IDR(s) is an efficient method for solving large nonsymmetric systems of linear equations. More...

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

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

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

Classes
class	Factory

struct	parameters_type

Public Types
using	value_type = ValueType

using	transposed_type = Idr< 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_subspace_dim () const
	Gets the subspace dimension of the solver. More...

void	set_subspace_dim (const size_type other)
	Sets the subspace dimension of the solver. More...

remove_complex< ValueType >	get_kappa () const
	Gets the kappa parameter of the solver. More...

void	set_kappa (const remove_complex< ValueType > other)
	Sets the kappa parameter of the solver. More...

bool	get_deterministic () const
	Gets the deterministic parameter of the solver. More...

void	set_deterministic (const bool other)
	Sets the deterministic parameter of the solver. More...

bool	get_complex_subspace () const
	Gets the complex_subspace parameter of the solver. More...

void	set_complex_subpsace (const bool other)
	Sets the complex_subspace parameter of the solver. More...

void	set_complex_subspace (const bool other)
	Sets the complex_subspace parameter of the solver. 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, Idr< 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< Idr< 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< Idr< 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< Idr< 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::Idr< ValueType >

IDR(s) is an efficient method for solving large nonsymmetric systems of linear equations.

The implementation follows the elegant variant that exploits the biorthogonality of the shadow vectors.

The method is based on the induced dimension reduction (IDR) theorem. Let \( P = [p_1, \ldots, p_s] \) be the shadow matrix — the \( s \) random, orthonormalized vectors that Ginkgo stores in a dense matrix — and let

\[ \mathcal{S} = \{ v \in \mathbb{C}^N : P^H v = 0 \} \]

be its left null space, that is, the orthogonal complement of the space spanned by the shadow vectors. Starting from the full Krylov space \( \mathcal{G}_0 = \mathcal{K}_N(A, r_0) \), the theorem states that the subspaces

\[ \mathcal{G}_j = (I - \omega_j A) (\mathcal{G}_{j-1} \cap \mathcal{S}), \qquad \omega_j \ne 0, \]

are nested, \( \mathcal{G}_j \subset \mathcal{G}_{j-1} \), and that \( \mathcal{G}_j = \{0\} \) for some \( j \le N \). IDR(s) forces the residuals into these shrinking spaces; in exact arithmetic it therefore reaches the true solution after at most \( N + N/s \) matrix-vector products.

References

Van Gijzen, M. B., Sonneveld, P. Algorithm 913: An Elegant IDR(s) Variant that Efficiently Exploits Biorthogonality Properties. ACM Transactions on Mathematical Software, 38 (1), Article 5, 2011. https://doi.org/10.1145/2049662.2049667 (the implemented variant; the IDR theorem is Theorem 2.1 in Section 2.1)
Sonneveld, P., Van Gijzen, M. B. IDR(s): A Family of Simple and Fast Algorithms for Solving Large Nonsymmetric Systems of Linear Equations. SIAM Journal on Scientific Computing, 31 (2), 1035–1062, 2008. https://doi.org/10.1137/070685804 (proof of the IDR theorem and of the \( N + N/s \) bound)

Template Parameters

ValueType precision of the elements of the system matrix.

Member Function Documentation

◆ apply_uses_initial_guess()

template<typename ValueType = default_precision>

bool gko::solver::Idr< 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::Idr< 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_complex_subspace()

template<typename ValueType = default_precision>

bool gko::solver::Idr< ValueType >::get_complex_subspace ( ) const

inline

Gets the complex_subspace parameter of the solver.

Returns: the complex_subspace parameter

References gko::solver::Idr< ValueType >::parameters_type::complex_subspace.

◆ get_deterministic()

template<typename ValueType = default_precision>

bool gko::solver::Idr< ValueType >::get_deterministic ( ) const

inline

Gets the deterministic parameter of the solver.

Returns: the deterministic parameter

References gko::solver::Idr< ValueType >::parameters_type::deterministic.

◆ get_kappa()

template<typename ValueType = default_precision>

remove_complex<ValueType> gko::solver::Idr< ValueType >::get_kappa ( ) const

inline

Gets the kappa parameter of the solver.

Returns: the kappa parameter

References gko::solver::Idr< ValueType >::parameters_type::kappa.

◆ get_subspace_dim()

template<typename ValueType = default_precision>

size_type gko::solver::Idr< ValueType >::get_subspace_dim ( ) const

inline

Gets the subspace dimension of the solver.

Returns: the subspace Dimension

References gko::solver::Idr< ValueType >::parameters_type::subspace_dim.

◆ parse()

template<typename ValueType = default_precision>

static parameters_type gko::solver::Idr< 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_complex_subpsace()

template<typename ValueType = default_precision>

void gko::solver::Idr< ValueType >::set_complex_subpsace ( const bool other )

inline

Sets the complex_subspace parameter of the solver.

Parameters

other the new complex_subspace parameter

References gko::solver::Idr< ValueType >::set_complex_subspace().

◆ set_complex_subspace()

template<typename ValueType = default_precision>

void gko::solver::Idr< ValueType >::set_complex_subspace ( const bool other )

inline

Sets the complex_subspace parameter of the solver.

Parameters

other the new complex_subspace parameter

References gko::solver::Idr< ValueType >::parameters_type::complex_subspace.

Referenced by gko::solver::Idr< ValueType >::set_complex_subpsace().

◆ set_deterministic()

template<typename ValueType = default_precision>

void gko::solver::Idr< ValueType >::set_deterministic ( const bool other )

inline

Sets the deterministic parameter of the solver.

Parameters

other the new deterministic parameter

References gko::solver::Idr< ValueType >::parameters_type::deterministic.

◆ set_kappa()

template<typename ValueType = default_precision>

void gko::solver::Idr< ValueType >::set_kappa ( const remove_complex< ValueType > other )

inline

Sets the kappa parameter of the solver.

Parameters

other the new kappa parameter

References gko::solver::Idr< ValueType >::parameters_type::kappa.

◆ set_subspace_dim()

template<typename ValueType = default_precision>

void gko::solver::Idr< ValueType >::set_subspace_dim ( const size_type other )

inline

Sets the subspace dimension of the solver.

Parameters

other the new subspace Dimension

References gko::solver::Idr< ValueType >::parameters_type::subspace_dim.

◆ transpose()

template<typename ValueType = default_precision>

std::unique_ptr<LinOp> gko::solver::Idr< 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/idr.hpp

Classes

Public Types

Public Member Functions

Static Public Member Functions

Detailed Description

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

Member Function Documentation

◆ apply_uses_initial_guess()

◆ conj_transpose()

◆ get_complex_subspace()

◆ get_deterministic()

◆ get_kappa()

◆ get_subspace_dim()

◆ parse()

◆ set_complex_subpsace()

◆ set_complex_subspace()

◆ set_deterministic()

◆ set_kappa()

◆ set_subspace_dim()

◆ transpose()

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