gko::preconditioner::Sor< ValueType, IndexType > Class Template Reference

This class generates the (S)SOR preconditioner. More...

#include <ginkgo/core/preconditioner/sor.hpp>

Inheritance diagram for gko::preconditioner::Sor< ValueType, IndexType >:

Collaboration diagram for gko::preconditioner::Sor< ValueType, IndexType >:

Classes
struct	parameters_type

Public Types
using	value_type = ValueType
using	index_type = IndexType
using	composition_type = Composition< ValueType >

Public Member Functions
const parameters_type &	get_parameters ()
	Returns the parameters used to construct the factory. More...
const parameters_type &	get_parameters () const
	Returns the parameters used to construct the factory. More...
std::unique_ptr< composition_type >	generate (std::shared_ptr< const LinOp > system_matrix) const
Public Member Functions inherited from gko::LinOpFactory
std::unique_ptr< LinOp >	generate (std::shared_ptr< const LinOp > input) const
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)

Static Public Member Functions
static parameters_type	build ()
	Creates a new parameter_type to set up the factory.
static parameters_type	parse (const config::pnode &config, const config::registry &context, const config::type_descriptor &td_for_child=config::make_type_descriptor< ValueType, IndexType >())

Friends
class	enable_parameters_type< parameters_type, Sor >

Detailed Description

template<typename ValueType = default_precision, typename IndexType = int32>
class gko::preconditioner::Sor< ValueType, IndexType >

This class generates the (S)SOR preconditioner.

The SOR preconditioner starts from a splitting of the matrix \(A\) into \(A = D + L + U\), where \(L\) contains all entries below the diagonal, and \(U\) contains all entries above the diagonal. The application of the preconditioner is then defined as solving \(M x = y\) with

\[ M = \frac{1}{\omega} (D + \omega L), \quad 0 < \omega < 2. \]

\(\omega\) is known as the relaxation factor. The preconditioner can be made symmetric, leading to the SSOR preconditioner. Here, \(M\) is defined as

\[ M = \frac{1}{\omega (2 - \omega)} (D + \omega L) D^{-1} (D + \omega U) , \quad 0 < \omega < 2. \]

This class is a factory, which will only generate the preconditioner. The resulting LinOp will represent the application of \(M^{-1}\).

References

• Saad, Y. Iterative Methods for Sparse Linear Systems. 2nd ed. SIAM, 2003, ch. 4.1. https://doi.org/10.1137/1.9780898718003

Template Parameters

ValueType	The value type of the internally used CSR matrix
IndexType	The index type of the internally used CSR matrix

Member Function Documentation

generate()

template<typename ValueType = default_precision, typename IndexType = int32>

std::unique_ptr<composition_type> gko::preconditioner::Sor< ValueType, IndexType >::generate

(

std::shared_ptr< const LinOp >

system_matrix

)

const

Parameters

system_matrix

the source matrix used to generate the preconditioner.

Note

This function overrides the default LinOpFactory::generate to return a Factorization instead of a generic LinOp, which would need to be cast to Factorization again to access its factors. It is only necessary because smart pointers aren't covariant.

get_parameters() [1/2]

template<typename ValueType = default_precision, typename IndexType = int32>

const parameters_type& gko::preconditioner::Sor< ValueType, IndexType >::get_parameters ( )

inline

Returns the parameters used to construct the factory.

Returns

the parameters used to construct the factory.

get_parameters() [2/2]

template<typename ValueType = default_precision, typename IndexType = int32>

const parameters_type& gko::preconditioner::Sor< ValueType, IndexType >::get_parameters ( ) const

inline

Returns the parameters used to construct the factory.

Returns

the parameters used to construct the factory.

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

• ginkgo/core/preconditioner/sor.hpp