preconditioned conjugate gradient method More...

#include <tcg.hh>

Detailed Description

template<class X, class Xstar, class Regularization = NoRegularization>
class Kaskade::TCG< X, Xstar, Regularization >

preconditioned conjugate gradient method

This implements a preconditioned IterateType::CG iteration for an operator \( A: X\to x^* \), preconditioned by a preconditioner \( B^{-1}: X^* \to X \). The termination is based on an estimate of the absolute energy error.

The implementation follows Deuflhard/Weiser, Section 5.3.3.

Definition at line 79 of file tcg.hh.

Inheritance diagram for Kaskade::TCG< X, Xstar, Regularization >:

Public Types
enum class	Result { Converged , Failed , EncounteredNonConvexity }

typedef ScalarTraits< typenameGetScalar< X >::type >::Real	Real
	the real field type corresponding to X::field_type More...

Public Member Functions
template<class Int = int, class enable = typename std::enable_if<!std::is_same<Regularization,NoRegularization>::value && std::is_same<Int,int>::value>::type>
	TCG (Dune::LinearOperator< X, Xstar > &op_, Dune::Preconditioner< X, Xstar > &prec_, DualPairing< X, Xstar > const &dp_, Regularization &regularization_, double relTol_=1e-3, size_t maxSteps_=100, Int verbose_=0)
	Set up conjugate gradient solver with absolute energy error termination criterion. More...

template<class Int = int, class enable = typename std::enable_if<std::is_same<Regularization,NoRegularization>::value && std::is_same<Int,int>::value>::type>
	TCG (Dune::LinearOperator< X, Xstar > &op_, Dune::Preconditioner< X, Xstar > &prec_, DualPairing< X, Xstar > const &dp_, double relTol_=1e-3, size_t maxSteps_=100, Int verbose_=0)
	Set up conjugate gradient solver with absolute energy error termination criterion. More...

virtual int	apply (X &u, X &q, Xstar &b, Dune::InverseOperatorResult &res)
	Apply inverse operator. More...

virtual void	apply (X &u, Xstar &b, Dune::InverseOperatorResult &res)
	Apply tcg and possibly forget second descent direction. More...

void	apply (X &u, Xstar &b)

virtual void	apply (X &x, X &b, double relTol, Dune::InverseOperatorResult &res)
	Apply inverse operator with given absolute tolerance. More...

void	setRelativeAccuracy (double relTol_)

void	setMaxSteps (size_t maxSteps_)

bool	localConvergenceLikely () const

bool	encounteredNonConvexity () const

Member Typedef Documentation

◆ Real

template<class X , class Xstar , class Regularization = NoRegularization>

typedef ScalarTraits<typenameGetScalar<X>::type>::Real Kaskade::TCG< X, Xstar, Regularization >::Real

the real field type corresponding to X::field_type

Definition at line 85 of file tcg.hh.

Member Enumeration Documentation

◆ Result

template<class X , class Xstar , class Regularization = NoRegularization>

enum class Kaskade::TCG::Result

strong

Enumerator
Converged
Failed
EncounteredNonConvexity

Definition at line 81 of file tcg.hh.

Constructor & Destructor Documentation

◆ TCG() [1/2]

template<class X , class Xstar , class Regularization = NoRegularization>

template<class Int = int, class enable = typename std::enable_if<!std::is_same<Regularization,NoRegularization>::value && std::is_same<Int,int>::value>::type>

Kaskade::TCG< X, Xstar, Regularization >::TCG	(	Dune::LinearOperator< X, Xstar > &	op_,
		Dune::Preconditioner< X, Xstar > &	prec_,
		DualPairing< X, Xstar > const &	dp_,
		Regularization &	regularization_,
		double	relTol_ = `1e-3`,
		size_t	maxSteps_ = `100`,
		Int	verbose_ = `0`
	)

inline

Set up conjugate gradient solver with absolute energy error termination criterion.

Parameters

verbose

Definition at line 93 of file tcg.hh.

◆ TCG() [2/2]

template<class X , class Xstar , class Regularization = NoRegularization>

template<class Int = int, class enable = typename std::enable_if<std::is_same<Regularization,NoRegularization>::value && std::is_same<Int,int>::value>::type>

Kaskade::TCG< X, Xstar, Regularization >::TCG	(	Dune::LinearOperator< X, Xstar > &	op_,
		Dune::Preconditioner< X, Xstar > &	prec_,
		DualPairing< X, Xstar > const &	dp_,
		double	relTol_ = `1e-3`,
		size_t	maxSteps_ = `100`,
		Int	verbose_ = `0`
	)

inline

Set up conjugate gradient solver with absolute energy error termination criterion.

Parameters

verbose

Definition at line 110 of file tcg.hh.

Member Function Documentation

◆ apply() [1/4]

template<class X , class Xstar , class Regularization = NoRegularization>

virtual int Kaskade::TCG< X, Xstar, Regularization >::apply	(	X &	u,
		X &	q,
		Xstar &	b,
		Dune::InverseOperatorResult &	res
	)

inlinevirtual

Apply inverse operator.

Parameters

u	the initial value (starting iterate)
b	the right hand side

Definition at line 127 of file tcg.hh.

Referenced by Kaskade::TCG< X, Xstar, Regularization >::apply().

◆ apply() [2/4]

template<class X , class Xstar , class Regularization = NoRegularization>

void Kaskade::TCG< X, Xstar, Regularization >::apply	(	X &	u,
		Xstar &	b
	)

inline

Definition at line 257 of file tcg.hh.

◆ apply() [3/4]

template<class X , class Xstar , class Regularization = NoRegularization>

virtual void Kaskade::TCG< X, Xstar, Regularization >::apply	(	X &	u,
		Xstar &	b,
		Dune::InverseOperatorResult &	res
	)

inlinevirtual

Apply tcg and possibly forget second descent direction.

Definition at line 252 of file tcg.hh.

◆ apply() [4/4]

template<class X , class Xstar , class Regularization = NoRegularization>

virtual void Kaskade::TCG< X, Xstar, Regularization >::apply	(	X &	x,
		X &	b,
		double	relTol,
		Dune::InverseOperatorResult &	res
	)

inlinevirtual

Apply inverse operator with given absolute tolerance.

Definition at line 266 of file tcg.hh.

◆ encounteredNonConvexity()

template<class X , class Xstar , class Regularization = NoRegularization>

bool Kaskade::TCG< X, Xstar, Regularization >::encounteredNonConvexity ( ) const

inline

Definition at line 277 of file tcg.hh.

◆ localConvergenceLikely()

template<class X , class Xstar , class Regularization = NoRegularization>

bool Kaskade::TCG< X, Xstar, Regularization >::localConvergenceLikely ( ) const

inline

Definition at line 275 of file tcg.hh.

◆ setMaxSteps()

template<class X , class Xstar , class Regularization = NoRegularization>

void Kaskade::TCG< X, Xstar, Regularization >::setMaxSteps ( size_t maxSteps_ )

inline

Definition at line 273 of file tcg.hh.

◆ setRelativeAccuracy()

template<class X , class Xstar , class Regularization = NoRegularization>

void Kaskade::TCG< X, Xstar, Regularization >::setRelativeAccuracy ( double relTol_ )

inline

Definition at line 271 of file tcg.hh.

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

tcg.hh

Detailed Description

Public Types

Public Member Functions

Member Typedef Documentation

◆ Real

Member Enumeration Documentation

◆ Result

Constructor & Destructor Documentation

◆ TCG() [1/2]

◆ TCG() [2/2]

Member Function Documentation

◆ apply() [1/4]

◆ apply() [2/4]

◆ apply() [3/4]

◆ apply() [4/4]

◆ encounteredNonConvexity()

◆ localConvergenceLikely()

◆ setMaxSteps()

◆ setRelativeAccuracy()