# concepts::GMRes< F > Class Template ReferenceLinear Solvers

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

`#include <gmres.hh>`

Inheritance diagram for concepts::GMRes< F >:

struct  R

## Public Types

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

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

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

## 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) More...

virtual const uint dimY () const
Returns the size of the source space of the operator (number of columns of the corresponding matrix) More...

Real epsilon () const
Returns the residual. More...

GMRes (Operator< F > &A, Real maxeps, int maxit=0, uint rs=0, uint relres=0, Operator< F > *W=0)
Constructor. More...

uint iterations () const
Returns the number of iterations. More...

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

virtual void operator() (const Function< c_type > &fncY, Function< c_type > &fncX)
Application operator for complex function `fncY`. More...

virtual void operator() (const Function< r_type > &fncY, Function< F > &fncX)
Application operator for real function `fncY`. More...

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

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

virtual void operator() (const Vector< c_type > &fncY, Vector< c_type > &fncX)
Application operator for complex function `fncY`. More...

virtual void operator() (const Vector< r_type > &fncY, Vector< F > &fncX)
Application operator for real vector `fncY`. More...

virtual void show_messages ()

virtual ~GMRes ()

## Protected Member Functions

virtual std::ostream & info (std::ostream &os) const

## Protected Attributes

uint dimX_
Dimension of image space and the source space. More...

uint dimY_

## Private Member Functions

virtual void apply_ () throw (NoConvergence, MissingFeature)
Intrinsic application method without argument. More...

virtual void apply_ (const Vector< F > &fncY, Vector< F > &fncX) throw (NoConvergence, MissingFeature)
Intrinsic application method, i.e. More...

## Private Attributes

Operator< F > & A_
Operator which is solved. More...

Real eps_
Current residual. More...

uint it_
Number of iterations. More...

Real maxeps_
Convergence criterion. More...

uint maxit_
Maximal number of iterations until abortion. More...

uint relres_
relres = 0: absolute residual, relres = 1: relative residual More...

uint rs_
Restart. More...

Operator< F > * W_
Optional preconditioner. More...

## 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 24 of file gmres.hh.

## ◆ c_type

template<class F >
 typedef Cmplxtype::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::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.

## ◆ GMRes()

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 34 of file gmres.hh.

## ◆ ~GMRes()

template<class F >
 virtual concepts::GMRes< F >::~GMRes ( )
virtual

## ◆ apply_() [1/2]

template<class F >
 virtual void concepts::GMRes< F >::apply_ ( ) throw ( NoConvergence, MissingFeature )
privatevirtual

Intrinsic application method without argument.

Implements concepts::VecOperator< F >.

## ◆ apply_() [2/2]

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

Intrinsic application method, i.e.

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

Implements concepts::VecOperator< F >.

## ◆ 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)

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)

Definition at line 98 of file compositions.hh.

## ◆ epsilon()

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 48 of file gmres.hh.

## ◆ info()

template<class F >
 virtual std::ostream& concepts::GMRes< F >::info ( std::ostream & os ) const
protectedvirtual

Reimplemented from concepts::VecOperator< F >.

## ◆ iterations()

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 43 of file gmres.hh.

## ◆ operator()() [1/7]

template<class F >
 void concepts::VecOperator< F >::operator() ( )
virtualinherited

Application method without second argument. Used for parallel solvers.

Reimplemented from concepts::Operator< F >.

## ◆ operator()() [2/7]

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()() [3/7]

template<class F >
 virtual void concepts::VecOperator< 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 from concepts::Operator< F >.

## ◆ operator()() [4/7]

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_()

## ◆ operator()() [5/7]

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()

## ◆ operator()() [6/7]

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()() [7/7]

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::Newton< F >, concepts::MumpsOverlap< F >, and concepts::Mumps< F >.

Definition at line 100 of file compositions.hh.

## ◆ A_

template<class F >
 Operator& concepts::GMRes< F >::A_
private

Operator which is solved.

Definition at line 71 of file gmres.hh.

## ◆ 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.

## ◆ eps_

template<class F >
 Real concepts::GMRes< F >::eps_
private

Current residual.

Definition at line 78 of file gmres.hh.

## ◆ it_

template<class F >
 uint concepts::GMRes< F >::it_
private

Number of iterations.

Definition at line 80 of file gmres.hh.

## ◆ maxeps_

template<class F >
 Real concepts::GMRes< F >::maxeps_
private

Convergence criterion.

Definition at line 74 of file gmres.hh.

## ◆ maxit_

template<class F >
 uint concepts::GMRes< F >::maxit_
private

Maximal number of iterations until abortion.

Definition at line 76 of file gmres.hh.

## ◆ relres_

template<class F >
 uint concepts::GMRes< F >::relres_
private

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

Definition at line 84 of file gmres.hh.

## ◆ rs_

template<class F >
 uint concepts::GMRes< F >::rs_
private

Restart.

Definition at line 82 of file gmres.hh.

## ◆ W_

template<class F >
 Operator* concepts::GMRes< F >::W_
private

Optional preconditioner.

Definition at line 69 of file gmres.hh.

The documentation for this class was generated from the following file:
Page URL: http://wiki.math.ethz.ch/bin/view/Concepts/WebHome
21 August 2020
© 2020 Eidgenössische Technische Hochschule Zürich