#include <ginkgo/core/factorization/par_ict.hpp>

Inheritance diagram for gko::factorization::ParIct< ValueType, IndexType >:

Classes
class	Factory

struct	parameters_type

Public Types
using	value_type = ValueType

using	index_type = IndexType

using	matrix_type = matrix::Csr< ValueType, IndexType >

Public Types inherited from gko::Composition< ValueType >
using	value_type = ValueType

using	transposed_type = Composition< ValueType >

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

Public Types inherited from gko::ConvertibleTo< ResultType >
using	result_type = ResultType

Public Member Functions
std::shared_ptr< const matrix_type >	get_l_factor () const

std::shared_ptr< const matrix_type >	get_lt_factor () const

const parameters_type &	get_parameters () const

Public Member Functions inherited from gko::Composition< ValueType >
const std::vector< std::shared_ptr< const LinOp > > &	get_operators () const noexcept

std::unique_ptr< LinOp >	transpose () const override

std::unique_ptr< LinOp >	conj_transpose () const override

Composition &	operator= (const Composition &)

Composition &	operator= (Composition &&)

	Composition (const Composition &)

	Composition (Composition &&)

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

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

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

ConcreteLinOp *	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< AbstractObject, PolymorphicBase >
std::unique_ptr< AbstractObject >	create_default (std::shared_ptr< const Executor > exec) const

std::unique_ptr< AbstractObject >	create_default () const

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

std::unique_ptr< AbstractObject >	clone () const

AbstractObject *	copy_from (const PolymorphicObject *other)

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

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

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

AbstractObject *	move_from (ptr_param< PolymorphicObject > other)

AbstractObject *	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

std::unique_ptr< PolymorphicObject >	create_default () const

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

std::unique_ptr< PolymorphicObject >	clone () const

PolymorphicObject *	copy_from (const PolymorphicObject *other)

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)

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)

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

PolymorphicObject *	move_from (ptr_param< PolymorphicObject > other)

PolymorphicObject *	clear ()

std::shared_ptr< const Executor >	get_executor () const noexcept

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< ConcreteLinOp >
void	convert_to (result_type *result) const override

void	move_to (result_type *result) override

Public Member Functions inherited from gko::ConvertibleTo< ResultType >
virtual void	convert_to (result_type *result) const =0

void	convert_to (ptr_param< result_type > result) const

virtual void	move_to (result_type *result)=0

void	move_to (ptr_param< result_type > result)

Static Public Member Functions
template<typename... Args>
static std::unique_ptr< Composition< ValueType > >	create (Args &&... args)=delete

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, IndexType >())

Static Public Member Functions inherited from gko::EnableCreateMethod< ConcreteType >
template<typename... Args>
static std::unique_ptr< ConcreteType >	create (Args &&... args)

Protected Member Functions
	ParIct (const Factory *factory, std::shared_ptr< const LinOp > system_matrix)

std::unique_ptr< Composition< ValueType > >	generate_l_lt (const std::shared_ptr< const LinOp > &system_matrix) const

Protected Member Functions inherited from gko::Composition< ValueType >
void	add_operators ()

template<typename... Rest>
void	add_operators (std::shared_ptr< const LinOp > oper, Rest &&... rest)

	Composition (std::shared_ptr< const Executor > exec)

template<typename Iterator , typename = std::void_t< typename std::iterator_traits<Iterator>::iterator_category>>
	Composition (Iterator begin, Iterator end)

template<typename... Rest>
	Composition (std::shared_ptr< const LinOp > oper, Rest &&... rest)

void	apply_impl (const LinOp b, LinOp x) const override

void	apply_impl (const LinOp alpha, const LinOp b, const LinOp beta, LinOp x) const override

Protected Member Functions inherited from gko::EnableLinOp< ConcreteLinOp, PolymorphicBase >
ConcreteLinOp *	self () noexcept

const ConcreteLinOp *	self () const noexcept

Protected Member Functions inherited from gko::EnablePolymorphicObject< ConcreteObject, PolymorphicBase >
std::unique_ptr< PolymorphicObject >	create_default_impl (std::shared_ptr< const Executor > exec) const override

PolymorphicObject *	copy_from_impl (const PolymorphicObject *other) override

PolymorphicObject *	copy_from_impl (std::unique_ptr< PolymorphicObject > other) override

PolymorphicObject *	move_from_impl (PolymorphicObject *other) override

PolymorphicObject *	move_from_impl (std::unique_ptr< PolymorphicObject > other) override

PolymorphicObject *	clear_impl () override

Protected Member Functions inherited from gko::PolymorphicObject
	PolymorphicObject (std::shared_ptr< const Executor > exec)

	PolymorphicObject (const PolymorphicObject &other)

Protected Member Functions inherited from gko::log::EnableLogging< PolymorphicObject >
void	log (Params &&... params) const

Additional Inherited Members
Protected Attributes inherited from gko::log::EnableLogging< PolymorphicObject >
std::vector< std::shared_ptr< const Logger > >	loggers_

Detailed Description

template<typename ValueType = default_precision, typename IndexType = int32>
class gko::factorization::ParIct< ValueType, IndexType >

ParICT is an incomplete threshold-based Cholesky factorization which is computed in parallel.

\(L\) is a lower triangular matrix which approximates a given symmetric positive definite matrix \(A\) with \(A \approx LL^T\). Here, \(L\) has a sparsity pattern that is improved iteratively based on its element-wise magnitude. The initial sparsity pattern is chosen based on the lower triangle of \(A\).

One iteration of the ParICT algorithm consists of the following steps:

Calculating the residual \(R = A - LL^T\)
Adding new non-zero locations from \(R\) to \(L\). The new non-zero locations are initialized based on the corresponding residual value.
Executing a fixed-point iteration on \(L\) according to \( F(L) = \begin{cases} \frac{1}{l_{jj}} \left(a_{ij}-\sum_{k=1}^{j-1}l_{ik}l_{jk}\right), \quad & i \neq j \\ \sqrt{a_{ij}-\sum_{k=1}^{j-1}l_{ik}l_{jk}}, \quad & i = j \\ \end{cases} \)
Removing the smallest entries (by magnitude) from \(L\)
Executing a fixed-point iteration on the (now sparser) \(L\)

This ParICT algorithm thus improves the sparsity pattern and the approximation of \(L\) simultaneously.

The implementation follows the design of H. Anzt et al., ParILUT - A Parallel Threshold ILU for GPUs, 2019 IEEE International Parallel and Distributed Processing Symposium (IPDPS), pp. 231–241.

Template Parameters

ValueType	Type of the values of all matrices used in this class
IndexType	Type of the indices of all matrices used in this class

Member Function Documentation

◆ generate_l_lt()

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

std::unique_ptr< Composition< ValueType > > gko::factorization::ParIct< ValueType, IndexType >::generate_l_lt ( const std::shared_ptr< const LinOp > & system_matrix ) const

protected

Generates the incomplete LL^T factors, which will be returned as a composition of the lower (first element of the composition) and the upper factor (second element). The dynamic type of L and L^T is matrix_type

Parameters

system_matrix the source matrix used to generate the factors.

Note: : system_matrix must be convertible to a Csr Matrix, otherwise, an exception is thrown.

Returns: A Composition, containing the incomplete LU factors for the given system_matrix (first element is L, then L^T)

◆ parse()

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

static parameters_type gko::factorization::ParIct< ValueType, IndexType >::parse	(	const config::pnode &	config,
		const config::registry &	context,
		const config::type_descriptor &	td_for_child = `config::make_type_descriptor< ValueType, IndexType >()`
	)

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/index type of this class.

Returns: parameters

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

ginkgo/core/factorization/par_ict.hpp

ParIct< ValueType, IndexType > Class Template Reference

ParIct< ValueType, IndexType > Class Template Reference#

Classes

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ generate_l_lt()

◆ parse()

ParIct< ValueType, IndexType > Class Template Reference

ParIct&lt; ValueType, IndexType &gt; Class Template Reference#

Classes

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ generate_l_lt()

◆ parse()

ParIct< ValueType, IndexType > Class Template Reference#