#include <deal.II/base/index_set.h>

Classes
class	ElementIterator

class	IntervalAccessor

class	IntervalIterator

struct	Range

Public Types
using	size_type = types::global_dof_index

using	value_type = signed int

Public Member Functions
	IndexSet ()

	IndexSet (const size_type size)

	IndexSet (const IndexSet &)=default

IndexSet &	operator= (const IndexSet &)=default

	IndexSet (IndexSet &&is) noexcept

IndexSet &	operator= (IndexSet &&is) noexcept

	IndexSet (const Epetra_BlockMap &map)

void	clear ()

void	set_size (const size_type size)

size_type	size () const

void	add_range (const size_type begin, const size_type end)

void	add_index (const size_type index)

template<typename ForwardIterator >
void	add_indices (const ForwardIterator &begin, const ForwardIterator &end)

void	add_indices (const IndexSet &other, const size_type offset=0)

bool	is_element (const size_type index) const

bool	is_contiguous () const

bool	is_empty () const

bool	is_ascending_and_one_to_one (const MPI_Comm &communicator) const

size_type	n_elements () const

size_type	nth_index_in_set (const size_type local_index) const

size_type	index_within_set (const size_type global_index) const

unsigned int	n_intervals () const

size_type	largest_range_starting_index () const

void	compress () const

bool	operator== (const IndexSet &is) const

bool	operator!= (const IndexSet &is) const

IndexSet	operator& (const IndexSet &is) const

IndexSet	get_view (const size_type begin, const size_type end) const

std::vector< IndexSet >	split_by_block (const std::vector< types::global_dof_index > &n_indices_per_block) const

void	subtract_set (const IndexSet &other)

IndexSet	tensor_product (const IndexSet &other) const

size_type	pop_back ()

size_type	pop_front ()

void	fill_index_vector (std::vector< size_type > &indices) const

template<typename VectorType >
void	fill_binary_vector (VectorType &vector) const

template<class StreamType >
void	print (StreamType &out) const

void	write (std::ostream &out) const

void	read (std::istream &in)

void	block_write (std::ostream &out) const

void	block_read (std::istream &in)

Epetra_Map	make_trilinos_map (const MPI_Comm &communicator=MPI_COMM_WORLD, const bool overlapping=false) const

Tpetra::Map< int, types::global_dof_index >	make_tpetra_map (const MPI_Comm &communicator=MPI_COMM_WORLD, const bool overlapping=false) const

std::size_t	memory_consumption () const

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

template<typename Vector >
void	fill_binary_vector (Vector &vector) const

Iterators
ElementIterator	begin () const

ElementIterator	at (const size_type global_index) const

ElementIterator	end () const

IntervalIterator	begin_intervals () const

IntervalIterator	end_intervals () const

Static Public Member Functions
static ::ExceptionBase &	ExcIndexNotPresent (size_type arg1)

Private Member Functions
void	do_compress () const

Private Attributes
std::vector< Range >	ranges

bool	is_compressed

size_type	index_space_size

size_type	largest_range

Threads::Mutex	compress_mutex

Related Functions
(Note that these are not member functions.)
IndexSet	complete_index_set (const IndexSet::size_type N)

Detailed Description

A class that represents a subset of indices among a larger set. For example, it can be used to denote the set of degrees of freedom within the range \([0,\text{dof\_handler.n\_dofs})\) that belongs to a particular subdomain, or those among all degrees of freedom that are stored on a particular processor in a distributed parallel computation.

This class can represent a collection of half-open ranges of indices as well as individual elements. For practical purposes it also stores the overall range these indices can assume. In other words, you need to specify the size of the index space \([0,\text{size})\) of which objects of this class are a subset.

There are two ways to iterate over the IndexSets: First, begin() and end() allow iteration over individual indices in the set. Second, begin_interval() and end_interval() allow iteration over the half-open ranges as described above.

The data structures used in this class along with a rationale can be found in the Distributed Computing paper.

Author: Wolfgang Bangerth, 2009

Definition at line 74 of file index_set.h.

Member Typedef Documentation

◆ size_type

using IndexSet::size_type = types::global_dof_index

size_type is the type used for storing the size and the individual entries in the IndexSet.

Definition at line 85 of file index_set.h.

◆ value_type

using IndexSet::value_type = signed int

One can see an IndexSet as a container of size size(), where the elements of the containers are bool values that are either false or true, depending on whether a particular index is an element of the IndexSet or not. In other words, an IndexSet is a bit like a vector in which the elements we store are booleans. In this view, the correct local alias indicating the type of the elements of the vector would then be bool.

On the other hand, bool has the disadvantage that it is not a numerical type that, for example, allows multiplication with a double. In other words, one can not easily use a vector of booleans in a place where other vectors are allowed. Consequently, we declare the type of the elements of such a vector as a signed integer. This uses the fact that in the C++ language, booleans are implicitly convertible to integers. In other words, declaring the type of the elements of the vector as a signed integer is only a small lie, but it is a useful one.

Definition at line 104 of file index_set.h.

Constructor & Destructor Documentation

◆ IndexSet() [1/5]

IndexSet::IndexSet ( )

inline

Default constructor.

Definition at line 1466 of file index_set.h.

◆ IndexSet() [2/5]

IndexSet::IndexSet ( const size_type size )

inlineexplicit

Constructor that also sets the overall size of the index range.

Definition at line 1474 of file index_set.h.

◆ IndexSet() [3/5]

IndexSet::IndexSet ( const IndexSet & )

default

Copy constructor.

◆ IndexSet() [4/5]

IndexSet::IndexSet ( IndexSet && is )

inlinenoexcept

Move constructor. Create a new IndexSet by transferring the internal data of the input set.

Definition at line 1482 of file index_set.h.

◆ IndexSet() [5/5]

IndexSet::IndexSet ( const Epetra_BlockMap & map )

explicit

Constructor from a Trilinos Epetra_BlockMap.

Definition at line 68 of file index_set.cc.

Member Function Documentation

◆ operator=() [1/2]

IndexSet& IndexSet::operator= ( const IndexSet & )

default

Copy assignment operator.

◆ operator=() [2/2]

IndexSet & IndexSet::operator= ( IndexSet && is )

inlinenoexcept

Move assignment operator. Transfer the internal data of the input set into the current one.

Definition at line 1499 of file index_set.h.

◆ clear()

void IndexSet::clear ( )

inline

Remove all indices from this index set. The index set retains its size, however.

Definition at line 1611 of file index_set.h.

◆ set_size()

void IndexSet::set_size ( const size_type size )

inline

Set the maximal size of the indices upon which this object operates.

This function can only be called if the index set does not yet contain any elements. This can be achieved by calling clear(), for example.

Definition at line 1623 of file index_set.h.

◆ size()

IndexSet::size_type IndexSet::size ( ) const

inline

Return the size of the index space of which this index set is a subset of.

Note that the result is not equal to the number of indices within this set. The latter information is returned by n_elements().

Definition at line 1635 of file index_set.h.

◆ add_range()

void IndexSet::add_range	(	const size_type	begin,
		const size_type	end
	)

inline

Add the half-open range \([\text{begin},\text{end})\) to the set of indices represented by this class.

Parameters

[in]	begin	The first element of the range to be added.
[in]	end	The past-the-end element of the range to be added.

Definition at line 1674 of file index_set.h.

◆ add_index()

void IndexSet::add_index ( const size_type index )

inline

Add an individual index to the set of indices.

Definition at line 1654 of file index_set.h.

◆ add_indices() [1/2]

template<typename ForwardIterator >

void IndexSet::add_indices	(	const ForwardIterator &	begin,
		const ForwardIterator &	end
	)

inline

Add a whole set of indices described by dereferencing every element of the iterator range [begin,end).

Parameters

[in]	begin	Iterator to the first element of range of indices to be added
[in]	end	The past-the-end iterator for the range of elements to be added.

Precondition: The condition begin<=end needs to be satisfied.

Definition at line 1704 of file index_set.h.

◆ add_indices() [2/2]

void IndexSet::add_indices	(	const IndexSet &	other,
		const size_type	offset = `0`
	)

Add the given IndexSet other to the current one, constructing the union of *this and other.

If the offset argument is nonzero, then every index in other is shifted by offset before being added to the current index set. This allows to construct, for example, one index set from several others that are supposed to represent index sets corresponding to different ranges (e.g., when constructing the set of nonzero entries of a block vector from the sets of nonzero elements of the individual blocks of a vector).

This function will generate an exception if any of the (possibly shifted) indices of the other index set lie outside the range [0,size()) represented by the current object.

Definition at line 382 of file index_set.cc.

◆ is_element()

bool IndexSet::is_element ( const size_type index ) const

inline

Return whether the specified index is an element of the index set.

Definition at line 1766 of file index_set.h.

◆ is_contiguous()

bool IndexSet::is_contiguous ( ) const

inline

Return whether the index set stored by this object defines a contiguous range. This is true also if no indices are stored at all.

Definition at line 1816 of file index_set.h.

◆ is_empty()

bool IndexSet::is_empty ( ) const

inline

Return whether the index set stored by this object contains no elements. This is similar, but faster than checking n_elements() == 0.

Definition at line 1825 of file index_set.h.

◆ is_ascending_and_one_to_one()

bool IndexSet::is_ascending_and_one_to_one ( const MPI_Comm & communicator ) const

Return whether the IndexSets are ascending with respect to MPI process number and 1:1, i.e., each index is contained in exactly one IndexSet (among those stored on the different processes), each process stores contiguous subset of indices, and the index set on process \(p+1\) starts at the index one larger than the last one stored on process \(p\). In case there is only one MPI process, this just means that the IndexSet is complete.

Definition at line 666 of file index_set.cc.

◆ n_elements()

IndexSet::size_type IndexSet::n_elements ( ) const

inline

Return the number of elements stored in this index set.

Definition at line 1833 of file index_set.h.

◆ nth_index_in_set()

IndexSet::size_type IndexSet::nth_index_in_set ( const size_type local_index ) const

inline

Return the global index of the local index with number local_index stored in this index set. local_index obviously needs to be less than n_elements().

Definition at line 1881 of file index_set.h.

◆ index_within_set()

IndexSet::size_type IndexSet::index_within_set ( const size_type global_index ) const

inline

Return the how-manyth element of this set (counted in ascending order) global_index is. global_index needs to be less than the size(). This function returns numbers::invalid_dof_index if the index global_index is not actually a member of this index set, i.e. if is_element(global_index) is false.

Definition at line 1922 of file index_set.h.

◆ n_intervals()

unsigned int IndexSet::n_intervals ( ) const

inline

Each index set can be represented as the union of a number of contiguous intervals of indices, where if necessary intervals may only consist of individual elements to represent isolated members of the index set.

This function returns the minimal number of such intervals that are needed to represent the index set under consideration.

Definition at line 1858 of file index_set.h.

◆ largest_range_starting_index()

IndexSet::size_type IndexSet::largest_range_starting_index ( ) const

inline

This function returns the local index of the beginning of the largest range.

In other words, the return value is nth_index_in_set(x), where x is the first index of the largest contiguous range of indices in the IndexSet. The return value is therefore equal to the number of elements in the set that come before the largest range.

This call assumes that the IndexSet is nonempty.

Definition at line 1867 of file index_set.h.

◆ compress()

void IndexSet::compress ( ) const

inline

Compress the internal representation by merging individual elements with contiguous ranges, etc. This function does not have any external effect.

Definition at line 1643 of file index_set.h.

◆ operator==()

bool IndexSet::operator== ( const IndexSet & is ) const

inline

Comparison for equality of index sets. This operation is only allowed if the size of the two sets is the same (though of course they do not have to have the same number of indices).

Definition at line 1970 of file index_set.h.

◆ operator!=()

bool IndexSet::operator!= ( const IndexSet & is ) const

inline

Comparison for inequality of index sets. This operation is only allowed if the size of the two sets is the same (though of course they do not have to have the same number of indices).

Definition at line 1983 of file index_set.h.

◆ operator&()

IndexSet IndexSet::operator& ( const IndexSet & is ) const

Return the intersection of the current index set and the argument given, i.e. a set of indices that are elements of both index sets. The two index sets must have the same size (though of course they do not have to have the same number of indices).

◆ get_view()

IndexSet IndexSet::get_view	(	const size_type	begin,
		const size_type	end
	)		const

This command takes an interval [begin, end) and returns the intersection of the current index set with the interval, shifted to the range [0, end-begin).

In other words, the result of this operation is the intersection of the set represented by the current object and the interval [begin, end), as seen within the interval [begin, end) by shifting the result of the intersection operation to the left by begin. This corresponds to the notion of a view: The interval [begin, end) is a window through which we see the set represented by the current object.

Definition at line 211 of file index_set.cc.

◆ split_by_block()

std::vector< IndexSet > IndexSet::split_by_block ( const std::vector< types::global_dof_index > & n_indices_per_block ) const

Split the set indices represented by this object into blocks given by the n_indices_per_block structure. The sum of its entries must match the global size of the current object.

Definition at line 238 of file index_set.cc.

◆ subtract_set()

void IndexSet::subtract_set ( const IndexSet & other )

Remove all elements contained in other from this set. In other words, if \(x\) is the current object and \(o\) the argument, then we compute \(x \leftarrow x \backslash o\).

Definition at line 258 of file index_set.cc.

◆ tensor_product()

IndexSet IndexSet::tensor_product ( const IndexSet & other ) const

Return a new IndexSet, with global size equal to this->size()*other.size(), containing for every element n of this IndexSet, the entries in the half open range [n*other.size(), (n+1)*other.size()) of the other IndexSet.

The name results from the perspective that one starts with an IndexSet and takes the tensor product with another IndexSet with other.size() elements; this results in a matrix of size this->size() times other.size() that has ones in exactly the rows for which this IndexSet contained an index and in the columns for which the other IndexSet contained an index. This matrix is then "unrolled" again by going through each row one by one and reindexing the entries of the matrix in consecutive order. A one in the matrix then corresponds to an entry in the reindexed IndexSet that is returned by this function.

Definition at line 330 of file index_set.cc.

◆ pop_back()

IndexSet::size_type IndexSet::pop_back ( )

Remove and return the last element of the last range. This function throws an exception if the IndexSet is empty.

Definition at line 342 of file index_set.cc.

◆ pop_front()

IndexSet::size_type IndexSet::pop_front ( )

Remove and return the first element of the first range. This function throws an exception if the IndexSet is empty.

Definition at line 360 of file index_set.cc.

◆ fill_index_vector()

void IndexSet::fill_index_vector ( std::vector< size_type > & indices ) const

Fill the given vector with all indices contained in this IndexSet.

Definition at line 507 of file index_set.cc.

◆ fill_binary_vector() [1/2]

template<typename VectorType >

void IndexSet::fill_binary_vector ( VectorType & vector ) const

Fill the given vector with either zero or one elements, providing a binary representation of this index set. The given vector is assumed to already have the correct size.

The given argument is filled with integer values zero and one, using vector.operator[]. Thus, any object that has such an operator can be used as long as it allows conversion of integers zero and one to elements of the vector. Specifically, this is the case for classes Vector, BlockVector, but also std::vector<bool>, std::vector<int>, and std::vector<double>.

◆ print()

template<class StreamType >

void IndexSet::print ( StreamType & out ) const

inline

Output a text representation of this IndexSet to the given stream. Used for testing.

Definition at line 2016 of file index_set.h.

◆ write()

void IndexSet::write ( std::ostream & out ) const

Write the IndexSet into a text based file format, that can be read in again using the read() function.

Definition at line 436 of file index_set.cc.

◆ read()

void IndexSet::read ( std::istream & in )

Construct the IndexSet from a text based representation given by the stream in written by the write() function.

Definition at line 451 of file index_set.cc.

◆ block_write()

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

Write the IndexSet into a binary, compact representation, that can be read in again using the block_read() function.

Definition at line 473 of file index_set.cc.

◆ block_read()

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

Construct the IndexSet from a binary representation given by the stream in written by the write_block() function.

Definition at line 487 of file index_set.cc.

◆ make_trilinos_map()

Epetra_Map IndexSet::make_trilinos_map	(	const MPI_Comm &	communicator = `MPI_COMM_WORLD`,
		const bool	overlapping = `false`
	)		const

Given an MPI communicator, create a Trilinos map object that represents a distribution of vector elements or matrix rows in which we will locally store those elements or rows for which we store the index in the current index set, and all the other elements/rows elsewhere on one of the other MPI processes.

The last argument only plays a role if the communicator is a parallel one, distributing computations across multiple processors. In that case, if the last argument is false, then it is assumed that the index sets this function is called with on all processors are mutually exclusive but together enumerate each index exactly once. In other words, if you call this function on two processors, then the index sets this function is called with must together have all possible indices from zero to size()-1, and no index must appear in both index sets. This corresponds, for example, to the case where we want to split the elements of vectors into unique subsets to be stored on different processors – no element should be owned by more than one processor, but each element must be owned by one.

On the other hand, if the second argument is true, then the index sets can be overlapping, and they also do not need to span the whole index set. This is a useful operation if we want to create vectors that not only contain the locally owned indices, but for example also the elements that correspond to degrees of freedom located on ghost cells. Another application of this method is to select a subset of the elements of a vector, e.g. for extracting only certain solution components.

Definition at line 596 of file index_set.cc.

◆ make_tpetra_map()

Tpetra::Map< int, types::global_dof_index > IndexSet::make_tpetra_map	(	const MPI_Comm &	communicator = `MPI_COMM_WORLD`,
		const bool	overlapping = `false`
	)		const

Definition at line 527 of file index_set.cc.

◆ memory_consumption()

std::size_t IndexSet::memory_consumption ( ) const

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

Definition at line 729 of file index_set.cc.

◆ serialize()

template<class Archive >

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

inline

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

Definition at line 2047 of file index_set.h.

◆ begin()

IndexSet::ElementIterator IndexSet::begin ( ) const

inline

Return an iterator that points at the first index that is contained in this IndexSet.

Definition at line 1519 of file index_set.h.

◆ at()

IndexSet::ElementIterator IndexSet::at ( const size_type global_index ) const

inline

Return an element iterator pointing to the element with global index global_index or the next larger element if the index is not in the set. This is equivalent to

auto p = begin();
while (*p<global_index)
  ++p;
return p;

If there is no element in this IndexSet at or behind global_index, this method will return end().

Definition at line 1531 of file index_set.h.

◆ end()

IndexSet::ElementIterator IndexSet::end ( ) const

inline

Return an iterator that points one after the last index that is contained in this IndexSet.

Definition at line 1581 of file index_set.h.

◆ begin_intervals()

IndexSet::IntervalIterator IndexSet::begin_intervals ( ) const

inline

Return an Iterator that points at the first interval of this IndexSet.

Definition at line 1590 of file index_set.h.

◆ end_intervals()

IndexSet::IntervalIterator IndexSet::end_intervals ( ) const

inline

Return an Iterator that points one after the last interval of this IndexSet.

Definition at line 1602 of file index_set.h.

◆ do_compress()

void IndexSet::do_compress ( ) const

private

Actually perform the compress() operation.

Definition at line 98 of file index_set.cc.

◆ fill_binary_vector() [2/2]

template<typename Vector >

void IndexSet::fill_binary_vector ( Vector & vector ) const

Definition at line 1997 of file index_set.h.

Friends And Related Function Documentation

◆ complete_index_set()

IndexSet complete_index_set ( const IndexSet::size_type N )

IndexSet is (N);

is.add_range(0, N);

This function exists so that one can create and initialize index sets that are complete in one step, or so one can write code like

if (my_index_set == complete_index_set(my_index_set.size())

...

Definition at line 1014 of file index_set.h.

Member Data Documentation

◆ ranges

std::vector<Range> IndexSet::ranges

mutableprivate

A set of contiguous ranges of indices that make up (part of) this index set. This variable is always kept sorted.

The variable is marked "mutable" so that it can be changed by compress(), though this of course doesn't change anything about the external representation of this index set.

Definition at line 953 of file index_set.h.

◆ is_compressed

bool IndexSet::is_compressed

mutableprivate

True if compress() has been called after the last change in the set of indices.

The variable is marked "mutable" so that it can be changed by compress(), though this of course doesn't change anything about the external representation of this index set.

Definition at line 963 of file index_set.h.

◆ index_space_size

size_type IndexSet::index_space_size

private

The overall size of the index range. Elements of this index set have to have a smaller number than this value.

Definition at line 969 of file index_set.h.

◆ largest_range

size_type IndexSet::largest_range

mutableprivate

This integer caches the index of the largest range in ranges. This gives O(1) access to the range with most elements, while general access costs O(log(n_ranges)). The largest range is needed for the methods is_element(), index_within_set(), nth_index_in_set. In many applications, the largest range contains most elements (the locally owned range), whereas there are only a few other elements (ghosts).

Definition at line 980 of file index_set.h.

◆ compress_mutex

Threads::Mutex IndexSet::compress_mutex

mutableprivate

A mutex that is used to synchronize operations of the do_compress() function that is called from many 'const' functions via compress().

Definition at line 986 of file index_set.h.

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

include/deal.II/base/index_set.h
source/base/index_set.cc

Classes

Public Types

Public Member Functions

Static Public Member Functions

Private Member Functions

Private Attributes

Related Functions

Detailed Description

Member Typedef Documentation

◆ size_type

◆ value_type

Constructor & Destructor Documentation

◆ IndexSet() [1/5]

◆ IndexSet() [2/5]

◆ IndexSet() [3/5]

◆ IndexSet() [4/5]

◆ IndexSet() [5/5]

Member Function Documentation

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ clear()

◆ set_size()

◆ size()

◆ add_range()

◆ add_index()

◆ add_indices() [1/2]

◆ add_indices() [2/2]

◆ is_element()

◆ is_contiguous()

◆ is_empty()

◆ is_ascending_and_one_to_one()

◆ n_elements()

◆ nth_index_in_set()

◆ index_within_set()

◆ n_intervals()

◆ largest_range_starting_index()

◆ compress()

◆ operator==()

◆ operator!=()

◆ operator&()

◆ get_view()

◆ split_by_block()

◆ subtract_set()

◆ tensor_product()

◆ pop_back()

◆ pop_front()

◆ fill_index_vector()

◆ fill_binary_vector() [1/2]

◆ print()

◆ write()

◆ read()

◆ block_write()

◆ block_read()

◆ make_trilinos_map()

◆ make_tpetra_map()

◆ memory_consumption()

◆ serialize()

◆ begin()

◆ at()

◆ end()

◆ begin_intervals()

◆ end_intervals()

◆ do_compress()

◆ fill_binary_vector() [2/2]

Friends And Related Function Documentation

◆ complete_index_set()

Member Data Documentation

◆ ranges

◆ is_compressed

◆ index_space_size

◆ largest_range

◆ compress_mutex