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

Inheritance diagram for RelaxationBlock< MatrixType, InverseNumberType, VectorType >:

Classes
class	AdditionalData

Public Types
using	size_type = types::global_dof_index

Public Member Functions
void	initialize (const MatrixType &A, const AdditionalData &parameters)

void	clear ()

void	invert_diagblocks ()

Protected Types
enum	Inversion { gauss_jordan , householder , svd }

Protected Member Functions
void	do_step (VectorType &dst, const VectorType &prev, const VectorType &src, const bool backward) 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

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

std::size_t	memory_consumption () const

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

static ::ExceptionBase &	ExcInverseNotAvailable ()

Protected Attributes
SmartPointer< const MatrixType, RelaxationBlock< MatrixType, InverseNumberType, VectorType > >	A

SmartPointer< const AdditionalData, RelaxationBlock< MatrixType, InverseNumberType, VectorType > >	additional_data

Inversion	inversion

Private Types
using	number = typename MatrixType::value_type

using	value_type = InverseNumberType

Private Member Functions
void	block_kernel (const size_type block_begin, const size_type block_end)

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 MatrixType, typename InverseNumberType = typename MatrixType::value_type, typename VectorType = Vector<double>>
class RelaxationBlock< MatrixType, InverseNumberType, VectorType >

Base class for the implementation of overlapping, multiplicative Schwarz relaxation methods and smoothers.

This class uses the infrastructure provided by PreconditionBlockBase. It adds functions to initialize with a block list and to do the relaxation step. The actual relaxation method with the interface expected by SolverRelaxation and MGSmootherRelaxation is in the derived classes.

This class allows for more general relaxation methods than PreconditionBlock, since the index sets may be arbitrary and overlapping, while there only contiguous, disjoint sets of equal size are allowed. As a drawback, this class cannot be used as a preconditioner, since its implementation relies on a straight forward implementation of the Gauss- Seidel process.

Parallel computations require you to specify an initialized ghost vector in AdditionalData::temp_ghost_vector.

Definition at line 56 of file relaxation_block.h.

Member Typedef Documentation

◆ number

template<typename MatrixType , typename InverseNumberType = typename MatrixType::value_type, typename VectorType = Vector<double>>

using RelaxationBlock< MatrixType, InverseNumberType, VectorType >::number = typename MatrixType::value_type

private

Define number type of matrix.

Definition at line 62 of file relaxation_block.h.

◆ value_type

template<typename MatrixType , typename InverseNumberType = typename MatrixType::value_type, typename VectorType = Vector<double>>

using RelaxationBlock< MatrixType, InverseNumberType, VectorType >::value_type = InverseNumberType

private

Value type for inverse matrices.

Definition at line 67 of file relaxation_block.h.

◆ size_type

template<typename MatrixType , typename InverseNumberType = typename MatrixType::value_type, typename VectorType = Vector<double>>

using RelaxationBlock< MatrixType, InverseNumberType, VectorType >::size_type = types::global_dof_index

Declare type for container size.

Definition at line 73 of file relaxation_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

◆ initialize()

template<typename MatrixType , typename InverseNumberType = typename MatrixType::value_type, typename VectorType = Vector<double>>

void RelaxationBlock< MatrixType, InverseNumberType, VectorType >::initialize	(	const MatrixType &	A,
		const AdditionalData &	parameters
	)

Initialize matrix and additional information. In a second step, the inverses of the diagonal blocks may be computed.

Note that AdditionalData, different from other preconditioners, defines quite large objects, and that therefore the object is not copied, but rather a pointer is stored. Thus, the lifetime of additional_data hast to exceed the lifetime of this object.

◆ clear()

template<typename MatrixType , typename InverseNumberType = typename MatrixType::value_type, typename VectorType = Vector<double>>

void RelaxationBlock< MatrixType, InverseNumberType, VectorType >::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.

◆ invert_diagblocks()

template<typename MatrixType , typename InverseNumberType = typename MatrixType::value_type, typename VectorType = Vector<double>>

void RelaxationBlock< MatrixType, InverseNumberType, VectorType >::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.

◆ do_step()

template<typename MatrixType , typename InverseNumberType = typename MatrixType::value_type, typename VectorType = Vector<double>>

void RelaxationBlock< MatrixType, InverseNumberType, VectorType >::do_step	(	VectorType &	dst,
		const VectorType &	prev,
		const VectorType &	src,
		const bool	backward
	)		const

protected

Perform one block relaxation step.

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

◆ block_kernel()

template<typename MatrixType , typename InverseNumberType = typename MatrixType::value_type, typename VectorType = Vector<double>>

void RelaxationBlock< MatrixType, InverseNumberType, VectorType >::block_kernel	(	const size_type	block_begin,
		const size_type	block_end
	)

private

Computes (the inverse of) a range of blocks.

◆ 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.

◆ memory_consumption()

template<typename number >

std::size_t PreconditionBlockBase< number >::memory_consumption

inlineinherited

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

Definition at line 665 of file precondition_block_base.h.

Member Data Documentation

◆ A

template<typename MatrixType , typename InverseNumberType = typename MatrixType::value_type, typename VectorType = Vector<double>>

SmartPointer<const MatrixType, RelaxationBlock<MatrixType, InverseNumberType, VectorType> > RelaxationBlock< MatrixType, InverseNumberType, VectorType >::A

protected

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 preconditioning vmult function of the derived classes.

Definition at line 252 of file relaxation_block.h.

◆ additional_data

template<typename MatrixType , typename InverseNumberType = typename MatrixType::value_type, typename VectorType = Vector<double>>

SmartPointer<const AdditionalData, RelaxationBlock<MatrixType, InverseNumberType, VectorType> > RelaxationBlock< MatrixType, InverseNumberType, VectorType >::additional_data

protected

Control information.

Definition at line 259 of file relaxation_block.h.

◆ 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/relaxation_block.h

Classes

Public Types

Public Member Functions

Protected Types

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Private Types

Private Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ number

◆ value_type

◆ size_type

Member Enumeration Documentation

◆ Inversion

Member Function Documentation

◆ initialize()

◆ clear()

◆ invert_diagblocks()

◆ do_step()

◆ block_kernel()

◆ 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()

◆ memory_consumption()

Member Data Documentation

◆ A

◆ additional_data

◆ inversion

◆ n_diagonal_blocks

◆ var_inverse_full

◆ var_inverse_householder

◆ var_inverse_svd

◆ var_diagonal

◆ var_store_diagonals

◆ var_same_diagonal

◆ var_inverses_ready