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

Inheritance diagram for SparsityPattern:

Public Types
using	size_type = SparsityPatternBase::size_type

using	const_iterator = SparsityPatternBase::const_iterator

using	iterator = SparsityPatternBase::iterator

Public Member Functions
void	reinit (const size_type m, const size_type n, const unsigned int max_per_row)

void	reinit (const size_type m, const size_type n, const std::vector< unsigned int > &row_lengths)

virtual void	reinit (const size_type m, const size_type n, const ArrayView< const unsigned int > &row_lengths)=0

Construction and setup
Constructors, destructor, functions initializing, copying and filling an object.
	SparsityPattern ()

	SparsityPattern (const SparsityPattern &)

	SparsityPattern (const size_type m, const size_type n, const unsigned int max_per_row)

	SparsityPattern (const size_type m, const size_type n, const std::vector< unsigned int > &row_lengths)

	SparsityPattern (const size_type m, const unsigned int max_per_row)

	SparsityPattern (const size_type m, const std::vector< unsigned int > &row_lengths)

	SparsityPattern (const SparsityPattern &original, const unsigned int max_per_row, const size_type extra_off_diagonals)

	~SparsityPattern () override=default

SparsityPattern &	operator= (const SparsityPattern &)

virtual void	reinit (const size_type m, const size_type n, const ArrayView< const unsigned int > &row_lengths) override

void	compress ()

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

void	copy_from (const DynamicSparsityPattern &dsp)

void	copy_from (const SparsityPattern &sp)

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

template<typename ForwardIterator >
void	add_entries (const size_type row, ForwardIterator begin, ForwardIterator end, const bool indices_are_sorted=false)

Querying information
bool	operator== (const SparsityPattern &) const

bool	stores_only_added_elements () const

std::size_t	memory_consumption () const

Accessing entries
size_type	operator() (const size_type i, const size_type j) const

Input/Output
void	block_write (std::ostream &out) const

void	block_read (std::istream &in)

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

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

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

Construction and Initialization
Constructors, destructor, functions initializing, copying and filling an object.
void	symmetrize ()

void	add (const size_type i, const size_type j)

Iterators
iterator	begin () const

iterator	begin (const size_type r) const

iterator	end () const

iterator	end (const size_type r) const

Querying information
bool	operator== (const SparsityPatternBase &) const

bool	empty () const

bool	exists (const size_type i, const size_type j) const

size_type	max_entries_per_row () const

size_type	bandwidth () const

std::size_t	n_nonzero_elements () const

bool	is_compressed () const

size_type	n_rows () const

size_type	n_cols () const

unsigned int	row_length (const size_type row) const

Accessing entries
size_type	column_number (const size_type row, const unsigned int index) const

size_type	row_position (const size_type i, const size_type j) const

std::pair< size_type, size_type >	matrix_position (const std::size_t global_index) const

Input/Output
void	print (std::ostream &out) const

void	print_gnuplot (std::ostream &out) const

void	print_svg (std::ostream &out) const

Static Public Member Functions
static ::ExceptionBase &	ExcIteratorRange (int arg1, int arg2)

static ::ExceptionBase &	ExcInvalidNumberOfPartitions (int arg1)

static ::ExceptionBase &	ExcNotCompressed ()

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

static ::ExceptionBase &	ExcMatrixIsCompressed ()

Static Public Attributes
static const size_type	invalid_entry = numbers::invalid_size_type

Protected Attributes
size_type	max_dim

size_type	rows

size_type	cols

std::size_t	max_vec_len

unsigned int	max_row_length

std::unique_ptr< std::size_t[]>	rowstart

std::unique_ptr< size_type[]>	colnums

bool	compressed

Private Attributes
bool	store_diagonal_first_in_row

Friends
template<typename number >
class	SparseMatrix

template<typename number >
class	SparseLUDecomposition

template<typename number >
class	SparseILU

template<typename number >
class	ChunkSparseMatrix

class	ChunkSparsityPattern

class	DynamicSparsityPattern

class	SparsityPatternIterators::Iterator

class	SparsityPatternIterators::Accessor

class	ChunkSparsityPatternIterators::Accessor

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

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

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

using	map_value_type = decltype(counter_map)::value_type

using	map_iterator = decltype(counter_map)::iterator

static std::mutex	mutex

void	check_no_subscribers () const noexcept

Detailed Description

This class stores a sparsity pattern in the compressed row storage (CSR) format to store data, and is used as the basis for the SparseMatrix class.

The elements of a SparsityPattern, corresponding to the places where SparseMatrix objects can store nonzero entries, are stored row-by-row. Within each row, elements are generally stored left-to-right in increasing column index order; the exception to this rule is that if the matrix is square (n_rows() == n_columns()), then the diagonal entry is stored as the first element in each row to make operations like applying a Jacobi or SSOR preconditioner faster. As a consequence, if you traverse the elements of a row of a SparsityPattern with the help of iterators into this object (using SparsityPattern::begin and SparsityPattern::end) you will find that the elements are not sorted by column index within each row whenever the matrix is square (the first item will be the diagonal, followed by the other entries sorted by column index).

While this class forms the basis upon which SparseMatrix objects base their storage format, and thus plays a central role in setting up linear systems, it is rarely set up directly due to the way it stores its information. Rather, one typically goes through an intermediate format first, see for example the step-2 tutorial program as well as the documentation module Sparsity.

You can iterate over entries in the pattern using begin(), end(), begin(row), and end(row). These functions return an iterator of type SparsityPatternIterators::Iterator. When dereferencing an iterator it, you have access to the member functions in SparsityPatternIterators::Accessor, like it->column() and it->row().

Definition at line 888 of file sparsity_pattern.h.

Member Typedef Documentation

◆ size_type

using SparsityPattern::size_type = SparsityPatternBase::size_type

Declare type for container size.

Definition at line 894 of file sparsity_pattern.h.

◆ const_iterator

using SparsityPattern::const_iterator = SparsityPatternBase::const_iterator

Typedef an iterator class that allows to walk over all nonzero elements of a sparsity pattern.

Definition at line 900 of file sparsity_pattern.h.

◆ iterator

using SparsityPattern::iterator = SparsityPatternBase::iterator

Typedef an iterator class that allows to walk over all nonzero elements of a sparsity pattern.

Since the iterator does not allow to modify the sparsity pattern, this type is the same as that for const_iterator.

Definition at line 909 of file sparsity_pattern.h.

Constructor & Destructor Documentation

◆ SparsityPattern() [1/7]

SparsityPattern::SparsityPattern ( )

Initialize the matrix empty, that is with no memory allocated. This is useful if you want such objects as member variables in other classes. You can make the structure usable by calling the reinit() function.

Definition at line 53 of file sparsity_pattern.cc.

◆ SparsityPattern() [2/7]

SparsityPattern::SparsityPattern ( const SparsityPattern & s )

Copy constructor. This constructor is only allowed to be called if the matrix structure to be copied is empty. This is so in order to prevent involuntary copies of objects for temporaries, which can use large amounts of computing time. However, copy constructors are needed if one wants to place a SparsityPattern in a container, e.g., to write such statements like v.push_back (SparsityPattern());, with v a std::vector of SparsityPattern objects.

Usually, it is sufficient to use the explicit keyword to disallow unwanted temporaries, but this does not work for std::vectors. Since copying a structure like this is not useful anyway because multiple matrices can use the same sparsity structure, copies are only allowed for empty objects, as described above.

Definition at line 62 of file sparsity_pattern.cc.

◆ SparsityPattern() [3/7]

SparsityPattern::SparsityPattern	(	const size_type	m,
		const size_type	n,
		const unsigned int	max_per_row
	)

Initialize a rectangular pattern of size m x n.

Parameters

[in]	m	The number of rows.
[in]	n	The number of columns.
[in]	max_per_row	Maximum number of nonzero entries per row.

Definition at line 78 of file sparsity_pattern.cc.

◆ SparsityPattern() [4/7]

SparsityPattern::SparsityPattern	(	const size_type	m,
		const size_type	n,
		const std::vector< unsigned int > &	row_lengths
	)

Initialize a rectangular pattern of size m x n.

Parameters

[in]	m	The number of rows.
[in]	n	The number of columns.
[in]	row_lengths	Possible number of nonzero entries for each row. This vector must have one entry for each row.

Definition at line 89 of file sparsity_pattern.cc.

◆ SparsityPattern() [5/7]

SparsityPattern::SparsityPattern	(	const size_type	m,
		const unsigned int	max_per_row
	)

Initialize a quadratic pattern of dimension m with at most max_per_row nonzero entries per row.

This constructor automatically enables optimized storage of diagonal elements. To avoid this, use the constructor taking row and column numbers separately.

Definition at line 100 of file sparsity_pattern.cc.

◆ SparsityPattern() [6/7]

SparsityPattern::SparsityPattern	(	const size_type	m,
		const std::vector< unsigned int > &	row_lengths
	)

Initialize a quadratic pattern of size m x m.

Parameters

[in]	m	The number of rows and columns.
[in]	row_lengths	Maximum number of nonzero entries for each row. This vector must have one entry for each row.

Definition at line 109 of file sparsity_pattern.cc.

◆ SparsityPattern() [7/7]

SparsityPattern::SparsityPattern	(	const SparsityPattern &	original,
		const unsigned int	max_per_row,
		const size_type	extra_off_diagonals
	)

Make a copy with extra off-diagonals.

This constructs objects intended for the application of the ILU(n)-method or other incomplete decompositions. Therefore, additional to the original entry structure, space for extra_off_diagonals side- diagonals is provided on both sides of the main diagonal.

max_per_row is the maximum number of nonzero elements per row which this structure is to hold. It is assumed that this number is sufficiently large to accommodate both the elements in original as well as the new off-diagonal elements created by this constructor. You will usually want to give the same number as you gave for original plus the number of side diagonals times two. You may however give a larger value if you wish to add further nonzero entries for the decomposition based on other criteria than their being on side- diagonals.

This function requires that original refers to a quadratic matrix structure. It must be compressed. The matrix structure is not compressed after this function finishes.

Definition at line 118 of file sparsity_pattern.cc.

◆ ~SparsityPattern()

SparsityPattern::~SparsityPattern ( )

overridedefault

Destructor.

Member Function Documentation

◆ operator=()

SparsityPattern & SparsityPattern::operator= ( const SparsityPattern & s )

Copy operator. For this the same holds as for the copy constructor: it is declared, defined and fine to be called, but the latter only for empty objects.

Definition at line 198 of file sparsity_pattern.cc.

◆ reinit() [1/4]

void SparsityPattern::reinit	(	const size_type	m,
		const size_type	n,
		const ArrayView< const unsigned int > &	row_lengths
	)

overridevirtual

Reallocate memory for a matrix of size m times n. The number of entries for each row is taken from the ArrayView row_lengths which has to give this number of each row \(i=0\ldots m-1\).

Implements SparsityPatternBase.

Definition at line 229 of file sparsity_pattern.cc.

◆ compress()

void SparsityPattern::compress ( )

This function compresses the sparsity structure that this object represents. It does so by eliminating unused entries and sorting the remaining ones to allow faster access by usage of binary search algorithms. A special sorting scheme is used for the diagonal entry of quadratic matrices, which is always the first entry of each row.

The memory which is no more needed is released.

SparseMatrix objects require the SparsityPattern objects they are initialized with to be compressed, to reduce memory requirements.

Definition at line 338 of file sparsity_pattern.cc.

◆ copy_from() [1/4]

template<typename ForwardIterator >

void SparsityPattern::copy_from	(	const size_type	n_rows,
		const size_type	n_cols,
		const ForwardIterator	begin,
		const ForwardIterator	end
	)

This function can be used as a replacement for reinit(), subsequent calls to add() and a final call to close() if you know exactly in advance the entries that will form the matrix sparsity pattern.

The first two parameters determine the size of the matrix. For the two last ones, note that a sparse matrix can be described by a sequence of rows, each of which is represented by a sequence of pairs of column indices and values. In the present context, the begin() and end() parameters designate iterators (of forward iterator type) into a container, one representing one row. The distance between begin() and end() should therefore be equal to n_rows(). These iterators may be iterators of std::vector, std::list, pointers into a C-style array, or any other iterator satisfying the requirements of a forward iterator. The objects pointed to by these iterators (i.e. what we get after applying operator* or operator-> to one of these iterators) must be a container itself that provides functions begin and end designating a range of iterators that describe the contents of one line. Dereferencing these inner iterators must either yield a pair of an unsigned integer as column index and a value of arbitrary type (such a type would be used if we wanted to describe a sparse matrix with one such object), or simply an unsigned integer (of we only wanted to describe a sparsity pattern). The function is able to determine itself whether an unsigned integer or a pair is what we get after dereferencing the inner iterators, through some template magic.

While the order of the outer iterators denotes the different rows of the matrix, the order of the inner iterator denoting the columns does not matter, as they are sorted internal to this function anyway.

Since that all sounds very complicated, consider the following example code, which may be used to fill a sparsity pattern:

std::vector<std::vector<unsigned int> > column_indices (n_rows);
for (unsigned int row=0; row<n_rows; ++row)
        // generate necessary columns in this row
  fill_row (column_indices[row]);
 
sparsity.copy_from (n_rows, n_cols,
                    column_indices.begin(),
                    column_indices.end());

Note that this example works since the iterators dereferenced yield containers with functions begin and end (namely std::vectors), and the inner iterators dereferenced yield unsigned integers as column indices. Note that we could have replaced each of the two std::vector occurrences by std::list, and the inner one by std::set as well.

Another example would be as follows, where we initialize a whole matrix, not only a sparsity pattern:

std::vector<std::map<unsigned int,double> > entries (n_rows);
for (unsigned int row=0; row<n_rows; ++row)
        // generate necessary pairs of columns
        // and corresponding values in this row
  fill_row (entries[row]);
 
sparsity.copy_from (n_rows, n_cols,
                    column_indices.begin(),
                    column_indices.end());
matrix.reinit (sparsity);
matrix.copy_from (column_indices.begin(),
                  column_indices.end());

This example works because dereferencing iterators of the inner type yields a pair of unsigned integers and a value, the first of which we take as column index. As previously, the outer std::vector could be replaced by std::list, and the inner std::map<unsigned int,double> could be replaced by std::vector<std::pair<unsigned int,double> >, or a list or set of such pairs, as they all return iterators that point to such pairs.

◆ copy_from() [2/4]

void SparsityPattern::copy_from ( const DynamicSparsityPattern & dsp )

Copy data from a DynamicSparsityPattern. Previous content of this object is lost, and the sparsity pattern is in compressed mode afterwards.

Definition at line 490 of file sparsity_pattern.cc.

◆ copy_from() [3/4]

void SparsityPattern::copy_from ( const SparsityPattern & sp )

Copy data from a SparsityPattern. Previous content of this object is lost, and the sparsity pattern is in compressed mode afterwards.

Definition at line 442 of file sparsity_pattern.cc.

◆ copy_from() [4/4]

template<typename number >

void SparsityPattern::copy_from ( const FullMatrix< number > & matrix )

Take a full matrix and use its nonzero entries to generate a sparse matrix entry pattern for this object.

Previous content of this object is lost, and the sparsity pattern is in compressed mode afterwards.

Once you have built a sparsity pattern with this function, you probably want to attach a SparseMatrix object to it. The original matrix object can then be copied into this SparseMatrix object using the version of SparseMatrix::copy_from() that takes a FullMatrix object as argument. Through this procedure, you can convert a FullMatrix into a SparseMatrix.

Definition at line 551 of file sparsity_pattern.cc.

◆ add_entries()

template<typename ForwardIterator >

void SparsityPattern::add_entries	(	const size_type	row,
		ForwardIterator	begin,
		ForwardIterator	end,
		const bool	indices_are_sorted = `false`
	)

Add several nonzero entries to the specified matrix row. This function may only be called for non-compressed sparsity patterns.

If some of the entries already exist, nothing bad happens.

Definition at line 733 of file sparsity_pattern.cc.

◆ operator==() [1/2]

bool SparsityPattern::operator== ( const SparsityPattern & ) const

Test for equality of two SparsityPatterns.

◆ stores_only_added_elements()

bool SparsityPattern::stores_only_added_elements ( ) const

Return whether this object stores only those entries that have been added explicitly, or if the sparsity pattern contains elements that have been added through other means (implicitly) while building it. For the current class, the result is false if and only if it is square because it then unconditionally stores the diagonal entries whether they have been added explicitly or not.

This function mainly serves the purpose of describing the current class in cases where several kinds of sparsity patterns can be passed as template arguments.

◆ memory_consumption()

std::size_t SparsityPattern::memory_consumption ( ) const

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

Definition at line 1038 of file sparsity_pattern.cc.

◆ operator()()

SparsityPattern::size_type SparsityPattern::operator()	(	const size_type	i,
		const size_type	j
	)		const

Return the index of the matrix element with row number i and column number j. If the matrix element is not a nonzero one, return SparsityPattern::invalid_entry.

This function is usually called by the SparseMatrix::operator()(). It may only be called for compressed sparsity patterns, since in this case searching whether the entry exists can be done quite fast with a binary sort algorithm because the column numbers are sorted.

If m is the number of entries in row, then the complexity of this function is log(m) if the sparsity pattern is compressed.

Note: This function is not cheap since it has to search through all of the elements of the given row i to find whether index j exists. Thus, it is more expensive than necessary in cases where you want to loop over all of the nonzero elements of this sparsity pattern (or of a sparse matrix associated with it) or of a single row. In such cases, it is more efficient to use iterators over the elements of the sparsity pattern or of the sparse matrix.

Definition at line 666 of file sparsity_pattern.cc.

◆ block_write()

void SparsityPattern::block_write ( std::ostream & out ) const

Write the data of this object en bloc to a file. This is done in a binary mode, so the output is neither readable by humans nor (probably) by other computers using a different operating system or number format.

The purpose of this function is that you can swap out matrices and sparsity pattern if you are short of memory, want to communicate between different programs, or allow objects to be persistent across different runs of the program.

Definition at line 967 of file sparsity_pattern.cc.

◆ block_read()

void SparsityPattern::block_read ( std::istream & in )

Read data that has previously been written by block_write() from a file. This is done using the inverse operations to the above function, so it is reasonably fast because the bitstream is not interpreted except for a few numbers up front.

The object is resized on this operation, and all previous contents are lost.

A primitive form of error checking is performed which will recognize the bluntest attempts to interpret some data as a vector stored bitwise to a file, but not more.

Definition at line 991 of file sparsity_pattern.cc.

◆ save()

template<class Archive >

void SparsityPattern::save	(	Archive &	ar,
		const unsigned int	version
	)		const

Write the data of this object to a stream for the purpose of serialization

◆ load()

template<class Archive >

void SparsityPattern::load	(	Archive &	ar,
		const unsigned int	version
	)

Read the data of this object from a stream for the purpose of serialization

◆ serialize()

template<class Archive >

void SparsityPattern::serialize	(	Archive &	archive,
		const unsigned int	version
	)

Write and read the data of this object from a stream for the purpose of serialization.

◆ reinit() [2/4]

void SparsityPatternBase::reinit	(	const size_type	m,
		const size_type	n,
		const unsigned int	max_per_row
	)

Since this class has to implement only one reinit() function, we need to bring all base reinit() functions into the scope so that the compiler can find them.

Definition at line 394 of file sparsity_pattern.cc.

◆ reinit() [3/4]

void SparsityPatternBase::reinit	(	const size_type	m,
		const size_type	n,
		const std::vector< unsigned int > &	row_lengths
	)

Since this class has to implement only one reinit() function, we need to bring all base reinit() functions into the scope so that the compiler can find them.

Definition at line 407 of file sparsity_pattern.cc.

◆ reinit() [4/4]

virtual void SparsityPatternBase::reinit	(	const size_type	m,
		const size_type	n,
		const ArrayView< const unsigned int > &	row_lengths
	)

virtual

Since this class has to implement only one reinit() function, we need to bring all base reinit() functions into the scope so that the compiler can find them.

Implements SparsityPatternBase.

◆ symmetrize()

void SparsityPatternBase::symmetrize ( )

inherited

Make the sparsity pattern symmetric by adding the sparsity pattern of the transpose object.

This function throws an exception if the sparsity pattern does not represent a quadratic matrix.

Definition at line 841 of file sparsity_pattern.cc.

◆ add()

void SparsityPatternBase::add	(	const size_type	i,
		const size_type	j
	)

inherited

Add a nonzero entry to the matrix. This function may only be called for non-compressed sparsity patterns.

If the entry already exists, nothing bad happens.

Definition at line 704 of file sparsity_pattern.cc.

◆ begin() [1/2]

iterator SparsityPatternBase::begin ( ) const

inherited

Iterator starting at the first entry of the matrix. The resulting iterator can be used to walk over all nonzero entries of the sparsity pattern.

The order in which elements are accessed depends on the storage scheme implemented by derived classes.

◆ begin() [2/2]

iterator SparsityPatternBase::begin ( const size_type r ) const

inherited

Iterator starting at the first entry of row r.

Note that if the given row is empty, i.e. does not contain any nonzero entries, then the iterator returned by this function equals end(r). Note also that the iterator may not be dereferenceable in that case.

The order in which elements are accessed depends on the storage scheme implemented by derived classes.

◆ end() [1/2]

iterator SparsityPatternBase::end ( ) const

inherited

Final iterator.

◆ end() [2/2]

iterator SparsityPatternBase::end ( const size_type r ) const

inherited

Final iterator of row r. It points to the first element past the end of line r, or past the end of the entire sparsity pattern.

Note that the end iterator is not necessarily dereferenceable. This is in particular the case if it is the end iterator for the last row of a matrix.

◆ operator==() [2/2]

bool SparsityPatternBase::operator== ( const SparsityPatternBase & ) const

inherited

Test for equality of two SparsityPatterns.

◆ empty()

bool SparsityPatternBase::empty ( ) const

inherited

Return whether the object is empty. It is empty if no memory is allocated, which is the same as that both dimensions are zero.

Definition at line 624 of file sparsity_pattern.cc.

◆ exists()

bool SparsityPatternBase::exists	(	const size_type	i,
		const size_type	j
	)		const

inherited

Check if a value at a certain position may be non-zero.

Definition at line 781 of file sparsity_pattern.cc.

◆ max_entries_per_row()

SparsityPatternBase::size_type SparsityPatternBase::max_entries_per_row ( ) const

inherited

Return the maximum number of entries per row. Before compression, this equals the number given to the constructor, while after compression, it equals the maximum number of entries actually allocated by the user.

Definition at line 647 of file sparsity_pattern.cc.

◆ bandwidth()

SparsityPatternBase::size_type SparsityPatternBase::bandwidth ( ) const

inherited

Compute the bandwidth of the matrix represented by this structure. The bandwidth is the maximum of \(|i-j|\) for which the index pair \((i,j)\) represents a nonzero entry of the matrix. Consequently, the maximum bandwidth a \(n\times m\) matrix can have is \(\max\{n-1,m-1\}\), a diagonal matrix has bandwidth 0, and there are at most \(2*q+1\) entries per row if the bandwidth is \(q\). The returned quantity is sometimes called "half bandwidth" in the literature.

Definition at line 947 of file sparsity_pattern.cc.

◆ n_nonzero_elements()

std::size_t SparsityPatternBase::n_nonzero_elements ( ) const

inherited

Return the number of nonzero elements of this matrix. Actually, it returns the number of entries in the sparsity pattern; if any of the entries should happen to be zero, it is counted anyway.

This function may only be called if the matrix struct is compressed. It does not make too much sense otherwise anyway.

◆ is_compressed()

bool SparsityPatternBase::is_compressed ( ) const

inherited

Return whether the structure is compressed or not.

◆ n_rows()

size_type SparsityPatternBase::n_rows ( ) const

inherited

Return number of rows of this matrix, which equals the dimension of the image space.

◆ n_cols()

size_type SparsityPatternBase::n_cols ( ) const

inherited

Return number of columns of this matrix, which equals the dimension of the range space.

◆ row_length()

unsigned int SparsityPatternBase::row_length ( const size_type row ) const

inherited

Number of entries in a specific row.

◆ column_number()

size_type SparsityPatternBase::column_number	(	const size_type	row,
		const unsigned int	index
	)		const

inherited

Access to column number field. Return the column number of the indexth entry in row. Note that if diagonal elements are optimized, the first element in each row is the diagonal element, i.e. column_number(row,0)==row.

If the sparsity pattern is already compressed, then (except for the diagonal element), the entries are sorted by columns, i.e. column_number(row,i) < column_number(row,i+1).

◆ row_position()

SparsityPatternBase::size_type SparsityPatternBase::row_position	(	const size_type	i,
		const size_type	j
	)		const

inherited

The index of a global matrix entry in its row.

This function is analogous to operator(), but it computes the index not with respect to the total field, but only with respect to the row j.

Definition at line 799 of file sparsity_pattern.cc.

◆ matrix_position()

std::pair< SparsityPatternBase::size_type, SparsityPatternBase::size_type > SparsityPatternBase::matrix_position ( const std::size_t global_index ) const

inherited

This is the inverse operation to operator()(): given a global index, find out row and column of the matrix entry to which it belongs. The returned value is the pair composed of row and column index.

This function may only be called if the sparsity pattern is closed. The global index must then be between zero and n_nonzero_elements().

If N is the number of rows of this matrix, then the complexity of this function is log(N).

Definition at line 817 of file sparsity_pattern.cc.

◆ print()

void SparsityPatternBase::print ( std::ostream & out ) const

inherited

Print the sparsity of the matrix. The output consists of one line per row of the format [i,j1,j2,j3,...]. i is the row number and jn are the allocated columns in this row.

Definition at line 875 of file sparsity_pattern.cc.

◆ print_gnuplot()

void SparsityPatternBase::print_gnuplot ( std::ostream & out ) const

inherited

Print the sparsity of the matrix in a format that gnuplot understands and which can be used to plot the sparsity pattern in a graphical way. The format consists of pairs i j of nonzero elements, each representing one entry of this matrix, one per line of the output file. Indices are counted from zero on, as usual. Since sparsity patterns are printed in the same way as matrices are displayed, we print the negative of the column index, which means that the (0,0) element is in the top left rather than in the bottom left corner.

Print the sparsity pattern in gnuplot by setting the data style to dots or points and use the plot command.

Definition at line 896 of file sparsity_pattern.cc.

◆ print_svg()

void SparsityPatternBase::print_svg ( std::ostream & out ) const

inherited

Prints the sparsity of the matrix in a .svg file which can be opened in a web browser. The .svg file contains squares which correspond to the entries in the matrix. An entry in the matrix which contains a non-zero value corresponds with a red square while a zero-valued entry in the matrix correspond with a white square.

Definition at line 914 of file sparsity_pattern.cc.

Friends And Related Function Documentation

◆ SparseMatrix

template<typename number >

friend class SparseMatrix

friend

Typedef for sparse matrix type used

Typedef for the sparse matrix type used.

Definition at line 1369 of file sparsity_pattern.h.

◆ SparseLUDecomposition

template<typename number >

friend class SparseLUDecomposition

friend

Definition at line 1371 of file sparsity_pattern.h.

◆ SparseILU

template<typename number >

friend class SparseILU

friend

Definition at line 1373 of file sparsity_pattern.h.

◆ ChunkSparseMatrix

template<typename number >

friend class ChunkSparseMatrix

friend

Definition at line 1375 of file sparsity_pattern.h.

◆ ChunkSparsityPattern

friend class ChunkSparsityPattern

friend

Definition at line 1377 of file sparsity_pattern.h.

◆ DynamicSparsityPattern

friend class DynamicSparsityPattern

friend

Definition at line 1378 of file sparsity_pattern.h.

◆ SparsityPatternIterators::Iterator

friend class SparsityPatternIterators::Iterator

friend

Definition at line 1381 of file sparsity_pattern.h.

◆ SparsityPatternIterators::Accessor

friend class SparsityPatternIterators::Accessor

friend

Definition at line 1382 of file sparsity_pattern.h.

◆ ChunkSparsityPatternIterators::Accessor

friend class ChunkSparsityPatternIterators::Accessor

friend

Definition at line 1383 of file sparsity_pattern.h.

Member Data Documentation

◆ store_diagonal_first_in_row

bool SparsityPattern::store_diagonal_first_in_row

private

Is special treatment of diagonals enabled?

Definition at line 1365 of file sparsity_pattern.h.

◆ invalid_entry

const SparsityPatternBase::size_type SparsityPatternBase::invalid_entry = numbers::invalid_size_type

staticinherited

Define a value which is used to indicate that a certain value in the colnums array is unused, i.e. does not represent a certain column number index.

Indices with this invalid value are used to insert new entries to the sparsity pattern using the add() member function, and are removed when calling compress().

You should not assume that the variable declared here has a certain value. The initialization is given here only to enable the compiler to perform some optimizations, but the actual value of the variable may change over time.

Definition at line 362 of file sparsity_pattern.h.

◆ max_dim

size_type SparsityPatternBase::max_dim

protectedinherited

Maximum number of rows that can be stored in the rowstart array. Since reallocation of that array only happens if the present one is too small, but never when the size of this matrix structure shrinks, max_dim might be larger than rows and in this case rowstart has more elements than are used.

Definition at line 762 of file sparsity_pattern.h.

◆ rows

size_type SparsityPatternBase::rows

protectedinherited

Number of rows that this sparsity structure shall represent.

Definition at line 767 of file sparsity_pattern.h.

◆ cols

size_type SparsityPatternBase::cols

protectedinherited

Number of columns that this sparsity structure shall represent.

Definition at line 772 of file sparsity_pattern.h.

◆ max_vec_len

std::size_t SparsityPatternBase::max_vec_len

protectedinherited

Size of the actually allocated array colnums. Here, the same applies as for the rowstart array, i.e. it may be larger than the actually used part of the array.

Definition at line 779 of file sparsity_pattern.h.

◆ max_row_length

unsigned int SparsityPatternBase::max_row_length

protectedinherited

Maximum number of elements per row. This is set to the value given to the reinit() function (or to the constructor), or to the maximum row length computed from the vectors in case the more flexible constructors or reinit versions are called. Its value is more or less meaningless after compress() has been called.

Definition at line 788 of file sparsity_pattern.h.

◆ rowstart

std::unique_ptr<std::size_t[]> SparsityPatternBase::rowstart

protectedinherited

Array which hold for each row which is the first element in colnums belonging to that row. Note that the size of the array is one larger than the number of rows, because the last element is used for row=rows, i.e. the row past the last used one. The value of rowstart[rows]} equals the index of the element past the end in colnums; this way, we are able to write loops like for (i=rowstart[k]; i<rowstart[k+1]; ++i) also for the last row.

Note that the actual size of the allocated memory may be larger than the region that is used. The actual number of elements that was allocated is stored in max_dim.

Definition at line 803 of file sparsity_pattern.h.

◆ colnums

std::unique_ptr<size_type[]> SparsityPatternBase::colnums

protectedinherited

Array of column numbers. In this array, we store for each non-zero element its column number. The column numbers for the elements in row r are stored within the index range rowstart[r]...rowstart[r+1]. Therefore to find out whether a given element (r,c) exists, we have to check whether the column number c exists in the above-mentioned range within this array. If it exists, say at position p within this array, the value of the respective element in the sparse matrix will also be at position p of the values array of that class.

At the beginning, all elements of this array are set to -1 indicating invalid (unused) column numbers (diagonal elements are preset if optimized storage is requested, though). Now, if nonzero elements are added, one column number in the row's respective range after the other is set to the column number of the added element. When compress is called, unused elements (indicated by column numbers -1) are eliminated by copying the column number of subsequent rows and the column numbers within each row (with possible exception of the diagonal element) are sorted, such that finding whether an element exists and determining its position can be done by a binary search.

Definition at line 827 of file sparsity_pattern.h.

◆ compressed

bool SparsityPatternBase::compressed

protectedinherited

Store whether the compress() function was called for this object.

Definition at line 832 of file sparsity_pattern.h.

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

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

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Attributes

Private Attributes

Friends

Subscriptor functionality

Detailed Description

Member Typedef Documentation

◆ size_type

◆ const_iterator

◆ iterator

Constructor & Destructor Documentation

◆ SparsityPattern() [1/7]

◆ SparsityPattern() [2/7]

◆ SparsityPattern() [3/7]

◆ SparsityPattern() [4/7]

◆ SparsityPattern() [5/7]

◆ SparsityPattern() [6/7]

◆ SparsityPattern() [7/7]

◆ ~SparsityPattern()

Member Function Documentation

◆ operator=()

◆ reinit() [1/4]

◆ compress()

◆ copy_from() [1/4]

◆ copy_from() [2/4]

◆ copy_from() [3/4]

◆ copy_from() [4/4]

◆ add_entries()

◆ operator==() [1/2]

◆ stores_only_added_elements()

◆ memory_consumption()

◆ operator()()

◆ block_write()

◆ block_read()

◆ save()

◆ load()

◆ serialize()

◆ reinit() [2/4]

◆ reinit() [3/4]

◆ reinit() [4/4]

◆ symmetrize()

◆ add()

◆ begin() [1/2]

◆ begin() [2/2]

◆ end() [1/2]

◆ end() [2/2]

◆ operator==() [2/2]

◆ empty()

◆ exists()

◆ max_entries_per_row()

◆ bandwidth()

◆ n_nonzero_elements()

◆ is_compressed()

◆ n_rows()

◆ n_cols()

◆ row_length()

◆ column_number()

◆ row_position()

◆ matrix_position()

◆ print()

◆ print_gnuplot()

◆ print_svg()

Friends And Related Function Documentation

◆ SparseMatrix

◆ SparseLUDecomposition

◆ SparseILU

◆ ChunkSparseMatrix

◆ ChunkSparsityPattern

◆ DynamicSparsityPattern

◆ SparsityPatternIterators::Iterator

◆ SparsityPatternIterators::Accessor

◆ ChunkSparsityPatternIterators::Accessor

Member Data Documentation

◆ store_diagonal_first_in_row

◆ invalid_entry

◆ max_dim

◆ rows