Accelerated flexible conjugate gradient method. More...

#include <dune/istl/solvers.hh>

Inheritance diagram for Dune::RestartedFCGSolver< X >:

Public Types
typedef X	domain_type
	Type of the domain of the operator to be inverted.

typedef Y	range_type
	Type of the range of the operator to be inverted.

typedef X::field_type	field_type
	The field type of the operator.

typedef FieldTraits< field_type >::real_type	real_type
	The real type of the field type (is the same if using real numbers, but differs for std::complex)

typedef Simd::Scalar< real_type >	scalar_real_type
	scalar type underlying the field_type

Public Member Functions
	RestartedFCGSolver (const LinearOperator< X, X > &op, Preconditioner< X, X > &prec, scalar_real_type reduction, int maxit, int verbose, int mmax=10)
	Constructor to initialize a RestartedFCG solver.

	RestartedFCGSolver (const LinearOperator< X, X > &op, const ScalarProduct< X > &sp, Preconditioner< X, X > &prec, scalar_real_type reduction, int maxit, int verbose, int mmax=10)
	Constructor to initialize a RestartedFCG solver.

	RestartedFCGSolver (std::shared_ptr< const LinearOperator< X, X > > op, std::shared_ptr< const ScalarProduct< X > > sp, std::shared_ptr< Preconditioner< X, X > > prec, scalar_real_type reduction, int maxit, int verbose, int mmax=10)
	Constructor to initialize a RestartedFCG solver.

	RestartedFCGSolver (std::shared_ptr< const LinearOperator< X, X > > op, std::shared_ptr< Preconditioner< X, X > > prec, const ParameterTree &configuration)
	Constructor to initialize a RestartedFCG solver.

	RestartedFCGSolver (std::shared_ptr< const LinearOperator< X, X > > op, std::shared_ptr< const ScalarProduct< X > > sp, std::shared_ptr< Preconditioner< X, X > > prec, const ParameterTree &config)

void	apply (X &x, X &b, InverseOperatorResult &res) override
	Apply inverse operator.

void	apply (X &x, X &b, double reduction, InverseOperatorResult &res) final
	Apply inverse operator with given reduction factor.

virtual void	apply (X &x, Y &b, InverseOperatorResult &res)=0
	Apply inverse operator,.

virtual void	apply (X &x, Y &b, double reduction, InverseOperatorResult &res)=0
	apply inverse operator, with given convergence criteria.

SolverCategory::Category	category () const override
	Category of the solver (see SolverCategory::Category)

std::string	name () const

Protected Types
using	Iteration = typename IterativeSolver< X, X >::template Iteration< unsigned int >

enum	{ iterationSpacing = 5 , normSpacing = 16 }

Protected Member Functions
void	printHeader (std::ostream &s) const
	helper function for printing header of solver output

template<typename CountType , typename DataType >
void	printOutput (std::ostream &s, const CountType &iter, const DataType &norm, const DataType &norm_old) const
	helper function for printing solver output

template<typename CountType , typename DataType >
void	printOutput (std::ostream &s, const CountType &iter, const DataType &norm) const
	helper function for printing solver output

Protected Attributes
int	_mmax

std::shared_ptr< const LinearOperator< X, X > >	_op

std::shared_ptr< Preconditioner< X, X > >	_prec

std::shared_ptr< const ScalarProduct< X > >	_sp

scalar_real_type	_reduction

int	_maxit

int	_verbose

SolverCategory::Category	_category

Detailed Description

template<class X>
class Dune::RestartedFCGSolver< X >

Accelerated flexible conjugate gradient method.

Flexible conjugate gradient method as in Y. Notay 'Flexible conjugate Gradients', SIAM J. Sci. Comput Vol. 22, No.4, pp. 1444-1460

This solver discard cyclic all old directions to speed up computing. In exact arithmetic it is exactly the same as the GeneralizedPCGSolver, but it is much faster, depending on the operator and dimension. On the other hand for large mmax it uses noticeably more memory.

Member Typedef Documentation

◆ domain_type

template<class X , class Y >

typedef X Dune::InverseOperator< X, Y >::domain_type

inherited

Type of the domain of the operator to be inverted.

◆ field_type

template<class X , class Y >

typedef X::field_type Dune::InverseOperator< X, Y >::field_type

inherited

The field type of the operator.

◆ Iteration

template<class X >

using Dune::RestartedFCGSolver< X >::Iteration = typename IterativeSolver<X,X>::template Iteration<unsigned int>

protected

◆ range_type

template<class X , class Y >

typedef Y Dune::InverseOperator< X, Y >::range_type

inherited

Type of the range of the operator to be inverted.

◆ real_type

template<class X , class Y >

typedef FieldTraits<field_type>::real_type Dune::InverseOperator< X, Y >::real_type

inherited

The real type of the field type (is the same if using real numbers, but differs for std::complex)

◆ scalar_real_type

template<class X , class Y >

typedef Simd::Scalar<real_type> Dune::InverseOperator< X, Y >::scalar_real_type

inherited

scalar type underlying the field_type

Member Enumeration Documentation

◆ anonymous enum

template<class X , class Y >

anonymous enum

protectedinherited

Enumerator
iterationSpacing
normSpacing

Constructor & Destructor Documentation

◆ RestartedFCGSolver() [1/5]

template<class X >

Dune::RestartedFCGSolver< X >::RestartedFCGSolver	(	const LinearOperator< X, X > &	op,
		Preconditioner< X, X > &	prec,
		scalar_real_type	reduction,
		int	maxit,
		int	verbose,
		int	mmax = `10`
	)

inline

Constructor to initialize a RestartedFCG solver.

Parameters

op	The operator we solve.
prec	The preconditioner to apply in each iteration of the loop. Has to inherit from Preconditioner.
reduction	The relative defect reduction to achieve when applying the operator.
maxit	The maximum number of iteration steps allowed when applying the operator.
verbose	The verbosity level.

Verbose levels are:

0 : print nothing
1 : print initial and final defect and statistics
2 : print line for each iteration

Parameters

mmax	is the maximal number of previous vectors which are orthogonalized against the new search direction.

◆ RestartedFCGSolver() [2/5]

template<class X >

Dune::RestartedFCGSolver< X >::RestartedFCGSolver	(	const LinearOperator< X, X > &	op,
		const ScalarProduct< X > &	sp,
		Preconditioner< X, X > &	prec,
		scalar_real_type	reduction,
		int	maxit,
		int	verbose,
		int	mmax = `10`
	)

inline

Constructor to initialize a RestartedFCG solver.

Parameters

op	The operator we solve.
sp	The scalar product to use, e. g. SeqScalarproduct.
prec	The preconditioner to apply in each iteration of the loop. Has to inherit from Preconditioner.
reduction	The relative defect reduction to achieve when applying the operator.
maxit	The maximum number of iteration steps allowed when applying the operator.
verbose	The verbosity level.

Verbose levels are:

0 : print nothing
1 : print initial and final defect and statistics
2 : print line for each iteration

Parameters

mmax	is the maximal number of previous vectors which are orthogonalized against the new search direction.

◆ RestartedFCGSolver() [3/5]

template<class X >

Dune::RestartedFCGSolver< X >::RestartedFCGSolver	(	std::shared_ptr< const LinearOperator< X, X > >	op,
		std::shared_ptr< const ScalarProduct< X > >	sp,
		std::shared_ptr< Preconditioner< X, X > >	prec,
		scalar_real_type	reduction,
		int	maxit,
		int	verbose,
		int	mmax = `10`
	)

inline

Constructor to initialize a RestartedFCG solver.

Parameters

op	The operator we solve.
sp	The scalar product to use, e. g. SeqScalarproduct.
prec	The preconditioner to apply in each iteration of the loop. Has to inherit from Preconditioner.
reduction	The relative defect reduction to achieve when applying the operator.
maxit	The maximum number of iteration steps allowed when applying the operator.
verbose	The verbosity level.

Verbose levels are:

0 : print nothing
1 : print initial and final defect and statistics
2 : print line for each iteration

Parameters

mmax	is the maximal number of previous vectors which are orthogonalized against the new search direction.

◆ RestartedFCGSolver() [4/5]

template<class X >

Dune::RestartedFCGSolver< X >::RestartedFCGSolver	(	std::shared_ptr< const LinearOperator< X, X > >	op,
		std::shared_ptr< Preconditioner< X, X > >	prec,
		const ParameterTree &	configuration
	)

inline

Constructor to initialize a RestartedFCG solver.

Constructor.

Parameters

op	The operator we solve
prec	The preconditioner to apply in each iteration of the loop.
configuration	ParameterTree containing iterative solver parameters.

ParameterTree Key	Meaning
reduction	The relative defect reduction to achieve when applying the operator
maxit	The maximum number of iteration steps allowed when applying the operator
verbose	The verbosity level

See ISTL_Factory for the ParameterTree layout and examples.

Additional parameter:

ParameterTree Key	Meaning
mmax	number of FCG cycles before restart. default=10

See ISTL_Factory for the ParameterTree layout and examples.

◆ RestartedFCGSolver() [5/5]

template<class X >

Dune::RestartedFCGSolver< X >::RestartedFCGSolver	(	std::shared_ptr< const LinearOperator< X, X > >	op,
		std::shared_ptr< const ScalarProduct< X > >	sp,
		std::shared_ptr< Preconditioner< X, X > >	prec,
		const ParameterTree &	config
	)

inline

Member Function Documentation

◆ apply() [1/4]

void Dune::IterativeSolver< X, X >::apply	(	X &	x,
		X &	b,
		double	reduction,
		InverseOperatorResult &	res
	)

inlinefinalinherited

Apply inverse operator with given reduction factor.

apply inverse operator, with given convergence criteria.

Warning: Right hand side b may be overwritten!

Parameters

x	The left hand side to store the result in.
b	The right hand side
reduction	The minimum defect reduction to achieve.
res	Object to store the statistics about applying the operator.

Exceptions

SolverAbort When the solver detects a problem and cannot continue

◆ apply() [2/4]

template<class X >

void Dune::RestartedFCGSolver< X >::apply	(	X &	x,
		X &	b,
		InverseOperatorResult &	res
	)

inlineoverride

Apply inverse operator.

Apply inverse operator,.

Warning: Note: right hand side b may be overwritten!

Parameters

x	The left hand side to store the result in.
b	The right hand side
res	Object to store the statistics about applying the operator.

Exceptions

SolverAbort When the solver detects a problem and cannot continue

Note: Currently, the RestartedFCGSolver aborts when a NaN or infinite defect is detected. However, -ffinite-math-only (implied by -ffast-math) can inhibit a result from becoming NaN that really should be NaN. E.g. numeric_limits<double>::quiet_NaN()*0.0==0.0 with gcc-5.3 -ffast-math.

◆ apply() [3/4]

template<class X , class Y >

virtual void Dune::InverseOperator< X, Y >::apply	(	X &	x,
		Y &	b,
		double	reduction,
		InverseOperatorResult &	res
	)

pure virtualinherited

apply inverse operator, with given convergence criteria.

Warning: Right hand side b may be overwritten!

Parameters

x	The left hand side to store the result in.
b	The right hand side
reduction	The minimum defect reduction to achieve.
res	Object to store the statistics about applying the operator.

Exceptions

SolverAbort When the solver detects a problem and cannot continue

Implemented in Dune::Cholmod< Vector, Index >.

◆ apply() [4/4]

template<class X , class Y >

virtual void Dune::InverseOperator< X, Y >::apply	(	X &	x,
		Y &	b,
		InverseOperatorResult &	res
	)

pure virtualinherited

Apply inverse operator,.

Warning: Note: right hand side b may be overwritten!

Parameters

x	The left hand side to store the result in.
b	The right hand side
res	Object to store the statistics about applying the operator.

Exceptions

SolverAbort When the solver detects a problem and cannot continue

Implemented in Dune::Cholmod< Vector, Index >, Dune::RestartedGMResSolver< X, Y, F >, and Dune::RestartedFlexibleGMResSolver< X, Y, F >.

◆ category()

SolverCategory::Category Dune::IterativeSolver< X, X >::category ( ) const

inlineoverridevirtualinherited

Category of the solver (see SolverCategory::Category)

Implements Dune::InverseOperator< X, Y >.

◆ name()

std::string Dune::IterativeSolver< X, X >::name ( ) const

inlineinherited

◆ printHeader()

template<class X , class Y >

void Dune::InverseOperator< X, Y >::printHeader ( std::ostream & s ) const

inlineprotectedinherited

helper function for printing header of solver output

◆ printOutput() [1/2]

template<class X , class Y >

template<typename CountType , typename DataType >

void Dune::InverseOperator< X, Y >::printOutput	(	std::ostream &	s,
		const CountType &	iter,
		const DataType &	norm
	)		const

inlineprotectedinherited

helper function for printing solver output

◆ printOutput() [2/2]

template<class X , class Y >

template<typename CountType , typename DataType >

void Dune::InverseOperator< X, Y >::printOutput	(	std::ostream &	s,
		const CountType &	iter,
		const DataType &	norm,
		const DataType &	norm_old
	)		const

inlineprotectedinherited

helper function for printing solver output

Member Data Documentation

◆ _category

SolverCategory::Category Dune::IterativeSolver< X, X >::_category

protectedinherited

◆ _maxit

int Dune::IterativeSolver< X, X >::_maxit

protectedinherited

◆ _mmax

template<class X >

int Dune::RestartedFCGSolver< X >::_mmax

protected

◆ _op

std::shared_ptr<const LinearOperator<X,X > > Dune::IterativeSolver< X, X >::_op

protectedinherited

◆ _prec

std::shared_ptr<Preconditioner<X,X > > Dune::IterativeSolver< X, X >::_prec

protectedinherited

◆ _reduction

scalar_real_type Dune::IterativeSolver< X, X >::_reduction

protectedinherited

◆ _sp

std::shared_ptr<const ScalarProduct<X> > Dune::IterativeSolver< X, X >::_sp

protectedinherited

◆ _verbose

int Dune::IterativeSolver< X, X >::_verbose

protectedinherited

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

solvers.hh

Public Types

Public Member Functions

Protected Types

Protected Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ domain_type

◆ field_type

◆ Iteration

◆ range_type

◆ real_type

◆ scalar_real_type

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ RestartedFCGSolver() [1/5]

◆ RestartedFCGSolver() [2/5]

◆ RestartedFCGSolver() [3/5]

◆ RestartedFCGSolver() [4/5]

◆ RestartedFCGSolver() [5/5]

Member Function Documentation

◆ apply() [1/4]

◆ apply() [2/4]

◆ apply() [3/4]

◆ apply() [4/4]

◆ category()

◆ name()

◆ printHeader()

◆ printOutput() [1/2]

◆ printOutput() [2/2]

Member Data Documentation

◆ _category

◆ _maxit

◆ _mmax

◆ _op

◆ _prec

◆ _reduction

◆ _sp

◆ _verbose