Iterative refinement (IR) is an iterative method that uses another coarse method to approximate the error of the current solution via the current residual. More...

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

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

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

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Classes
class	Factory

struct	parameters_type

Public Types
using	value_type = ValueType

using	transposed_type = Ir< ValueType >

Public Types inherited from gko::EnablePolymorphicAssignment< Ir< ValueType > >
using	result_type = Ir< ValueType >

Public Types inherited from gko::ConvertibleTo< Ir< ValueType > >
using	result_type = Ir< 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...

std::shared_ptr< const LinOp >	get_solver () const
	Returns the solver operator used as the inner solver. More...

void	set_solver (std::shared_ptr< const LinOp > new_solver)
	Sets the solver operator used as the inner solver. More...

Ir &	operator= (const Ir &)
	Copy-assigns an IR solver. More...

Ir &	operator= (Ir &&)
	Move-assigns an IR solver. More...

	Ir (const Ir &)
	Copy-constructs an IR solver. More...

	Ir (Ir &&)
	Move-constructs an IR solver. More...

const parameters_type &	get_parameters () const

Public Member Functions inherited from gko::EnableLinOp< Ir< ValueType > >
const Ir< ValueType > *	apply (ptr_param< const LinOp > b, ptr_param< LinOp > x) const

Ir< ValueType > *	apply (ptr_param< const LinOp > b, ptr_param< LinOp > x)

const Ir< ValueType > *	apply (ptr_param< const LinOp > alpha, ptr_param< const LinOp > b, ptr_param< const LinOp > beta, ptr_param< LinOp > x) const

Ir< ValueType > *	apply (ptr_param< const LinOp > alpha, ptr_param< const LinOp > b, ptr_param< const LinOp > beta, ptr_param< LinOp > x)

Public Member Functions inherited from gko::EnableAbstractPolymorphicObject< Ir< ValueType >, LinOp >
std::unique_ptr< Ir< ValueType > >	create_default (std::shared_ptr< const Executor > exec) const

std::unique_ptr< Ir< ValueType > >	create_default () const

std::unique_ptr< Ir< ValueType > >	clone (std::shared_ptr< const Executor > exec) const

std::unique_ptr< Ir< ValueType > >	clone () const

Ir< ValueType > *	copy_from (const PolymorphicObject *other)

std::enable_if_t< std::is_base_of< PolymorphicObject, std::decay_t< Derived > >::value, Ir< ValueType > > *	copy_from (std::unique_ptr< Derived > &&other)

std::enable_if_t< std::is_base_of< PolymorphicObject, std::decay_t< Derived > >::value, Ir< ValueType > > *	copy_from (const std::unique_ptr< Derived > &other)

Ir< ValueType > *	copy_from (const std::shared_ptr< const PolymorphicObject > &other)

Ir< ValueType > *	move_from (ptr_param< PolymorphicObject > other)

Ir< ValueType > *	clear ()

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

const LinOp *	apply (ptr_param< const LinOp > b, ptr_param< LinOp > x) const

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

const LinOp *	apply (ptr_param< const LinOp > alpha, ptr_param< const LinOp > b, ptr_param< const LinOp > beta, ptr_param< LinOp > x) const

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::EnableAbstractPolymorphicObject< LinOp >
std::unique_ptr< LinOp >	create_default (std::shared_ptr< const Executor > exec) const

std::unique_ptr< LinOp >	create_default () const

std::unique_ptr< LinOp >	clone (std::shared_ptr< const Executor > exec) const

std::unique_ptr< LinOp >	clone () const

LinOp *	copy_from (const PolymorphicObject *other)

std::enable_if_t< std::is_base_of< PolymorphicObject, std::decay_t< Derived > >::value, LinOp > *	copy_from (std::unique_ptr< Derived > &&other)

std::enable_if_t< std::is_base_of< PolymorphicObject, std::decay_t< Derived > >::value, LinOp > *	copy_from (const std::unique_ptr< Derived > &other)

LinOp *	copy_from (const std::shared_ptr< const PolymorphicObject > &other)

LinOp *	move_from (ptr_param< PolymorphicObject > other)

LinOp *	clear ()

Public Member Functions inherited from gko::PolymorphicObject
PolymorphicObject &	operator= (const PolymorphicObject &)

std::unique_ptr< PolymorphicObject >	create_default (std::shared_ptr< const Executor > exec) const
	Creates a new "default" object of the same dynamic type as this object. More...

std::unique_ptr< PolymorphicObject >	create_default () const
	Creates a new "default" object of the same dynamic type as this object. More...

std::unique_ptr< PolymorphicObject >	clone (std::shared_ptr< const Executor > exec) const
	Creates a clone of the object. More...

std::unique_ptr< PolymorphicObject >	clone () const
	Creates a clone of the object. More...

PolymorphicObject *	copy_from (const PolymorphicObject *other)
	Copies another object into this object. More...

template<typename Derived , typename Deleter >
std::enable_if_t< std::is_base_of< PolymorphicObject, std::decay_t< Derived > >::value, PolymorphicObject > *	copy_from (std::unique_ptr< Derived, Deleter > &&other)
	Moves another object into this object. More...

template<typename Derived , typename Deleter >
std::enable_if_t< std::is_base_of< PolymorphicObject, std::decay_t< Derived > >::value, PolymorphicObject > *	copy_from (const std::unique_ptr< Derived, Deleter > &other)
	Copies another object into this object. More...

PolymorphicObject *	copy_from (const std::shared_ptr< const PolymorphicObject > &other)
	Copies another object into this object. More...

PolymorphicObject *	move_from (ptr_param< PolymorphicObject > other)
	Moves another object into this object. More...

PolymorphicObject *	clear ()
	Transforms the object into its default state. More...

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::EnablePolymorphicAssignment< Ir< ValueType > >
void	convert_to (result_type *result) const override
	Converts the implementer to an object of type result_type. More...

void	move_to (result_type *result) override
	Converts the implementer to an object of type result_type by moving data from this object. More...

Public Member Functions inherited from gko::ConvertibleTo< Ir< ValueType > >
void	convert_to (ptr_param< result_type > result) const

void	move_to (ptr_param< result_type > result)

Public Member Functions inherited from gko::solver::EnableSolverBase< Ir< 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< Ir< 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...

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

Friends
class	EnableLinOp< Ir >

class	EnablePolymorphicObject< Ir, LinOp >

class	EnableApplyWithInitialGuess< Ir >

Detailed Description

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

Iterative refinement (IR) is an iterative method that uses another coarse method to approximate the error of the current solution via the current residual.

Moreover, it can be also considered as preconditioned Richardson iteration with relaxation factor = 1.

For any approximation of the solution solution to the system Ax = b, the residual is defined as: residual = b - A solution. The error in solution, e = x - solution (with x being the exact solution) can be obtained as the solution to the residual equation Ae = residual, since A e = Ax - A solution = b - A solution = residual. Then, the real solution is computed as x = relaxation_factor * solution + e. Instead of accurately solving the residual equation Ae = residual, the solution of the system e can be approximated to obtain the approximation error using a coarse method solver, which is used to update solution, and the entire process is repeated with the updated solution. This yields the iterative refinement method:

solution = initial_guess
while not converged:
    residual = b - A solution
    error = solver(A, residual)
    solution = solution + relaxation_factor * error

With relaxation_factor equal to 1 (default), the solver is Iterative Refinement, with relaxation_factor equal to a value other than 1, the solver is a Richardson iteration, with possibility for additional preconditioning.

Assuming that solver has accuracy c, i.e., | e - error | <= c | e |, iterative refinement will converge with a convergence rate of c. Indeed, from e - error = x - solution - error = x - solution* (where solution* denotes the value stored in solution after the update) and e = inv(A) residual = inv(A)b - inv(A) A solution = x - solution it follows that | x - solution* | <= c | x - solution |.

Unless otherwise specified via the solver factory parameter, this implementation uses the identity operator (i.e. the solver that approximates the solution of a system Ax = b by setting x := b) as the default inner solver. Such a setting results in a relaxation method known as the Richardson iteration with parameter 1, which is guaranteed to converge for matrices whose spectrum is strictly contained within the unit disc around 1 (i.e., all its eigenvalues lambda have to satisfy the equation `|relaxation_factor * lambda - 1| < 1).

Template Parameters

ValueType precision of matrix elements

Constructor & Destructor Documentation

◆ Ir() [1/2]

template<typename ValueType = default_precision>

gko::solver::Ir< ValueType >::Ir ( const Ir< ValueType > & )

Copy-constructs an IR solver.

Inherits the executor, shallow-copies inner solver, stopping criterion and system matrix.

◆ Ir() [2/2]

template<typename ValueType = default_precision>

gko::solver::Ir< ValueType >::Ir ( Ir< ValueType > && )

Move-constructs an IR solver.

Preserves the executor, moves inner solver, stopping criterion and system matrix. The moved-from object is empty (0x0 and nullptr inner solver, stopping criterion and system matrix)

Member Function Documentation

◆ apply_uses_initial_guess()

template<typename ValueType = default_precision>

bool gko::solver::Ir< 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.

References gko::solver::provided.

◆ conj_transpose()

template<typename ValueType = default_precision>

std::unique_ptr<LinOp> gko::solver::Ir< 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_solver()

template<typename ValueType = default_precision>

std::shared_ptr<const LinOp> gko::solver::Ir< ValueType >::get_solver ( ) const

inline

Returns the solver operator used as the inner solver.

Returns: the solver operator used as the inner solver

◆ operator=() [1/2]

template<typename ValueType = default_precision>

Ir& gko::solver::Ir< ValueType >::operator= ( const Ir< ValueType > & )

Copy-assigns an IR solver.

Preserves the executor, shallow-copies inner solver, stopping criterion and system matrix. If the executors mismatch, clones inner solver, stopping criterion and system matrix onto this executor.

◆ operator=() [2/2]

template<typename ValueType = default_precision>

Ir& gko::solver::Ir< ValueType >::operator= ( Ir< ValueType > && )

Move-assigns an IR solver.

Preserves the executor, moves inner solver, stopping criterion and system matrix. If the executors mismatch, clones inner solver, stopping criterion and system matrix onto this executor. The moved-from object is empty (0x0 and nullptr inner solver, stopping criterion and system matrix)

◆ set_solver()

template<typename ValueType = default_precision>

void gko::solver::Ir< ValueType >::set_solver ( std::shared_ptr< const LinOp > new_solver )

Sets the solver operator used as the inner solver.

Parameters

new_solver the new inner solver

◆ transpose()

template<typename ValueType = default_precision>

std::unique_ptr<LinOp> gko::solver::Ir< 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/ir.hpp

Classes

Public Types

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

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

Constructor & Destructor Documentation

◆ Ir() [1/2]

◆ Ir() [2/2]

Member Function Documentation

◆ apply_uses_initial_guess()

◆ conj_transpose()

◆ get_solver()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ set_solver()

◆ transpose()

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