPtr< ILinearIterator< X, Y > >	clone ()
	clone

virtual std::string	config_string () const
	returns information about configuration parameters

SmartPtr< IConvergenceCheck< X > >	convergence_check ()
	returns the convergence check

ConstSmartPtr< IConvergenceCheck< X > >	convergence_check () const
	returns the convergence check

number	defect () const
	returns the current defect

	ILinearOperatorInverse ()
	constructor setting convergence check to (100, 1e-12, 1e-12, true)

	ILinearOperatorInverse (SmartPtr< IConvergenceCheck< X > > spConvCheck)
	Default constructor.

virtual bool	init (SmartPtr< ILinearOperator< Y, X > > J, const Y &u)
	initializes for the inverse for a linearized operator at linearization point u

virtual bool	init (SmartPtr< ILinearOperator< Y, X > > L)
	initializes for the inverse for a linear operator

SmartPtr< ILinearOperator< Y, X > >	linear_operator ()
	returns the current Operator this Inverse Operator is initialized for

virtual const char *	name () const =0
	returns the name of the operator inverse

number	reduction () const
	returns the current relative reduction

void	set_convergence_check (SmartPtr< IConvergenceCheck< X > > spConvCheck)
	set the convergence check

virtual int	standard_offset () const
	returns the standard offset for output

int	step () const
	returns the current number of steps

virtual bool	supports_parallel () const =0
	returns if parallel solving is supported

virtual	~ILinearOperatorInverse ()
	virtual destructor

Public Member Functions inherited from ug::ILinearIterator< X, Y >
SmartPtr< IDamping< X, Y > >	damping ()
	returns the scaling

	ILinearIterator ()
	constructor

	ILinearIterator (const ILinearIterator< X, Y > &parent)
	copy constructor

void	set_damp (number factor)
	sets the damping to a constant factor

void	set_damp (SmartPtr< IDamping< X, Y > > spScaling)
	sets a scaling for the correction

virtual	~ILinearIterator ()
	virtual destructor

Protected Attributes
SmartPtr< IConvergenceCheck< X > >	m_spConvCheck
	smart pointer holding the convergence check

SmartPtr< ILinearOperator< Y, X > >	m_spLinearOperator
	Operator that is inverted by this Inverse Operator.

Protected Attributes inherited from ug::ILinearIterator< X, Y >
SmartPtr< IDamping< X, Y > >	m_spDamping
	the scaling

Detailed Description

template<typename X, typename Y = X>
class ug::ILinearOperatorInverse< X, Y >

describes an inverse linear mapping X->Y

This class is the base class for the inversion of linear operator given in form of the ILinearOperator interface class. Given a operator L, the basic usage of this class is to invert this operator, i.e. to compute the solution u of

L*u = f     i.e. u := L^{-1} f

This application has been split up into three steps:

init(): This method initializes the inverse operator. The inverse operator is initialized the way that, its application will be the inverse application of the operator L passed in by this function. The prepare method can only be called, when this method has been called once.
apply(): This method performs the inversion. Before this method is called the init and prepare methods have to be called.

This splitting has been made, since initialization and preparation may be computationally expansive. Thus, the user of this class has the choice when to call this initialization/preparation. E.g. when the operator is applied several times on the same vectors, those have only to be prepared once and the init of the operator is only needed once.

Template Parameters

X	domain space
Y	range space

Member Typedef Documentation

◆ codomain_function_type

template<typename X , typename Y = X>

typedef Y ug::ILinearOperatorInverse< X, Y >::codomain_function_type

Range space.

◆ domain_function_type

template<typename X , typename Y = X>

typedef X ug::ILinearOperatorInverse< X, Y >::domain_function_type

Domain space.

Constructor & Destructor Documentation

◆ ILinearOperatorInverse() [1/2]

template<typename X , typename Y = X>

ug::ILinearOperatorInverse< X, Y >::ILinearOperatorInverse ( )

inline

constructor setting convergence check to (100, 1e-12, 1e-12, true)

References new().

◆ ILinearOperatorInverse() [2/2]

template<typename X , typename Y = X>

ug::ILinearOperatorInverse< X, Y >::ILinearOperatorInverse ( SmartPtr< IConvergenceCheck< X > > spConvCheck )

inline

Default constructor.

◆ ~ILinearOperatorInverse()

template<typename X , typename Y = X>

virtual ug::ILinearOperatorInverse< X, Y >::~ILinearOperatorInverse ( )

inlinevirtual

virtual destructor

Member Function Documentation

◆ apply()

template<typename X , typename Y = X>

virtual bool ug::ILinearOperatorInverse< X, Y >::apply	(	Y &	u,
		const X &	f
	)

pure virtual

applies inverse operator, i.e. returns u = A^{-1} f

This method applies the inverse operator, i.e. u = A^{-1} f. The domain function f remains unchanged. Note, that this method can always be implemented by creating a copy of f and calling apply_return_defect with this copy.

Parameters

[in]	f	right-hand side
[out]	u	solution

Returns: bool success flag

Implements ug::ILinearIterator< X, Y >.

Implemented in ug::PrimalSubassembledMatrixInverse< TAlgebra >, ug::PrimalSubassembledMatrixInverse< algebra_type >, ug::AnalyzingSolver< M, X, Y >, and ug::IMatrixOperatorInverse< M, X, Y >.

Referenced by ug::OperatorInverseIterator< TAlgebra >::apply(), ug::SchurInverseWithOperator< TAlgebra >::apply(), ug::SchurInverseWithFullMatrix< TAlgebra >::apply(), ug::SchurInverseWithAutoFullMatrix< TAlgebra >::apply(), ug::PowerMethod< TAlgebra >::calculate_max_eigenvalue(), and ug::PowerMethod< TAlgebra >::calculate_min_eigenvalue().

◆ apply_return_defect()

template<typename X , typename Y = X>

virtual bool ug::ILinearOperatorInverse< X, Y >::apply_return_defect	(	Y &	u,
		X &	f
	)

pure virtual

applies inverse operator, i.e. returns u = A^{-1} f and returns defect d := f - A*u

This method applies the inverse operator, i.e. u = A^{-1} f. The domain function f is changed in the way, that the defect d := f - A*u is returned in the function. This is always useful, when the inverting algorithm can (or must) update the defect during computation (this is e.g. the case for the geometric multigrid method). Note, that this method can always be implemented by calling apply and then computing d := f - A*u.

Parameters

[in,out]	f	right-hand side
[out]	u	solution

Returns: bool success flag

Implemented in ug::PrimalSubassembledMatrixInverse< TAlgebra >, ug::PrimalSubassembledMatrixInverse< algebra_type >, ug::AnalyzingSolver< M, X, Y >, and ug::IMatrixOperatorInverse< M, X, Y >.

Referenced by ug::IPreconditionedLinearOperatorInverse< X >::apply(), ug::SchurInverseWithOperator< TAlgebra >::apply_return_defect(), ug::SchurInverseWithFullMatrix< TAlgebra >::apply_return_defect(), ug::SchurInverseWithAutoFullMatrix< TAlgebra >::apply_return_defect(), ug::OperatorInverseIterator< TAlgebra >::apply_update_defect(), and ug::ILinearOperatorInverse< X, Y >::apply_update_defect().

◆ apply_update_defect()

template<typename X , typename Y = X>

virtual bool ug::ILinearOperatorInverse< X, Y >::apply_update_defect	(	Y &	c,
		X &	d
	)

inlinevirtual

compute new correction c = B*d and update defect d := d - A*c

This method applies the inverse operator, i.e. c = B*d. The domain function d is changed in the way, that the defect d := d - A*c is returned in the function. This is always useful, when the iterating algorithm can (or must) update the defect during computation (this is e.g. the case for the geometric multigrid method). Note, that this method can always be implemented by calling apply and then computing d := d - A*c.

Parameters

[in,out]	d	defect
[out]	u	correction

Returns: bool success flag

Implements ug::ILinearIterator< X, Y >.

References ug::ILinearOperatorInverse< X, Y >::apply_return_defect().

Referenced by ug::LinearSolver< TVector >::compute_correction().

◆ clone()

template<typename X , typename Y = X>

virtual SmartPtr< ILinearIterator< X, Y > > ug::ILinearOperatorInverse< X, Y >::clone ( )

inlinevirtual

clone

Implements ug::ILinearIterator< X, Y >.

Reimplemented in ug::IExternalSolver< TAlgebra >.

References SPNULL, and UG_THROW.

◆ config_string()

template<typename X , typename Y = X>

virtual std::string ug::ILinearOperatorInverse< X, Y >::config_string ( ) const

inlinevirtual

returns information about configuration parameters

this should return necessary information about parameters and possibly calling config_string of subcomponents.

Returns: std::string necessary information about configuration parameters

Reimplemented from ug::ILinearIterator< X, Y >.

Reimplemented in ug::IPreconditionedLinearOperatorInverse< X >, ug::IPreconditionedLinearOperatorInverse< TVector >, ug::IPreconditionedLinearOperatorInverse< ug::ParallelVector >, ug::IPreconditionedLinearOperatorInverse< vector_type >, ug::AgglomeratingSolver< TAlgebra >, ug::AnalyzingSolver< M, X, Y >, ug::BiCGStab< TVector >, ug::GMRES< TVector >, and ug::LU< TAlgebra >.

References ug::ILinearOperatorInverse< X, Y >::name().

Referenced by ug::SchurInverseWithOperator< TAlgebra >::config_string(), ug::SchurInverseWithFullMatrix< TAlgebra >::config_string(), ug::SchurInverseWithAutoFullMatrix< TAlgebra >::config_string(), and ug::SchurPrecond< TAlgebra >::config_string().

◆ convergence_check() [1/2]

template<typename X , typename Y = X>

SmartPtr< IConvergenceCheck< X > > ug::ILinearOperatorInverse< X, Y >::convergence_check ( )

inline

returns the convergence check

References ug::ILinearOperatorInverse< X, Y >::m_spConvCheck.

◆ convergence_check() [2/2]

template<typename X , typename Y = X>

ConstSmartPtr< IConvergenceCheck< X > > ug::ILinearOperatorInverse< X, Y >::convergence_check ( ) const

inline

returns the convergence check

References ug::ILinearOperatorInverse< X, Y >::m_spConvCheck.

Referenced by ug::LU< TAlgebra >::apply(), ug::AutoLinearSolver< TVector >::apply_return_defect(), ug::BiCGStab< TVector >::apply_return_defect(), ug::CG< TVector >::apply_return_defect(), ug::GMRES< TVector >::apply_return_defect(), ug::LinearSolver< TVector >::apply_return_defect(), ug::ILinearOperatorInverse< X, Y >::defect(), ug::AutoLinearSolver< TVector >::prepare_conv_check(), ug::BiCGStab< TVector >::prepare_conv_check(), ug::CG< TVector >::prepare_conv_check(), ug::FETISolver< TAlgebra >::prepare_conv_check(), ug::GMRES< TVector >::prepare_conv_check(), ug::LinearSolver< TVector >::prepare_conv_check(), ug::ILinearOperatorInverse< X, Y >::reduction(), and ug::ILinearOperatorInverse< X, Y >::step().

◆ defect()

template<typename X , typename Y = X>

number ug::ILinearOperatorInverse< X, Y >::defect ( ) const

inline

returns the current defect

References ug::ILinearOperatorInverse< X, Y >::convergence_check().

Referenced by ug::AutoLinearSolver< TVector >::apply_return_defect().

◆ init() [1/2]

template<typename X , typename Y = X>

virtual bool ug::ILinearOperatorInverse< X, Y >::init	(	SmartPtr< ILinearOperator< Y, X > >	J,
		const Y &	u
	)

inlinevirtual

initializes for the inverse for a linearized operator at linearization point u

This method passes the linear operator J(u) that should be inverted by this operator. As second argument the linearization point is passed. This is needed e.g. for the geometric multigrid method, that inverts a linearized operator based on coarser grid operators, that have to be initialized based on the linearization point.

Parameters

[in]	J	linearized operator to invert
[in]	u	linearization point

Returns: bool success flag

Implements ug::ILinearIterator< X, Y >.

Reimplemented in ug::IMatrixOperatorInverse< M, X, Y >, ug::AnalyzingSolver< M, X, Y >, and ug::LU< TAlgebra >.

References ug::ILinearOperatorInverse< X, Y >::m_spLinearOperator.

◆ init() [2/2]

template<typename X , typename Y = X>

virtual bool ug::ILinearOperatorInverse< X, Y >::init ( SmartPtr< ILinearOperator< Y, X > > L )

inlinevirtual

initializes for the inverse for a linear operator

This method passes the operator L that is inverted by this operator. In addition some preparation step can be made.

Parameters

[in] L linear operator to invert

Returns: bool success flag

Implements ug::ILinearIterator< X, Y >.

Reimplemented in ug::IMatrixOperatorInverse< M, X, Y >, ug::AnalyzingSolver< M, X, Y >, and ug::LU< TAlgebra >.

References ug::ILinearOperatorInverse< X, Y >::m_spLinearOperator.

Referenced by ug::PowerMethod< TAlgebra >::calculate_max_eigenvalue(), ug::PowerMethod< TAlgebra >::calculate_min_eigenvalue(), ug::OperatorInverseIterator< TAlgebra >::init(), ug::OperatorInverseIterator< TAlgebra >::init(), ug::SchurInverseWithOperator< TAlgebra >::init(), ug::SchurInverseWithFullMatrix< TAlgebra >::init(), ug::SchurInverseWithAutoFullMatrix< TAlgebra >::init(), and ug::AutoLinearSolver< TVector >::init_op().

◆ linear_operator()

template<typename X , typename Y = X>

SmartPtr< ILinearOperator< Y, X > > ug::ILinearOperatorInverse< X, Y >::linear_operator ( )

inline

returns the current Operator this Inverse Operator is initialized for

References ug::ILinearOperatorInverse< X, Y >::m_spLinearOperator, ug::ILinearOperatorInverse< X, Y >::name(), and UG_THROW.

Referenced by ug::IPreconditionedLinearOperatorInverse< X >::apply(), ug::AutoLinearSolver< TVector >::apply_return_defect(), ug::BiCGStab< TVector >::apply_return_defect(), ug::CG< TVector >::apply_return_defect(), ug::GMRES< TVector >::apply_return_defect(), ug::LinearSolver< TVector >::apply_return_defect(), and ug::AutoLinearSolver< TVector >::compute_correction().

◆ name()

template<typename X , typename Y = X>

virtual const char * ug::ILinearOperatorInverse< X, Y >::name ( ) const

pure virtual

returns the name of the operator inverse

This method returns the name of the inverse operator. This function is typically needed, when the inverse operator is used inside of another and some debug output should be printed