Reference documentation for deal.II version GIT 6da2e5d553 2022-07-01 18:55:02+00:00
Sparsity patterns
Collaboration diagram for Sparsity patterns:

## Modules

Exceptions and assertions

## Classes

class  BlockSparsityPatternBase< SparsityPatternType >

class  BlockSparsityPattern

class  BlockDynamicSparsityPattern

class  ChunkSparsityPatternIterators::Accessor

class  ChunkSparsityPatternIterators::Iterator

class  ChunkSparsityPattern

class  DynamicSparsityPatternIterators::Accessor

class  DynamicSparsityPatternIterators::Iterator

class  DynamicSparsityPattern

struct  DynamicSparsityPattern::Line

class  SparsityPatternBase

class  SparsityPattern

class  TrilinosWrappers::SparsityPattern

## Functions

BlockSparsityPatternBase< SparsityPatternType >::BlockSparsityPatternBase ()

BlockSparsityPatternBase< SparsityPatternType >::BlockSparsityPatternBase (const size_type n_block_rows, const size_type n_block_columns)

BlockSparsityPatternBase< SparsityPatternType >::BlockSparsityPatternBase (const BlockSparsityPatternBase &bsp)

BlockSparsityPatternBase< SparsityPatternType >::~BlockSparsityPatternBase () override

void BlockSparsityPatternBase< SparsityPatternType >::reinit (const size_type n_block_rows, const size_type n_block_columns)

BlockSparsityPatternBaseBlockSparsityPatternBase< SparsityPatternType >::operator= (const BlockSparsityPatternBase &)

void BlockSparsityPatternBase< SparsityPatternType >::collect_sizes ()

SparsityPatternType & BlockSparsityPatternBase< SparsityPatternType >::block (const size_type row, const size_type column)

const SparsityPatternType & BlockSparsityPatternBase< SparsityPatternType >::block (const size_type row, const size_type column) const

const BlockIndicesBlockSparsityPatternBase< SparsityPatternType >::get_row_indices () const

const BlockIndicesBlockSparsityPatternBase< SparsityPatternType >::get_column_indices () const

void BlockSparsityPatternBase< SparsityPatternType >::compress ()

size_type BlockSparsityPatternBase< SparsityPatternType >::n_block_rows () const

size_type BlockSparsityPatternBase< SparsityPatternType >::n_block_cols () const

bool BlockSparsityPatternBase< SparsityPatternType >::empty () const

size_type BlockSparsityPatternBase< SparsityPatternType >::max_entries_per_row () const

void BlockSparsityPatternBase< SparsityPatternType >::add (const size_type i, const size_type j)

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

size_type BlockSparsityPatternBase< SparsityPatternType >::n_rows () const

size_type BlockSparsityPatternBase< SparsityPatternType >::n_cols () const

bool BlockSparsityPatternBase< SparsityPatternType >::exists (const size_type i, const size_type j) const

unsigned int BlockSparsityPatternBase< SparsityPatternType >::row_length (const size_type row) const

size_type BlockSparsityPatternBase< SparsityPatternType >::n_nonzero_elements () const

void BlockSparsityPatternBase< SparsityPatternType >::print (std::ostream &out) const

void BlockSparsityPatternBase< SparsityPatternType >::print_gnuplot (std::ostream &out) const

void BlockSparsityPatternBase< SparsityPatternType >::print_svg (std::ostream &out) const

ChunkSparsityPatternIterators::Accessor::Accessor (const ChunkSparsityPattern *matrix, const size_type row)

ChunkSparsityPatternIterators::Accessor::Accessor (const ChunkSparsityPattern *matrix)

size_type ChunkSparsityPatternIterators::Accessor::row () const

std::size_t ChunkSparsityPatternIterators::Accessor::reduced_index () const

size_type ChunkSparsityPatternIterators::Accessor::column () const

bool ChunkSparsityPatternIterators::Accessor::is_valid_entry () const

bool ChunkSparsityPatternIterators::Accessor::operator== (const Accessor &) const

bool ChunkSparsityPatternIterators::Accessor::operator< (const Accessor &) const

ChunkSparsityPatternIterators::Iterator::Iterator (const ChunkSparsityPattern *sp, const size_type row)

IteratorChunkSparsityPatternIterators::Iterator::operator++ ()

Iterator ChunkSparsityPatternIterators::Iterator::operator++ (int)

const AccessorChunkSparsityPatternIterators::Iterator::operator* () const

const AccessorChunkSparsityPatternIterators::Iterator::operator-> () const

bool ChunkSparsityPatternIterators::Iterator::operator== (const Iterator &) const

bool ChunkSparsityPatternIterators::Iterator::operator!= (const Iterator &) const

bool ChunkSparsityPatternIterators::Iterator::operator< (const Iterator &) const

ChunkSparsityPattern::ChunkSparsityPattern ()

ChunkSparsityPattern::ChunkSparsityPattern (const ChunkSparsityPattern &)

ChunkSparsityPattern::ChunkSparsityPattern (const size_type m, const size_type n, const size_type max_chunks_per_row, const size_type chunk_size)

ChunkSparsityPattern::ChunkSparsityPattern (const size_type m, const size_type n, const std::vector< size_type > &row_lengths, const size_type chunk_size)

ChunkSparsityPattern::ChunkSparsityPattern (const size_type n, const size_type max_per_row, const size_type chunk_size)

ChunkSparsityPattern::ChunkSparsityPattern (const size_type m, const std::vector< size_type > &row_lengths, const size_type chunk_size)

ChunkSparsityPattern::~ChunkSparsityPattern () override=default

ChunkSparsityPatternChunkSparsityPattern::operator= (const ChunkSparsityPattern &)

void ChunkSparsityPattern::reinit (const size_type m, const size_type n, const size_type max_per_row, const size_type chunk_size)

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

void ChunkSparsityPattern::reinit (const size_type m, const size_type n, const ArrayView< const size_type > &row_lengths, const size_type chunk_size)

void ChunkSparsityPattern::compress ()

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

template<typename SparsityPatternType >
void ChunkSparsityPattern::copy_from (const SparsityPatternType &dsp, const size_type chunk_size)

template<typename number >
void ChunkSparsityPattern::copy_from (const FullMatrix< number > &matrix, const size_type chunk_size)

template<typename Sparsity >
void ChunkSparsityPattern::create_from (const size_type m, const size_type n, const Sparsity &sparsity_pattern_for_chunks, const size_type chunk_size, const bool optimize_diagonal=true)

bool ChunkSparsityPattern::empty () const

size_type ChunkSparsityPattern::get_chunk_size () const

size_type ChunkSparsityPattern::max_entries_per_row () const

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

void ChunkSparsityPattern::symmetrize ()

size_type ChunkSparsityPattern::n_rows () const

size_type ChunkSparsityPattern::n_cols () const

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

size_type ChunkSparsityPattern::row_length (const size_type row) const

size_type ChunkSparsityPattern::bandwidth () const

size_type ChunkSparsityPattern::n_nonzero_elements () const

bool ChunkSparsityPattern::is_compressed () const

bool ChunkSparsityPattern::stores_only_added_elements () const

iterator ChunkSparsityPattern::begin () const

iterator ChunkSparsityPattern::end () const

iterator ChunkSparsityPattern::begin (const size_type r) const

iterator ChunkSparsityPattern::end (const size_type r) const

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

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

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

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

std::size_t ChunkSparsityPattern::memory_consumption () const

DynamicSparsityPatternIterators::Accessor::Accessor (const DynamicSparsityPattern *sparsity_pattern, const size_type row, const unsigned int index_within_row)

DynamicSparsityPatternIterators::Accessor::Accessor (const DynamicSparsityPattern *sparsity_pattern)

DynamicSparsityPatternIterators::Accessor::Accessor ()

size_type DynamicSparsityPatternIterators::Accessor::row () const

size_type DynamicSparsityPatternIterators::Accessor::index () const

size_type DynamicSparsityPatternIterators::Accessor::column () const

bool DynamicSparsityPatternIterators::Accessor::operator== (const Accessor &) const

bool DynamicSparsityPatternIterators::Accessor::operator< (const Accessor &) const

DynamicSparsityPatternIterators::Iterator::Iterator (const DynamicSparsityPattern *sp, const size_type row, const unsigned int index_within_row)

DynamicSparsityPatternIterators::Iterator::Iterator (const DynamicSparsityPattern *sp)

DynamicSparsityPatternIterators::Iterator::Iterator ()=default

IteratorDynamicSparsityPatternIterators::Iterator::operator++ ()

Iterator DynamicSparsityPatternIterators::Iterator::operator++ (int)

const AccessorDynamicSparsityPatternIterators::Iterator::operator* () const

const AccessorDynamicSparsityPatternIterators::Iterator::operator-> () const

bool DynamicSparsityPatternIterators::Iterator::operator== (const Iterator &) const

bool DynamicSparsityPatternIterators::Iterator::operator!= (const Iterator &) const

bool DynamicSparsityPatternIterators::Iterator::operator< (const Iterator &) const

int DynamicSparsityPatternIterators::Iterator::operator- (const Iterator &p) const

DynamicSparsityPattern::DynamicSparsityPattern ()

DynamicSparsityPattern::DynamicSparsityPattern (const DynamicSparsityPattern &)

DynamicSparsityPattern::DynamicSparsityPattern (const size_type m, const size_type n, const IndexSet &rowset=IndexSet())

DynamicSparsityPattern::DynamicSparsityPattern (const IndexSet &indexset)

DynamicSparsityPattern::DynamicSparsityPattern (const size_type n)

DynamicSparsityPatternDynamicSparsityPattern::operator= (const DynamicSparsityPattern &)

void DynamicSparsityPattern::reinit (const size_type m, const size_type n, const IndexSet &rowset=IndexSet())

void DynamicSparsityPattern::compress ()

bool DynamicSparsityPattern::empty () const

size_type DynamicSparsityPattern::max_entries_per_row () const

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

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

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

DynamicSparsityPattern DynamicSparsityPattern::get_view (const IndexSet &rows) const

void DynamicSparsityPattern::symmetrize ()

template<typename SparsityPatternTypeLeft , typename SparsityPatternTypeRight >
void DynamicSparsityPattern::compute_mmult_pattern (const SparsityPatternTypeLeft &left, const SparsityPatternTypeRight &right)

template<typename SparsityPatternTypeLeft , typename SparsityPatternTypeRight >
void DynamicSparsityPattern::compute_Tmmult_pattern (const SparsityPatternTypeLeft &left, const SparsityPatternTypeRight &right)

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

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

size_type DynamicSparsityPattern::n_rows () const

size_type DynamicSparsityPattern::n_cols () const

size_type DynamicSparsityPattern::row_length (const size_type row) const

void DynamicSparsityPattern::clear_row (const size_type row)

size_type DynamicSparsityPattern::column_number (const size_type row, const size_type index) const

size_type DynamicSparsityPattern::column_index (const size_type row, const size_type col) const

void DynamicSparsityPattern::Line::add (const size_type col_num)

template<typename ForwardIterator >
void DynamicSparsityPattern::Line::add_entries (ForwardIterator begin, ForwardIterator end, const bool indices_are_sorted)

size_type DynamicSparsityPattern::Line::memory_consumption () const

## Variables

static const size_type BlockSparsityPatternBase< SparsityPatternType >::invalid_entry = SparsityPattern::invalid_entry

const ChunkSparsityPatternChunkSparsityPatternIterators::Accessor::sparsity_pattern

SparsityPatternIterators::Accessor ChunkSparsityPatternIterators::Accessor::reduced_accessor

size_type ChunkSparsityPatternIterators::Accessor::chunk_row

size_type ChunkSparsityPatternIterators::Accessor::chunk_col

Accessor ChunkSparsityPatternIterators::Iterator::accessor

static const size_type ChunkSparsityPattern::invalid_entry = SparsityPattern::invalid_entry

const DynamicSparsityPatternDynamicSparsityPatternIterators::Accessor::sparsity_pattern

size_type DynamicSparsityPatternIterators::Accessor::current_row

std::vector< size_type >::const_iterator DynamicSparsityPatternIterators::Accessor::current_entry

std::vector< size_type >::const_iterator DynamicSparsityPatternIterators::Accessor::end_of_row

Accessor DynamicSparsityPatternIterators::Iterator::accessor

std::vector< size_typeDynamicSparsityPattern::Line::entries

## Friends

class ChunkSparsityPatternIterators::Accessor::Iterator

class DynamicSparsityPatternIterators::Accessor::Iterator

## Iterators

bool DynamicSparsityPattern::have_entries

size_type DynamicSparsityPattern::rows

size_type DynamicSparsityPattern::cols

IndexSet DynamicSparsityPattern::rowset

std::vector< LineDynamicSparsityPattern::lines

class DynamicSparsityPattern::DynamicSparsityPatternIterators::Accessor

iterator DynamicSparsityPattern::begin () const

iterator DynamicSparsityPattern::end () const

iterator DynamicSparsityPattern::begin (const size_type r) const

iterator DynamicSparsityPattern::end (const size_type r) const

size_type DynamicSparsityPattern::bandwidth () const

size_type DynamicSparsityPattern::n_nonzero_elements () const

const IndexSetDynamicSparsityPattern::row_index_set () const

IndexSet DynamicSparsityPattern::nonempty_cols () const

IndexSet DynamicSparsityPattern::nonempty_rows () const

static bool DynamicSparsityPattern::stores_only_added_elements ()

size_type DynamicSparsityPattern::memory_consumption () const

## Detailed Description

Almost all finite element formulations lead to matrices that are "sparse", i.e., for which the number of nonzero elements per row is (i) relatively small compared to the overall size of the matrix, and (ii) bounded by a fixed number that does not grow if the mesh is refined. For such cases, it is more efficient to not store all elements of the matrix, but only those that are actually (or may be) nonzero. This requires storing, for each row, the column indices of the nonzero entries (we call this the "sparsity pattern") as well as the actual values of these nonzero entries. (In practice, it sometimes happens that some of the nonzero values are, in fact, zero. Sparsity patterns and sparse matrices only intend to provision space for entries that may be nonzero, and do so at a time when we don't know yet what values these entries will ultimately have; they may have a zero value if a coefficient or cell happens to have particular values.)

In deal.II, sparsity patterns are typically separated from the actual sparse matrices (with the exception of the SparseMatrixEZ class and some classes from interfaces to external libraries such as PETSc). The reason is that one often has several matrices that share the same sparsity pattern; examples include the stiffness and mass matrices necessary for time stepping schemes, or the left and right hand side matrix of generalized eigenvalue problems. It would therefore be wasteful if each of them had to store their sparsity pattern separately.

Consequently, deal.II has sparsity pattern classes that matrix classes build on. There are two main groups of sparsity pattern classes, as discussed below:

#### "Static" sparsity patterns

The main sparse matrix class in deal.II, SparseMatrix, only stores a value for each matrix entry, but not where these entries are located. For this, it relies on the information it gets from a sparsity pattern object associated with this matrix. This sparsity pattern object must be of type SparsityPattern.

Because matrices are large objects and because it is comparatively expensive to change them, SparsityPattern objects are built in two phases: first, in a "dynamic" phase, one allocates positions where one expects matrices built on it to have nonzero entries; in a second "static" phase, the representation of these nonzero locations is "compressed" into the usual Compressed Sparse Row (CSR) format. After this, no new nonzero locations may be added. Only after compression can a sparsity pattern be associated to a matrix, since the latter requires the efficient compressed data format of the former. Building a sparsity pattern during the dynamic phase often happens with the DoFTools::make_sparsity_pattern() function. Although this may appear a restriction, it is typically not a significant problem to first build a sparsity pattern and then to write into the matrix only in the previously allocated locations, since in finite element codes it is normally quite clear which elements of a matrix can possibly be nonzero and which are definitely zero.

The advantage of this two-phase generation of a sparsity pattern is that when it is actually used with a matrix, a very efficient format is available. In particular, the locations of entries are stored in a linear array that allows for rapid access friendly to modern CPU types with deep hierarchies of caches. Consequently, the static SparsityPattern class is the only one on which deal.II's main SparseMatrix class can work.

The main drawback of static sparsity patterns is that their efficient construction requires a reasonably good guess how many entries each of the rows may maximally have. During the actual construction, for example in the DoFTools::make_sparsity_pattern() function, only at most as many entries can be allocated as previously stated. This is a problem because it is often difficult to estimate the maximal number of entries per row. Consequently, a common strategy is to first build and intermediate sparsity pattern that uses a less efficient storage scheme during construction of the sparsity pattern and later copy it directly into the static, compressed form. Most tutorial programs do this, starting at step-2 (see also, for example the step-11, step-18, and step-27 tutorial programs).

#### "Dynamic" or "compressed" sparsity patterns

As explained above, it is often complicated to obtain good estimates for the maximal number of entries in each row of a sparsity pattern. Consequently, any attempts to allocate a regular SparsityPattern with bad estimates requires huge amounts of memory, almost all of which will not be used and be de-allocated upon compression.

To avoid this, deal.II contains a "dynamic" or "compressed" sparsity pattern called DynamicSparsityPattern that only allocates as much memory as necessary to hold the currently added entries. While this saves much memory compared to the worst-case behavior mentioned above, it requires the use of less efficient storage schemes for insertion of elements, and the frequent allocation of memory often also takes significant compute time. The tradeoff to avoid excessive memory allocation cannot be avoided, however.

The class is typically used in the following way

* DynamicSparsityPattern dsp (dof_handler.n_dofs());
* DoFTools::make_sparsity_pattern (dof_handler,
*                                  dsp);
* constraints.condense (dsp);
*
* SparsityPattern final_sparsity_pattern;
* final_sparsity_pattern.copy_from (dsp);
* 

The intermediate, compressed sparsity pattern is directly copied into the "compressed" form of the final static pattern.

#### Dynamic block sparsity patterns

The class BlockDynamicSparsityPattern implements an array of dynamic sparsity patterns for constructing block matrices. See the documentation and step-22 for more information.

## ◆ size_type [1/6]

template<typename SparsityPatternType >
 using BlockSparsityPatternBase< SparsityPatternType >::size_type = types::global_dof_index

Declare type for container size.

Definition at line 84 of file block_sparsity_pattern.h.

## ◆ size_type [2/6]

Declare the type for container size.

Definition at line 68 of file chunk_sparsity_pattern.h.

## ◆ size_type [3/6]

Declare the type for container size.

Definition at line 172 of file chunk_sparsity_pattern.h.

## ◆ size_type [4/6]

Declare the type for container size.

Definition at line 250 of file chunk_sparsity_pattern.h.

## ◆ const_iterator [1/2]

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

Definition at line 255 of file chunk_sparsity_pattern.h.

## ◆ iterator [1/2]

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 264 of file chunk_sparsity_pattern.h.

## ◆ size_type [5/6]

 using DynamicSparsityPatternIterators::size_type = typedef types::global_dof_index

Declare type for container size.

Definition at line 55 of file dynamic_sparsity_pattern.h.

## ◆ size_type [6/6]

Declare the type for container size.

Definition at line 326 of file dynamic_sparsity_pattern.h.

## ◆ iterator [2/2]

Typedef an for 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 335 of file dynamic_sparsity_pattern.h.

## ◆ const_iterator [2/2]

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

Definition at line 341 of file dynamic_sparsity_pattern.h.

## ◆ BlockSparsityPatternBase() [1/3]

template<class 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 25 of file block_sparsity_pattern.cc.

## ◆ BlockSparsityPatternBase() [2/3]

template<class SparsityPatternBase >
 BlockSparsityPatternBase< SparsityPatternBase >::BlockSparsityPatternBase ( const size_type n_block_rows, const size_type n_block_columns )

Initialize the matrix with the given number of block rows and columns. The blocks themselves are still empty, and you have to call collect_sizes() after you assign them sizes.

Definition at line 33 of file block_sparsity_pattern.cc.

## ◆ BlockSparsityPatternBase() [3/3]

template<class SparsityPatternBase >
 BlockSparsityPatternBase< SparsityPatternBase >::BlockSparsityPatternBase ( const BlockSparsityPatternBase< SparsityPatternType > & bsp )

Copy constructor. This constructor is only allowed to be called if the sparsity pattern to be copied is empty, i.e. there are no block allocated at present. This is for the same reason as for the SparsityPattern, see there for the details.

Definition at line 45 of file block_sparsity_pattern.cc.

## ◆ ~BlockSparsityPatternBase()

template<class SparsityPatternBase >
 override

Destructor.

Definition at line 62 of file block_sparsity_pattern.cc.

## ◆ reinit() [1/5]

template<class SparsityPatternBase >
 void BlockSparsityPatternBase< SparsityPatternBase >::reinit ( const size_type n_block_rows, const size_type n_block_columns )

Resize the matrix, by setting the number of block rows and columns. This deletes all blocks and replaces them with uninitialized ones, i.e. ones for which also the sizes are not yet set. You have to do that by calling the reinit() functions of the blocks themselves. Do not forget to call collect_sizes() after that on this object.

The reason that you have to set sizes of the blocks yourself is that the sizes may be varying, the maximum number of elements per row may be varying, etc. It is simpler not to reproduce the interface of the SparsityPattern class here but rather let the user call whatever function they desire.

Definition at line 77 of file block_sparsity_pattern.cc.

## ◆ operator=() [1/3]

template<typename SparsityPatternType >
 BlockSparsityPatternBase< SparsityPatternBase > & BlockSparsityPatternBase< SparsityPatternBase >::operator= ( const BlockSparsityPatternBase< SparsityPatternType > & )

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 110 of file block_sparsity_pattern.cc.

## ◆ collect_sizes()

template<class SparsityPatternBase >
 void BlockSparsityPatternBase< SparsityPatternBase >::collect_sizes

This function collects the sizes of the sub-objects and stores them in internal arrays, in order to be able to relay global indices into the matrix to indices into the subobjects. You must call this function each time after you have changed the size of the sub-objects.

Definition at line 129 of file block_sparsity_pattern.cc.

## ◆ block() [1/2]

template<typename SparsityPatternType >
 SparsityPatternType & BlockSparsityPatternBase< SparsityPatternType >::block ( const size_type row, const size_type column )
inline

Access the block with the given coordinates.

Definition at line 756 of file block_sparsity_pattern.h.

## ◆ block() [2/2]

template<typename SparsityPatternType >
 const SparsityPatternType & BlockSparsityPatternBase< SparsityPatternType >::block ( const size_type row, const size_type column ) const
inline

Access the block with the given coordinates. Version for constant objects.

Definition at line 768 of file block_sparsity_pattern.h.

## ◆ get_row_indices()

template<typename SparsityPatternType >
 const BlockIndices & BlockSparsityPatternBase< SparsityPatternType >::get_row_indices
inline

Grant access to the object describing the distribution of row indices to the individual blocks.

Definition at line 781 of file block_sparsity_pattern.h.

## ◆ get_column_indices()

template<typename SparsityPatternType >
 const BlockIndices & BlockSparsityPatternBase< SparsityPatternType >::get_column_indices
inline

Grant access to the object describing the distribution of column indices to the individual blocks.

Definition at line 790 of file block_sparsity_pattern.h.

## ◆ compress() [1/3]

template<class SparsityPatternBase >
 void BlockSparsityPatternBase< SparsityPatternBase >::compress

This function compresses the sparsity structures that this object represents. It simply calls compress for all sub-objects.

Definition at line 168 of file block_sparsity_pattern.cc.

## ◆ n_block_rows()

template<typename SparsityPatternType >
 BlockSparsityPatternBase< SparsityPatternType >::size_type BlockSparsityPatternBase< SparsityPatternType >::n_block_rows
inline

Return the number of blocks in a column.

Definition at line 951 of file block_sparsity_pattern.h.

## ◆ n_block_cols()

template<typename SparsityPatternType >
 BlockSparsityPatternBase< SparsityPatternType >::size_type BlockSparsityPatternBase< SparsityPatternType >::n_block_cols
inline

Return the number of blocks in a row.

Definition at line 942 of file block_sparsity_pattern.h.

## ◆ empty() [1/3]

template<class SparsityPatternBase >
 bool BlockSparsityPatternBase< SparsityPatternBase >::empty

Return whether the object is empty. It is empty if no memory is allocated, which is the same as that both dimensions are zero. This function is just the concatenation of the respective call to all sub- matrices.

Definition at line 179 of file block_sparsity_pattern.cc.

## ◆ max_entries_per_row() [1/3]

template<class SparsityPatternBase >
 BlockSparsityPatternBase< SparsityPatternBase >::size_type BlockSparsityPatternBase< SparsityPatternBase >::max_entries_per_row

Return the maximum number of entries per row. It returns the maximal number of entries per row accumulated over all blocks in a row, and the maximum over all rows.

Definition at line 192 of file block_sparsity_pattern.cc.

## ◆ add() [1/4]

template<typename SparsityPatternType >
 void BlockSparsityPatternBase< SparsityPatternType >::add ( const size_type i, const size_type j )
inline

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.

This function simply finds out to which block (i,j) belongs and then relays to that block.

Definition at line 799 of file block_sparsity_pattern.h.

## ◆ add_entries() [1/3]

template<typename SparsityPatternType >
template<typename ForwardIterator >
 void BlockSparsityPatternBase< SparsityPatternType >::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.

This function simply finds out to which blocks (row,col) for col in the iterator range belong and then relays to those blocks.

Definition at line 818 of file block_sparsity_pattern.h.

## ◆ n_rows() [1/3]

template<class SparsityPatternBase >

Return number of rows of this matrix, which equals the dimension of the image space. It is the sum of rows of the (block-)rows of sub-matrices.

Definition at line 211 of file block_sparsity_pattern.cc.

## ◆ n_cols() [1/3]

template<class SparsityPatternBase >

Return number of columns of this matrix, which equals the dimension of the range space. It is the sum of columns of the (block-)columns of sub- matrices.

Definition at line 225 of file block_sparsity_pattern.cc.

## ◆ exists() [1/3]

template<typename SparsityPatternType >
 bool BlockSparsityPatternBase< SparsityPatternType >::exists ( const size_type i, const size_type j ) const
inline

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

Definition at line 906 of file block_sparsity_pattern.h.

## ◆ row_length() [1/3]

template<typename SparsityPatternType >
 unsigned int BlockSparsityPatternBase< SparsityPatternType >::row_length ( const size_type row ) const
inline

Number of entries in a specific row, added up over all the blocks that form this row.

Definition at line 924 of file block_sparsity_pattern.h.

## ◆ n_nonzero_elements() [1/3]

template<class SparsityPatternBase >
 BlockSparsityPatternBase< SparsityPatternBase >::size_type BlockSparsityPatternBase< SparsityPatternBase >::n_nonzero_elements

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.

In the present context, it is the sum of the values as returned by the sub-objects.

Definition at line 239 of file block_sparsity_pattern.cc.

## ◆ print() [1/3]

template<class SparsityPatternBase >
 void BlockSparsityPatternBase< 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 252 of file block_sparsity_pattern.cc.

## ◆ print_gnuplot() [1/3]

template<class SparsityPatternBase >
 void BlockSparsityPatternBase< 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. This is the same functionality implemented for usual sparsity patterns, see SparsityPatternBase::print_gnuplot().

Definition at line 309 of file block_sparsity_pattern.cc.

## ◆ print_svg()

template<class SparsityPatternBase >
 void BlockSparsityPatternBase< SparsityPatternBase >::print_svg ( std::ostream & out ) const

Print the sparsity of the matrix in svg format. This is the same functionality implemented for usual sparsity patterns, see SparsityPatternBase::print_svg().

Definition at line 336 of file block_sparsity_pattern.cc.

## ◆ Accessor() [1/5]

 ChunkSparsityPatternIterators::Accessor::Accessor ( const ChunkSparsityPattern * matrix, const size_type row )

Constructor.

## ◆ Accessor() [2/5]

 ChunkSparsityPatternIterators::Accessor::Accessor ( const ChunkSparsityPattern * matrix )

Constructor. Construct the end accessor for the given sparsity pattern.

## ◆ row() [1/2]

 size_type ChunkSparsityPatternIterators::Accessor::row ( ) const

Row number of the element represented by this object. This function can only be called for entries for which is_valid_entry() is true.

## ◆ reduced_index()

 std::size_t ChunkSparsityPatternIterators::Accessor::reduced_index ( ) const

Return the global index from the reduced sparsity pattern.

## ◆ column() [1/2]

 size_type ChunkSparsityPatternIterators::Accessor::column ( ) const

Column number of the element represented by this object. This function can only be called for entries for which is_valid_entry() is true.

## ◆ is_valid_entry()

 bool ChunkSparsityPatternIterators::Accessor::is_valid_entry ( ) const

Return whether the sparsity pattern entry pointed to by this iterator is valid or not. Note that after compressing the sparsity pattern, all entries are valid. However, before compression, the sparsity pattern allocated some memory to be used while still adding new nonzero entries; if you create iterators in this phase of the sparsity pattern's lifetime, you will iterate over elements that are not valid. If this is so, then this function will return false.

## ◆ operator==() [1/4]

 bool ChunkSparsityPatternIterators::Accessor::operator== ( const Accessor & ) const

Comparison. True, if both iterators point to the same matrix position.

## ◆ operator<() [1/4]

 bool ChunkSparsityPatternIterators::Accessor::operator< ( const Accessor & ) const

Comparison operator. Result is true if either the first row number is smaller or if the row numbers are equal and the first index is smaller.

This function is only valid if both iterators point into the same sparsity pattern.

## ◆ advance() [1/2]

 void ChunkSparsityPatternIterators::Accessor::advance ( )
protected

Move the accessor to the next nonzero entry in the matrix.

## ◆ Iterator() [1/4]

 ChunkSparsityPatternIterators::Iterator::Iterator ( const ChunkSparsityPattern * sp, const size_type row )

Constructor. Create an iterator into the sparsity pattern sp for the given row and the index within it.

## ◆ operator++() [1/4]

 Iterator& ChunkSparsityPatternIterators::Iterator::operator++ ( )

Prefix increment.

## ◆ operator++() [2/4]

 Iterator ChunkSparsityPatternIterators::Iterator::operator++ ( int )

Postfix increment.

## ◆ operator*() [1/2]

 const Accessor& ChunkSparsityPatternIterators::Iterator::operator* ( ) const

Dereferencing operator.

## ◆ operator->() [1/2]

 const Accessor* ChunkSparsityPatternIterators::Iterator::operator-> ( ) const

Dereferencing operator.

## ◆ operator==() [2/4]

 bool ChunkSparsityPatternIterators::Iterator::operator== ( const Iterator & ) const

Comparison. True, if both iterators point to the same matrix position.

## ◆ operator!=() [1/2]

 bool ChunkSparsityPatternIterators::Iterator::operator!= ( const Iterator & ) const

Inverse of ==.

## ◆ operator<() [2/4]

 bool ChunkSparsityPatternIterators::Iterator::operator< ( const Iterator & ) const

Comparison operator. Result is true if either the first row number is smaller or if the row numbers are equal and the first index is smaller.

This function is only valid if both iterators point into the same matrix.

## ◆ ChunkSparsityPattern() [1/6]

 ChunkSparsityPattern::ChunkSparsityPattern ( )

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 25 of file chunk_sparsity_pattern.cc.

## ◆ ChunkSparsityPattern() [2/6]

 ChunkSparsityPattern::ChunkSparsityPattern ( const ChunkSparsityPattern & 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 ChunkSparsityPattern in a container, e.g., to write such statements like v.push_back (ChunkSparsityPattern());, with v a vector of ChunkSparsityPattern objects.

Usually, it is sufficient to use the explicit keyword to disallow unwanted temporaries, but this does not work for std::vector. 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 32 of file chunk_sparsity_pattern.cc.

## ◆ ChunkSparsityPattern() [3/6]

 ChunkSparsityPattern::ChunkSparsityPattern ( const size_type m, const size_type n, const size_type max_chunks_per_row, const size_type chunk_size )

Initialize a rectangular matrix.

• m number of rows
• n number of columns
• max_per_row maximum number of nonzero entries per row

Definition at line 48 of file chunk_sparsity_pattern.cc.

## ◆ ChunkSparsityPattern() [4/6]

 ChunkSparsityPattern::ChunkSparsityPattern ( const size_type m, const size_type n, const std::vector< size_type > & row_lengths, const size_type chunk_size )

Initialize a rectangular matrix.

• m number of rows
• n number of columns
• row_lengths possible number of nonzero entries for each row. This vector must have one entry for each row.

Definition at line 60 of file chunk_sparsity_pattern.cc.

## ◆ ChunkSparsityPattern() [5/6]

 ChunkSparsityPattern::ChunkSparsityPattern ( const size_type n, const size_type max_per_row, const size_type chunk_size )

Initialize a quadratic matrix of dimension n 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 73 of file chunk_sparsity_pattern.cc.

## ◆ ChunkSparsityPattern() [6/6]

 ChunkSparsityPattern::ChunkSparsityPattern ( const size_type m, const std::vector< size_type > & row_lengths, const size_type chunk_size )

Initialize a quadratic matrix.

• m number of rows and columns
• row_lengths possible number of nonzero entries for each row. This vector must have one entry for each row.

Definition at line 82 of file chunk_sparsity_pattern.cc.

## ◆ ~ChunkSparsityPattern()

 ChunkSparsityPattern::~ChunkSparsityPattern ( )
overridedefault

Destructor.

## ◆ operator=() [2/3]

 ChunkSparsityPattern & ChunkSparsityPattern::operator= ( const ChunkSparsityPattern & 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 95 of file chunk_sparsity_pattern.cc.

## ◆ reinit() [2/5]

 void ChunkSparsityPattern::reinit ( const size_type m, const size_type n, const size_type max_per_row, const size_type chunk_size )

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 116 of file chunk_sparsity_pattern.cc.

## ◆ reinit() [3/5]

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

Reallocate memory for a matrix of size m x 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...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.

If the number of rows equals the number of columns then diagonal elements are stored first in each row to allow optimized access in relaxation methods of SparseMatrix.

Definition at line 260 of file chunk_sparsity_pattern.cc.

## ◆ reinit() [4/5]

 void ChunkSparsityPattern::reinit ( const size_type m, const size_type n, const ArrayView< const size_type > & row_lengths, const size_type chunk_size )

Same as above, but with an ArrayView argument instead.

Definition at line 131 of file chunk_sparsity_pattern.cc.

## ◆ compress() [2/3]

 void ChunkSparsityPattern::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 ChunkSparsityPattern objects they are initialized with to be compressed, to reduce memory requirements.

Definition at line 174 of file chunk_sparsity_pattern.cc.

## ◆ copy_from() [1/3]

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

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 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 integer (if we only wanted to describe a sparsity pattern). The function is able to determine itself whether an 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<size_type> > column_indices (n_rows);
for (size_type 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());
types::global_dof_index size_type
size_type n_cols() const
size_type n_rows() const

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 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<size_type,double> > entries (n_rows);
for (size_type 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());
@ matrix
Contents is actually a matrix.

This example works because dereferencing iterators of the inner type yields a pair of 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<size_type,double> could be replaced by std::vector<std::pair<size_type,double> >, or a list or set of such pairs, as they all return iterators that point to such pairs.

## ◆ copy_from() [2/3]

template<typename SparsityPatternType >
 void ChunkSparsityPattern::copy_from ( const SparsityPatternType & dsp, const size_type chunk_size )

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

Definition at line 183 of file chunk_sparsity_pattern.cc.

## ◆ copy_from() [3/3]

template<typename number >
 void ChunkSparsityPattern::copy_from ( const FullMatrix< number > & matrix, const size_type chunk_size )

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.

Definition at line 225 of file chunk_sparsity_pattern.cc.

## ◆ create_from()

template<typename Sparsity >
 void ChunkSparsityPattern::create_from ( const size_type m, const size_type n, const Sparsity & sparsity_pattern_for_chunks, const size_type chunk_size, const bool optimize_diagonal = true )

Set the sparsity pattern of the chunk sparsity pattern to be given by chunk_size*chunksize blocks of the sparsity pattern for chunks specified. Note that the final number of rows m of the sparsity pattern will be approximately sparsity_pattern_for_chunks.n_rows() * chunk_size (modulo padding elements in the last chunk) and similarly for the number of columns n.

This is a special initialization option in case you can tell the position of the chunk already from the beginning without generating the sparsity pattern using make_sparsity_pattern calls. This bypasses the search for chunks but of course needs to be handled with care in order to give a correct sparsity pattern.

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

Definition at line 295 of file chunk_sparsity_pattern.cc.

## ◆ empty() [2/3]

 bool ChunkSparsityPattern::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 320 of file chunk_sparsity_pattern.cc.

## ◆ get_chunk_size()

 size_type ChunkSparsityPattern::get_chunk_size ( ) const

Return the chunk size given as argument when constructing this object.

## ◆ max_entries_per_row() [2/3]

 ChunkSparsityPattern::size_type ChunkSparsityPattern::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 328 of file chunk_sparsity_pattern.cc.

## ◆ add() [2/4]

 void ChunkSparsityPattern::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 336 of file chunk_sparsity_pattern.cc.

## ◆ symmetrize() [1/2]

 void ChunkSparsityPattern::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 357 of file chunk_sparsity_pattern.cc.

## ◆ n_rows() [2/3]

 size_type ChunkSparsityPattern::n_rows ( ) const
inline

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

## ◆ n_cols() [2/3]

 size_type ChunkSparsityPattern::n_cols ( ) const
inline

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

## ◆ exists() [2/3]

 bool ChunkSparsityPattern::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 346 of file chunk_sparsity_pattern.cc.

## ◆ row_length() [2/3]

 ChunkSparsityPattern::size_type ChunkSparsityPattern::row_length ( const size_type row ) const

Number of entries in a specific row.

Definition at line 370 of file chunk_sparsity_pattern.cc.

## ◆ bandwidth() [1/2]

 ChunkSparsityPattern::size_type ChunkSparsityPattern::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 $$\max\{n-1,m-1\}$$.

Definition at line 520 of file chunk_sparsity_pattern.cc.

## ◆ n_nonzero_elements() [2/3]

 ChunkSparsityPattern::size_type ChunkSparsityPattern::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.

Definition at line 398 of file chunk_sparsity_pattern.cc.

## ◆ is_compressed()

 bool ChunkSparsityPattern::is_compressed ( ) const

Return whether the structure is compressed or not.

## ◆ stores_only_added_elements() [1/2]

 bool ChunkSparsityPattern::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 true 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.

Definition at line 535 of file chunk_sparsity_pattern.cc.

## ◆ begin() [1/4]

 iterator ChunkSparsityPattern::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.

## ◆ end() [1/4]

 iterator ChunkSparsityPattern::end ( ) const

Final iterator.

## ◆ begin() [2/4]

 iterator ChunkSparsityPattern::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.

## ◆ end() [2/4]

 iterator ChunkSparsityPattern::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.

## ◆ block_write()

 void ChunkSparsityPattern::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 of 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 546 of file chunk_sparsity_pattern.cc.

 void ChunkSparsityPattern::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 562 of file chunk_sparsity_pattern.cc.

## ◆ print() [2/3]

 void ChunkSparsityPattern::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 455 of file chunk_sparsity_pattern.cc.

## ◆ print_gnuplot() [2/3]

 void ChunkSparsityPattern::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 486 of file chunk_sparsity_pattern.cc.

## ◆ memory_consumption() [1/3]

 std::size_t ChunkSparsityPattern::memory_consumption ( ) const

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

Definition at line 588 of file chunk_sparsity_pattern.cc.

## ◆ Accessor() [3/5]

 DynamicSparsityPatternIterators::Accessor::Accessor ( const DynamicSparsityPattern * sparsity_pattern, const size_type row, const unsigned int index_within_row )
inline

Constructor.

Definition at line 745 of file dynamic_sparsity_pattern.h.

## ◆ Accessor() [4/5]

 DynamicSparsityPatternIterators::Accessor::Accessor ( const DynamicSparsityPattern * sparsity_pattern )
inline

Constructor. Construct the end accessor for the given sparsity pattern.

Definition at line 781 of file dynamic_sparsity_pattern.h.

## ◆ Accessor() [5/5]

 DynamicSparsityPatternIterators::Accessor::Accessor ( )
inline

Default constructor creating a dummy accessor. This constructor is here only to be able to store accessors in STL containers such as std::vector.

Definition at line 790 of file dynamic_sparsity_pattern.h.

## ◆ row() [2/2]

 size_type DynamicSparsityPatternIterators::Accessor::row ( ) const
inline

Row number of the element represented by this object.

Definition at line 799 of file dynamic_sparsity_pattern.h.

## ◆ index()

 size_type DynamicSparsityPatternIterators::Accessor::index ( ) const
inline

Index within the current row of the element represented by this object.

Definition at line 819 of file dynamic_sparsity_pattern.h.

## ◆ column() [2/2]

 size_type DynamicSparsityPatternIterators::Accessor::column ( ) const
inline

Column number of the element represented by this object.

Definition at line 809 of file dynamic_sparsity_pattern.h.

## ◆ operator==() [3/4]

 bool DynamicSparsityPatternIterators::Accessor::operator== ( const Accessor & other ) const
inline

Comparison. True, if both iterators point to the same matrix position.

Definition at line 835 of file dynamic_sparsity_pattern.h.

## ◆ operator<() [3/4]

 bool DynamicSparsityPatternIterators::Accessor::operator< ( const Accessor & other ) const
inline

Comparison operator. Result is true if either the first row number is smaller or if the row numbers are equal and the first index is smaller.

This function is only valid if both iterators point into the same sparsity pattern.

Definition at line 851 of file dynamic_sparsity_pattern.h.

## ◆ advance() [2/2]

 void DynamicSparsityPatternIterators::Accessor::advance ( )
inlineprotected

Move the accessor to the next nonzero entry in the matrix.

Definition at line 878 of file dynamic_sparsity_pattern.h.

## ◆ Iterator() [2/4]

 DynamicSparsityPatternIterators::Iterator::Iterator ( const DynamicSparsityPattern * sp, const size_type row, const unsigned int index_within_row )
inline

Constructor. Create an iterator into the sparsity pattern sp for the given global index (i.e., the index of the given element counting from the zeroth row).

Definition at line 906 of file dynamic_sparsity_pattern.h.

## ◆ Iterator() [3/4]

 DynamicSparsityPatternIterators::Iterator::Iterator ( const DynamicSparsityPattern * sp )
inline

Constructor. Create an invalid (end) iterator into the sparsity pattern sp.

Definition at line 914 of file dynamic_sparsity_pattern.h.

## ◆ Iterator() [4/4]

 DynamicSparsityPatternIterators::Iterator::Iterator ( )
default

Default constructor creating an invalid iterator. This constructor is here only to be able to store iterators in STL containers such as std::vector.

## ◆ operator++() [3/4]

 Iterator & DynamicSparsityPatternIterators::Iterator::operator++ ( )
inline

Prefix increment.

Definition at line 921 of file dynamic_sparsity_pattern.h.

## ◆ operator++() [4/4]

 Iterator DynamicSparsityPatternIterators::Iterator::operator++ ( int )
inline

Postfix increment.

Definition at line 930 of file dynamic_sparsity_pattern.h.

## ◆ operator*() [2/2]

 const Accessor & DynamicSparsityPatternIterators::Iterator::operator* ( ) const
inline

Dereferencing operator.

Definition at line 940 of file dynamic_sparsity_pattern.h.

## ◆ operator->() [2/2]

 const Accessor * DynamicSparsityPatternIterators::Iterator::operator-> ( ) const
inline

Dereferencing operator.

Definition at line 948 of file dynamic_sparsity_pattern.h.

## ◆ operator==() [4/4]

 bool DynamicSparsityPatternIterators::Iterator::operator== ( const Iterator & other ) const
inline

Comparison. True, if both iterators point to the same matrix position.

Definition at line 955 of file dynamic_sparsity_pattern.h.

## ◆ operator!=() [2/2]

 bool DynamicSparsityPatternIterators::Iterator::operator!= ( const Iterator & other ) const
inline

Inverse of ==.

Definition at line 963 of file dynamic_sparsity_pattern.h.

## ◆ operator<() [4/4]

 bool DynamicSparsityPatternIterators::Iterator::operator< ( const Iterator & other ) const
inline

Comparison operator. Result is true if either the first row number is smaller or if the row numbers are equal and the first index is smaller.

This function is only valid if both iterators point into the same matrix.

Definition at line 969 of file dynamic_sparsity_pattern.h.

## ◆ operator-()

 int DynamicSparsityPatternIterators::Iterator::operator- ( const Iterator & p ) const
inline

Return the distance between the current iterator and the argument. The distance is given by how many times one has to apply operator++ to the current iterator to get the argument (for a positive return value), or operator-- (for a negative return value).

Definition at line 977 of file dynamic_sparsity_pattern.h.

## ◆ DynamicSparsityPattern() [1/5]

 DynamicSparsityPattern::DynamicSparsityPattern ( )

Initialize as an empty object. 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 222 of file dynamic_sparsity_pattern.cc.

## ◆ DynamicSparsityPattern() [2/5]

 DynamicSparsityPattern::DynamicSparsityPattern ( const DynamicSparsityPattern & s )

Copy constructor. This constructor is only allowed to be called if the sparsity 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 you want to place a DynamicSparsityPattern in a container, e.g. to write such statements like v.push_back (DynamicSparsityPattern());, with v a vector of DynamicSparsityPattern objects.

Definition at line 231 of file dynamic_sparsity_pattern.cc.

## ◆ DynamicSparsityPattern() [3/5]

 DynamicSparsityPattern::DynamicSparsityPattern ( const size_type m, const size_type n, const IndexSet & rowset = IndexSet() )

Initialize a rectangular sparsity pattern with m rows and n columns. The rowset restricts the storage to elements in rows of this set. Adding elements outside of this set has no effect. The default argument keeps all entries.

Definition at line 248 of file dynamic_sparsity_pattern.cc.

## ◆ DynamicSparsityPattern() [4/5]

 DynamicSparsityPattern::DynamicSparsityPattern ( const IndexSet & indexset )

Create a square SparsityPattern using the given index set. The total size is given by the size of indexset and only rows corresponding to indices in indexset are stored on the current processor.

Definition at line 260 of file dynamic_sparsity_pattern.cc.

## ◆ DynamicSparsityPattern() [5/5]

 DynamicSparsityPattern::DynamicSparsityPattern ( const size_type n )

Initialize a square pattern of dimension n.

Definition at line 270 of file dynamic_sparsity_pattern.cc.

## ◆ operator=() [3/3]

 DynamicSparsityPattern & DynamicSparsityPattern::operator= ( const DynamicSparsityPattern & 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 282 of file dynamic_sparsity_pattern.cc.

## ◆ reinit() [5/5]

 void DynamicSparsityPattern::reinit ( const size_type m, const size_type n, const IndexSet & rowset = IndexSet() )

Reallocate memory and set up data structures for a new sparsity pattern with m rows and n columns. The rowset restricts the storage to elements in rows of this set. Adding elements outside of this set has no effect. The default argument keeps all entries.

Definition at line 301 of file dynamic_sparsity_pattern.cc.

## ◆ compress() [3/3]

 void DynamicSparsityPattern::compress ( )

Since this object is kept compressed at all times anyway, this function does nothing, but is declared to make the interface of this class as much alike as that of the SparsityPattern class.

Definition at line 326 of file dynamic_sparsity_pattern.cc.

## ◆ empty() [3/3]

 bool DynamicSparsityPattern::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 332 of file dynamic_sparsity_pattern.cc.

## ◆ max_entries_per_row() [3/3]

 DynamicSparsityPattern::size_type DynamicSparsityPattern::max_entries_per_row ( ) const

Return the maximum number of entries per row. Note that this number may change as entries are added.

Definition at line 340 of file dynamic_sparsity_pattern.cc.

## ◆ add() [3/4]

 void DynamicSparsityPattern::add ( const size_type i, const size_type j )
inline

Add a nonzero entry. If the entry already exists, this call does nothing.

Definition at line 1031 of file dynamic_sparsity_pattern.h.

## ◆ add_entries() [2/3]

template<typename ForwardIterator >
 void DynamicSparsityPattern::add_entries ( const size_type row, ForwardIterator begin, ForwardIterator end, const bool indices_are_unique_and_sorted = false )
inline

Add several nonzero entries to the specified row. Already existing entries are ignored.

Definition at line 1050 of file dynamic_sparsity_pattern.h.

## ◆ exists() [3/3]

 bool DynamicSparsityPattern::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 357 of file dynamic_sparsity_pattern.cc.

## ◆ get_view()

 DynamicSparsityPattern DynamicSparsityPattern::get_view ( const IndexSet & rows ) const

Return a view of this sparsity pattern. That is, for all rows in rows extract non-empty columns. The resulting sparsity pattern will have number of rows equal rows.n_elements().

Definition at line 432 of file dynamic_sparsity_pattern.cc.

## ◆ symmetrize() [2/2]

 void DynamicSparsityPattern::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 square matrix.

Definition at line 386 of file dynamic_sparsity_pattern.cc.

## ◆ compute_mmult_pattern()

template<typename SparsityPatternTypeLeft , typename SparsityPatternTypeRight >
 template void DynamicSparsityPattern::compute_mmult_pattern ( const SparsityPatternTypeLeft & left, const SparsityPatternTypeRight & right )

Construct and store in this object the sparsity pattern corresponding to the product of left and right sparsity pattern.

Definition at line 496 of file dynamic_sparsity_pattern.cc.

## ◆ compute_Tmmult_pattern()

template<typename SparsityPatternTypeLeft , typename SparsityPatternTypeRight >
 template void DynamicSparsityPattern::compute_Tmmult_pattern ( const SparsityPatternTypeLeft & left, const SparsityPatternTypeRight & right )

Construct and store in this object the sparsity pattern corresponding to the product of transposed left and non-transpose right sparsity pattern.

Definition at line 455 of file dynamic_sparsity_pattern.cc.

## ◆ print() [3/3]

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

Print the sparsity pattern. 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 525 of file dynamic_sparsity_pattern.cc.

## ◆ print_gnuplot() [3/3]

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

Print the sparsity pattern 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, 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 543 of file dynamic_sparsity_pattern.cc.

## ◆ n_rows() [3/3]

 DynamicSparsityPattern::size_type DynamicSparsityPattern::n_rows ( ) const
inline

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

Definition at line 1015 of file dynamic_sparsity_pattern.h.

## ◆ n_cols() [3/3]

 types::global_dof_index DynamicSparsityPattern::n_cols ( ) const
inline

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

Definition at line 1023 of file dynamic_sparsity_pattern.h.

## ◆ row_length() [3/3]

 types::global_dof_index DynamicSparsityPattern::row_length ( const size_type row ) const
inline

Number of entries in a specific row. This function can only be called if the given row is a member of the index set of rows that we want to store.

Definition at line 1071 of file dynamic_sparsity_pattern.h.

## ◆ clear_row()

 void DynamicSparsityPattern::clear_row ( const size_type row )

Clear all entries stored in a specific row.

Definition at line 413 of file dynamic_sparsity_pattern.cc.

## ◆ column_number()

 types::global_dof_index DynamicSparsityPattern::column_number ( const size_type row, const size_type index ) const
inline

Access to column number field. Return the column number of the indexth entry in row.

Definition at line 1089 of file dynamic_sparsity_pattern.h.

## ◆ column_index()

 types::global_dof_index DynamicSparsityPattern::column_index ( const size_type row, const size_type col ) const

Return index of column col in row row. If the column does not exist in this sparsity pattern, the returned value will be 'numbers::invalid_size_type'.

Definition at line 656 of file dynamic_sparsity_pattern.cc.

## ◆ begin() [3/4]

 DynamicSparsityPattern::iterator DynamicSparsityPattern::begin ( ) const
inline

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.

Note the discussion in the general documentation of this class about the order in which elements are accessed.

Note
If the sparsity pattern has been initialized with an IndexSet that denotes which rows to store, then iterators will simply skip over rows that are not stored. In other words, they will look like empty rows, but no exception will be generated when iterating over such rows.

Definition at line 1104 of file dynamic_sparsity_pattern.h.

## ◆ end() [3/4]

 DynamicSparsityPattern::iterator DynamicSparsityPattern::end ( ) const
inline

Final iterator.

Definition at line 1114 of file dynamic_sparsity_pattern.h.

## ◆ begin() [4/4]

 DynamicSparsityPattern::iterator DynamicSparsityPattern::begin ( const size_type r ) const
inline

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.

Note also the discussion in the general documentation of this class about the order in which elements are accessed.

Note
If the sparsity pattern has been initialized with an IndexSet that denotes which rows to store, then iterators will simply skip over rows that are not stored. In other words, they will look like empty rows, but no exception will be generated when iterating over such rows.

Definition at line 1122 of file dynamic_sparsity_pattern.h.

## ◆ end() [4/4]

 DynamicSparsityPattern::iterator DynamicSparsityPattern::end ( const size_type r ) const
inline

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.

Definition at line 1180 of file dynamic_sparsity_pattern.h.

## ◆ bandwidth() [2/2]

 DynamicSparsityPattern::size_type DynamicSparsityPattern::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.

Definition at line 566 of file dynamic_sparsity_pattern.cc.

## ◆ n_nonzero_elements() [3/3]

 DynamicSparsityPattern::size_type DynamicSparsityPattern::n_nonzero_elements ( ) const

Return the number of nonzero elements allocated through this sparsity pattern.

Definition at line 586 of file dynamic_sparsity_pattern.cc.

## ◆ row_index_set()

 const IndexSet & DynamicSparsityPattern::row_index_set ( ) const
inline

Return the IndexSet that sets which rows are active on the current processor. It corresponds to the IndexSet given to this class in the constructor or in the reinit function.

Definition at line 1194 of file dynamic_sparsity_pattern.h.

## ◆ nonempty_cols()

 IndexSet DynamicSparsityPattern::nonempty_cols ( ) const

Return the IndexSet that contains entries for all columns in which at least one element exists in this sparsity pattern.

Note
In a parallel context, this only considers the locally stored rows.

Definition at line 603 of file dynamic_sparsity_pattern.cc.

## ◆ nonempty_rows()

 IndexSet DynamicSparsityPattern::nonempty_rows ( ) const

Return the IndexSet that contains entries for all rows in which at least one element exists in this sparsity pattern.

Note
In a parallel context, this only considers the locally stored rows.

Definition at line 617 of file dynamic_sparsity_pattern.cc.

## ◆ stores_only_added_elements() [2/2]

 bool DynamicSparsityPattern::stores_only_added_elements ( )
inlinestatic

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 always true.

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.

Definition at line 1202 of file dynamic_sparsity_pattern.h.

## ◆ memory_consumption() [2/3]

 DynamicSparsityPattern::size_type DynamicSparsityPattern::memory_consumption ( ) const

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

Definition at line 641 of file dynamic_sparsity_pattern.cc.

## ◆ add() [4/4]

 void DynamicSparsityPattern::Line::add ( const size_type col_num )
inline

Add the given column number to this line.

Definition at line 990 of file dynamic_sparsity_pattern.h.

## ◆ add_entries() [3/3]

template<typename ForwardIterator >
 template void DynamicSparsityPattern::Line::add_entries ( ForwardIterator begin, ForwardIterator end, const bool indices_are_sorted )

Add the columns specified by the iterator range to this line.

Definition at line 34 of file dynamic_sparsity_pattern.cc.

## ◆ memory_consumption() [3/3]

 DynamicSparsityPattern::size_type DynamicSparsityPattern::Line::memory_consumption ( ) const

estimates memory consumption.

Definition at line 216 of file dynamic_sparsity_pattern.cc.

## ◆ invalid_entry [1/2]

template<typename SparsityPatternType >
 const size_type BlockSparsityPatternBase< SparsityPatternType >::invalid_entry = SparsityPattern::invalid_entry
static

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.

This value is only an alias to the respective value of the SparsityPattern class.

Definition at line 94 of file block_sparsity_pattern.h.

## ◆ sparsity_pattern [1/2]

 const ChunkSparsityPattern* ChunkSparsityPatternIterators::Accessor::sparsity_pattern
protected

The sparsity pattern we operate on accessed.

Definition at line 134 of file chunk_sparsity_pattern.h.

## ◆ reduced_accessor

 SparsityPatternIterators::Accessor ChunkSparsityPatternIterators::Accessor::reduced_accessor
protected

The accessor of the (reduced) sparsity pattern.

Definition at line 139 of file chunk_sparsity_pattern.h.

## ◆ chunk_row

 size_type ChunkSparsityPatternIterators::Accessor::chunk_row
protected

Current chunk row number.

Definition at line 144 of file chunk_sparsity_pattern.h.

## ◆ chunk_col

 size_type ChunkSparsityPatternIterators::Accessor::chunk_col
protected

Current chunk col number.

Definition at line 149 of file chunk_sparsity_pattern.h.

## ◆ accessor [1/2]

 Accessor ChunkSparsityPatternIterators::Iterator::accessor
private

Store an object of the accessor class.

Definition at line 230 of file chunk_sparsity_pattern.h.

## ◆ invalid_entry [2/2]

 const size_type ChunkSparsityPattern::invalid_entry = SparsityPattern::invalid_entry
static

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 280 of file chunk_sparsity_pattern.h.

## ◆ sparsity_pattern [2/2]

 const DynamicSparsityPattern* DynamicSparsityPatternIterators::Accessor::sparsity_pattern
protected

The sparsity pattern we operate on accessed.

Definition at line 131 of file dynamic_sparsity_pattern.h.

## ◆ current_row

 size_type DynamicSparsityPatternIterators::Accessor::current_row
protected

The row we currently point into.

Definition at line 136 of file dynamic_sparsity_pattern.h.

## ◆ current_entry

 std::vector::const_iterator DynamicSparsityPatternIterators::Accessor::current_entry
protected

A pointer to the element within the current row that we currently point to.

Definition at line 142 of file dynamic_sparsity_pattern.h.

## ◆ end_of_row

 std::vector::const_iterator DynamicSparsityPatternIterators::Accessor::end_of_row
protected

A pointer to the end of the current row. We store this to make comparison against the end of line iterator cheaper as it otherwise needs to do the IndexSet translation from row index to the index within the 'lines' array of DynamicSparsityPattern.

Definition at line 150 of file dynamic_sparsity_pattern.h.

## ◆ accessor [2/2]

 Accessor DynamicSparsityPatternIterators::Iterator::accessor
private

Store an object of the accessor class.

Definition at line 272 of file dynamic_sparsity_pattern.h.

## ◆ have_entries

 bool DynamicSparsityPattern::have_entries
private

A flag that stores whether any entries have been added so far.

Definition at line 673 of file dynamic_sparsity_pattern.h.

## ◆ rows

 size_type DynamicSparsityPattern::rows
private

Number of rows that this sparsity structure shall represent.

Definition at line 678 of file dynamic_sparsity_pattern.h.

## ◆ cols

 size_type DynamicSparsityPattern::cols
private

Number of columns that this sparsity structure shall represent.

Definition at line 683 of file dynamic_sparsity_pattern.h.

## ◆ rowset

 IndexSet DynamicSparsityPattern::rowset
private

A set that contains the valid rows.

Definition at line 689 of file dynamic_sparsity_pattern.h.

## ◆ entries

 std::vector DynamicSparsityPattern::Line::entries

Storage for the column indices of this row. This array is always kept sorted.

Definition at line 705 of file dynamic_sparsity_pattern.h.

## ◆ lines

 std::vector DynamicSparsityPattern::lines
private

Actual data: store for each row the set of nonzero entries.

Definition at line 733 of file dynamic_sparsity_pattern.h.

## ◆ Iterator [1/2]

 friend class Iterator
friend

Definition at line 158 of file chunk_sparsity_pattern.h.

## ◆ Iterator [2/2]

 friend class Iterator
friend

Definition at line 159 of file dynamic_sparsity_pattern.h.

## ◆ DynamicSparsityPatternIterators::Accessor

 friend class DynamicSparsityPatternIterators::Accessor
friend

Definition at line 736 of file dynamic_sparsity_pattern.h.