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

#include <cg.hh>

Inheritance diagram for concepts::CG< F >:

Collaboration diagram for concepts::CG< F >:

Public Types
typedef Cmplxtype< F >::type	c_type
	Real type of data type.
typedef Realtype< F >::type	r_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)
	Constructor.
	CG (Operator< F > &A, Operator< F > &Minv, Real maxeps, int maxit=0, bool relres=0, bool throwing=true)
	Constructor.
virtual const uint	dimX () const
	Returns the size of the image space of the operator (number of rows of the corresponding matrix)
virtual const uint	dimY () const
	Returns the size of the source space of the operator (number of columns of the corresponding matrix)
Real	epsilon () const
	Returns the residual.
uint	iterations () const
	Returns the number of iterations.
virtual void	operator() (const Vector< r_type > &fncY, Vector< F > &fncX)
	Application operator for real vector `fncY`.
void	operator() (const Matrix< c_type > &mX, Matrix< c_type > &mY)
	Application method to complex matrices. Calls apply_()
virtual void	operator() (const Function< c_type > &fncY, Function< c_type > &fncX)
	Application operator for complex function `fncY`.
virtual void	operator() (const Function< r_type > &fncY, Function< F > &fncX)
	Application operator for real function `fncY`.
virtual void	operator() (const Vector< c_type > &fncY, Vector< c_type > &fncX)
	Application operator for complex function `fncY`.
void	operator() (const Matrix< r_type > &mX, Matrix< F > &mY)
	Application method to real matrices. Calls function apply()
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_
Private Member Functions
virtual void	apply_ (const Vector< F > &fncY, Vector< F > &fncX)
	Intrinsic application method, i.e.
Private Attributes
Operator< F > &	A_
	Operator which is solved.
Real	eps_
	Current residual.
uint	it_
	Number of iterations.
Real	maxeps_
	Convergence criterion.
uint	maxit_
	Maximal number of iterations until abortion.
bool	relres_
	false: absolute residual, true: relative residual
bool	throwing_
	false: best solution is given, when non converging true: exception is thrown, when non converging
Operator< F > *	W_
	Optional preconditioner.

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

Definition at line 32 of file cg.hh.

Member Typedef Documentation

template<class F>

typedef Cmplxtype<F>::type concepts::VecOperator< F >::c_type [inherited]

Real type of data type.

Reimplemented from concepts::Operator< F >.

Definition at line 112 of file compositions.hh.

template<class F>

typedef Realtype<F>::type concepts::VecOperator< F >::r_type [inherited]

Real type of data type.

Reimplemented from concepts::Operator< F >.

Definition at line 110 of file compositions.hh.

template<class F>

typedef F concepts::Operator< F >::type [inherited]

Type of data, e.g. matrix entries.

Reimplemented in concepts::AfterIteration< F >, and concepts::SubMatrixN< F >.

Definition at line 43 of file compositions.hh.

Constructor & Destructor Documentation

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 42 of file cg.hh.

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 58 of file cg.hh.

Member Function Documentation

template<class F>

virtual void concepts::CG< F >::apply_	(	const Vector< F > &	fncY,
		Vector< F > &	fncX
	)		`[private, virtual]`

Intrinsic application method, i.e.

real Operator and real Vector or complex Operator and real Vector.

Implements concepts::VecOperator< F >.

template<class F>

virtual const uint concepts::Operator< F >::dimX ( ) const [inline, virtual, inherited]

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

Definition at line 87 of file compositions.hh.

template<class F>

virtual const uint concepts::Operator< F >::dimY ( ) const [inline, virtual, inherited]

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

Definition at line 92 of file compositions.hh.

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 72 of file cg.hh.

template<class F>

std::ostream& concepts::CG< F >::info ( std::ostream & os ) const [protected, virtual]

Returns information in an output stream.

Reimplemented from concepts::VecOperator< F >.

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.

Definition at line 67 of file cg.hh.

template<class F>

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

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.

template<class F>

virtual void concepts::VecOperator< F >::operator()	(	const Function< r_type > &	fncY,
		Function< F > &	fncX
	)		`[virtual, inherited]`

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 from concepts::Operator< F >.

template<class F>

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

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 >.

template<class F>

void concepts::VecOperator< F >::operator()	(	const Matrix< c_type > &	mX,
		Matrix< c_type > &	mY
	)		`[inherited]`

Application method to complex matrices. Calls apply_()

template<class F>

void concepts::VecOperator< F >::operator()	(	const Matrix< r_type > &	mX,
		Matrix< F > &	mY
	)		`[inherited]`

Application method to real matrices. Calls function apply()

template<class F>

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

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.

Member Data Documentation

template<class F>

Operator<F>& concepts::CG< F >::A_ [private]

Operator which is solved.

Definition at line 79 of file cg.hh.

template<class F>

uint concepts::Operator< F >::dimX_ [protected, inherited]

Dimension of image space and the source space.

Definition at line 96 of file compositions.hh.

template<class F>

uint concepts::Operator< F >::dimY_ [protected, inherited]

Definition at line 96 of file compositions.hh.

template<class F>

Real concepts::CG< F >::eps_ [private]

Current residual.

Definition at line 86 of file cg.hh.

template<class F>

uint concepts::CG< F >::it_ [private]

Number of iterations.

Definition at line 88 of file cg.hh.

template<class F>

Real concepts::CG< F >::maxeps_ [private]

Convergence criterion.

Definition at line 82 of file cg.hh.

template<class F>

uint concepts::CG< F >::maxit_ [private]

Maximal number of iterations until abortion.

Definition at line 84 of file cg.hh.

template<class F>

bool concepts::CG< F >::relres_ [private]

false: absolute residual, true: relative residual

Definition at line 90 of file cg.hh.

template<class F>

bool concepts::CG< F >::throwing_ [private]

false: best solution is given, when non converging true: exception is thrown, when non converging

Definition at line 94 of file cg.hh.

template<class F>

Operator<F>* concepts::CG< F >::W_ [private]

Optional preconditioner.

Definition at line 77 of file cg.hh.

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

operator/cg.hh

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Detailed Description

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

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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