#include <deal.II/lac/precondition_block.h>

Inheritance diagram for PreconditionBlock< MatrixType, inverse_type >:

[legend]

Classes
class	AdditionalData

Public Types
using	size_type = types::global_dof_index

Public Member Functions
	PreconditionBlock (bool store_diagonals=false)

	~PreconditionBlock () override=default

void	initialize (const MatrixType &A, const AdditionalData parameters)

void	clear ()

bool	empty () const

value_type	el (size_type i, size_type j) const

void	invert_diagblocks ()

template<typename number2 >
void	forward_step (Vector< number2 > &dst, const Vector< number2 > &prev, const Vector< number2 > &src, const bool transpose_diagonal) const

template<typename number2 >
void	backward_step (Vector< number2 > &dst, const Vector< number2 > &prev, const Vector< number2 > &src, const bool transpose_diagonal) const

size_type	block_size () const

std::size_t	memory_consumption () const

template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

EnableObserverPointer functionality
Classes derived from EnableObserverPointer provide a facility to subscribe to this object. This is mostly used by the ObserverPointer class.
void	subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const

void	unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const

unsigned int	n_subscriptions () const

template<typename StreamType >
void	list_subscribers (StreamType &stream) const

void	list_subscribers () const

Static Public Member Functions
static ::ExceptionBase &	ExcWrongBlockSize (int arg1, int arg2)

static ::ExceptionBase &	ExcInverseMatricesAlreadyExist ()

static ::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)

static ::ExceptionBase &	ExcNoSubscriber (std::string arg1, std::string arg2)

Protected Types
enum	Inversion { gauss_jordan , householder , svd }

Protected Member Functions
void	initialize (const MatrixType &A, const std::vector< size_type > &permutation, const std::vector< size_type > &inverse_permutation, const AdditionalData parameters)

void	set_permutation (const std::vector< size_type > &permutation, const std::vector< size_type > &inverse_permutation)

void	invert_permuted_diagblocks ()

void	reinit (unsigned int nblocks, size_type blocksize, bool compress, Inversion method=gauss_jordan)

void	inverses_computed (bool are_they)

bool	same_diagonal () const

bool	store_diagonals () const

bool	inverses_ready () const

unsigned int	size () const

template<typename number2 >
void	inverse_vmult (size_type i, Vector< number2 > &dst, const Vector< number2 > &src) const

template<typename number2 >
void	inverse_Tvmult (size_type i, Vector< number2 > &dst, const Vector< number2 > &src) const

FullMatrix< number > &	inverse (size_type i)

const FullMatrix< number > &	inverse (size_type i) const

Householder< number > &	inverse_householder (size_type i)

const Householder< number > &	inverse_householder (size_type i) const

LAPACKFullMatrix< number > &	inverse_svd (size_type i)

const LAPACKFullMatrix< number > &	inverse_svd (size_type i) const

FullMatrix< number > &	diagonal (size_type i)

const FullMatrix< number > &	diagonal (size_type i) const

void	log_statistics () const

Static Protected Member Functions
static ::ExceptionBase &	ExcDiagonalsNotStored ()

static ::ExceptionBase &	ExcInverseNotAvailable ()

Protected Attributes
size_type	blocksize

ObserverPointer< const MatrixType, PreconditionBlock< MatrixType, inverse_type > >	A

double	relaxation

std::vector< size_type >	permutation

std::vector< size_type >	inverse_permutation

Inversion	inversion

Private Types
using	number = typename MatrixType::value_type

using	value_type = inverse_type

using	map_value_type = decltype(counter_map)::value_type

using	map_iterator = decltype(counter_map)::iterator

Private Member Functions
void	check_no_subscribers () const noexcept

Private Attributes
std::atomic< unsigned int >	counter

std::map< std::string, unsigned int >	counter_map

std::vector< std::atomic< bool > * >	validity_pointers

const std::type_info *	object_info

unsigned int	n_diagonal_blocks

std::vector< FullMatrix< number > >	var_inverse_full

std::vector< Householder< number > >	var_inverse_householder

std::vector< LAPACKFullMatrix< number > >	var_inverse_svd

std::vector< FullMatrix< number > >	var_diagonal

bool	var_store_diagonals

bool	var_same_diagonal

bool	var_inverses_ready

Static Private Attributes
static std::mutex	mutex

Detailed Description

template<typename MatrixType, typename inverse_type = typename MatrixType::value_type>
class PreconditionBlock< MatrixType, inverse_type >

Base class for actual block preconditioners. This class assumes the MatrixType consisting of invertible blocks of blocksize on the diagonal and provides the inversion of the diagonal blocks of the matrix. It is not necessary for this class that the matrix be block diagonal; rather, it applies to matrices of arbitrary structure with the minimal property of having invertible blocks on the diagonal. The matrix must have access to individual matrix entries.

The block matrix structure used by this class is given, e.g., for the DG method for the transport equation. For a downstream numbering the matrices even have got a block lower left matrix structure, i.e. the matrices are empty above the diagonal blocks.

Note: This class is intended to be used for matrices whose structure is given by local contributions from disjoint cells, such as for DG methods. It is not intended for problems where the block structure results from different physical variables such as in the Stokes equations considered in step-22.

For all matrices that are empty above and below the diagonal blocks (i.e. for all block diagonal matrices) the BlockJacobi preconditioner is a direct solver. For all matrices that are empty only above the diagonal blocks (e.g. the matrices one gets by the DG method with downstream numbering) BlockSOR is a direct solver.

This first implementation of the PreconditionBlock assumes the matrix has blocks each of the same block size. Varying block sizes within the matrix must still be implemented if needed.

The first template parameter denotes the type of number representation in the sparse matrix, the second denotes the type of number representation in which the inverted diagonal block matrices are stored within this class by invert_diagblocks(). If you don't want to use the block inversion as an exact solver, but rather as a preconditioner, you may probably want to store the inverted blocks with less accuracy than the original matrix; for example, number==double, inverse_type=float might be a viable choice.

See also: Block (linear algebra)

Definition at line 81 of file precondition_block.h.

Member Typedef Documentation

◆ number

template<typename MatrixType , typename inverse_type = typename MatrixType::value_type>

using PreconditionBlock< MatrixType, inverse_type >::number = typename MatrixType::value_type

private

Define number type of matrix.

Definition at line 88 of file precondition_block.h.

◆ value_type

template<typename MatrixType , typename inverse_type = typename MatrixType::value_type>

using PreconditionBlock< MatrixType, inverse_type >::value_type = inverse_type

private

Value type for inverse matrices.

Definition at line 93 of file precondition_block.h.

◆ size_type

template<typename MatrixType , typename inverse_type = typename MatrixType::value_type>

using PreconditionBlock< MatrixType, inverse_type >::size_type = types::global_dof_index

Declare type for container size.

Definition at line 99 of file precondition_block.h.

◆ map_value_type

using EnableObserverPointer::map_value_type = decltype(counter_map)::value_type

privateinherited

The data type used in counter_map.

Definition at line 238 of file enable_observer_pointer.h.

◆ map_iterator

using EnableObserverPointer::map_iterator = decltype(counter_map)::iterator

privateinherited

The iterator type used in counter_map.

Definition at line 243 of file enable_observer_pointer.h.

Member Enumeration Documentation

◆ Inversion

template<typename number >

enum PreconditionBlockBase::Inversion

inherited

Choose a method for inverting the blocks, and thus the data type for the inverses.

Enumerator
gauss_jordan	Use the standard Gauss-Jacobi method implemented in FullMatrix::inverse().
householder	Use QR decomposition of the Householder class.
svd	Use the singular value decomposition of LAPACKFullMatrix.

Definition at line 70 of file precondition_block_base.h.

Constructor & Destructor Documentation

◆ PreconditionBlock()

template<typename MatrixType , typename inverse_type = typename MatrixType::value_type>

PreconditionBlock< MatrixType, inverse_type >::PreconditionBlock ( bool store_diagonals = false )

Constructor.

◆ ~PreconditionBlock()

template<typename MatrixType , typename inverse_type = typename MatrixType::value_type>

PreconditionBlock< MatrixType, inverse_type >::~PreconditionBlock ( )

overridedefault

Destructor.

Member Function Documentation

◆ initialize() [1/2]

template<typename MatrixType , typename inverse_type = typename MatrixType::value_type>

void PreconditionBlock< MatrixType, inverse_type >::initialize	(	const MatrixType &	A,
		const AdditionalData	parameters
	)

Initialize matrix and block size. We store the matrix and the block size in the preconditioner object. In a second step, the inverses of the diagonal blocks may be computed.

Additionally, a relaxation parameter for derived classes may be provided.

◆ initialize() [2/2]

template<typename MatrixType , typename inverse_type = typename MatrixType::value_type>

void PreconditionBlock< MatrixType, inverse_type >::initialize	(	const MatrixType &	A,
		const std::vector< size_type > &	permutation,
		const std::vector< size_type > &	inverse_permutation,
		const AdditionalData	parameters
	)

protected

Initialize matrix and block size for permuted preconditioning. Additionally to the parameters of the other initialize() function, we hand over two index vectors with the permutation and its inverse. For the meaning of these vectors see PreconditionBlockSOR.

In a second step, the inverses of the diagonal blocks may be computed. Make sure you use invert_permuted_diagblocks() to yield consistent data.

Additionally, a relaxation parameter for derived classes may be provided.

◆ set_permutation()

template<typename MatrixType , typename inverse_type = typename MatrixType::value_type>

void PreconditionBlock< MatrixType, inverse_type >::set_permutation	(	const std::vector< size_type > &	permutation,
		const std::vector< size_type > &	inverse_permutation
	)

protected

Set either the permutation of rows or the permutation of blocks, depending on the size of the vector.

If the size of the permutation vectors is equal to the dimension of the linear system, it is assumed that rows are permuted individually. In this case, set_permutation() must be called before initialize(), since the diagonal blocks are built from the permuted entries of the matrix.

If the size of the permutation vector is not equal to the dimension of the system, the diagonal blocks are computed from the unpermuted entries. Instead, the relaxation methods step() and Tstep() are executed applying the blocks in the order given by the permutation vector. They will throw an exception if length of this vector is not equal to the number of blocks.

Note: Permutation of blocks can only be applied to the relaxation operators step() and Tstep(), not to the preconditioning operators vmult() and Tvmult().; It is safe to call set_permutation() before initialize(), while the other order is only admissible for block permutation.

◆ invert_permuted_diagblocks()

template<typename MatrixType , typename inverse_type = typename MatrixType::value_type>

void PreconditionBlock< MatrixType, inverse_type >::invert_permuted_diagblocks ( )

protected

Replacement of invert_diagblocks() for permuted preconditioning.

◆ clear()

template<typename MatrixType , typename inverse_type = typename MatrixType::value_type>

void PreconditionBlock< MatrixType, inverse_type >::clear ( )

Deletes the inverse diagonal block matrices if existent, sets the blocksize to 0, hence leaves the class in the state that it had directly after calling the constructor.

◆ empty()

template<typename MatrixType , typename inverse_type = typename MatrixType::value_type>

bool PreconditionBlock< MatrixType, inverse_type >::empty ( ) const

Check whether the object is empty.

◆ el()

template<typename MatrixType , typename inverse_type = typename MatrixType::value_type>

value_type PreconditionBlock< MatrixType, inverse_type >::el	(	size_type	i,
		size_type	j
	)		const

Read-only access to entries. This function is only possible if the inverse diagonal blocks are stored.

◆ invert_diagblocks()

template<typename MatrixType , typename inverse_type = typename MatrixType::value_type>

void PreconditionBlock< MatrixType, inverse_type >::invert_diagblocks ( )

Stores the inverse of the diagonal blocks in inverse. This costs some additional memory - for DG methods about 1/3 (for double inverses) or 1/6 (for float inverses) of that used for the matrix - but it makes the preconditioning much faster.

It is not allowed to call this function twice (will produce an error) before a call of clear(...) because at the second time there already exist the inverse matrices.

After this function is called, the lock on the matrix given through the use_matrix function is released, i.e. you may overwrite of delete it. You may want to do this in case you use this matrix to precondition another matrix.

◆ forward_step()

template<typename MatrixType , typename inverse_type = typename MatrixType::value_type>

template<typename number2 >

void PreconditionBlock< MatrixType, inverse_type >::forward_step	(	Vector< number2 > &	dst,
		const Vector< number2 > &	prev,
		const Vector< number2 > &	src,
		const bool	transpose_diagonal
	)		const

Perform one block relaxation step in forward numbering.

Depending on the arguments dst and pref, this performs an SOR step (both reference the same vector) of a Jacobi step (both different vectors). For the Jacobi step, the calling function must copy dst to pref after this.

Note: If a permutation is set, it is automatically honored by this function.

◆ backward_step()

template<typename MatrixType , typename inverse_type = typename MatrixType::value_type>

template<typename number2 >

void PreconditionBlock< MatrixType, inverse_type >::backward_step	(	Vector< number2 > &	dst,
		const Vector< number2 > &	prev,
		const Vector< number2 > &	src,
		const bool	transpose_diagonal
	)		const

Perform one block relaxation step in backward numbering.

Depending on the arguments dst and pref, this performs an SOR step (both reference the same vector) of a Jacobi step (both different vectors). For the Jacobi step, the calling function must copy dst to pref after this.

Note: If a permutation is set, it is automatically honored by this function.

◆ block_size()

template<typename MatrixType , typename inverse_type = typename MatrixType::value_type>

size_type PreconditionBlock< MatrixType, inverse_type >::block_size ( ) const

Return the size of the blocks.

◆ memory_consumption()

template<typename MatrixType , typename inverse_type = typename MatrixType::value_type>

std::size_t PreconditionBlock< MatrixType, inverse_type >::memory_consumption ( ) const

Determine an estimate for the memory consumption (in bytes) of this object.

◆ subscribe()

void EnableObserverPointer::subscribe	(	std::atomic< bool > *const	validity,
		const std::string &	identifier = `""`
	)		const

inherited

Subscribes a user of the object by storing the pointer validity. The subscriber may be identified by text supplied as identifier.

Definition at line 131 of file enable_observer_pointer.cc.

◆ unsubscribe()

void EnableObserverPointer::unsubscribe	(	std::atomic< bool > *const	validity,
		const std::string &	identifier = `""`
	)		const

inherited

Unsubscribes a user from the object.

Note: The identifier and the validity pointer must be the same as the one supplied to subscribe().

Definition at line 151 of file enable_observer_pointer.cc.

◆ n_subscriptions()

unsigned int EnableObserverPointer::n_subscriptions ( ) const

inlineinherited

Return the present number of subscriptions to this object. This allows to use this class for reference counted lifetime determination where the last one to unsubscribe also deletes the object.

Definition at line 322 of file enable_observer_pointer.h.

◆ list_subscribers() [1/2]

template<typename StreamType >

void EnableObserverPointer::list_subscribers ( StreamType & stream ) const

inlineinherited

List the subscribers to the input stream.

Definition at line 339 of file enable_observer_pointer.h.

◆ list_subscribers() [2/2]

void EnableObserverPointer::list_subscribers ( ) const

inherited

List the subscribers to deallog.

Definition at line 199 of file enable_observer_pointer.cc.

◆ serialize()

template<class Archive >

void EnableObserverPointer::serialize	(	Archive &	ar,
		const unsigned int	version
	)

inlineinherited

Read or write the data of this object to or from a stream for the purpose of serialization using the BOOST serialization library.

This function does not actually serialize any of the member variables of this class. The reason is that what this class stores is only who subscribes to this object, but who does so at the time of storing the contents of this object does not necessarily have anything to do with who subscribes to the object when it is restored. Consequently, we do not want to overwrite the subscribers at the time of restoring, and then there is no reason to write the subscribers out in the first place.

Definition at line 331 of file enable_observer_pointer.h.

◆ check_no_subscribers()

void EnableObserverPointer::check_no_subscribers ( ) const

privatenoexceptinherited

Check that there are no objects subscribing to this object. If this check passes then it is safe to destroy the current object. It this check fails then this function will either abort or print an error message to deallog (by using the AssertNothrow mechanism), but will not throw an exception.

Note: Since this function is just a consistency check it does nothing in release mode.; If this function is called when there is an uncaught exception then, rather than aborting, this function prints an error message to the standard error stream and returns.

Definition at line 53 of file enable_observer_pointer.cc.

◆ reinit()

template<typename number >

void PreconditionBlockBase< number >::reinit	(	unsigned int	nblocks,
		size_type	blocksize,
		bool	compress,
		Inversion	method = `gauss_jordan`
	)

void PreconditionBlockBase< number >::inverse_vmult	(	size_type	i,
		Vector< number2 > &	dst,
		const Vector< number2 > &	src
	)		const

inlineinherited

Multiply with the inverse block at position i.

Definition at line 419 of file precondition_block_base.h.

◆ inverse_Tvmult()

template<typename number >

template<typename number2 >

void PreconditionBlockBase< number >::inverse_Tvmult	(	size_type	i,
		Vector< number2 > &	dst,
		const Vector< number2 > &	src
	)		const

◆ n_diagonal_blocks

template<typename number >

unsigned int PreconditionBlockBase< number >::n_diagonal_blocks

privateinherited

The number of (inverse) diagonal blocks, if only one is stored.

Definition at line 249 of file precondition_block_base.h.

◆ var_inverse_full

template<typename number >

std::vector<FullMatrix<number> > PreconditionBlockBase< number >::var_inverse_full

privateinherited

Storage of the inverse matrices of the diagonal blocks matrices as FullMatrix<number> matrices, if Inversion gauss_jordan is used. Using number=float saves memory in comparison with number=double, but may introduce numerical instability.

Definition at line 257 of file precondition_block_base.h.

◆ var_inverse_householder

template<typename number >

std::vector<Householder<number> > PreconditionBlockBase< number >::var_inverse_householder

privateinherited

Storage of the inverse matrices of the diagonal blocks matrices as Householder matrices if Inversion householder is used. Using number=float saves memory in comparison with number=double, but may introduce numerical instability.

Definition at line 265 of file precondition_block_base.h.

◆ var_inverse_svd

template<typename number >

std::vector<LAPACKFullMatrix<number> > PreconditionBlockBase< number >::var_inverse_svd

privateinherited

Storage of the inverse matrices of the diagonal blocks matrices as LAPACKFullMatrix matrices if Inversion svd is used. Using number=float saves memory in comparison with number=double, but may introduce numerical instability.

Definition at line 273 of file precondition_block_base.h.

◆ var_diagonal

template<typename number >

std::vector<FullMatrix<number> > PreconditionBlockBase< number >::var_diagonal

privateinherited

Storage of the original diagonal blocks.

Used by the blocked SSOR method.

Definition at line 280 of file precondition_block_base.h.

◆ var_store_diagonals

template<typename number >

bool PreconditionBlockBase< number >::var_store_diagonals

privateinherited

This is true, if the field var_diagonal is to be used.

Definition at line 286 of file precondition_block_base.h.

◆ var_same_diagonal

template<typename number >

bool PreconditionBlockBase< number >::var_same_diagonal

privateinherited

This is true, if only one inverse is stored.

Definition at line 291 of file precondition_block_base.h.

◆ var_inverses_ready

template<typename number >

bool PreconditionBlockBase< number >::var_inverses_ready

privateinherited

The inverse matrices are usable. Set by the parent class via inverses_computed().

Definition at line 297 of file precondition_block_base.h.

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

include/deal.II/lac/precondition_block.h

Classes

Public Types

Public Member Functions

Static Public Member Functions

Protected Types

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Private Types

Private Member Functions

Private Attributes

Static Private Attributes

Detailed Description

Member Typedef Documentation

◆ number

◆ value_type

◆ size_type

◆ map_value_type

◆ map_iterator

Member Enumeration Documentation

◆ Inversion

Constructor & Destructor Documentation

◆ PreconditionBlock()

◆ ~PreconditionBlock()

Member Function Documentation

◆ initialize() [1/2]

◆ initialize() [2/2]

◆ set_permutation()

◆ invert_permuted_diagblocks()

◆ clear()

◆ empty()

◆ el()

◆ invert_diagblocks()

◆ forward_step()

◆ backward_step()

◆ block_size()

◆ memory_consumption()

◆ subscribe()

◆ unsubscribe()

◆ n_subscriptions()

◆ list_subscribers() [1/2]

◆ list_subscribers() [2/2]

◆ serialize()

◆ check_no_subscribers()

◆ reinit()

◆ inverses_computed()

◆ same_diagonal()

◆ store_diagonals()

◆ inverses_ready()

◆ size()

◆ inverse_vmult()

◆ inverse_Tvmult()

◆ inverse() [1/2]

◆ inverse() [2/2]

◆ inverse_householder() [1/2]

◆ inverse_householder() [2/2]

◆ inverse_svd() [1/2]

◆ inverse_svd() [2/2]

◆ diagonal() [1/2]

◆ diagonal() [2/2]

◆ log_statistics()

Member Data Documentation

◆ blocksize

◆ A

◆ relaxation

◆ permutation

◆ inverse_permutation

◆ counter

◆ counter_map

◆ validity_pointers

◆ object_info

◆ mutex

◆ inversion

◆ n_diagonal_blocks

◆ var_inverse_full

◆ var_inverse_householder

◆ var_inverse_svd

◆ var_diagonal

◆ var_store_diagonals

◆ var_same_diagonal