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

Inheritance diagram for PreconditionBlockSOR< MatrixType, inverse_type >:

Public Types
using	size_type = types::global_dof_index

using	number = typename MatrixType::value_type

Public Member Functions
	PreconditionBlockSOR ()

template<typename number2 >
void	vmult (Vector< number2 > &, const Vector< number2 > &) const

template<typename number2 >
void	vmult_add (Vector< number2 > &, const Vector< number2 > &) const

template<typename number2 >
void	Tvmult (Vector< number2 > &, const Vector< number2 > &) const

template<typename number2 >
void	Tvmult_add (Vector< number2 > &, const Vector< number2 > &) const

template<typename number2 >
void	step (Vector< number2 > &dst, const Vector< number2 > &rhs) const

template<typename number2 >
void	Tstep (Vector< number2 > &dst, const Vector< number2 > &rhs) const

Protected Types
enum	Inversion

Protected Member Functions
	PreconditionBlockSOR (bool store)

template<typename number2 >
void	forward (Vector< number2 > &, const Vector< number2 > &, const bool transpose_diagonal, const bool adding) const

template<typename number2 >
void	backward (Vector< number2 > &, const Vector< number2 > &, const bool transpose_diagonal, const bool adding) const

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

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	clear ()

bool	empty () const

value_type	el (size_type i, size_type j) const

void	invert_diagblocks ()

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

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

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

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

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

FullMatrix< typename MatrixType::value_type > &	inverse (size_type i)

const FullMatrix< typename MatrixType::value_type > &	inverse (size_type i) const

Householder< typename MatrixType::value_type > &	inverse_householder (size_type i)

const Householder< typename MatrixType::value_type > &	inverse_householder (size_type i) const

LAPACKFullMatrix< typename MatrixType::value_type > &	inverse_svd (size_type i)

const LAPACKFullMatrix< typename MatrixType::value_type > &	inverse_svd (size_type i) const

FullMatrix< typename MatrixType::value_type > &	diagonal (size_type i)

const FullMatrix< typename MatrixType::value_type > &	diagonal (size_type i) const

void	log_statistics () const

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

static ::ExceptionBase &	ExcInverseMatricesAlreadyExist ()

static ::ExceptionBase &	ExcDiagonalsNotStored ()

static ::ExceptionBase &	ExcInverseNotAvailable ()

Protected Attributes
size_type	blocksize

SmartPointer< const MatrixType, PreconditionBlock< MatrixType, typename MatrixType::value_type > >	A

double	relaxation

std::vector< size_type >	permutation

std::vector< size_type >	inverse_permutation

Inversion	inversion

Private Types
using	value_type = typename MatrixType::value_type

Private Attributes
unsigned int	n_diagonal_blocks

std::vector< FullMatrix< typename MatrixType::value_type > >	var_inverse_full

std::vector< Householder< typename MatrixType::value_type > >	var_inverse_householder

std::vector< LAPACKFullMatrix< typename MatrixType::value_type > >	var_inverse_svd

std::vector< FullMatrix< typename MatrixType::value_type > >	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.
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)

using	map_value_type = decltype(counter_map)::value_type

using	map_iterator = decltype(counter_map)::iterator

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

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

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

void	check_no_subscribers () const noexcept

Detailed Description

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

Block SOR preconditioning. This class satisfies the relaxation concept.

The functions vmult and Tvmult execute a (transposed) block-SOR step, based on the blocks in PreconditionBlock. The elements outside the diagonal blocks may be distributed arbitrarily.

See PreconditionBlock for requirements on the matrix. The blocks used in this class must be contiguous and non-overlapping. An overlapping Schwarz relaxation method can be found in RelaxationBlockSOR; that class does not offer preconditioning, though.

Permutations

Optionally, the entries of the source vector can be treated in the order of the indices in the permutation vector set by set_permutation (or the opposite order for Tvmult()). The inverse permutation is used for storing elements back into this vector. This functionality is automatically enabled after a call to set_permutation() with vectors of nonzero size.

Note: The diagonal blocks, like the matrix, are not permuted! Therefore, the permutation vector can only swap whole blocks. It may not change the order inside blocks or swap single indices between blocks.

Instantiations

Note: Instantiations for this template are provided for <float> and <double>; others can be generated in application programs (see the section on Template instantiations in the manual).

Definition at line 653 of file precondition_block.h.

Member Typedef Documentation

◆ value_type

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

privateinherited

Value type for inverse matrices.

Definition at line 94 of file precondition_block.h.

Member Enumeration Documentation

◆ Inversion

enum PreconditionBlockBase::Inversion

inherited

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

Definition at line 70 of file precondition_block_base.h.

Member Function Documentation

◆ initialize() [1/2]

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

inherited

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]

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

protectedinherited

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()

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

protectedinherited

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()

void PreconditionBlock< MatrixType, typename MatrixType::value_type >::invert_permuted_diagblocks ( )

protectedinherited

Replacement of invert_diagblocks() for permuted preconditioning.

◆ clear()

void PreconditionBlock< MatrixType, typename MatrixType::value_type >::clear ( )

inherited

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()

bool PreconditionBlock< MatrixType, typename MatrixType::value_type >::empty ( ) const

inherited

Check whether the object is empty.

◆ el()

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

inherited

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

◆ invert_diagblocks()

void PreconditionBlock< MatrixType, typename MatrixType::value_type >::invert_diagblocks ( )

inherited

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()

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

inherited

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()

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

inherited

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()

size_type PreconditionBlock< MatrixType, typename MatrixType::value_type >::block_size ( ) const

inherited

Return the size of the blocks.

◆ memory_consumption()

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

inherited

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

◆ ExcWrongBlockSize()

static ::ExceptionBase & PreconditionBlock< MatrixType, typename MatrixType::value_type >::ExcWrongBlockSize	(	int	arg1,
		int	arg2
	)

staticinherited

For non-overlapping block preconditioners, the block size must divide the matrix size. If not, this exception gets thrown.

Note: The message that will be printed by this exception reads:
<< "The blocksize " << arg1 << " and the size of the matrix " << arg2 << " do not match."

◆ ExcInverseMatricesAlreadyExist()

static ::ExceptionBase & PreconditionBlock< MatrixType, typename MatrixType::value_type >::ExcInverseMatricesAlreadyExist ( )

staticinherited

Exception

◆ reinit()

void PreconditionBlockBase< typename MatrixType::value_type >::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 110 of file precondition_block_base.h.

◆ inverses_computed()

void PreconditionBlockBase< typename MatrixType::value_type >::inverses_computed ( bool are_they )

inlineinherited

Tell the class that inverses are computed.

Definition at line 119 of file precondition_block_base.h.

◆ same_diagonal()

bool PreconditionBlockBase< typename MatrixType::value_type >::same_diagonal

inlineinherited

Does the matrix use only one diagonal block?

Definition at line 125 of file precondition_block_base.h.

◆ store_diagonals()

bool PreconditionBlockBase< typename MatrixType::value_type >::store_diagonals

inlineinherited

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

Definition at line 131 of file precondition_block_base.h.

◆ inverses_ready()

bool PreconditionBlockBase< typename MatrixType::value_type >::inverses_ready

inlineinherited

Return true, if inverses are ready for use.

Definition at line 137 of file precondition_block_base.h.

◆ size()

unsigned int PreconditionBlockBase< typename MatrixType::value_type >::size

inlineinherited

The number of blocks.

Definition at line 143 of file precondition_block_base.h.

◆ inverse_vmult()

void PreconditionBlockBase< typename MatrixType::value_type >::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 150 of file precondition_block_base.h.

◆ inverse_Tvmult()

void PreconditionBlockBase< typename MatrixType::value_type >::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 159 of file precondition_block_base.h.

◆ inverse() [1/2]

FullMatrix< typename MatrixType::value_type > & PreconditionBlockBase< typename MatrixType::value_type >::inverse ( size_type i )

inlineinherited

Access to the inverse diagonal blocks if Inversion is gauss_jordan.

Definition at line 167 of file precondition_block_base.h.

◆ inverse() [2/2]

const FullMatrix< typename MatrixType::value_type > & PreconditionBlockBase< typename MatrixType::value_type >::inverse ( size_type i ) const

inlineinherited

Access to the inverse diagonal blocks.

Definition at line 185 of file precondition_block_base.h.

◆ inverse_householder() [1/2]

Householder< typename MatrixType::value_type > & PreconditionBlockBase< typename MatrixType::value_type >::inverse_householder ( size_type i )

inlineinherited

Access to the inverse diagonal blocks if Inversion is householder.

Definition at line 173 of file precondition_block_base.h.

◆ inverse_householder() [2/2]

const Householder< typename MatrixType::value_type > & PreconditionBlockBase< typename MatrixType::value_type >::inverse_householder ( size_type i ) const

inlineinherited

Access to the inverse diagonal blocks if Inversion is householder.

Definition at line 191 of file precondition_block_base.h.

◆ inverse_svd() [1/2]

LAPACKFullMatrix< typename MatrixType::value_type > & PreconditionBlockBase< typename MatrixType::value_type >::inverse_svd ( size_type i )

inlineinherited

Access to the inverse diagonal blocks if Inversion is householder.

Definition at line 179 of file precondition_block_base.h.

◆ inverse_svd() [2/2]

const LAPACKFullMatrix< typename MatrixType::value_type > & PreconditionBlockBase< typename MatrixType::value_type >::inverse_svd ( size_type i ) const

inlineinherited

Access to the inverse diagonal blocks if Inversion is householder.

Definition at line 197 of file precondition_block_base.h.

◆ diagonal() [1/2]

FullMatrix< typename MatrixType::value_type > & PreconditionBlockBase< typename MatrixType::value_type >::diagonal ( size_type i )

inlineinherited

Access to the diagonal blocks.

Definition at line 203 of file precondition_block_base.h.

◆ diagonal() [2/2]

const FullMatrix< typename MatrixType::value_type > & PreconditionBlockBase< typename MatrixType::value_type >::diagonal ( size_type i ) const

inlineinherited

Access to the diagonal blocks.

Definition at line 209 of file precondition_block_base.h.

◆ log_statistics()

void PreconditionBlockBase< typename MatrixType::value_type >::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 217 of file precondition_block_base.h.

◆ ExcDiagonalsNotStored()

static ::ExceptionBase & PreconditionBlockBase< typename MatrixType::value_type >::ExcDiagonalsNotStored ( )

staticinherited

You are trying to access a diagonal block (not its inverse), but you decided not to store the diagonal blocks.

◆ ExcInverseNotAvailable()

static ::ExceptionBase & PreconditionBlockBase< typename MatrixType::value_type >::ExcInverseNotAvailable ( )

staticinherited

You are accessing a diagonal block, assuming that it has a certain type. But, the method used for inverting the diagonal blocks does not use this type

Member Data Documentation

◆ blocksize

size_type PreconditionBlock< MatrixType, typename MatrixType::value_type >::blocksize

protectedinherited

Size of the blocks. Each diagonal block is assumed to be of the same size.

Definition at line 338 of file precondition_block.h.

◆ A

SmartPointer<const MatrixType, PreconditionBlock<MatrixType, typename MatrixType::value_type > > PreconditionBlock< MatrixType, typename MatrixType::value_type >::A

protectedinherited

Pointer to the matrix. Make sure that the matrix exists as long as this class needs it, i.e. until calling invert_diagblocks, or (if the inverse matrices should not be stored) until the last call of the preconditoining vmult function of the derived classes.

Definition at line 346 of file precondition_block.h.

◆ relaxation

double PreconditionBlock< MatrixType, typename MatrixType::value_type >::relaxation

protectedinherited

Relaxation parameter to be used by derived classes.

Definition at line 350 of file precondition_block.h.

◆ permutation

std::vector<size_type> PreconditionBlock< MatrixType, typename MatrixType::value_type >::permutation

protectedinherited

The permutation vector

Definition at line 355 of file precondition_block.h.

◆ inverse_permutation

std::vector<size_type> PreconditionBlock< MatrixType, typename MatrixType::value_type >::inverse_permutation

protectedinherited

The inverse permutation vector

Definition at line 360 of file precondition_block.h.

◆ inversion

Inversion PreconditionBlockBase< typename MatrixType::value_type >::inversion

protectedinherited

The method used for inverting blocks.

Definition at line 243 of file precondition_block_base.h.

◆ n_diagonal_blocks

unsigned int PreconditionBlockBase< typename MatrixType::value_type >::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

std::vector<FullMatrix<typename MatrixType::value_type > > PreconditionBlockBase< typename MatrixType::value_type >::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

std::vector<Householder<typename MatrixType::value_type > > PreconditionBlockBase< typename MatrixType::value_type >::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

std::vector<LAPACKFullMatrix<typename MatrixType::value_type > > PreconditionBlockBase< typename MatrixType::value_type >::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

std::vector<FullMatrix<typename MatrixType::value_type > > PreconditionBlockBase< typename MatrixType::value_type >::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

bool PreconditionBlockBase< typename MatrixType::value_type >::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

bool PreconditionBlockBase< typename MatrixType::value_type >::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

bool PreconditionBlockBase< typename MatrixType::value_type >::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 files:

include/deal.II/lac/precondition_block.h
source/lac/precondition_block_ez.cc

Public Types

Public Member Functions

Protected Types

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Private Types

Private Attributes

Subscriptor functionality

Detailed Description

Permutations

Instantiations

Member Typedef Documentation

◆ value_type

Member Enumeration Documentation

◆ Inversion

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()

◆ ExcWrongBlockSize()

◆ ExcInverseMatricesAlreadyExist()

◆ 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()

◆ ExcDiagonalsNotStored()

◆ ExcInverseNotAvailable()

Member Data Documentation

◆ blocksize

◆ A

◆ relaxation

◆ permutation

◆ inverse_permutation

◆ inversion

◆ n_diagonal_blocks

◆ var_inverse_full

◆ var_inverse_householder

◆ var_inverse_svd

◆ var_diagonal

◆ var_store_diagonals

◆ var_same_diagonal

◆ var_inverses_ready