gsGradientMethod< T > Class Template Reference

Detailed Description

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

The gradient method.

Iterates x^{new} = x - damping * precond * ( mat * x - rhs ),

where by default damping = 1 and precond = identity.

Inheritance diagram for gsGradientMethod< T >:

Collaboration diagram for gsGradientMethod< T >:

Public Member Functions
bool	adaptiveStepSize () const
	Returns true iff adaptive step sizes are activated.
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 >
	gsGradientMethod (const OperatorType &mat, const LinOpPtr &precond, T step_size)
	Constructor using a matrix (operator) and optionally a preconditionner.
template<typename OperatorType >
	gsGradientMethod (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	setAdaptiveStepSize ()
	Activate adaptive step size. Then in each step, the step size is chosen such that the norm of the residual is minimized.
void	setMaxIterations (index_t max_iters)
	Set the maximum number of iterations (default: 1000)
gsGradientMethod &	setOptions (const gsOptionList &opt)
	Set the options based on a gsOptionList.
void	setPreconditioner (const LinOpPtr &precond)
	Set the preconditionner.
void	setStepSize (T step_size)
	Set the step size.
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	stepSize () const
	Returns the chosen step size.
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, T step_size)
	Constructor using a matrix (operator) and optionally a preconditionner.
template<typename OperatorType >
static uPtr	make (const OperatorType &mat, const LinOpPtr &precond=LinOpPtr())
	Constructor 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

gsGradientMethod() [1/2]

template<class T = real_t>

template<typename OperatorType >

gsGradientMethod ( 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

In each step, the step width is chosen such that the residual is minimized (adaptive step sizes)

gsGradientMethod() [2/2]

template<class T = real_t>

template<typename OperatorType >

gsGradientMethod ( const OperatorType &  mat, const LinOpPtr &  precond, T  step_size  )

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
step_size	The step size

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() [1/2]

template<class T = real_t>

template<typename OperatorType >

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

inlinestatic

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
step_size	The step size

make() [2/2]

template<class T = real_t>

template<typename OperatorType >

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

inlinestatic

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

In each step, the step width is chosen such that the residual is minimized (adaptive step sizes)

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