Reference documentation for deal.II version Git 8668eb52a3 2020-04-08 14:09:01 +0200
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Public Types | Static Public Member Functions | Static Public Attributes | Protected Attributes | Friends | List of all members
SparsityPatternBase Class Referenceabstract

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

Inheritance diagram for SparsityPatternBase:

Public Types

using size_type = types::global_dof_index
using const_iterator = SparsityPatternIterators::Iterator
using iterator = SparsityPatternIterators::Iterator

Public Member Functions

Construction and Initialization

Constructors, destructor, functions initializing, copying and filling an object.

 SparsityPatternBase ()
 ~SparsityPatternBase () override=default
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
void symmetrize ()
void add (const size_type i, const size_type j)
iterator begin () const
iterator end () const
iterator begin (const size_type r) 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
std::size_t memory_consumption () 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_typematrix_position (const std::size_t global_index) const
void print (std::ostream &out) const
void print_gnuplot (std::ostream &out) const
void print_svg (std::ostream &out) const
template<class Archive >
void save (Archive &ar, const unsigned int version) const
template<class Archive >
void load (Archive &ar, const unsigned int version)
- Public Member Functions inherited from Subscriptor
 Subscriptor ()
 Subscriptor (const Subscriptor &)
 Subscriptor (Subscriptor &&) noexcept
virtual ~Subscriptor ()
Subscriptoroperator= (const Subscriptor &)
Subscriptoroperator= (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 ::ExceptionBaseExcNotCompressed ()
static ::ExceptionBaseExcNotEnoughSpace (int arg1, int arg2)
static ::ExceptionBaseExcMatrixIsCompressed ()
- Static Public Member Functions inherited from Subscriptor
static ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)
static ::ExceptionBaseExcNoSubscriber (std::string arg1, std::string arg2)

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


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

Detailed Description

A class that can store which elements of a matrix are nonzero (or, in fact, may be nonzero) and for which we have to allocate memory to store their values. This class is an example of the "static" type of sparsity patters (see Sparsity patterns). It uses the compressed row storage (CSR) format to store data, and is used as the basis for the derived SparsityPattern class and SparseMatrix class.

The elements of a SparsityPatternBase, corresponding to the places where SparseMatrix objects can store nonzero entries, are stored row-by-row. The ordering of non-zero elements within each row (i.e. increasing column index order) depends on the derived classes.

Wolfgang Bangerth, Guido Kanschat and others

Definition at line 329 of file sparsity_pattern.h.

Member Typedef Documentation

◆ size_type

Declare type for container size.

Definition at line 335 of file sparsity_pattern.h.

◆ const_iterator

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

Definition at line 341 of file sparsity_pattern.h.

◆ 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 350 of file sparsity_pattern.h.

Constructor & Destructor Documentation

◆ SparsityPatternBase()

SparsityPatternBase::SparsityPatternBase ( )

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 40 of file

◆ ~SparsityPatternBase()

SparsityPatternBase::~SparsityPatternBase ( )


Member Function Documentation

◆ reinit() [1/3]

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

Reallocate memory and set up data structures for a new matrix with m rows and n columns, with at most max_per_row nonzero entries per row.

This function simply maps its operations to the other reinit() function.

Definition at line 217 of file

◆ reinit() [2/3]

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

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

If m*n==0 all memory is freed, resulting in a total reinitialization of the object. If it is nonzero, new memory is only allocated if the new size extends the old one. This is done to save time and to avoid fragmentation of the heap.

Definition at line 614 of file

◆ reinit() [3/3]

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

Same as above, but with an ArrayView argument instead.

The derived classes are responsible for implementation of this function.

Implemented in SparsityPattern.

◆ symmetrize()

void SparsityPatternBase::symmetrize ( )

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

◆ add()

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

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

◆ begin() [1/2]

iterator SparsityPatternBase::begin ( ) const

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.

◆ end() [1/2]

iterator SparsityPatternBase::end ( ) const

Final iterator.

◆ begin() [2/2]

iterator SparsityPatternBase::begin ( const size_type  r) const

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() [2/2]

iterator SparsityPatternBase::end ( const size_type  r) const

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==()

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

Test for equality of two SparsityPatterns.

◆ empty()

bool SparsityPatternBase::empty ( ) const

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

◆ exists()

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

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

Definition at line 781 of file

◆ max_entries_per_row()

SparsityPatternBase::size_type SparsityPatternBase::max_entries_per_row ( ) const

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

◆ bandwidth()

SparsityPatternBase::size_type SparsityPatternBase::bandwidth ( ) const

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 948 of file

◆ n_nonzero_elements()

std::size_t SparsityPatternBase::n_nonzero_elements ( ) const

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

Return whether the structure is compressed or not.

◆ n_rows()

size_type SparsityPatternBase::n_rows ( ) const

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

◆ n_cols()

size_type SparsityPatternBase::n_cols ( ) const

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

Number of entries in a specific row.

◆ memory_consumption()

std::size_t SparsityPatternBase::memory_consumption ( ) const

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

Definition at line 1031 of file

◆ column_number()

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

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

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

◆ matrix_position()

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

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

◆ print()

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

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

◆ print_gnuplot()

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

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

◆ print_svg()

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

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

◆ save()

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

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

Friends And Related Function Documentation

◆ SparseMatrix

template<typename number >
friend class SparseMatrix

Typedef for sparse matrix type used

Typedef for the sparse matrix type used.

Definition at line 806 of file sparsity_pattern.h.

Member Data Documentation

◆ invalid_entry

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

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 366 of file sparsity_pattern.h.

◆ max_dim

size_type SparsityPatternBase::max_dim

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 732 of file sparsity_pattern.h.

◆ rows

size_type SparsityPatternBase::rows

Number of rows that this sparsity structure shall represent.

Definition at line 737 of file sparsity_pattern.h.

◆ cols

size_type SparsityPatternBase::cols

Number of columns that this sparsity structure shall represent.

Definition at line 742 of file sparsity_pattern.h.

◆ max_vec_len

std::size_t SparsityPatternBase::max_vec_len

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 749 of file sparsity_pattern.h.

◆ max_row_length

unsigned int SparsityPatternBase::max_row_length

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 758 of file sparsity_pattern.h.

◆ rowstart

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

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 773 of file sparsity_pattern.h.

◆ colnums

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

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 797 of file sparsity_pattern.h.

◆ compressed

bool SparsityPatternBase::compressed

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

Definition at line 802 of file sparsity_pattern.h.

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