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

Inheritance diagram for SparseMIC< number >:

Public Types
using	size_type = types::global_dof_index

using	AdditionalData = typename SparseLUDecomposition< number >::AdditionalData

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

Public Member Functions
	SparseMIC ()

virtual	~SparseMIC () override

virtual void	clear () override

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

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

static ::ExceptionBase &	ExcNoSubscriber (std::string arg1, std::string 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 >
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	print_as_numpy_arrays (std::ostream &out, const unsigned int precision=9) 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 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 49 of file sparse_mic.h.

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

include/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

template<typename number>
class SparseMIC< number >