Ginkgo  Generated from pipelines/130473384 branch based on develop. Ginkgo version 1.1.1
A numerical linear algebra library targeting many-core architectures
Classes | Public Types | Public Member Functions | Static Public Member Functions | Friends | List of all members
gko::solver::Ir< ValueType > Class Template Reference

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>

Collaboration diagram for gko::solver::Ir< ValueType >:
[legend]

Classes

class  Factory
 
struct  parameters_type
 

Public Types

using value_type = 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::shared_ptr< const LinOpget_system_matrix () const
 Returns the system operator (matrix) of the linear system. More...
 
std::shared_ptr< const LinOpget_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...
 
const parameters_typeget_parameters () const
 
- Public Member Functions inherited from gko::EnableLinOp< Ir< ValueType > >
const Ir< ValueType > * apply (const LinOp *b, LinOp *x) const
 
Ir< ValueType > * apply (const LinOp *b, LinOp *x)
 
const Ir< ValueType > * apply (const LinOp *alpha, const LinOp *b, const LinOp *beta, LinOp *x) const
 
Ir< ValueType > * apply (const LinOp *alpha, const LinOp *b, const LinOp *beta, 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)
 
Ir< ValueType > * copy_from (std::unique_ptr< PolymorphicObject > other)
 
Ir< ValueType > * clear ()
 
- Public Member Functions inherited from gko::LinOp
LinOpapply (const LinOp *b, LinOp *x)
 Applies a linear operator to a vector (or a sequence of vectors). More...
 
const LinOpapply (const LinOp *b, LinOp *x) const
 Applies a linear operator to a vector (or a sequence of vectors). More...
 
LinOpapply (const LinOp *alpha, const LinOp *b, const LinOp *beta, LinOp *x)
 Performs the operation x = alpha * op(b) + beta * x. More...
 
const LinOpapply (const LinOp *alpha, const LinOp *b, const LinOp *beta, 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...
 
- Public Member Functions inherited from gko::EnableAbstractPolymorphicObject< LinOp >
std::unique_ptr< LinOpcreate_default (std::shared_ptr< const Executor > exec) const
 
std::unique_ptr< LinOpcreate_default () const
 
std::unique_ptr< LinOpclone (std::shared_ptr< const Executor > exec) const
 
std::unique_ptr< LinOpclone () const
 
LinOpcopy_from (const PolymorphicObject *other)
 
LinOpcopy_from (std::unique_ptr< PolymorphicObject > other)
 
LinOpclear ()
 
- Public Member Functions inherited from gko::PolymorphicObject
PolymorphicObjectoperator= (const PolymorphicObject &)
 
std::unique_ptr< PolymorphicObjectcreate_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< PolymorphicObjectcreate_default () const
 Creates a new "default" object of the same dynamic type as this object. More...
 
std::unique_ptr< PolymorphicObjectclone (std::shared_ptr< const Executor > exec) const
 Creates a clone of the object. More...
 
std::unique_ptr< PolymorphicObjectclone () const
 Creates a clone of the object. More...
 
PolymorphicObjectcopy_from (const PolymorphicObject *other)
 Copies another object into this object. More...
 
PolymorphicObjectcopy_from (std::unique_ptr< PolymorphicObject > other)
 Moves another object into this object. More...
 
PolymorphicObjectclear ()
 Transforms the object into its default state. More...
 
std::shared_ptr< const Executorget_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
 Adds a new logger to the list of subscribed loggers. More...
 
void remove_logger (const Logger *logger) override
 Removes a logger from the list of subscribed loggers. More...
 
- 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...
 

Static Public Member Functions

static auto build () -> decltype(Factory ::create())
 

Friends

class EnableLinOp< Ir >
 
class EnablePolymorphicObject< Ir, LinOp >
 

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.

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 = 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 + error

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 `|lambda - 1| < 1).

Template Parameters
ValueTypeprecision of matrix elements

Member Function Documentation

◆ 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

◆ get_system_matrix()

template<typename ValueType = default_precision>
std::shared_ptr<const LinOp> gko::solver::Ir< ValueType >::get_system_matrix ( ) const
inline

Returns the system operator (matrix) of the linear system.

Returns
the system operator (matrix)

◆ set_solver()

template<typename ValueType = default_precision>
void gko::solver::Ir< ValueType >::set_solver ( std::shared_ptr< const LinOp new_solver)
inline

Sets the solver operator used as the inner solver.

Parameters
new_solverthe new inner solver

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