#include <cg.hh>

Inheritance diagram for concepts::CG< F >:

Public Types
typedef Realtype< F >::type	r_type
	Real type of data type.

typedef Cmplxtype< F >::type	c_type
	Real type of data type.

typedef F	type
	Type of data, e.g. matrix entries.

Public Member Functions
	CG (Operator< F > &A, Real maxeps, int maxit=0, uint relres=false, bool throwing=true)

	CG (Operator< F > &A, Operator< F > &Minv, Real maxeps, int maxit=0, bool relres=0, bool throwing=true)

uint	iterations () const

Real	epsilon () const

virtual void	operator() (const Function< r_type > &fncY, Function< F > &fncX)

virtual void	operator() (const Function< c_type > &fncY, Function< c_type > &fncX)

virtual void	operator() (const Vector< r_type > &fncY, Vector< F > &fncX)

virtual void	operator() (const Vector< c_type > &fncY, Vector< c_type > &fncX)

void	operator() (const Matrix< r_type > &mX, Matrix< F > &mY)
	Application method to real matrices. Calls function apply()

void	operator() (const Matrix< c_type > &mX, Matrix< c_type > &mY)
	Application method to complex matrices. Calls apply_()

void	operator() ()
	Application method without second argument. Used for parallel solvers.

virtual void	operator() (const Function< r_type > &fncY, Function< F > &fncX)

virtual const uint	dimX () const

virtual const uint	dimY () const

virtual void	show_messages ()

Protected Member Functions
std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.

Protected Attributes
uint	dimX_
	Dimension of image space and the source space.

uint	dimY_

Detailed Description

template<class F>
class concepts::CG< F >

Solves a symmetric system of linear equations with conjugate gradients (CG).

Constructing an object of this class does not solve the given system. Use the application operator to solve the system. If you want to specify a starting vector for the cg iterations, set fncX before calling the application operator to this starting value. fncX also holds the result after the solve.

The application operator throws NoConvergence if the desired residual maxeps is not reached within the given number of iterations maxit.

Test:: test::CgTest

Examples: RobinBCs.cc, howToGetStarted.cc, hpFEM2d-simple.cc, hpFEM2d.cc, inhomDirichletBCs.cc, inhomNeumannBCs.cc, linearFEM1d-simple.cc, and linearFEM1d.cc.

Definition at line 39 of file cg.hh.

Member Typedef Documentation

◆ c_type

template<class F >

typedef Cmplxtype<F>::type concepts::VecOperator< F >::c_type

inherited

Real type of data type.

Definition at line 120 of file compositions.hh.

◆ r_type

template<class F >

typedef Realtype<F>::type concepts::VecOperator< F >::r_type

inherited

Real type of data type.

Definition at line 118 of file compositions.hh.

◆ type

template<class F >

typedef F concepts::Operator< F >::type

inherited

Type of data, e.g. matrix entries.

Definition at line 45 of file compositions.hh.

Constructor & Destructor Documentation

◆ CG() [1/2]

template<class F >

concepts::CG< F >::CG	(	Operator< F > &	A,
		Real	maxeps,
		int	maxit = `0`,
		uint	relres = `false`,
		bool	throwing = `true`
	)

inline

Constructor.

Parameters

A	Matrix
maxeps	Maximal residual
maxit	Maximal number of iterations
relres	Relative residual
throwing	In the case of non convergence an exception is thrown and the best solution is not given back.

Definition at line 49 of file cg.hh.

◆ CG() [2/2]

template<class F >

concepts::CG< F >::CG	(	Operator< F > &	A,
		Operator< F > &	Minv,
		Real	maxeps,
		int	maxit = `0`,
		bool	relres = `0`,
		bool	throwing = `true`
	)

inline

Constructor.

Parameters

A	Matrix
Minv	Preconditioner for A, ie. Minv should approximate and it has to be symmetric positive definite
maxeps	Maximal residual
maxit	Maximal number of iterations
relres	Relative residual
throwing	In the case of non convergence an exception is thrown and the best solution is not given back.

Definition at line 87 of file cg.hh.

Member Function Documentation

◆ dimX()

template<class F >

virtual const uint concepts::Operator< F >::dimX ( ) const

inlinevirtualinherited

Returns the size of the image space of the operator (number of rows of the corresponding matrix)

Examples: hpFEM2d-simple.cc, hpFEM2d.cc, and matfileTutorial.cc.

Definition at line 93 of file compositions.hh.

◆ dimY()

template<class F >

virtual const uint concepts::Operator< F >::dimY ( ) const

inlinevirtualinherited

Returns the size of the source space of the operator (number of columns of the corresponding matrix)

Examples: matfileTutorial.cc.

Definition at line 98 of file compositions.hh.

◆ epsilon()

template<class F >

Real concepts::CG< F >::epsilon ( ) const

inline

Returns the residual. Calling this method makes only sence after a linear system has been solved.

Definition at line 123 of file cg.hh.

◆ info()

template<class F >

std::ostream & concepts::CG< F >::info ( std::ostream & os ) const

protectedvirtual

Returns information in an output stream.

Reimplemented from concepts::VecOperator< F >.

◆ iterations()

template<class F >

uint concepts::CG< F >::iterations ( ) const

inline

Returns the number of iterations. Calling this method makes only sense after a linear system has been solved.

Examples: hpFEM2d.cc.

Definition at line 118 of file cg.hh.

◆ operator()() [1/5]

template<class F >

void concepts::VecOperator< F >::operator() ( )

virtualinherited

Application method without second argument. Used for parallel solvers.

Reimplemented from concepts::Operator< F >.

◆ operator()() [2/5]

template<class F >

virtual void concepts::VecOperator< F >::operator()	(	const Function< c_type > &	fncY,
		Function< c_type > &	fncX
	)

virtualinherited

Application operator for complex function fncY.

Computes fncX = A(fncY) where A is this operator. fncX becomes complex.

In derived classes its enough to implement the operator() for complex Operator's. If a real counterpart is not implemented, the function fncY is splitted into real and imaginary part and the application operator for real functions is called for each. Then the result is combined.

If in a derived class the operator() for complex Operator's is not implemented, a exception is thrown from here.

Reimplemented from concepts::Operator< F >.

◆ operator()() [3/5]

template<class F >

virtual void concepts::Operator< F >::operator()	(	const Function< r_type > &	fncY,
		Function< F > &	fncX
	)

virtualinherited

Application operator for real function fncY.

Computes fncX = A(fncY) where A is this operator.

fncX becomes the type of the operator, for real data it becomes real, for complex data it becomes complex.

In derived classes its enough to implement the operator() for real Operator's. If a complex counterpart is not implemented, the function fncY is transformed to a complex function and then the application operator for complex functions is called.

If in a derived class the operator() for real Operator's is not implemented, a exception is thrown from here.

Reimplemented in aglowav::C2W< F >, aglowav2::C2W< F >, aglowav::W2C< F >, aglowav2::W2C< F >, aglowav::C2_tl2< F >, aglowav::C2tl2< F >, aglowav::CGt2< F >, aglowav::ComposeN< F >, aglowav2::Operator00< F >, bem::D< F >, bem::D_1< F >, concepts::TrivExtendRestrict< F >, sparseqr::GivensRotations< F >, vectorial::BlockOperator< F >, concepts::TrivExtendRestrict< Real >, sparseqr::GivensRotations< Real >, concepts::AfterIteration< F >, concepts::Compose< F, H >, concepts::DDSolver< F, G >, concepts::Multiple< F >, concepts::LiCoI< F >, concepts::LiCo< F >, concepts::DenseMatrix< F >, concepts::DiagonalMatrix< F >, concepts::Permutation< F >, concepts::Matrix< F >, concepts::Matrix< F::type >, and concepts::DiagonalSolver< F >.

◆ operator()() [4/5]

template<class F >

virtual void concepts::VecOperator< F >::operator()	(	const Vector< c_type > &	fncY,
		Vector< c_type > &	fncX
	)

virtualinherited

Application operator for complex function fncY.

Computes fncX = A(fncY) where A is this operator. fncX becomes complex.

In derived classes its enough to implement the operator() for complex Operator's. If a real counterpart is not implemented, the vector fncY is splitted into real and imaginary part and the application operator for real vectors is called for each. Then the result is combined

If in a derived class the operator() for complex Operator's i not implemented, a exception is thrown from here.

◆ operator()() [5/5]

template<class F >

virtual void concepts::VecOperator< F >::operator()	(	const Vector< r_type > &	fncY,
		Vector< F > &	fncX
	)

virtualinherited

Application operator for real vector fncY.

Computes fncX = A(fncY) where A is this operator.

Type of fncX becomes that of the operator, for real data it becomes real, for complex data it becomes complex.

In derived classes its enough to implement the operator() for real Operator's. If a complex counterpart is not implemented, the vector fncY is transformed to a complex vector and then the application for complex vectors is called.

If in a derived class the operator() for real Operator's is not implemented, a exception is thrown from here.

◆ show_messages()

template<class F >

virtual void concepts::Operator< F >::show_messages ( )

inlinevirtualinherited

Reimplemented in concepts::MumpsOverlap< F >.

Definition at line 100 of file compositions.hh.

Member Data Documentation

◆ dimX_

template<class F >

uint concepts::Operator< F >::dimX_

protectedinherited

Dimension of image space and the source space.

Definition at line 104 of file compositions.hh.

◆ dimY_

template<class F >

uint concepts::Operator< F >::dimY_

protectedinherited

Definition at line 104 of file compositions.hh.

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

operator/cg.hh

Class documentation of Concepts

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ c_type

◆ r_type

◆ type

Constructor & Destructor Documentation

◆ CG() [1/2]

◆ CG() [2/2]

Member Function Documentation

◆ dimX()

◆ dimY()

◆ epsilon()

◆ info()

◆ iterations()

◆ operator()() [1/5]

◆ operator()() [2/5]

◆ operator()() [3/5]

◆ operator()() [4/5]

◆ operator()() [5/5]

◆ show_messages()

Member Data Documentation

◆ dimX_

◆ dimY_