concepts::GMRes< F > Class Template Reference

Solves a system of linear equations with general minimal residuals (GMRes). More...

#include <gmres.hh>

Inheritance diagram for concepts::GMRes< F >:

Collaboration diagram for concepts::GMRes< F >:

List of all members.

Classes
struct	R
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
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.
	GMRes (Operator< F > &A, Real maxeps, int maxit=0, uint rs=0, uint relres=0, Operator< F > *W=0)
	Constructor.
uint	iterations () const
	Returns the number of iterations.
void	operator() (const Matrix< c_type > &mX, Matrix< c_type > &mY)
	Application method to complex matrices. Calls apply_()
virtual void	operator() (const Vector< r_type > &fncY, Vector< F > &fncX)
	Application operator for real vector fncY.
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()
virtual	~GMRes ()
Protected Member Functions
virtual 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) throw (NoConvergence, MissingFeature)
	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.
uint	relres_
	relres = 0: absolute residual, relres = 1: relative residual
uint	rs_
	Restart.
Operator< F > *	W_
	Optional preconditioner.

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Detailed Description

template<class F>
class concepts::GMRes< F >

Solves a system of linear equations with general minimal residuals (GMRes).

Examples:

linearDG1d.cc.

Definition at line 22 of file gmres.hh.

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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.

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Constructor & Destructor Documentation

template<class F>

concepts::GMRes< F >::GMRes	(	Operator< F > &	A,
		Real	maxeps,
		int	maxit = 0,
		uint	rs = 0,
		uint	relres = 0,
		Operator< F > *	W = 0
	)		[inline]

Constructor.

Parameters:

A	A matrix
maxeps	Maximal residual
maxit	Maximal number of iterations
rs	Restart
relres	0: absolute residual, 1: relative residual
W	Optional preconditioner

Definition at line 32 of file gmres.hh.

template<class F>

virtual concepts::GMRes< F >::~GMRes

(

)

[virtual]

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Member Function Documentation

template<class F>

virtual void concepts::GMRes< F >::apply_	(	const Vector< F > &	fncY,
		Vector< F > &	fncX
	)		throw (NoConvergence, MissingFeature) [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::GMRes< F >::epsilon

(

)

const [inline]

Returns the residual.

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

Definition at line 46 of file gmres.hh.

template<class F>

virtual std::ostream& concepts::GMRes< F >::info

(

std::ostream &

os

)

const [protected, virtual]

Returns information in an output stream.

Reimplemented from concepts::VecOperator< F >.

template<class F>

uint concepts::GMRes< F >::iterations

(

)

const [inline]

Returns the number of iterations.

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

Definition at line 41 of file gmres.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.

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Member Data Documentation

template<class F>

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

Operator which is solved.

Definition at line 69 of file gmres.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::GMRes< F >::eps_ [private]

Current residual.

Definition at line 76 of file gmres.hh.

template<class F>

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

Number of iterations.

Definition at line 78 of file gmres.hh.

template<class F>

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

Convergence criterion.

Definition at line 72 of file gmres.hh.

template<class F>

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

Maximal number of iterations until abortion.

Definition at line 74 of file gmres.hh.

template<class F>

uint concepts::GMRes< F >::relres_ [private]

relres = 0: absolute residual, relres = 1: relative residual

Definition at line 82 of file gmres.hh.

template<class F>

uint concepts::GMRes< F >::rs_ [private]

Restart.

Definition at line 80 of file gmres.hh.

template<class F>

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

Optional preconditioner.

Definition at line 67 of file gmres.hh.

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

• operator/gmres.hh