ParILU is an incomplete LU factorization which is computed in parallel. More...

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

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

Collaboration diagram for gko::factorization::ParIlu< 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 >

using	l_matrix_type = matrix_type

using	u_matrix_type = matrix_type

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

using	transposed_type = Composition< ValueType >

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

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

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

std::shared_ptr< const matrix_type >	get_u_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
	Returns a list of operators of the composition. More...

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...

Composition &	operator= (const Composition &)
	Copy-assigns a Composition. More...

Composition &	operator= (Composition &&)
	Move-assigns a Composition. More...

	Composition (const Composition &)
	Copy-constructs a Composition. More...

	Composition (Composition &&)
	Move-constructs a Composition. More...

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

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

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

Composition< 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< Composition< ValueType >, LinOp >
std::unique_ptr< Composition< ValueType > >	create_default (std::shared_ptr< const Executor > exec) const

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

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

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

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

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

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

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

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

Composition< 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...

virtual bool	apply_uses_initial_guess () const
	Returns true if the linear operator uses the data given in x as an initial guess. 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< Composition< 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< Composition< ValueType > >
void	convert_to (ptr_param< result_type > result) const

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 Public Member Functions inherited from gko::EnableCreateMethod< Composition< ValueType > >
static std::unique_ptr< Composition< ValueType > >	create (Args &&... args)

Detailed Description

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

ParILU is an incomplete LU factorization which is computed in parallel.

$L$ is a lower unitriangular, while $U$ is an upper triangular matrix, which approximate a given matrix $A$ with $A \approx LU$ . Here, $L$ and $U$ have the same sparsity pattern as $A$ , which is also called ILU(0).

The ParILU algorithm generates the incomplete factors iteratively, using a fixed-point iteration of the form

$F(L, U) = \begin{cases} \frac{1}{u_{jj}} \left(a_{ij}-\sum_{k=1}^{j-1}l_{ik}u_{kj}\right), \quad & i>j \\ a_{ij}-\sum_{k=1}^{i-1}l_{ik}u_{kj}, \quad & i\leq j \end{cases}$

In general, the entries of $L$ and $U$ can be iterated in parallel and in asynchronous fashion, the algorithm asymptotically converges to the incomplete factors $L$ and $U$ fulfilling $\left(R = A - L \cdot U\right)\vert_\mathcal{S} = 0\vert_\mathcal{S}$ where $\mathcal{S}$ is the pre-defined sparsity pattern (in case of ILU(0) the sparsity pattern of the system matrix $A$ ). The number of ParILU sweeps needed for convergence depends on the parallelism level: For sequential execution, a single sweep is sufficient, for fine-grained parallelism, the number of sweeps necessary to get a good approximation of the incomplete factors depends heavily on the problem. On the OpenMP executor, 3 sweeps usually give a decent approximation in our experiments, while GPU executors can take 10 or more iterations.

The ParILU algorithm in Ginkgo follows the design of E. Chow and A. Patel, Fine-grained Parallel Incomplete LU Factorization, SIAM Journal on Scientific Computing, 37, C169-C193 (2015).

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

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

ginkgo/core/factorization/par_ilu.hpp

Classes

Public Types

Public Member Functions

Static Public Member Functions

Detailed Description

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

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