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

Inheritance diagram for PreconditionBlock< MatrixType, inverse_type >:

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

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

static ::ExceptionBase &	ExcInverseMatricesAlreadyExist ()

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

SmartPointer< 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

Private Attributes
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

Subscriptor functionality
Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class.
using	map_value_type = decltype(counter_map)::value_type

using	map_iterator = decltype(counter_map)::iterator

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

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

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

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

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

static std::mutex	mutex

void	check_no_subscribers () const noexcept

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. Still the matrix must have access to single matrix entries. Therefore, BlockMatrixArray and similar classes are not a possible matrix class template arguments.

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 82 of file precondition_block.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.

Member Function Documentation

◆ reinit()

template<typename number >

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

inlineinherited

Resize to this number of diagonal blocks with the given block size. If compress is true, then only one block will be stored.

Definition at line 333 of file precondition_block_base.h.

◆ inverses_computed()

template<typename number >

void PreconditionBlockBase< number >::inverses_computed ( bool are_they )

inlineinherited

Tell the class that inverses are computed.

Definition at line 598 of file precondition_block_base.h.

◆ same_diagonal()

template<typename number >

bool PreconditionBlockBase< number >::same_diagonal

inlineinherited

Does the matrix use only one diagonal block?

Definition at line 582 of file precondition_block_base.h.

◆ store_diagonals()

template<typename number >

bool PreconditionBlockBase< number >::store_diagonals

inlineinherited

Check, whether diagonal blocks (not their inverses) should be stored.

Definition at line 590 of file precondition_block_base.h.

◆ inverses_ready()

template<typename number >

bool PreconditionBlockBase< number >::inverses_ready

inlineinherited

Return true, if inverses are ready for use.

Definition at line 606 of file precondition_block_base.h.

◆ size()

template<typename number >

unsigned int PreconditionBlockBase< number >::size

inlineinherited

The number of blocks.

Definition at line 411 of file precondition_block_base.h.

◆ inverse_vmult()

template<typename number >

template<typename number2 >

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

inlineinherited

Multiply with the transposed inverse block at position i.

Definition at line 448 of file precondition_block_base.h.

◆ inverse() [1/2]

template<typename number >

FullMatrix< number > & PreconditionBlockBase< number >::inverse ( size_type i )

inlineinherited

Access to the inverse diagonal blocks if Inversion is gauss_jordan.

Definition at line 526 of file precondition_block_base.h.

◆ inverse() [2/2]

template<typename number >

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

inlineinherited

Access to the inverse diagonal blocks.

Definition at line 476 of file precondition_block_base.h.

◆ inverse_householder() [1/2]

template<typename number >

Householder< number > & PreconditionBlockBase< number >::inverse_householder ( size_type i )

inlineinherited

Access to the inverse diagonal blocks if Inversion is householder.

Definition at line 540 of file precondition_block_base.h.

◆ inverse_householder() [2/2]

template<typename number >

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

inlineinherited

Access to the inverse diagonal blocks if Inversion is householder.

Definition at line 488 of file precondition_block_base.h.

◆ inverse_svd() [1/2]

template<typename number >

LAPACKFullMatrix< number > & PreconditionBlockBase< number >::inverse_svd ( size_type i )

inlineinherited

Access to the inverse diagonal blocks if Inversion is householder.

Definition at line 554 of file precondition_block_base.h.

◆ inverse_svd() [2/2]

template<typename number >

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

inlineinherited

Access to the inverse diagonal blocks if Inversion is householder.

Definition at line 500 of file precondition_block_base.h.

◆ diagonal() [1/2]

template<typename number >

FullMatrix< number > & PreconditionBlockBase< number >::diagonal ( size_type i )

inlineinherited

Access to the diagonal blocks.

Definition at line 568 of file precondition_block_base.h.

◆ diagonal() [2/2]

template<typename number >

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

inlineinherited

Access to the diagonal blocks.

Definition at line 512 of file precondition_block_base.h.

◆ log_statistics()

template<typename number >

void PreconditionBlockBase< number >::log_statistics

inlineinherited

Print some statistics about the inverses to deallog. Output depends on Inversion. It is richest for svd, where we obtain statistics on extremal singular values and condition numbers.

Definition at line 614 of file precondition_block_base.h.

Member Data Documentation

◆ inversion

template<typename number >

Inversion PreconditionBlockBase< number >::inversion

protectedinherited

The method used for inverting blocks.

Definition at line 243 of file precondition_block_base.h.

◆ 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 Attributes

Subscriptor functionality

Detailed Description

Member Enumeration Documentation

◆ Inversion

Member Function Documentation

◆ 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

◆ inversion

◆ n_diagonal_blocks

◆ var_inverse_full

◆ var_inverse_householder

◆ var_inverse_svd

◆ var_diagonal

◆ var_store_diagonals

◆ var_same_diagonal

◆ var_inverses_ready