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

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

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

[legend]

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

[legend]

Classes
class	Factory

struct	parameters_type

Public Types
using	value_type = ValueType

Public Member Functions
size_type	get_krylov_dim () const
	Returns the Krylov dimension. More...

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

cb_gmres::storage_precision	get_storage_precision () const
	Returns the storage precision used internally. 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...

virtual bool	apply_uses_initial_guess () const
	Returns true if the linear operator uses the data given in x as an initial guess. 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, CbGmres< 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< CbGmres< 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< CbGmres< 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< CbGmres< 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::CbGmres< ValueType >

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

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 CB-GMRES are merged into 2 separate steps. Classical Gram-Schmidt with reorthogonalization is used.

The Krylov basis can be stored in reduced precision (compressed) to reduce memory accesses, while all computations (including Krylov basis operations) are performed in the same arithmetic precision ValueType. By default, the Krylov basis are stored in one precision lower than ValueType.

Mathematically CB-GMRES is the same algorithm as standard GMRES — the Arnoldi process produces an orthonormal basis \( V_m \) and an upper Hessenberg \( \bar H_m \) with \( A V_m = V_{m+1} \bar H_m \), and the iterate is chosen as

\[ x_m = x_0 + V_m y_m, \qquad y_m = \arg\min_{y} \| \beta e_1 - \bar H_m y \|_2. \]

The "compressed basis" variant stores the columns of \( V_m \) in a precision lower than ValueType: each basis vector is cast down to the storage type when written and cast back up when read. The Hessenberg matrix, the Givens rotations, and the working residual all stay in full ValueType precision, so the final approximation has the same accuracy as standard GMRES while the basis storage and the bandwidth needed to apply it are reduced. See the storage_precision enum for the supported compression options.

Template Parameters

ValueType the arithmetic precision and the precision of matrix elements

Member Function Documentation

◆ get_krylov_dim()

template<typename ValueType = default_precision>

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

inline

Returns the Krylov dimension.

Returns: the Krylov dimension

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

◆ get_storage_precision()

template<typename ValueType = default_precision>

cb_gmres::storage_precision gko::solver::CbGmres< ValueType >::get_storage_precision ( ) const

inline

Returns the storage precision used internally.

Returns: the storage precision used internally

References gko::solver::CbGmres< ValueType >::parameters_type::storage_precision.

◆ parse()

template<typename ValueType = default_precision>

static parameters_type gko::solver::CbGmres< 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::CbGmres< ValueType >::set_krylov_dim ( size_type other )

inline

Sets the Krylov dimension.

Parameters

other the new Krylov dimension

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

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

ginkgo/core/solver/cb_gmres.hpp

Classes

Public Types

Public Member Functions

Static Public Member Functions

Detailed Description

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

Member Function Documentation

◆ get_krylov_dim()

◆ get_storage_precision()

◆ parse()

◆ set_krylov_dim()

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