gsGMRes< T > Class Template Reference

Detailed Description

template<class T = real_t>
class gismo::gsGMRes< T >

The generalized minimal residual (GMRES) method.

Inheritance diagram for gsGMRes< T >:

Collaboration diagram for gsGMRes< T >:

Public Member Functions
virtual std::string	detail () const
	Prints the object as a string with extended details.
T	error () const
	The relative residual error of the current iterate. More...
void	finalizeIteration (VectorType &x)
	Some post-processing might be required.
template<typename OperatorType >
	gsGMRes (const OperatorType &mat, const LinOpPtr &precond=LinOpPtr())
	Constructor using a matrix (operator) and optionally a preconditionner. More...
bool	initIteration (const VectorType &rhs, VectorType &x)
	Init the iteration.
index_t	iterations () const
	The number of iterations needed to reach the error criteria.
LinOpPtr	preconditioner () const
	Get the preconditioner.
void	setMaxIterations (index_t max_iters)
	Set the maximum number of iterations (default: 1000)
virtual gsIterativeSolver &	setOptions (const gsOptionList &opt)
	Set the options based on a gsOptionList.
void	setPreconditioner (const LinOpPtr &precond)
	Set the preconditionner.
void	setTolerance (T tol)
	Set the tolerance for the error criteria on the relative residual error (default: 1e-10)
index_t	size () const
	Returns the size of the linear system.
void	solve (const VectorType &rhs, VectorType &x)
	Solves the linear system and stores the solution in x. More...
void	solveDetailed (const VectorType &rhs, VectorType &x, VectorType &error_history)
	Solves the linear system and stores the solution in x and records the error histroy. More...
bool	step (VectorType &x)
	Perform one step, requires initIteration.
T	tolerance () const
	The chosen tolerance for the error criteria on the relative residual error.
LinOpPtr	underlying () const
	Get the underlying matrix/operator to be solved for.

Static Public Member Functions
static gsOptionList	defaultOptions ()
	Returns a list of default options.
template<typename OperatorType >
static uPtr	make (const OperatorType &mat, const LinOpPtr &precond=LinOpPtr())
	Make function using a matrix (operator) and optionally a preconditionner. More...

Protected Attributes
T	m_error
	The relative error as absolute_error/m_rhs_norm.
const LinOpPtr	m_mat
	The matrix/operator to be solved for.
index_t	m_max_iters
	The upper bound for the number of iterations.
index_t	m_num_iter
	The number of iterations performed.
LinOpPtr	m_precond
	The preconditioner.
T	m_rhs_norm
	The norm of the right-hand-side.
gsOptionList::Real	m_tol
	The tolerance for m_error to be reached.

Private Member Functions
std::ostream &	print (std::ostream &os) const
	Prints the object as a string.
void	solveUpperTriangular (const VectorType &R, const VectorType &gg)

Related Functions
(Note that these are not member functions.)
template<class T >
std::ostream &	operator<< (std::ostream &os, const gsIterativeSolver< T > &b)
	Print (as string) operator for iterative solvers. More...

Constructor & Destructor Documentation

gsGMRes ( const OperatorType &  mat, const LinOpPtr &  precond = LinOpPtr()  )

inlineexplicit

Constructor using a matrix (operator) and optionally a preconditionner.

Parameters

mat	The operator to be solved for, see gsIterativeSolver for details
precond	The preconditioner, defaulted to the identity

Member Function Documentation

T error ( ) const

inlineinherited

The relative residual error of the current iterate.

This is the Euclidean norm of the residual, devided by the Euclidean norm of the right-hand side.

static uPtr make ( const OperatorType &  mat, const LinOpPtr &  precond = LinOpPtr()  )

inlinestatic

Make function using a matrix (operator) and optionally a preconditionner.

Parameters

mat	The operator to be solved for, see gsIterativeSolver for details
precond	The preconditioner, defaulted to the identity

void solve ( const VectorType &  rhs, VectorType &  x  )

inlineinherited

Solves the linear system and stores the solution in x.

Solves the linear system of equations

Parameters

[in]	rhs	the right hand side of the linear system
[in,out]	x	starting value; the solution is stored in here

void solveDetailed ( const VectorType &  rhs, VectorType &  x, VectorType &  error_history  )

inlineinherited

Solves the linear system and stores the solution in x and records the error histroy.

Solves the linear system of equations

Parameters

[in]	rhs	the right hand side of the linear system
[in,out]	x	starting value; the solution is stored in here
[out]	error_history	the error history is stored here

void solveUpperTriangular ( const VectorType &  R, const VectorType &  gg  )

inlineprivate

Solves the Upper triangular system Ry = gg and stores the solution in the private member y.

Friends And Related Function Documentation

std::ostream & operator<< ( std::ostream &  os, const gsIterativeSolver< T > &  b  )

related

Print (as string) operator for iterative solvers.