A block-Jacobi preconditioner is a block-diagonal linear operator, obtained by inverting the diagonal blocks of the source operator. More...

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

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

[legend]

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

[legend]

Classes
class	Factory

struct	parameters_type

Public Types
using	value_type = ValueType

using	index_type = IndexType

using	mat_data = matrix_data< ValueType, IndexType >

using	transposed_type = Jacobi< ValueType, IndexType >

Public Types inherited from gko::EnablePolymorphicAssignment< Jacobi< ValueType, IndexType > >
using	result_type = Jacobi< ValueType, IndexType >

Public Types inherited from gko::ConvertibleTo< Jacobi< ValueType, IndexType > >
using	result_type = Jacobi< ValueType, IndexType >

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

Public Types inherited from gko::WritableToMatrixData< ValueType, IndexType >
using	value_type = ValueType

using	index_type = IndexType

Public Member Functions
size_type	get_num_blocks () const noexcept
	Returns the number of blocks of the operator. More...

const block_interleaved_storage_scheme< index_type > &	get_storage_scheme () const noexcept
	Returns the storage scheme used for storing Jacobi blocks. More...

const value_type *	get_blocks () const noexcept
	Returns the pointer to the memory used for storing the block data. More...

const remove_complex< value_type > *	get_conditioning () const noexcept
	Returns an array of 1-norm condition numbers of the blocks. More...

size_type	get_num_stored_elements () const noexcept
	Returns the number of elements explicitly stored in the matrix. More...

void	convert_to (matrix::Dense< value_type > *result) const override
	Converts the implementer to an object of type result_type. More...

void	move_to (matrix::Dense< value_type > *result) override
	Converts the implementer to an object of type result_type by moving data from this object. More...

void	write (mat_data &data) const override
	Writes a matrix to a matrix_data structure. 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...

Jacobi &	operator= (const Jacobi &other)
	Copy-assigns a Jacobi preconditioner. More...

Jacobi &	operator= (Jacobi &&other)
	Move-assigns a Jacobi preconditioner. More...

	Jacobi (const Jacobi &other)
	Copy-constructs a Jacobi preconditioner. More...

	Jacobi (Jacobi &&other)
	Move-assigns a Jacobi preconditioner. More...

const parameters_type &	get_parameters () const

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

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

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

Jacobi< ValueType, IndexType > *	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< Jacobi< ValueType, IndexType >, LinOp >
std::unique_ptr< Jacobi< ValueType, IndexType > >	create_default (std::shared_ptr< const Executor > exec) const

std::unique_ptr< Jacobi< ValueType, IndexType > >	create_default () const

std::unique_ptr< Jacobi< ValueType, IndexType > >	clone (std::shared_ptr< const Executor > exec) const

std::unique_ptr< Jacobi< ValueType, IndexType > >	clone () const

Jacobi< ValueType, IndexType > *	copy_from (const PolymorphicObject *other)

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

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

Jacobi< ValueType, IndexType > *	copy_from (const std::shared_ptr< const PolymorphicObject > &other)

Jacobi< ValueType, IndexType > *	move_from (ptr_param< PolymorphicObject > other)

Jacobi< ValueType, IndexType > *	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< Jacobi< ValueType, IndexType > >
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< Jacobi< ValueType, IndexType > >
void	convert_to (ptr_param< result_type > result) const

void	move_to (ptr_param< result_type > result)

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

void	move_to (ptr_param< result_type > result)

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

Friends
class	EnableLinOp< Jacobi >

class	EnablePolymorphicObject< Jacobi, LinOp >

Detailed Description

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

A block-Jacobi preconditioner is a block-diagonal linear operator, obtained by inverting the diagonal blocks of the source operator.

The Jacobi class implements the inversion of the diagonal blocks using Gauss-Jordan elimination with column pivoting, and stores the inverse explicitly in a customized format.

If the diagonal blocks of the matrix are not explicitly set by the user, the implementation will try to automatically detect the blocks by first finding the natural blocks of the matrix, and then applying the supervariable agglomeration procedure on them. However, if problem-specific knowledge regarding the block diagonal structure is available, it is usually beneficial to explicitly pass the starting rows of the diagonal blocks, as the block detection is merely a heuristic and cannot perfectly detect the diagonal block structure. The current implementation supports blocks of up to 32 rows / columns.

The implementation also includes an improved, adaptive version of the block-Jacobi preconditioner, which can store some of the blocks in lower precision and thus improve the performance of preconditioner application by reducing the amount of memory transfers. This variant can be enabled by setting the Jacobi::Factory's storage_optimization parameter. Refer to the documentation of the parameter for more details.

Template Parameters

ValueType	precision of matrix elements
IndexType	integral type used to store pointers to the start of each block

Note: The current implementation supports blocks of up to 32 rows / columns.; When using the adaptive variant, there may be a trade-off in terms of slightly longer preconditioner generation due to extra work required to detect the optimal precision of the blocks.; When the max_block_size is set to 1, specialized kernels are used, both for generation (inverting the diagonals) and application (diagonal scaling) to reduce the overhead involved in the usual (adaptive) block case.

Constructor & Destructor Documentation

◆ Jacobi() [1/2]

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

gko::preconditioner::Jacobi< ValueType, IndexType >::Jacobi ( const Jacobi< ValueType, IndexType > & other )

Copy-constructs a Jacobi preconditioner.

Inherits executor, copies all data and parameters.

◆ Jacobi() [2/2]

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

gko::preconditioner::Jacobi< ValueType, IndexType >::Jacobi ( Jacobi< ValueType, IndexType > && other )

Move-assigns a Jacobi preconditioner.

Inherits executor, moves all data and parameters. The moved-from object will be empty (0x0 and default parameters).

Member Function Documentation

◆ conj_transpose()

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

std::unique_ptr<LinOp> gko::preconditioner::Jacobi< ValueType, IndexType >::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.

◆ convert_to()

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

void gko::preconditioner::Jacobi< ValueType, IndexType >::convert_to ( matrix::Dense< value_type > * result ) const

overridevirtual

Converts the implementer to an object of type result_type.

Parameters

result the object used to store the result of the conversion

Implements gko::ConvertibleTo< matrix::Dense< ValueType > >.

◆ get_blocks()

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

const value_type* gko::preconditioner::Jacobi< ValueType, IndexType >::get_blocks ( ) const

inlinenoexcept

Returns the pointer to the memory used for storing the block data.

Element (i, j) of block b is stored in position (get_block_pointers()[b] + i) * stride + j of the array.

Returns: the pointer to the memory used for storing the block data

References gko::array< ValueType >::get_const_data().

◆ get_conditioning()

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

const remove_complex<value_type>* gko::preconditioner::Jacobi< ValueType, IndexType >::get_conditioning ( ) const

inlinenoexcept

Returns an array of 1-norm condition numbers of the blocks.

Returns: an array of 1-norm condition numbers of the blocks

Note: This value is valid only if adaptive precision variant is used, and implementations of the standard non-adaptive variant are allowed to omit the calculation of condition numbers.

References gko::array< ValueType >::get_const_data().

◆ get_num_blocks()

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

size_type gko::preconditioner::Jacobi< ValueType, IndexType >::get_num_blocks ( ) const

inlinenoexcept

Returns the number of blocks of the operator.

Returns: the number of blocks of the operator

◆ get_num_stored_elements()

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

size_type gko::preconditioner::Jacobi< ValueType, IndexType >::get_num_stored_elements ( ) const

inlinenoexcept

Returns the number of elements explicitly stored in the matrix.

Returns: the number of elements explicitly stored in the matrix

References gko::array< ValueType >::get_num_elems().

◆ get_storage_scheme()

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

const block_interleaved_storage_scheme<index_type>& gko::preconditioner::Jacobi< ValueType, IndexType >::get_storage_scheme ( ) const

inlinenoexcept

Returns the storage scheme used for storing Jacobi blocks.

Returns: the storage scheme used for storing Jacobi blocks

◆ move_to()

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

void gko::preconditioner::Jacobi< ValueType, IndexType >::move_to ( matrix::Dense< value_type > * result )

overridevirtual

Converts the implementer to an object of type result_type by moving data from this object.

This method is used when the implementer is a temporary object, and move semantics can be used.

Parameters

result the object used to emplace the result of the conversion

Note: ConvertibleTo::move_to can be implemented by simply calling ConvertibleTo::convert_to. However, this operation can often be optimized by exploiting the fact that implementer's data can be moved to the result.

Implements gko::ConvertibleTo< matrix::Dense< ValueType > >.

◆ operator=() [1/2]

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

Jacobi& gko::preconditioner::Jacobi< ValueType, IndexType >::operator= ( const Jacobi< ValueType, IndexType > & other )

Copy-assigns a Jacobi preconditioner.

Preserves executor, copies all data and parameters.

◆ operator=() [2/2]

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

Jacobi& gko::preconditioner::Jacobi< ValueType, IndexType >::operator= ( Jacobi< ValueType, IndexType > && other )

Move-assigns a Jacobi preconditioner.

Preserves executor, moves all data and parameters. The moved-from object will be empty (0x0 and default parameters).

◆ transpose()

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

std::unique_ptr<LinOp> gko::preconditioner::Jacobi< ValueType, IndexType >::transpose ( ) const

overridevirtual

Returns a LinOp representing the transpose of the Transposable object.

Returns: a pointer to the new transposed object

Implements gko::Transposable.

◆ write()

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

void gko::preconditioner::Jacobi< ValueType, IndexType >::write ( mat_data & data ) const

overridevirtual

Writes a matrix to a matrix_data structure.

Parameters

data	the matrix_data structure

Implements gko::WritableToMatrixData< ValueType, IndexType >.

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

ginkgo/core/preconditioner/jacobi.hpp

Classes

Public Types

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

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

Constructor & Destructor Documentation

◆ Jacobi() [1/2]

◆ Jacobi() [2/2]

Member Function Documentation

◆ conj_transpose()

◆ convert_to()

◆ get_blocks()

◆ get_conditioning()

◆ get_num_blocks()

◆ get_num_stored_elements()

◆ get_storage_scheme()

◆ move_to()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ transpose()

◆ write()

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