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 >:

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

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Classes
struct	parameters_type
class	Factory

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< default_precision, int32 > >
using	result_type
Public Types inherited from gko::WritableToMatrixData< default_precision, int32 >
using	value_type
using	index_type

Public Member Functions
size_type	get_num_blocks () const noexcept
	Returns the number of blocks of the operator.
const block_interleaved_storage_scheme< index_type > &	get_storage_scheme () const noexcept
	Returns the storage scheme used for storing Jacobi blocks.
const value_type *	get_blocks () const noexcept
	Returns the pointer to the memory used for storing the block data.
const remove_complex< value_type > *	get_conditioning () const noexcept
	Returns an array of 1-norm condition numbers of the blocks.
size_type	get_num_stored_elements () const noexcept
	Returns the number of elements explicitly stored in the matrix.
void	convert_to (matrix::Dense< value_type > *result) const override
void	move_to (matrix::Dense< value_type > *result) override
void	write (mat_data &data) const override
std::unique_ptr< LinOp >	transpose () const override
	Returns a LinOp representing the transpose of the Transposable object.
std::unique_ptr< LinOp >	conj_transpose () const override
	Returns a LinOp representing the conjugate transpose of the Transposable object.
Jacobi &	operator= (const Jacobi &other)
	Copy-assigns a Jacobi preconditioner.
Jacobi &	operator= (Jacobi &&other)
	Move-assigns a Jacobi preconditioner.
	Jacobi (const Jacobi &other)
	Copy-constructs a Jacobi preconditioner.
	Jacobi (Jacobi &&other)
	Move-assigns a Jacobi preconditioner.
const parameters_type &	get_parameters () const
Public Member Functions inherited from gko::EnableLinOp< Jacobi< default_precision, int32 > >
const Jacobi< default_precision, int32 > *	apply (ptr_param< const LinOp > b, ptr_param< LinOp > x) const
Public Member Functions inherited from gko::EnablePolymorphicAssignment< Jacobi< default_precision, int32 > >
void	convert_to (result_type *result) const override
void	move_to (result_type *result) override
Public Member Functions inherited from gko::WritableToMatrixData< default_precision, int32 >
virtual void	write (matrix_data< default_precision, int32 > &data) const=0
	Writes a matrix to a matrix_data structure.

Static Public Member Functions
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 >())
	Create the parameters from the property_tree.

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.

◆ 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

◆ 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.

◆ 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

◆ 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

◆ 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).

◆ parse()

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

parameters_type gko::preconditioner::Jacobi< 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

Note: Jacobi does not support block_pointers and storage_optimization array.

◆ 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.

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

Constructor & Destructor Documentation

◆ Jacobi() [1/2]

◆ Jacobi() [2/2]

Member Function Documentation

◆ conj_transpose()

◆ get_blocks()

◆ get_conditioning()

◆ get_num_blocks()

◆ get_num_stored_elements()

◆ get_storage_scheme()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ parse()

◆ transpose()