gsBiCgStab< T > Class Template Reference

Detailed Description

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

Biconjugate gradient stabilized solver.

Inheritance diagram for gsBiCgStab< T >:

Collaboration diagram for gsBiCgStab< 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.
virtual void	finalizeIteration (VectorType &)
	Some post-processing might be required.
template<typename OperatorType >
	gsBiCgStab (const OperatorType &mat, const LinOpPtr &precond=LinOpPtr())
	Constructor using a matrix (operator) and optionally a preconditionner.
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.
std::ostream &	print (std::ostream &os) const
	Prints the object as a string.
void	setMaxIterations (index_t max_iters)
	Set the maximum number of iterations (default: 1000)
gsBiCgStab &	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.
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.
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.

Private 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.

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

Constructor & Destructor Documentation

gsBiCgStab()

template<class T = real_t>

template<typename OperatorType >

gsBiCgStab ( 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

error()

template<class T = real_t>

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.

make()

template<class T = real_t>

template<typename OperatorType >

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

solve()

template<class T = real_t>

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

solveDetailed()

template<class T = real_t>

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