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

Inheritance diagram for SparseMIC< number >:

Public Types
typedef types::global_dof_index	size_type

typedef SparseLUDecomposition< number >::AdditionalData	AdditionalData

Public Types inherited from SparseLUDecomposition< number >
typedef SparseMatrix< number >::size_type	size_type

Public Member Functions
	SparseMIC ()

virtual	~SparseMIC ()

virtual void	clear ()

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

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

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 &&)

virtual	~Subscriptor ()

Subscriptor &	operator= (const Subscriptor &)

Subscriptor &	operator= (Subscriptor &&)

void	subscribe (const char *identifier=0) const

void	unsubscribe (const char *identifier=0) const

unsigned int	n_subscriptions () const

void	list_subscribers () const

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

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

static ::ExceptionBase &	ExcInvalidStrengthening (double arg1)

static ::ExceptionBase &	ExcDecompositionNotStable (int arg1, double arg2)

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, char *arg2, std::string &arg3)

static ::ExceptionBase &	ExcNoSubscriber (char arg1, char arg2)

Private Member Functions
number	get_rowsum (const size_type row) const

Private Attributes
std::vector< number >	diag

std::vector< number >	inv_diag

std::vector< number >	inner_sums

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

typedef number	value_type

typedef numbers::NumberTraits< number >::real_type	real_type

typedef SparseMatrixIterators::Iterator< number, true >	const_iterator

typedef SparseMatrixIterators::Iterator< number, false >	iterator

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)

	SparseMatrix (const SparsityPattern &sparsity)

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

virtual	~SparseMatrix ()

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

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

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)

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

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 &&)

virtual	~Subscriptor ()

Subscriptor &	operator= (const Subscriptor &)

Subscriptor &	operator= (Subscriptor &&)

void	subscribe (const char *identifier=0) const

void	unsubscribe (const char *identifier=0) const

unsigned int	n_subscriptions () 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, char *arg2, std::string &arg3)

static ::ExceptionBase &	ExcNoSubscriber (char arg1, char arg2)

Protected Attributes inherited from SparseLUDecomposition< number >
double	strengthen_diagonal

std::vector< const size_type * >	prebuilt_lower_bound

Detailed Description

template<typename number>
class SparseMIC< number >

Implementation of the Modified Incomplete Cholesky (MIC(0)) preconditioner for symmetric matrices. This class conforms to the state and usage specification in SparseLUDecomposition.

The decomposition

Let a symmetric, positive-definite, sparse matrix \(A\) be in the form \(A = D - L - L^T\), where \(D\) is the diagonal part of \(A\) and \(-L\) is a strictly lower triangular matrix. The MIC(0) decomposition of the matrix \(A\) is defined by \(B = (X-L)X^{-1}(X-L^T)\), where \(X\) is a diagonal matrix defined by the condition \(\text{rowsum}(A) = \text{rowsum}(B)\).

Author: Stephen "Cheffo" Kolaroff, 2002, unified interface: Ralf Hartmann 2003; extension for full compatibility with LinearOperator class: Jean-Paul Pelteret, 2015.

Definition at line 47 of file sparse_mic.h.

Member Typedef Documentation

◆ size_type

template<typename number >

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

Declare type for container size.

Definition at line 53 of file sparse_mic.h.

◆ AdditionalData

template<typename number >

typedef SparseLUDecomposition<number>::AdditionalData SparseMIC< number >::AdditionalData

Make the AdditionalData type in the base class accessible to this class as well.

Definition at line 78 of file sparse_mic.h.

Constructor & Destructor Documentation

◆ SparseMIC()

template<typename number >

SparseMIC< number >::SparseMIC ( )

Constructor. Does nothing, so you have to call decompose sometimes afterwards.

◆ ~SparseMIC()

template<typename number >

virtual SparseMIC< number >::~SparseMIC ( )

virtual

Destructor.

Member Function Documentation

◆ clear()

template<typename number >

virtual void SparseMIC< number >::clear ( )

virtual

Deletes all member variables. Leaves the class in the state that it had directly after calling the constructor

Reimplemented from SparseLUDecomposition< number >.

◆ initialize()

template<typename number >

template<typename somenumber >

template void SparseMIC< 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 MIC decomposition.

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

◆ vmult()

template<typename number >

template<typename somenumber >

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

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

Call initialize before calling this function.

◆ Tvmult()

template<typename number >

template<typename somenumber >

template void SparseMIC< 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 \(dst=(LU)^{-1}src\).

Call initialize before calling this function.

Note: This function has not yet been implemented

◆ memory_consumption()

template<typename number >

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

virtual

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

Reimplemented from SparseLUDecomposition< number >.

◆ get_rowsum()

template<typename number >

number SparseMIC< number >::get_rowsum ( const size_type row ) const

private

Compute the row-th "inner sum".

Member Data Documentation

◆ diag

template<typename number >

std::vector<number> SparseMIC< number >::diag

private

Values of the computed diagonal.

Definition at line 158 of file sparse_mic.h.

◆ inv_diag

template<typename number >

std::vector<number> SparseMIC< number >::inv_diag

private

Inverses of the the diagonal: precomputed for faster vmult.

Definition at line 163 of file sparse_mic.h.

◆ inner_sums

template<typename number >

std::vector<number> SparseMIC< number >::inner_sums

private

Values of the computed "inner sums", i.e. per-row sums of the elements laying on the right side of the diagonal.

Definition at line 169 of file sparse_mic.h.

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

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

Public Types

Public Member Functions

Static Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<typename number> class SparseMIC< number >

The decomposition

Member Typedef Documentation

◆ size_type

◆ AdditionalData

Constructor & Destructor Documentation

◆ SparseMIC()

◆ ~SparseMIC()

Member Function Documentation

◆ clear()

◆ initialize()

◆ vmult()

◆ Tvmult()

◆ memory_consumption()

◆ get_rowsum()

Member Data Documentation

◆ diag

◆ inv_diag

◆ inner_sums

template<typename number>
class SparseMIC< number >