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

Inheritance diagram for SparseILU< number >:

Public Types
using	size_type = typename SparseLUDecomposition< number >::size_type

using	AdditionalData = typename SparseLUDecomposition< number >::AdditionalData

Public Types inherited from SparseLUDecomposition< number >
using	size_type = typename SparseMatrix< number >::size_type

Public Member Functions
	SparseILU ()=default

template<typename somenumber >
void	initialize (const SparseMatrix< somenumber > &matrix, const AdditionalData &parameters=AdditionalData())

template<typename somenumber >
void	vmult (Vector< somenumber > &dst, const Vector< somenumber > &src) const

template<typename somenumber >
void	Tvmult (Vector< somenumber > &dst, const Vector< somenumber > &src) const

std::size_t	memory_consumption () const override

Public Member Functions inherited from SparseLUDecomposition< number >
virtual	~SparseLUDecomposition () override=0

virtual void	clear () override

template<typename somenumber >
void	initialize (const SparseMatrix< somenumber > &matrix, const AdditionalData parameters)

bool	empty () const

size_type	m () const

size_type	n () const

template<class OutVector , class InVector >
void	vmult_add (OutVector &dst, const InVector &src) const

template<class OutVector , class InVector >
void	Tvmult_add (OutVector &dst, const InVector &src) const

Public Member Functions inherited from Subscriptor
	Subscriptor ()

	Subscriptor (const Subscriptor &)

	Subscriptor (Subscriptor &&) noexcept

virtual	~Subscriptor ()

Subscriptor &	operator= (const Subscriptor &)

Subscriptor &	operator= (Subscriptor &&) noexcept

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 Public Member Functions
static ::ExceptionBase &	ExcInvalidStrengthening (double arg1)

static ::ExceptionBase &	ExcZeroPivot (size_type arg1)

Static Public Member Functions inherited from SparseLUDecomposition< number >
static ::ExceptionBase &	ExcInvalidStrengthening (double arg1)

Static Public Member Functions inherited from Subscriptor
static ::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)

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

Additional Inherited Members
Protected Types inherited from SparseMatrix< number >
using	size_type = types::global_dof_index

using	value_type = number

using	real_type = typename numbers::NumberTraits< number >::real_type

using	const_iterator = SparseMatrixIterators::Iterator< number, true >

using	iterator = SparseMatrixIterators::Iterator< number, false >

Protected Member Functions inherited from SparseLUDecomposition< number >
	SparseLUDecomposition ()

template<typename somenumber >
void	copy_from (const SparseMatrix< somenumber > &matrix)

virtual void	strengthen_diagonal_impl ()

virtual number	get_strengthen_diagonal (const number rowsum, const size_type row) const

void	prebuild_lower_bound ()

Protected Member Functions inherited from SparseMatrix< number >
void	prepare_add ()

void	prepare_set ()

	SparseMatrix ()

	SparseMatrix (const SparseMatrix &)

	SparseMatrix (SparseMatrix< number > &&m) noexcept

	SparseMatrix (const SparsityPattern &sparsity)

	SparseMatrix (const SparsityPattern &sparsity, const IdentityMatrix &id)

virtual	~SparseMatrix () override

SparseMatrix< number > &	operator= (const SparseMatrix< number > &)

SparseMatrix< number > &	operator= (SparseMatrix< number > &&m) noexcept

SparseMatrix< number > &	operator= (const IdentityMatrix &id)

SparseMatrix &	operator= (const double d)

virtual void	reinit (const SparsityPattern &sparsity)

bool	empty () const

size_type	m () const

size_type	n () const

size_type	get_row_length (const size_type row) const

std::size_t	n_nonzero_elements () const

std::size_t	n_actually_nonzero_elements (const double threshold=0.) const

const SparsityPattern &	get_sparsity_pattern () const

std::size_t	memory_consumption () const

void	compress (::VectorOperation::values)

void	set (const size_type i, const size_type j, const number value)

template<typename number2 >
void	set (const std::vector< size_type > &indices, const FullMatrix< number2 > &full_matrix, const bool elide_zero_values=false)

template<typename number2 >
void	set (const std::vector< size_type > &row_indices, const std::vector< size_type > &col_indices, const FullMatrix< number2 > &full_matrix, const bool elide_zero_values=false)

template<typename number2 >
void	set (const size_type row, const std::vector< size_type > &col_indices, const std::vector< number2 > &values, const bool elide_zero_values=false)

template<typename number2 >
void	set (const size_type row, const size_type n_cols, const size_type col_indices, const number2 values, const bool elide_zero_values=false)

void	add (const size_type i, const size_type j, const number value)

template<typename number2 >
void	add (const std::vector< size_type > &indices, const FullMatrix< number2 > &full_matrix, const bool elide_zero_values=true)

template<typename number2 >
void	add (const std::vector< size_type > &row_indices, const std::vector< size_type > &col_indices, const FullMatrix< number2 > &full_matrix, const bool elide_zero_values=true)

template<typename number2 >
void	add (const size_type row, const std::vector< size_type > &col_indices, const std::vector< number2 > &values, const bool elide_zero_values=true)

template<typename number2 >
void	add (const size_type row, const size_type n_cols, const size_type col_indices, const number2 values, const bool elide_zero_values=true, const bool col_indices_are_sorted=false)

SparseMatrix &	operator*= (const number factor)

SparseMatrix &	operator/= (const number factor)

void	symmetrize ()

template<typename somenumber >
SparseMatrix< number > &	copy_from (const SparseMatrix< somenumber > &source)

template<typename ForwardIterator >
void	copy_from (const ForwardIterator begin, const ForwardIterator end)

template<typename somenumber >
void	copy_from (const FullMatrix< somenumber > &matrix)

SparseMatrix< number > &	copy_from (const TrilinosWrappers::SparseMatrix &matrix)

template<typename somenumber >
void	add (const number factor, const SparseMatrix< somenumber > &matrix)

const number &	operator() (const size_type i, const size_type j) const

number &	operator() (const size_type i, const size_type j)

number	el (const size_type i, const size_type j) const

number	diag_element (const size_type i) const

number &	diag_element (const size_type i)

template<class OutVector , class InVector >
void	vmult (OutVector &dst, const InVector &src) const

template<class OutVector , class InVector >
void	Tvmult (OutVector &dst, const InVector &src) const

template<class OutVector , class InVector >
void	vmult_add (OutVector &dst, const InVector &src) const

template<class OutVector , class InVector >
void	Tvmult_add (OutVector &dst, const InVector &src) const

template<typename somenumber >
somenumber	matrix_norm_square (const Vector< somenumber > &v) const

template<typename somenumber >
somenumber	matrix_scalar_product (const Vector< somenumber > &u, const Vector< somenumber > &v) const

template<typename somenumber >
somenumber	residual (Vector< somenumber > &dst, const Vector< somenumber > &x, const Vector< somenumber > &b) const

template<typename numberB , typename numberC >
void	mmult (SparseMatrix< numberC > &C, const SparseMatrix< numberB > &B, const Vector< number > &V=Vector< number >(), const bool rebuild_sparsity_pattern=true) const

template<typename numberB , typename numberC >
void	Tmmult (SparseMatrix< numberC > &C, const SparseMatrix< numberB > &B, const Vector< number > &V=Vector< number >(), const bool rebuild_sparsity_pattern=true) const

real_type	l1_norm () const

real_type	linfty_norm () const

real_type	frobenius_norm () const

template<typename somenumber >
void	precondition_Jacobi (Vector< somenumber > &dst, const Vector< somenumber > &src, const number omega=1.) const

template<typename somenumber >
void	precondition_SSOR (Vector< somenumber > &dst, const Vector< somenumber > &src, const number omega=1., const std::vector< std::size_t > &pos_right_of_diagonal=std::vector< std::size_t >()) const

template<typename somenumber >
void	precondition_SOR (Vector< somenumber > &dst, const Vector< somenumber > &src, const number om=1.) const

template<typename somenumber >
void	precondition_TSOR (Vector< somenumber > &dst, const Vector< somenumber > &src, const number om=1.) const

template<typename somenumber >
void	SSOR (Vector< somenumber > &v, const number omega=1.) const

template<typename somenumber >
void	SOR (Vector< somenumber > &v, const number om=1.) const

template<typename somenumber >
void	TSOR (Vector< somenumber > &v, const number om=1.) const

template<typename somenumber >
void	PSOR (Vector< somenumber > &v, const std::vector< size_type > &permutation, const std::vector< size_type > &inverse_permutation, const number om=1.) const

template<typename somenumber >
void	TPSOR (Vector< somenumber > &v, const std::vector< size_type > &permutation, const std::vector< size_type > &inverse_permutation, const number om=1.) const

template<typename somenumber >
void	Jacobi_step (Vector< somenumber > &v, const Vector< somenumber > &b, const number om=1.) const

template<typename somenumber >
void	SOR_step (Vector< somenumber > &v, const Vector< somenumber > &b, const number om=1.) const

template<typename somenumber >
void	TSOR_step (Vector< somenumber > &v, const Vector< somenumber > &b, const number om=1.) const

template<typename somenumber >
void	SSOR_step (Vector< somenumber > &v, const Vector< somenumber > &b, const number om=1.) const

const_iterator	begin () const

iterator	begin ()

const_iterator	end () const

iterator	end ()

const_iterator	begin (const size_type r) const

iterator	begin (const size_type r)

const_iterator	end (const size_type r) const

iterator	end (const size_type r)

template<class StreamType >
void	print (StreamType &out, const bool across=false, const bool diagonal_first=true) const

void	print_formatted (std::ostream &out, const unsigned int precision=3, const bool scientific=true, const unsigned int width=0, const char *zero_string=" ", const double denominator=1.) const

void	print_pattern (std::ostream &out, const double threshold=0.) const

void	block_write (std::ostream &out) const

void	block_read (std::istream &in)

Protected Member Functions inherited from Subscriptor
	Subscriptor ()

	Subscriptor (const Subscriptor &)

	Subscriptor (Subscriptor &&) noexcept

virtual	~Subscriptor ()

Subscriptor &	operator= (const Subscriptor &)

Subscriptor &	operator= (Subscriptor &&) noexcept

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 Protected Member Functions inherited from SparseMatrix< number >
static ::ExceptionBase &	ExcInvalidIndex (int arg1, int arg2)

static ::ExceptionBase &	ExcDifferentSparsityPatterns ()

static ::ExceptionBase &	ExcIteratorRange (int arg1, int arg2)

static ::ExceptionBase &	ExcSourceEqualsDestination ()

Static Protected Member Functions inherited from Subscriptor
static ::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)

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

Protected Attributes inherited from SparseLUDecomposition< number >
double	strengthen_diagonal

std::vector< const size_type * >	prebuilt_lower_bound

Related Functions inherited from SparseMatrix< number >
template<typename Number >
void	sum (const SparseMatrix< Number > &local, const MPI_Comm &mpi_communicator, SparseMatrix< Number > &global)

Detailed Description

template<typename number>
class SparseILU< number >

This class computes an Incomplete LU (ILU) decomposition of a sparse matrix, using either the same sparsity pattern or a different one. By incomplete we mean that unlike the exact decomposition, the incomplete one is also computed using sparse factors, and entries in the decomposition that do not fit into the given sparsity structure are discarded.

The algorithm used by this class is essentially a copy of the algorithm given in the book Y. Saad: "Iterative methods for sparse linear systems", second edition, in section 10.3.2.

Usage and state management

Refer to SparseLUDecomposition documentation for suggested usage and state management. This class is used in the step-22 tutorial program.

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).

Author: Wolfgang Bangerth, 2008, 2009; unified interface: Ralf Hartmann

Definition at line 61 of file sparse_ilu.h.

Member Typedef Documentation

◆ size_type

template<typename number>

using SparseILU< number >::size_type = typename SparseLUDecomposition<number>::size_type

Declare type for container size.

Definition at line 67 of file sparse_ilu.h.

◆ AdditionalData

template<typename number>

using SparseILU< number >::AdditionalData = typename SparseLUDecomposition<number>::AdditionalData

Make SparseLUDecomposition::AdditionalData accessible to this class as well.

Definition at line 81 of file sparse_ilu.h.

Constructor & Destructor Documentation

◆ SparseILU()

template<typename number>

SparseILU< number >::SparseILU ( )

default

Constructor. Does nothing.

Call the initialize function before using this object as preconditioner.

Member Function Documentation

◆ initialize()

template<typename number>

template<typename somenumber >

template void SparseILU< number >::initialize< float >	(	const SparseMatrix< somenumber > &	matrix,
		const AdditionalData &	parameters = `AdditionalData()`
	)

Perform the incomplete LU factorization of the given matrix.

This function needs to be called before an object of this class is used as preconditioner.

For more details about possible parameters, see the class documentation of SparseLUDecomposition and the documentation of the SparseLUDecomposition::AdditionalData class.

According to the parameters, this function creates a new SparsityPattern or keeps the previous sparsity or takes the sparsity given by the user to data. Then, this function performs the LU decomposition.

After this function is called the preconditioner is ready to be used.

◆ vmult()

template<typename number>

template<typename somenumber >

template void SparseILU< number >::vmult< float >	(	Vector< somenumber > &	dst,
		const Vector< somenumber > &	src
	)		const

Apply the incomplete decomposition, i.e. do one forward-backward step \(dst=(LU)^{-1}src\).

The initialize() function needs to be called before.

◆ Tvmult()

template<typename number>

template<typename somenumber >

template void SparseILU< number >::Tvmult< float >	(	Vector< somenumber > &	dst,
		const Vector< somenumber > &	src
	)		const

Apply the transpose of the incomplete decomposition, i.e. do one forward- backward step \(dst=(LU)^{-T}src\).

The initialize() function needs to be called before.

◆ memory_consumption()

template<typename number>

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

overridevirtual

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

Reimplemented from SparseLUDecomposition< number >.

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

deal.II/lac/sparse_ilu.h
source/lac/sparse_ilu.cc

Public Types

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

template<typename number> class SparseILU< number >

Usage and state management

Member Typedef Documentation

◆ size_type

◆ AdditionalData

Constructor & Destructor Documentation

◆ SparseILU()

Member Function Documentation

◆ initialize()

◆ vmult()

◆ Tvmult()

◆ memory_consumption()

template<typename number>
class SparseILU< number >