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

Inheritance diagram for SparseDirectUMFPACK:

Classes
class	AdditionalData

Public Types
using	size_type = types::global_dof_index

Public Member Functions
	SparseDirectUMFPACK ()

	~SparseDirectUMFPACK () override

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

Setting up a sparse factorization
void	initialize (const SparsityPattern &sparsity_pattern)

template<class Matrix >
void	factorize (const Matrix &matrix)

template<class Matrix >
void	initialize (const Matrix &matrix, const AdditionalData additional_data=AdditionalData())

Functions that represent the inverse of a matrix
void	vmult (Vector< double > &dst, const Vector< double > &src) const

void	vmult (BlockVector< double > &dst, const BlockVector< double > &src) const

void	Tvmult (Vector< double > &dst, const Vector< double > &src) const

void	Tvmult (BlockVector< double > &dst, const BlockVector< double > &src) const

size_type	m () const

size_type	n () const

Functions that solve linear systems
void	solve (Vector< double > &rhs_and_solution, const bool transpose=false) const

void	solve (Vector< std::complex< double > > &rhs_and_solution, const bool transpose=false) const

void	solve (BlockVector< double > &rhs_and_solution, const bool transpose=false) const

void	solve (BlockVector< std::complex< double > > &rhs_and_solution, const bool transpose=false) const

template<class Matrix >
void	solve (const Matrix &matrix, Vector< double > &rhs_and_solution, const bool transpose=false)

template<class Matrix >
void	solve (const Matrix &matrix, Vector< std::complex< double > > &rhs_and_solution, const bool transpose=false)

template<class Matrix >
void	solve (const Matrix &matrix, BlockVector< double > &rhs_and_solution, const bool transpose=false)

template<class Matrix >
void	solve (const Matrix &matrix, BlockVector< std::complex< double > > &rhs_and_solution, const bool transpose=false)

Subscriptor functionality
Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class.
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

Static Public Member Functions
static ::ExceptionBase &	ExcUMFPACKError (std::string arg1, int arg2)

static ::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)

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

Private Types
using	map_value_type = decltype(counter_map)::value_type

using	map_iterator = decltype(counter_map)::iterator

Private Member Functions
void	clear ()

template<typename number >
void	sort_arrays (const SparseMatrixEZ< number > &)

template<typename number >
void	sort_arrays (const SparseMatrix< number > &)

template<typename number >
void	sort_arrays (const BlockSparseMatrix< number > &)

void	check_no_subscribers () const noexcept

Private Attributes
size_type	n_rows

size_type	n_cols

void *	symbolic_decomposition

void *	numeric_decomposition

std::vector< types::suitesparse_index >	Ap

std::vector< types::suitesparse_index >	Ai

std::vector< double >	Ax

std::vector< double >	Az

std::vector< double >	control

std::atomic< unsigned int >	counter

std::map< std::string, unsigned int >	counter_map

std::vector< std::atomic< bool > * >	validity_pointers

const std::type_info *	object_info

Static Private Attributes
static std::mutex	mutex

Detailed Description

This class provides an interface to the sparse direct solver UMFPACK, which is part of the SuiteSparse library (see this link). UMFPACK is a set of routines for solving non-symmetric sparse linear systems, Ax=b, using the Unsymmetric-pattern MultiFrontal method and direct sparse LU factorization. Matrices may have symmetric or unsymmetric sparsity patterns, and may have unsymmetric entries. The use of this class is explained in the step-22 and step-29 tutorial programs.

This matrix class implements the usual interface of preconditioners, that is a function initialize(const SparseMatrix<double>&matrix,const AdditionalData) for initializing and the whole set of vmult() functions common to all matrices. Implemented here are only vmult() and vmult_add(), which perform multiplication with the inverse matrix. Furthermore, this class provides an older interface, consisting of the functions factorize() and solve(). Both interfaces are interchangeable.

Note: This class exists if the UMFPACK interface was not explicitly disabled during configuration.; UMFPACK has its own license, independent of that of deal.II. If you want to use the UMFPACK you have to accept that license. It is linked to from the deal.II ReadMe file. UMFPACK is included courtesy of its author, Timothy A. Davis.

Instantiations

There are instantiations of this class for SparseMatrix<double>, SparseMatrix<float>, SparseMatrixEZ<float>, SparseMatrixEZ<double>, BlockSparseMatrix<double>, and BlockSparseMatrix<float>.

This class is not instantiated for the matrix types in namespace PETScWrappers or TrilinosWrappers. However, PETScWrappers::SparseDirectMUMPS can be used for PETSc matrices, and in fact even works for parallel computations.

Definition at line 91 of file sparse_direct.h.

Member Typedef Documentation

◆ size_type

using SparseDirectUMFPACK::size_type = types::global_dof_index

Declare type for container size.

Definition at line 97 of file sparse_direct.h.

◆ map_value_type

using Subscriptor::map_value_type = decltype(counter_map)::value_type

privateinherited

The data type used in counter_map.

Definition at line 229 of file subscriptor.h.

◆ map_iterator

using Subscriptor::map_iterator = decltype(counter_map)::iterator

privateinherited

The iterator type used in counter_map.

Definition at line 234 of file subscriptor.h.

Constructor & Destructor Documentation

◆ SparseDirectUMFPACK()

SparseDirectUMFPACK::SparseDirectUMFPACK ( )

Constructor. See the documentation of this class for the meaning of the parameters to this function.

Definition at line 73 of file sparse_direct.cc.

◆ ~SparseDirectUMFPACK()

SparseDirectUMFPACK::~SparseDirectUMFPACK ( )

override

Destructor.

Definition at line 60 of file sparse_direct.cc.

Member Function Documentation

◆ initialize() [1/2]

void SparseDirectUMFPACK::initialize ( const SparsityPattern & sparsity_pattern )

This function does nothing. It is only here to provide a interface consistent with other sparse direct solvers.

Definition at line 67 of file sparse_direct.cc.

◆ factorize()

template<class Matrix >

void SparseDirectUMFPACK::factorize ( const Matrix & matrix )

Factorize the matrix. This function may be called multiple times for different matrices, after the object of this class has been initialized for a certain sparsity pattern. You may therefore save some computing time if you want to invert several matrices with the same sparsity pattern. However, note that the bulk of the computing time is actually spent in the factorization, so this functionality may not always be of large benefit.

In contrast to the other direct solver classes, the initialization method does nothing. Therefore initialize is not automatically called by this method, when the initialization step has not been performed yet.

This function copies the contents of the matrix into its own storage; the matrix can therefore be deleted after this operation, even if subsequent solves are required.

Definition at line 252 of file sparse_direct.cc.

◆ initialize() [2/2]

template<class Matrix >

void SparseDirectUMFPACK::initialize	(	const Matrix &	matrix,
		const AdditionalData	additional_data = AdditionalData() )

Initialize memory and call SparseDirectUMFPACK::factorize.

Definition at line 788 of file sparse_direct.cc.

◆ vmult() [1/2]

void SparseDirectUMFPACK::vmult	(	Vector< double > &	dst,
		const Vector< double > &	src ) const

Preconditioner interface function. Usually, given the source vector, this method returns an approximate solution of Ax = b. As this class provides a wrapper to a direct solver, here it is actually the exact solution (exact within the range of numerical accuracy of course).

In other words, this function actually multiplies with the exact inverse of the matrix, \(A^{-1}\).

Definition at line 795 of file sparse_direct.cc.

◆ vmult() [2/2]

void SparseDirectUMFPACK::vmult	(	BlockVector< double > &	dst,
		const BlockVector< double > &	src ) const

Same as before, but for block vectors.

Definition at line 804 of file sparse_direct.cc.

◆ Tvmult() [1/2]

void SparseDirectUMFPACK::Tvmult	(	Vector< double > &	dst,
		const Vector< double > &	src ) const

Same as before, but uses the transpose of the matrix, i.e. this function multiplies with \(A^{-T}\).

Definition at line 813 of file sparse_direct.cc.

◆ Tvmult() [2/2]

void SparseDirectUMFPACK::Tvmult	(	BlockVector< double > &	dst,
		const BlockVector< double > &	src ) const

Same as before, but for block vectors

Definition at line 823 of file sparse_direct.cc.

◆ m()

SparseDirectUMFPACK::size_type SparseDirectUMFPACK::m ( ) const

Return the dimension of the codomain (or range) space. Note that the matrix is of dimension \(m \times n\).

Definition at line 831 of file sparse_direct.cc.

◆ n()

SparseDirectUMFPACK::size_type SparseDirectUMFPACK::n ( ) const

Return the dimension of the domain space. Note that the matrix is of dimension \(m \times n\).

Definition at line 838 of file sparse_direct.cc.

◆ solve() [1/8]

void SparseDirectUMFPACK::solve	(	Vector< double > &	rhs_and_solution,
		const bool	transpose = false ) const

Solve for a certain right hand side vector. This function may be called multiple times for different right hand side vectors after the matrix has been factorized. This yields substantial savings in computing time, since the actual solution is fast, compared to the factorization of the matrix.

The solution will be returned in place of the right hand side vector.

Parameters

[in,out]	rhs_and_solution	A vector that contains the right hand side \(b\) of a linear system \(Ax=b\) upon calling this function, and that contains the solution \(x\) of the linear system after calling this function.
[in]	transpose	If set to true, this function solves the linear \(A^T x = b\) instead of \(Ax=b\).

Precondition: You need to call factorize() before this function can be called.

Definition at line 377 of file sparse_direct.cc.

◆ solve() [2/8]

void SparseDirectUMFPACK::solve	(	Vector< std::complex< double > > &	rhs_and_solution,
		const bool	transpose = false ) const

Like the previous function, but for a complex-valued right hand side and solution vector.

If the matrix that was previously factorized had complex-valued entries, then the rhs_and_solution vector will, upon return from this function, simply contain the solution of the linear system \(Ax=b\). If the matrix was real-valued, then this is also true, but the solution will simply be computed by applying the factorized \(A^{-1}\) to both the real and imaginary parts of the right hand side vector.

Definition at line 417 of file sparse_direct.cc.

◆ solve() [3/8]

void SparseDirectUMFPACK::solve	(	BlockVector< double > &	rhs_and_solution,
		const bool	transpose = false ) const

Same as before, but for block vectors.

Definition at line 532 of file sparse_direct.cc.

◆ solve() [4/8]

void SparseDirectUMFPACK::solve	(	BlockVector< std::complex< double > > &	rhs_and_solution,
		const bool	transpose = false ) const

Same as before, but for complex-valued block vectors.

Definition at line 547 of file sparse_direct.cc.

◆ solve() [5/8]

template<class Matrix >

void SparseDirectUMFPACK::solve	(	const Matrix &	matrix,
		Vector< double > &	rhs_and_solution,
		const bool	transpose = false )

Call the two functions factorize() and solve() in that order, i.e. perform the whole solution process for the given right hand side vector.

The solution will be returned in place of the right hand side vector.

Definition at line 573 of file sparse_direct.cc.

◆ solve() [6/8]

template<class Matrix >

void SparseDirectUMFPACK::solve	(	const Matrix &	matrix,
		Vector< std::complex< double > > &	rhs_and_solution,
		const bool	transpose = false )

Same as before, but for complex-valued solution vectors.

Definition at line 585 of file sparse_direct.cc.

◆ solve() [7/8]

template<class Matrix >

void SparseDirectUMFPACK::solve	(	const Matrix &	matrix,
		BlockVector< double > &	rhs_and_solution,
		const bool	transpose = false )

Same as before, but for block vectors.

Definition at line 609 of file sparse_direct.cc.

◆ solve() [8/8]

template<class Matrix >

void SparseDirectUMFPACK::solve	(	const Matrix &	matrix,
		BlockVector< std::complex< double > > &	rhs_and_solution,
		const bool	transpose = false )

Same as before, but for complex-valued block vectors.

Definition at line 621 of file sparse_direct.cc.

◆ clear()

void SparseDirectUMFPACK::clear ( )

private

Free all memory that hasn't been freed yet.

Definition at line 86 of file sparse_direct.cc.

◆ sort_arrays() [1/3]

template<typename number >

void SparseDirectUMFPACK::sort_arrays ( const SparseMatrixEZ< number > & matrix )

private

Make sure that the arrays Ai and Ap are sorted in each row. UMFPACK wants it this way. We need to have three versions of this function, one for the usual SparseMatrix, one for the SparseMatrixEZ, and one for the BlockSparseMatrix classes

Definition at line 174 of file sparse_direct.cc.

◆ sort_arrays() [2/3]

template<typename number >

void SparseDirectUMFPACK::sort_arrays ( const SparseMatrix< number > & matrix )

private

Definition at line 128 of file sparse_direct.cc.

◆ sort_arrays() [3/3]

template<typename number >

void SparseDirectUMFPACK::sort_arrays ( const BlockSparseMatrix< number > & matrix )

private

Definition at line 203 of file sparse_direct.cc.

◆ subscribe()

void Subscriptor::subscribe	(	std::atomic< bool > *const	validity,
		const std::string &	identifier = "" ) const

inherited

Subscribes a user of the object by storing the pointer validity. The subscriber may be identified by text supplied as identifier.

Definition at line 135 of file subscriptor.cc.

◆ unsubscribe()

void Subscriptor::unsubscribe	(	std::atomic< bool > *const	validity,
		const std::string &	identifier = "" ) const

inherited

Unsubscribes a user from the object.

Note: The identifier and the validity pointer must be the same as the one supplied to subscribe().

Definition at line 155 of file subscriptor.cc.

◆ n_subscriptions()

unsigned int Subscriptor::n_subscriptions ( ) const

inlineinherited

Return the present number of subscriptions to this object. This allows to use this class for reference counted lifetime determination where the last one to unsubscribe also deletes the object.

Definition at line 300 of file subscriptor.h.

◆ list_subscribers() [1/2]

template<typename StreamType >

void Subscriptor::list_subscribers ( StreamType & stream ) const

inlineinherited

List the subscribers to the input stream.

Definition at line 317 of file subscriptor.h.

◆ list_subscribers() [2/2]

void Subscriptor::list_subscribers ( ) const

inherited

List the subscribers to deallog.

Definition at line 203 of file subscriptor.cc.

◆ serialize()

template<class Archive >

void Subscriptor::serialize	(	Archive &	ar,
		const unsigned int	version )

inlineinherited

Read or write the data of this object to or from a stream for the purpose of serialization using the BOOST serialization library.

This function does not actually serialize any of the member variables of this class. The reason is that what this class stores is only who subscribes to this object, but who does so at the time of storing the contents of this object does not necessarily have anything to do with who subscribes to the object when it is restored. Consequently, we do not want to overwrite the subscribers at the time of restoring, and then there is no reason to write the subscribers out in the first place.

Definition at line 309 of file subscriptor.h.

◆ check_no_subscribers()

void Subscriptor::check_no_subscribers ( ) const

privatenoexceptinherited

Check that there are no objects subscribing to this object. If this check passes then it is safe to destroy the current object. It this check fails then this function will either abort or print an error message to deallog (by using the AssertNothrow mechanism), but will not throw an exception.

Note: Since this function is just a consistency check it does nothing in release mode.; If this function is called when there is an uncaught exception then, rather than aborting, this function prints an error message to the standard error stream and returns.

Definition at line 52 of file subscriptor.cc.

Member Data Documentation

◆ n_rows

size_type SparseDirectUMFPACK::n_rows

private

The dimension of the range space, i.e., the number of rows of the matrix.

Definition at line 368 of file sparse_direct.h.

◆ n_cols

size_type SparseDirectUMFPACK::n_cols

private

The dimension of the domain space, i.e., the number of columns of the matrix.

Definition at line 374 of file sparse_direct.h.

◆ symbolic_decomposition

void* SparseDirectUMFPACK::symbolic_decomposition

private

The UMFPACK routines allocate objects in which they store information about symbolic and numeric values of the decomposition. The actual data type of these objects is opaque, and only passed around as void pointers.

Definition at line 381 of file sparse_direct.h.

◆ numeric_decomposition

void* SparseDirectUMFPACK::numeric_decomposition

private

Definition at line 382 of file sparse_direct.h.

◆ Ap

std::vector<types::suitesparse_index> SparseDirectUMFPACK::Ap

private

The arrays in which we store the data for the solver. These are documented in the descriptions of the umfpack_*_symbolic() and umfpack_*_numeric() functions, but in short:

Ap is the array saying which row starts where in Ai
Ai is the array that stores the column indices of nonzero entries
Ax is the array that stores the values of nonzero entries; if the matrix is complex-valued, then it stores the real parts
Az is the array that stores the imaginary parts of nonzero entries, and is used only if the matrix is complex-valued.

Definition at line 419 of file sparse_direct.h.

◆ Ai

std::vector<types::suitesparse_index> SparseDirectUMFPACK::Ai

private

Definition at line 420 of file sparse_direct.h.

◆ Ax

std::vector<double> SparseDirectUMFPACK::Ax

private

Definition at line 421 of file sparse_direct.h.

◆ Az

std::vector<double> SparseDirectUMFPACK::Az

private

Definition at line 422 of file sparse_direct.h.

◆ control

std::vector<double> SparseDirectUMFPACK::control

private

Control and work arrays for the solver routines.

Definition at line 427 of file sparse_direct.h.

◆ counter

std::atomic<unsigned int> Subscriptor::counter

mutableprivateinherited

Store the number of objects which subscribed to this object. Initially, this number is zero, and upon destruction it shall be zero again (i.e. all objects which subscribed should have unsubscribed again).

The creator (and owner) of an object is counted in the map below if HE manages to supply identification.

We use the mutable keyword in order to allow subscription to constant objects also.

This counter may be read from and written to concurrently in multithreaded code: hence we use the std::atomic class template.

Definition at line 218 of file subscriptor.h.

◆ counter_map

std::map<std::string, unsigned int> Subscriptor::counter_map

mutableprivateinherited

In this map, we count subscriptions for each different identification string supplied to subscribe().

Definition at line 224 of file subscriptor.h.

◆ validity_pointers

std::vector<std::atomic<bool> *> Subscriptor::validity_pointers

mutableprivateinherited

In this vector, we store pointers to the validity bool in the SmartPointer objects that subscribe to this class.

Definition at line 240 of file subscriptor.h.

◆ object_info

const std::type_info* Subscriptor::object_info

mutableprivateinherited

Pointer to the typeinfo object of this object, from which we can later deduce the class name. Since this information on the derived class is neither available in the destructor, nor in the constructor, we obtain it in between and store it here.

Definition at line 248 of file subscriptor.h.

◆ mutex

std::mutex Subscriptor::mutex

staticprivateinherited

A mutex used to ensure data consistency when accessing the mutable members of this class. This lock is used in the subscribe() and unsubscribe() functions, as well as in list_subscribers().

Definition at line 271 of file subscriptor.h.

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

include/deal.II/lac/sparse_direct.h
source/lac/sparse_direct.cc

Classes

Public Types

Public Member Functions

Static Public Member Functions

Private Types

Private Member Functions

Private Attributes

Static Private Attributes

Detailed Description

Instantiations

Member Typedef Documentation

◆ size_type

◆ map_value_type

◆ map_iterator

Constructor & Destructor Documentation

◆ SparseDirectUMFPACK()

◆ ~SparseDirectUMFPACK()

Member Function Documentation

◆ initialize() [1/2]

◆ factorize()

◆ initialize() [2/2]

◆ vmult() [1/2]

◆ vmult() [2/2]

◆ Tvmult() [1/2]

◆ Tvmult() [2/2]

◆ m()

◆ n()

◆ solve() [1/8]

◆ solve() [2/8]

◆ solve() [3/8]

◆ solve() [4/8]

◆ solve() [5/8]

◆ solve() [6/8]

◆ solve() [7/8]

◆ solve() [8/8]

◆ clear()

◆ sort_arrays() [1/3]

◆ sort_arrays() [2/3]

◆ sort_arrays() [3/3]

◆ subscribe()

◆ unsubscribe()

◆ n_subscriptions()

◆ list_subscribers() [1/2]

◆ list_subscribers() [2/2]

◆ serialize()

◆ check_no_subscribers()

Member Data Documentation

◆ n_rows

◆ n_cols

◆ symbolic_decomposition

◆ numeric_decomposition

◆ Ap

◆ Ai

◆ Ax

◆ Az

◆ control

◆ counter

◆ counter_map

◆ validity_pointers

◆ object_info

◆ mutex