GMRES or the generalized minimal residual method is an iterative type Krylov subspace method which is suitable for nonsymmetric linear systems. More...

#include <ginkgo/core/solver/gmres.hpp>

Inheritance diagram for gko::solver::Gmres< ValueType >:

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Collaboration diagram for gko::solver::Gmres< ValueType >:

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Classes
class	Factory

struct	parameters_type

Public Types
using	value_type = ValueType

using	transposed_type = Gmres< ValueType >

Public Member Functions
std::unique_ptr< LinOp >	transpose () const override
	Returns a LinOp representing the transpose of the Transposable object. More...

std::unique_ptr< LinOp >	conj_transpose () const override
	Returns a LinOp representing the conjugate transpose of the Transposable object. More...

bool	apply_uses_initial_guess () const override
	Return true as iterative solvers use the data in x as an initial guess. More...

size_type	get_krylov_dim () const
	Gets the Krylov dimension of the solver. More...

void	set_krylov_dim (size_type other)
	Sets the Krylov dimension. More...

remove_complex< ValueType >	get_restart_ratio () const
	Returns the restart ratio. More...

void	set_restart_ratio (remove_complex< ValueType > other)
	Sets the restart ratio. More...

const parameters_type &	get_parameters () const

Public Member Functions inherited from gko::LinOp
void	apply (ptr_param< const LinOp > b, ptr_param< LinOp > x) const
	Applies a linear operator to a vector (or a sequence of vectors). More...

void	apply (ptr_param< const LinOp > alpha, ptr_param< const LinOp > b, ptr_param< const LinOp > beta, ptr_param< LinOp > x) const
	Performs the operation x = alpha * op(b) + beta * x. More...

const dim< 2 > &	get_size () const noexcept
	Returns the size of the operator. More...

LinOp &	operator= (const LinOp &)=default
	Copy-assigns a LinOp. More...

LinOp &	operator= (LinOp &&other)
	Move-assigns a LinOp. More...

	LinOp (const LinOp &)=default
	Copy-constructs a LinOp. More...

	LinOp (LinOp &&other)
	Move-constructs a LinOp. More...

Public Member Functions inherited from gko::PolymorphicObject
virtual void	validate_data () const
	Throws gko::InvalidData exception if we found the data inside the object does not fulfill certain property up to our knowledge.

PolymorphicObject &	operator= (const PolymorphicObject &)

std::shared_ptr< const Executor >	get_executor () const noexcept
	Returns the Executor of the object. More...

Public Member Functions inherited from gko::log::EnableLogging< PolymorphicObject >
void	add_logger (std::shared_ptr< const Logger > logger) override

void	remove_logger (const Logger *logger) override

void	remove_logger (ptr_param< const Logger > logger)

const std::vector< std::shared_ptr< const Logger > > &	get_loggers () const override

void	clear_loggers () override

Public Member Functions inherited from gko::log::Loggable
void	remove_logger (ptr_param< const Logger > logger)

Public Member Functions inherited from gko::solver::EnablePreconditionedIterativeSolver< ValueType, Gmres< ValueType > >
	EnablePreconditionedIterativeSolver (std::shared_ptr< const LinOp > system_matrix, std::shared_ptr< const stop::CriterionFactory > stop_factory, std::shared_ptr< const LinOp > preconditioner)

	EnablePreconditionedIterativeSolver (std::shared_ptr< const LinOp > system_matrix, const FactoryParameters &params)

Public Member Functions inherited from gko::solver::EnableSolverBase< Gmres< ValueType > >
EnableSolverBase &	operator= (const EnableSolverBase &other)
	Creates a shallow copy of the provided system matrix, clones it onto this executor if executors don't match.

EnableSolverBase &	operator= (EnableSolverBase &&other)
	Moves the provided system matrix, clones it onto this executor if executors don't match. More...

	EnableSolverBase (std::shared_ptr< const LinOp > system_matrix)

	EnableSolverBase (const EnableSolverBase &other)
	Creates a shallow copy of the provided system matrix.

	EnableSolverBase (EnableSolverBase &&other)
	Moves the provided system matrix. More...

int	get_num_workspace_ops () const override

std::vector< std::string >	get_workspace_op_names () const override

std::vector< int >	get_workspace_scalars () const override
	Returns the IDs of all scalars (workspace vectors with system dimension-independent size, usually 1 x num_rhs).

std::vector< int >	get_workspace_vectors () const override
	Returns the IDs of all vectors (workspace vectors with system dimension-dependent size, usually system_matrix_size x num_rhs).

Public Member Functions inherited from gko::solver::SolverBase< LinOp >
std::shared_ptr< const LinOp >	get_system_matrix () const
	Returns the system matrix, with its concrete type, used by the solver. More...

Public Member Functions inherited from gko::solver::EnableIterativeBase< Gmres< ValueType > >
EnableIterativeBase &	operator= (const EnableIterativeBase &other)
	Creates a shallow copy of the provided stopping criterion, clones it onto this executor if executors don't match.

EnableIterativeBase &	operator= (EnableIterativeBase &&other)
	Moves the provided stopping criterion, clones it onto this executor if executors don't match. More...

	EnableIterativeBase (std::shared_ptr< const stop::CriterionFactory > stop_factory)

	EnableIterativeBase (const EnableIterativeBase &other)
	Creates a shallow copy of the provided stopping criterion.

	EnableIterativeBase (EnableIterativeBase &&other)
	Moves the provided stopping criterion. More...

void	set_stop_criterion_factory (std::shared_ptr< const stop::CriterionFactory > new_stop_factory) override
	Sets the stopping criterion of the solver. More...

Public Member Functions inherited from gko::solver::IterativeBase
std::shared_ptr< const stop::CriterionFactory >	get_stop_criterion_factory () const
	Gets the stopping criterion factory of the solver. More...

Public Member Functions inherited from gko::solver::EnablePreconditionable< Gmres< ValueType > >
void	set_preconditioner (std::shared_ptr< const LinOp > new_precond) override
	Sets the preconditioner operator used by the Preconditionable. More...

EnablePreconditionable &	operator= (const EnablePreconditionable &other)
	Creates a shallow copy of the provided preconditioner, clones it onto this executor if executors don't match.

EnablePreconditionable &	operator= (EnablePreconditionable &&other)
	Moves the provided preconditioner, clones it onto this executor if executors don't match. More...

	EnablePreconditionable (std::shared_ptr< const LinOp > preconditioner)

	EnablePreconditionable (const EnablePreconditionable &other)
	Creates a shallow copy of the provided preconditioner.

	EnablePreconditionable (EnablePreconditionable &&other)
	Moves the provided preconditioner. More...

Public Member Functions inherited from gko::Preconditionable
virtual std::shared_ptr< const LinOp >	get_preconditioner () const
	Returns the preconditioner operator used by the Preconditionable. More...

Static Public Member Functions
static auto	build () -> decltype(Factory ::create())

static parameters_type	parse (const config::pnode &config, const config::registry &context, const config::type_descriptor &td_for_child=config::make_type_descriptor< ValueType >())
	Create the parameters from the property_tree. More...

Detailed Description

template<typename ValueType = default_precision>
class gko::solver::Gmres< ValueType >

GMRES or the generalized minimal residual method is an iterative type Krylov subspace method which is suitable for nonsymmetric linear systems.

The Arnoldi process builds an orthonormal basis \( V_m \) of the Krylov subspace

\[ \mathcal{K}_m(A, r_0) = \mathrm{span}\{r_0, A r_0, A^2 r_0, \ldots, A^{m-1} r_0\}, \]

and produces an upper Hessenberg matrix \( \bar H_m \) satisfying the Arnoldi relation \( A V_m = V_{m+1} \bar H_m \). GMRES then chooses the approximate solution \( x_m = x_0 + V_m y_m \) with \( y_m \) minimizing the residual norm over the subspace,

\[ y_m = \arg\min_{y \in \mathbb{R}^m} \| \beta e_1 - \bar H_m y \|_2, \qquad \beta = \| r_0 \|_2. \]

The implementation in Ginkgo makes use of the merged kernel to make the best use of data locality. The inner operations in one iteration of GMRES are merged into 2 separate steps. Modified Gram-Schmidt is used.

Template Parameters

ValueType precision of matrix elements

Member Function Documentation

◆ apply_uses_initial_guess()

template<typename ValueType = default_precision>

bool gko::solver::Gmres< ValueType >::apply_uses_initial_guess ( ) const

inlineoverridevirtual

Return true as iterative solvers use the data in x as an initial guess.

Returns: true as iterative solvers use the data in x as an initial guess.

Reimplemented from gko::LinOp.

◆ conj_transpose()

template<typename ValueType = default_precision>

std::unique_ptr<LinOp> gko::solver::Gmres< ValueType >::conj_transpose ( ) const

overridevirtual

Returns a LinOp representing the conjugate transpose of the Transposable object.

Returns: a pointer to the new conjugate transposed object

Implements gko::Transposable.

◆ get_krylov_dim()

template<typename ValueType = default_precision>

size_type gko::solver::Gmres< ValueType >::get_krylov_dim ( ) const

inline

Gets the Krylov dimension of the solver.

Returns: the Krylov dimension

References gko::solver::Gmres< ValueType >::parameters_type::krylov_dim.

◆ get_restart_ratio()

template<typename ValueType = default_precision>

remove_complex<ValueType> gko::solver::Gmres< ValueType >::get_restart_ratio ( ) const

inline

Returns the restart ratio.

Returns: the restart ratio

References gko::solver::Gmres< ValueType >::parameters_type::restart_ratio.

◆ parse()

template<typename ValueType = default_precision>

static parameters_type gko::solver::Gmres< ValueType >::parse	(	const config::pnode &	config,
		const config::registry &	context,
		const config::type_descriptor &	td_for_child = `config::make_type_descriptor< ValueType >()`
	)

static

Create the parameters from the property_tree.

Because this is directly tied to the specific type, the value/index type settings within config are ignored and type_descriptor is only used for children configs.

Parameters

config	the property tree for setting
context	the registry
td_for_child	the type descriptor for children configs. The default uses the value type of this class.

Returns: parameters

◆ set_krylov_dim()

template<typename ValueType = default_precision>

void gko::solver::Gmres< ValueType >::set_krylov_dim ( size_type other )

inline

Sets the Krylov dimension.

Parameters

other the new Krylov dimension

References gko::solver::Gmres< ValueType >::parameters_type::krylov_dim.

◆ set_restart_ratio()

template<typename ValueType = default_precision>

void gko::solver::Gmres< ValueType >::set_restart_ratio ( remove_complex< ValueType > other )

inline

Sets the restart ratio.

Parameters

other the new restart ratio

References gko::solver::Gmres< ValueType >::parameters_type::restart_ratio.

◆ transpose()

template<typename ValueType = default_precision>

std::unique_ptr<LinOp> gko::solver::Gmres< ValueType >::transpose ( ) const

overridevirtual

Returns a LinOp representing the transpose of the Transposable object.

Returns: a pointer to the new transposed object

Implements gko::Transposable.

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

ginkgo/core/solver/gmres.hpp

Classes

Public Types

Public Member Functions

Static Public Member Functions

Detailed Description

template<typename ValueType = default_precision> class gko::solver::Gmres< ValueType >

Member Function Documentation

◆ apply_uses_initial_guess()

◆ conj_transpose()

◆ get_krylov_dim()

◆ get_restart_ratio()

◆ parse()

◆ set_krylov_dim()

◆ set_restart_ratio()

◆ transpose()

template<typename ValueType = default_precision>
class gko::solver::Gmres< ValueType >