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

Inheritance diagram for PreconditionBlockBase< number >:

Public Types
enum	Inversion { gauss_jordan, householder, svd }

typedef types::global_dof_index	size_type

Public Member Functions
	PreconditionBlockBase (bool store_diagonals=false, Inversion method=gauss_jordan)

	~PreconditionBlockBase ()

void	clear ()

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

void	inverses_computed (bool are_they)

void	set_same_diagonal ()

bool	same_diagonal () const

bool	store_diagonals () const

bool	inverses_ready () const

bool	empty () const

unsigned int	size () const

number	el (size_type i, size_type j) 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)

Householder< number > &	inverse_householder (size_type i)

LAPACKFullMatrix< number > &	inverse_svd (size_type i)

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

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

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

std::size_t	memory_consumption () const

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

static ::ExceptionBase &	ExcInverseNotAvailable ()

Protected Attributes
Inversion	inversion

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

Detailed Description

template<typename number>
class PreconditionBlockBase< number >

A class storing the inverse diagonal blocks for block preconditioners and block relaxation methods.

This class does the book keeping for preconditioners and relaxation methods based on inverting blocks on the diagonal of a matrix. It allows us to either store all diagonal blocks and their inverses or the same block for each entry, and it keeps track of the choice. Thus, after initializing it and filling the inverse diagonal blocks correctly, a derived class can use inverse() with an integer argument referring to the block number.

Additionally, it allows the storage of the original diagonal blocks, not only the inverses. These are for instance used in the intermediate step of the SSOR preconditioner.

Author: Guido Kanschat

Date: 2010

Definition at line 54 of file precondition_block_base.h.

Member Typedef Documentation

◆ size_type

template<typename number>

typedef types::global_dof_index PreconditionBlockBase< number >::size_type

Declare type for container size.

Definition at line 60 of file precondition_block_base.h.

Member Enumeration Documentation

◆ Inversion

template<typename number>

enum PreconditionBlockBase::Inversion

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 66 of file precondition_block_base.h.

Constructor & Destructor Documentation

◆ PreconditionBlockBase()

template<typename number >

PreconditionBlockBase< number >::PreconditionBlockBase	(	bool	store_diagonals = `false`,
		Inversion	method = `gauss_jordan`
	)

inline

Constructor initializing default values.

Definition at line 296 of file precondition_block_base.h.

◆ ~PreconditionBlockBase()

template<typename number>

PreconditionBlockBase< number >::~PreconditionBlockBase ( )

The virtual destructor

Member Function Documentation

◆ clear()

template<typename number >

void PreconditionBlockBase< number >::clear ( )

inline

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

Definition at line 310 of file precondition_block_base.h.

◆ reinit()

template<typename number >

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

inline

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 328 of file precondition_block_base.h.

◆ inverses_computed()

template<typename number >

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

inline

Tell the class that inverses are computed.

Definition at line 602 of file precondition_block_base.h.

◆ set_same_diagonal()

template<typename number>

void PreconditionBlockBase< number >::set_same_diagonal ( )

Use only the inverse of the first diagonal block to save memory and computation time.

Possible applications: computing on a cartesian grid, all diagonal blocks are the same or all diagonal blocks are at least similar and inversion of one of them still yields a preconditioner.

◆ same_diagonal()

template<typename number >

bool PreconditionBlockBase< number >::same_diagonal ( ) const

inline

Does the matrix use only one diagonal block?

Definition at line 586 of file precondition_block_base.h.

◆ store_diagonals()

template<typename number >

bool PreconditionBlockBase< number >::store_diagonals ( ) const

inline

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

Definition at line 594 of file precondition_block_base.h.

◆ inverses_ready()

template<typename number >

bool PreconditionBlockBase< number >::inverses_ready ( ) const

inline

Return true, if inverses are ready for use.

Definition at line 610 of file precondition_block_base.h.

◆ empty()

template<typename number>

bool PreconditionBlockBase< number >::empty ( ) const

Check whether the object is empty.

◆ size()

template<typename number >

unsigned int PreconditionBlockBase< number >::size ( ) const

inline

The number of blocks.

Definition at line 407 of file precondition_block_base.h.

◆ el()

template<typename number>

number PreconditionBlockBase< number >::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.

◆ inverse_vmult()

template<typename number >

template<typename number2 >

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

inline

Multiply with the inverse block at position i.

Definition at line 416 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

inline

Multiply with the transposed inverse block at position i.

Definition at line 445 of file precondition_block_base.h.

◆ inverse() [1/2]

template<typename number >

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

inline

Access to the inverse diagonal blocks if Inversion is gauss_jordan.

Definition at line 527 of file precondition_block_base.h.

◆ inverse_householder() [1/2]

template<typename number >

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

inline

Access to the inverse diagonal blocks if Inversion is householder.

Definition at line 542 of file precondition_block_base.h.

◆ inverse_svd() [1/2]

template<typename number >

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

inline

Access to the inverse diagonal blocks if Inversion is householder.

Definition at line 557 of file precondition_block_base.h.

◆ inverse() [2/2]

template<typename number >

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

inline

Access to the inverse diagonal blocks.

Definition at line 473 of file precondition_block_base.h.

◆ inverse_householder() [2/2]

template<typename number >

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

inline

Access to the inverse diagonal blocks if Inversion is householder.

Definition at line 486 of file precondition_block_base.h.

◆ inverse_svd() [2/2]

template<typename number >

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

inline

Access to the inverse diagonal blocks if Inversion is householder.

Definition at line 499 of file precondition_block_base.h.

◆ diagonal() [1/2]

template<typename number >

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

inline

Access to the diagonal blocks.

Definition at line 572 of file precondition_block_base.h.

◆ diagonal() [2/2]

template<typename number >

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

inline

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 ( ) const

inline

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 618 of file precondition_block_base.h.

◆ memory_consumption()

template<typename number >

std::size_t PreconditionBlockBase< number >::memory_consumption ( ) const

inline

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

Definition at line 666 of file precondition_block_base.h.

Member Data Documentation

◆ inversion

template<typename number>

Inversion PreconditionBlockBase< number >::inversion

protected

The method used for inverting blocks.

Definition at line 235 of file precondition_block_base.h.

◆ n_diagonal_blocks

template<typename number>

unsigned int PreconditionBlockBase< number >::n_diagonal_blocks

private

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

Definition at line 241 of file precondition_block_base.h.

◆ var_inverse_full

template<typename number>

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

private

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 249 of file precondition_block_base.h.

◆ var_inverse_householder

template<typename number>

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

private

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 257 of file precondition_block_base.h.

◆ var_inverse_svd

template<typename number>

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

private

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 265 of file precondition_block_base.h.

◆ var_diagonal

template<typename number>

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

private

Storage of the original diagonal blocks.

Used by the blocked SSOR method.

Definition at line 272 of file precondition_block_base.h.

◆ var_store_diagonals

template<typename number>

bool PreconditionBlockBase< number >::var_store_diagonals

private

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

Definition at line 278 of file precondition_block_base.h.

◆ var_same_diagonal

template<typename number>

bool PreconditionBlockBase< number >::var_same_diagonal

private

This is true, if only one inverse is stored.

Definition at line 283 of file precondition_block_base.h.

◆ var_inverses_ready

template<typename number>

bool PreconditionBlockBase< number >::var_inverses_ready

private

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

Definition at line 289 of file precondition_block_base.h.

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

deal.II/lac/precondition_block_base.h

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Private Attributes

Detailed Description

template<typename number> class PreconditionBlockBase< number >

Member Typedef Documentation

◆ size_type

Member Enumeration Documentation

◆ Inversion

Constructor & Destructor Documentation

◆ PreconditionBlockBase()

◆ ~PreconditionBlockBase()

Member Function Documentation

◆ clear()

◆ reinit()

◆ inverses_computed()

◆ set_same_diagonal()

◆ same_diagonal()

◆ store_diagonals()

◆ inverses_ready()

◆ empty()

◆ size()

◆ el()

◆ inverse_vmult()

◆ inverse_Tvmult()

◆ inverse() [1/2]

◆ inverse_householder() [1/2]

◆ inverse_svd() [1/2]

◆ inverse() [2/2]

◆ inverse_householder() [2/2]

◆ inverse_svd() [2/2]

◆ diagonal() [1/2]

◆ diagonal() [2/2]

◆ log_statistics()

◆ memory_consumption()

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

template<typename number>
class PreconditionBlockBase< number >