Reference documentation for deal.II version Git 5109843 2018-03-21 23:56:40 +0700
IndexSet Class Reference

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

## Classes

class  ElementIterator

class  IntervalAccessor

class  IntervalIterator

struct  Range

## Public Types

typedef types::global_dof_index size_type

typedef signed int value_type

## Public Member Functions

IndexSet ()

IndexSet (const size_type size)

IndexSet (const IndexSet &)=default

IndexSetoperator= (const IndexSet &)=default

IndexSet (IndexSet &&is) noexcept

IndexSetoperator= (IndexSet &&is) noexcept

IndexSet (const Epetra_Map &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 unsigned int 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 unsigned int local_index) const

size_type index_within_set (const size_type global_index) const

unsigned int n_intervals () const

unsigned int 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

void subtract_set (const IndexSet &other)

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

std::size_t memory_consumption () const

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

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< Rangeranges

bool is_compressed

size_type index_space_size

size_type largest_range

## Related Functions

(Note that these are not member functions.)

IndexSet complete_index_set (const unsigned int 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.

Definition at line 68 of file index_set.h.

## Member Typedef Documentation

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

Definition at line 73 of file index_set.h.

 typedef signed int IndexSet::value_type

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 typedef 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 98 of file index_set.h.

## Constructor & Destructor Documentation

 IndexSet::IndexSet ( )
inline

Default constructor.

Definition at line 1395 of file index_set.h.

 IndexSet::IndexSet ( const size_type size )
inlineexplicit

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

Definition at line 1405 of file index_set.h.

 IndexSet::IndexSet ( const IndexSet & )
default

Copy constructor.

 IndexSet::IndexSet ( IndexSet && is )
inlinenoexcept

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

Definition at line 1415 of file index_set.h.

 IndexSet::IndexSet ( const Epetra_Map & map )
explicit

Constructor from a trilinos Epetra_Map.

Definition at line 68 of file index_set.cc.

## Member Function Documentation

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

Copy assignment operator.

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

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

Definition at line 1433 of file index_set.h.

 void IndexSet::clear ( )
inline

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

Definition at line 1549 of file index_set.h.

 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 1562 of file index_set.h.

 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 1575 of file index_set.h.

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

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 98 of file index_set.cc.

 void IndexSet::add_index ( const size_type index )
inline

Add an individual index to the set of indices.

Definition at line 1596 of file index_set.h.

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 1619 of file index_set.h.

 void IndexSet::add_indices ( const IndexSet & other, const unsigned int 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 400 of file index_set.cc.

 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 1645 of file index_set.h.

 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 1698 of file index_set.h.

 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 1708 of file index_set.h.

 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 618 of file index_set.cc.

 IndexSet::size_type IndexSet::n_elements ( ) const
inline

Return the number of elements stored in this index set.

Definition at line 1717 of file index_set.h.

 IndexSet::size_type IndexSet::nth_index_in_set ( const unsigned int 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 1769 of file index_set.h.

 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 1811 of file index_set.h.

 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 1745 of file index_set.h.

 unsigned int IndexSet::largest_range_starting_index ( ) const
inline

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

Definition at line 1755 of file index_set.h.

 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 1584 of file index_set.h.

 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 1860 of file index_set.h.

 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 1875 of file index_set.h.

 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).

Definition at line 199 of file index_set.cc.

 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 254 of file index_set.cc.

 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 288 of file index_set.cc.

 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 362 of file index_set.cc.

 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 379 of file index_set.cc.

 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 526 of file index_set.cc.

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>.

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 1913 of file index_set.h.

 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 455 of file index_set.cc.

 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 470 of file index_set.cc.

 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 492 of file index_set.cc.

 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 507 of file index_set.cc.

 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 549 of file index_set.cc.

 std::size_t IndexSet::memory_consumption ( ) const

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

Definition at line 679 of file index_set.cc.

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 1946 of file index_set.h.

 IndexSet::ElementIterator IndexSet::begin ( ) const
inline

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

Definition at line 1453 of file index_set.h.

 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 1465 of file index_set.h.

 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 1516 of file index_set.h.

 IndexSet::IntervalIterator IndexSet::begin_intervals ( ) const
inline

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

Definition at line 1526 of file index_set.h.

 IndexSet::IntervalIterator IndexSet::end_intervals ( ) const
inline

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

Definition at line 1539 of file index_set.h.

 void IndexSet::do_compress ( ) const
private

Actually perform the compress() operation.

Definition at line 130 of file index_set.cc.

## Friends And Related Function Documentation

 IndexSet complete_index_set ( const unsigned int N )
related

Create and return an index set of size $$N$$ that contains every single index within this range. In essence, this function returns an index set created by

IndexSet is (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 908 of file index_set.h.

## Member Data Documentation

 std::vector 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 848 of file index_set.h.

 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 858 of file index_set.h.

 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 864 of file index_set.h.

 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 875 of file index_set.h.