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// $Id: index_set.h 30036 2013-07-18 16:55:32Z maier $
//
// Copyright (C) 2009 - 2013 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#ifndef __deal2__index_set_h
#define __deal2__index_set_h
#include <deal.II/base/config.h>
#include <deal.II/base/utilities.h>
#include <deal.II/base/exceptions.h>
#include <vector>
#include <algorithm>
#ifdef DEAL_II_WITH_TRILINOS
# include <Epetra_Map.h>
#endif
#if defined(DEAL_II_WITH_MPI) || defined(DEAL_II_WITH_PETSC)
#include <mpi.h>
#else
typedef int MPI_Comm;
# ifndef MPI_COMM_WORLD
# define MPI_COMM_WORLD 0
# endif
#endif
DEAL_II_NAMESPACE_OPEN
/**
* 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.
*
* The data structures used in this class along with a rationale can be found
* in the @ref distributed_paper "Distributed Computing paper".
*
* @author Wolfgang Bangerth, 2009
*/
class IndexSet
{
public:
/**
* Default constructor.
*/
IndexSet ();
/**
* Constructor that also sets the
* overall size of the index
* range.
*/
explicit IndexSet (const types::global_dof_index size);
/**
* Remove all indices from this
* index set. The index set retains
* its size, however.
*/
void clear ();
/**
* 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.
*/
void set_size (const types::global_dof_index size);
/**
* 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().
*/
types::global_dof_index size () const;
/**
* Add the half-open range
* $[\text{begin},\text{end})$ to
* the set of indices represented
* by this class.
*/
void add_range (const types::global_dof_index begin,
const types::global_dof_index end);
/**
* Add an individual index to the
* set of indices.
*/
void add_index (const types::global_dof_index index);
/**
* Add a whole set of indices
* described by dereferencing
* every element of the the
* iterator range
* <code>[begin,end)</code>.
*/
template <typename ForwardIterator>
void add_indices (const ForwardIterator &begin,
const ForwardIterator &end);
/**
* Add the given IndexSet @p other to the
* current one, constructing the union of
* *this and @p other.
*
* If the @p offset argument is nonzero, then every
* index in @p other is shifted by @p 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 @p other index set
* lie outside the range <code>[0,size())</code> represented
* by the current object.
*/
void add_indices(const IndexSet &other,
const unsigned int offset = 0);
/**
* Return whether the specified
* index is an element of the
* index set.
*/
bool is_element (const types::global_dof_index index) const;
/**
* Return whether the index set
* stored by this object defines
* a contiguous range. This is
* true also if no indices are
* stored at all.
*/
bool is_contiguous () const;
/**
* Return the number of elements
* stored in this index set.
*/
types::global_dof_index n_elements () const;
/**
* Return the global index of the local
* index with number @p local_index
* stored in this index set. @p
* local_index obviously needs to be less
* than n_elements().
*/
types::global_dof_index nth_index_in_set (const unsigned int local_index) const;
/**
* Return the how-manyth element of this
* set (counted in ascending order) @p
* global_index is. @p global_index needs
* to be less than the size(). This
* function throws an exception if the
* index @p global_index is not actually
* a member of this index set, i.e. if
* is_element(global_index) is false.
*/
types::global_dof_index index_within_set (const types::global_dof_index global_index) const;
/**
* 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.
*/
unsigned int n_intervals () const;
/**
* Compress the internal
* representation by merging
* individual elements with
* contiguous ranges, etc. This
* function does not have any
* external effect.
*/
void compress () const;
/**
* 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).
*/
bool operator == (const IndexSet &is) const;
/**
* 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).
*/
bool 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).
*/
IndexSet operator & (const IndexSet &is) const;
/**
* This command takes an interval
* <tt>[begin, end)</tt> and returns
* the intersection of the current
* index set with the interval, shifted
* to the range <tt>[0,
* end-begin)</tt>.
*
* In other words, the result of this operation is the
* intersection of the set represented by the current object
* and the interval <tt>[begin, end)</tt>, as seen
* <i>within the interval <tt>[begin, end)</tt></i> by
* shifting the result of the intersection operation to
* the left by <tt>begin</tt>. This corresponds to the notion
* of a <i>view</i>: The interval <tt>[begin, end)</tt> is
* a <i>window</i> through which we see the set represented
* by the current object.
*/
IndexSet get_view (const types::global_dof_index begin,
const types::global_dof_index end) const;
/**
* Removes all elements contained in @p
* other from this set. In other words,
* if $x$ is the current object and $o$
* the argument, then we compute $x
* \leftarrow x \backslash o$.
*/
void subtract_set (const IndexSet &other);
/**
* Fills the given vector with all
* indices contained in this IndexSet.
*/
void fill_index_vector(std::vector<types::global_dof_index> &indices) 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
* <code>vector.operator[]</code>. 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 <typename Vector>
void fill_binary_vector (Vector &vector) const;
/**
* Outputs a text representation of this
* IndexSet to the given stream. Used for
* testing.
*/
template <class STREAM>
void print(STREAM &out) const;
/**
* Writes the IndexSet into a text based
* file format, that can be read in again
* using the read() function.
*/
void write(std::ostream &out) const;
/**
* Constructs the IndexSet from a text
* based representation given by the
* stream @param in written by the
* write() function.
*/
void read(std::istream &in);
/**
* Writes the IndexSet into a binary,
* compact representation, that can be
* read in again using the block_read()
* function.
*/
void block_write(std::ostream &out) const;
/**
* Constructs the IndexSet from a binary
* representation given by the stream
* @param in written by the write_block()
* function.
*/
void block_read(std::istream &in);
#ifdef DEAL_II_WITH_TRILINOS
/**
* 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 on 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, though they still
* need to contain each index
* exactly once on all processors
* taken together. 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.
*/
Epetra_Map make_trilinos_map (const MPI_Comm &communicator = MPI_COMM_WORLD,
const bool overlapping = false) const;
#endif
/**
* Determine an estimate for the memory
* consumption (in bytes) of this
* object.
*/
std::size_t memory_consumption () const;
DeclException1 (ExcIndexNotPresent, types::global_dof_index,
<< "The global index " << arg1
<< " is not an element of this set.");
/**
* Write or read the data of this object to or
* from a stream for the purpose of serialization
*/
template <class Archive>
void serialize (Archive &ar, const unsigned int version);
private:
/**
* A type that denotes the half
* open index range
* <code>[begin,end)</code>.
*
* The nth_index_in_set denotes
* the how many-th index within
* this IndexSet the first
* element of the current range
* is. This information is only
* accurate if
* IndexSet::compress() has been
* called after the last
* insertion.
*/
struct Range
{
types::global_dof_index begin;
types::global_dof_index end;
types::global_dof_index nth_index_in_set;
/**
* Default constructor. Since there is no useful choice for
* a default constructed interval, this constructor simply
* creates something that resembles an invalid range. We
* need this constructor for serialization purposes, but the
* invalid range should be filled with something read from
* the archive before it is used, so we should hopefully
* never get to see an invalid range in the wild.
**/
Range ();
/**
* Constructor. Create a half-open interval with the given indices.
*
* @param i1 Left end point of the interval.
* @param i2 First index greater than the last index of the indicated range.
**/
Range (const types::global_dof_index i1,
const types::global_dof_index i2);
friend
inline bool operator< (const Range &range_1,
const Range &range_2)
{
return ((range_1.begin < range_2.begin)
||
((range_1.begin == range_2.begin)
&&
(range_1.end < range_2.end)));
}
static bool end_compare(const IndexSet::Range &x, const IndexSet::Range &y)
{
return x.end < y.end;
}
static bool nth_index_compare (const IndexSet::Range &x,
const IndexSet::Range &y)
{
return (x.nth_index_in_set+(x.end-x.begin) <
y.nth_index_in_set+(y.end-y.begin));
}
friend
inline bool operator== (const Range &range_1,
const Range &range_2)
{
return ((range_1.begin == range_2.begin)
&&
(range_1.end == range_2.end));
}
std::size_t memory_consumption () const
{
return sizeof(Range);
}
/**
* Write or read the data of this object to or
* from a stream for the purpose of serialization
*/
template <class Archive>
void serialize (Archive &ar, const unsigned int version);
};
/**
* 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.
*/
mutable std::vector<Range> ranges;
/**
* 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.
*/
mutable bool is_compressed;
/**
* The overall size of the index
* range. Elements of this index
* set have to have a smaller
* number than this value.
*/
types::global_dof_index index_space_size;
/**
* This integer caches the index of the
* largest range in @p ranges. This gives
* <tt>O(1)</tt> access to the range with
* most elements, while general access
* costs <tt>O(log(n_ranges))</tt>. The
* largest range is needed for the
* methods @p is_element(), @p
* index_within_set(), @p
* 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).
*/
mutable types::global_dof_index largest_range;
/**
* Actually perform the compress()
* operation.
*/
void do_compress() const;
};
/**
* 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
* @code
* IndexSet is (N);
* is.add_range(0, N);
* @endcode
* 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
* @code
* if (my_index_set == complete_index_set(my_index_set.size())
* ...
* @endcode
*
* @relates IndexSet
*/
inline
IndexSet complete_index_set (const unsigned int N)
{
IndexSet is (N);
is.add_range(0, N);
return is;
}
/* ------------------ inline functions ------------------ */
inline
IndexSet::Range::Range ()
:
begin(numbers::invalid_dof_index),
end(numbers::invalid_dof_index)
{}
inline
IndexSet::Range::Range (const types::global_dof_index i1,
const types::global_dof_index i2)
:
begin(i1),
end(i2)
{}
inline
IndexSet::IndexSet ()
:
is_compressed (true),
index_space_size (0),
largest_range (deal_II_numbers::invalid_unsigned_int)
{}
inline
IndexSet::IndexSet (const types::global_dof_index size)
:
is_compressed (true),
index_space_size (size),
largest_range (deal_II_numbers::invalid_unsigned_int)
{}
inline
void
IndexSet::clear ()
{
ranges.clear ();
largest_range = 0;
is_compressed = true;
}
inline
void
IndexSet::set_size (const types::global_dof_index sz)
{
Assert (ranges.empty(),
ExcMessage ("This function can only be called if the current "
"object does not yet contain any elements."));
index_space_size = sz;
is_compressed = true;
}
inline
types::global_dof_index
IndexSet::size () const
{
return index_space_size;
}
inline
void
IndexSet::compress () const
{
if (is_compressed == true)
return;
do_compress();
}
inline
void
IndexSet::add_range (const types::global_dof_index begin,
const types::global_dof_index end)
{
Assert ((begin < index_space_size)
||
((begin == index_space_size) && (end == index_space_size)),
ExcIndexRangeType<types::global_dof_index> (begin, 0, index_space_size));
Assert (end <= index_space_size,
ExcIndexRangeType<types::global_dof_index> (end, 0, index_space_size+1));
Assert (begin <= end,
ExcIndexRangeType<types::global_dof_index> (begin, 0, end));
if (begin != end)
{
const Range new_range(begin,end);
// the new index might be larger than the last
// index present in the ranges. Then we can
// skip the binary search
if (ranges.size() == 0 || begin > ranges.back().end)
ranges.push_back(new_range);
else
ranges.insert (Utilities::lower_bound (ranges.begin(),
ranges.end(),
new_range),
new_range);
is_compressed = false;
}
}
inline
void
IndexSet::add_index (const types::global_dof_index index)
{
Assert (index < index_space_size,
ExcIndexRangeType<types::global_dof_index> (index, 0, index_space_size));
const Range new_range(index, index+1);
if (ranges.size() == 0 || index > ranges.back().end)
ranges.push_back(new_range);
else if (index == ranges.back().end)
ranges.back().end++;
else
ranges.insert (Utilities::lower_bound (ranges.begin(),
ranges.end(),
new_range),
new_range);
is_compressed = false;
}
template <typename ForwardIterator>
inline
void
IndexSet::add_indices (const ForwardIterator &begin,
const ForwardIterator &end)
{
// insert each element of the
// range. if some of them happen to
// be consecutive, merge them to a
// range
for (ForwardIterator p=begin; p!=end;)
{
const types::global_dof_index begin_index = *p;
types::global_dof_index end_index = begin_index + 1;
ForwardIterator q = p;
++q;
while ((q != end) && (*q == end_index))
{
++end_index;
++q;
}
add_range (begin_index, end_index);
p = q;
}
}
inline
void
IndexSet::add_indices(const IndexSet &other,
const unsigned int offset)
{
if ((this == &other) && (offset == 0))
return;
for (std::vector<Range>::iterator range = other.ranges.begin();
range != other.ranges.end();
++range)
{
add_range(range->begin+offset, range->end+offset);
}
compress();
}
inline
bool
IndexSet::is_element (const types::global_dof_index index) const
{
if (ranges.empty() == false)
{
compress ();
// fast check whether the index is in the
// largest range
Assert (largest_range < ranges.size(), ExcInternalError());
if (index >= ranges[largest_range].begin &&
index < ranges[largest_range].end)
return true;
// get the element after which
// we would have to insert a
// range that consists of all
// elements from this element
// to the end of the index
// range plus one. after this
// call we know that if
// p!=end() then
// p->begin<=index unless there
// is no such range at all
//
// if the searched for element
// is an element of this range,
// then we're done. otherwise,
// the element can't be in one
// of the following ranges
// because otherwise p would be
// a different iterator
//
// since we already know the position
// relative to the largest range (we
// called compress!), we can perform
// the binary search on ranges with
// lower/higher number compared to the
// largest range
std::vector<Range>::const_iterator
p = std::upper_bound (ranges.begin() + (index<ranges[largest_range].begin?
0 : largest_range+1),
index<ranges[largest_range].begin ?
ranges.begin() + largest_range:
ranges.end(),
Range (index, size()+1));
if (p == ranges.begin())
return ((index >= p->begin) && (index < p->end));
Assert ((p == ranges.end()) || (p->begin > index),
ExcInternalError());
// now move to that previous
// range
--p;
Assert (p->begin <= index, ExcInternalError());
return (p->end > index);
}
// didn't find this index, so it's
// not in the set
return false;
}
inline
bool
IndexSet::is_contiguous () const
{
compress ();
return (ranges.size() <= 1);
}
inline
types::global_dof_index
IndexSet::n_elements () const
{
// make sure we have
// non-overlapping ranges
compress ();
types::global_dof_index v = 0;
if (!ranges.empty())
{
Range &r = ranges.back();
v = r.nth_index_in_set + r.end - r.begin;
}
#ifdef DEBUG
types::global_dof_index s = 0;
for (std::vector<Range>::iterator range = ranges.begin();
range != ranges.end();
++range)
s += (range->end - range->begin);
Assert(s==v, ExcInternalError());
#endif
return v;
}
inline
types::global_dof_index
IndexSet::nth_index_in_set (const unsigned int n) const
{
// to make this call thread-safe, compress()
// must not be called through this function
Assert (is_compressed == true, ExcMessage ("IndexSet must be compressed."));
Assert (n < n_elements(), ExcIndexRangeType<types::global_dof_index> (n, 0, n_elements()));
// first check whether the index is in the
// largest range
Assert (largest_range < ranges.size(), ExcInternalError());
std::vector<Range>::const_iterator main_range=ranges.begin()+largest_range;
if (n>=main_range->nth_index_in_set &&
n<main_range->nth_index_in_set+(main_range->end-main_range->begin))
return main_range->begin + (n-main_range->nth_index_in_set);
// find out which chunk the local index n
// belongs to by using a binary search. the
// comparator is based on the end of the
// ranges. Use the position relative to main_range to
// subdivide the ranges
Range r (n,n+1);
r.nth_index_in_set = n;
std::vector<Range>::const_iterator range_begin, range_end;
if (n<main_range->nth_index_in_set)
{
range_begin = ranges.begin();
range_end = main_range;
}
else
{
range_begin = main_range + 1;
range_end = ranges.end();
}
std::vector<Range>::const_iterator
p = Utilities::lower_bound(range_begin, range_end, r,
Range::nth_index_compare);
if (p != ranges.end())
return p->begin + (n-p->nth_index_in_set);
else
{
Assert (false, ExcInternalError());
return numbers::invalid_dof_index;
}
}
inline
types::global_dof_index
IndexSet::index_within_set (const types::global_dof_index n) const
{
// to make this call thread-safe, compress()
// must not be called through this function
Assert (is_compressed == true, ExcMessage ("IndexSet must be compressed."));
Assert (is_element(n) == true, ExcIndexNotPresent (n));
Assert (n < size(), ExcIndexRangeType<types::global_dof_index> (n, 0, size()));
// check whether the index is in the largest
// range. use the result to perform a
// one-sided binary search afterward
Assert (largest_range < ranges.size(), ExcInternalError());
std::vector<Range>::const_iterator main_range=ranges.begin()+largest_range;
if (n >= main_range->begin && n < main_range->end)
return (n-main_range->begin) + main_range->nth_index_in_set;
Range r(n, n);
std::vector<Range>::const_iterator range_begin, range_end;
if (n<main_range->begin)
{
range_begin = ranges.begin();
range_end = main_range;
}
else
{
range_begin = main_range + 1;
range_end = ranges.end();
}
std::vector<Range>::const_iterator
p = Utilities::lower_bound(range_begin, range_end, r,
Range::end_compare);
Assert(p!=ranges.end(), ExcInternalError());
Assert(p->begin<=n, ExcInternalError());
Assert(n<p->end, ExcInternalError());
return (n-p->begin) + p->nth_index_in_set;
}
inline
bool
IndexSet::operator == (const IndexSet &is) const
{
Assert (size() == is.size(),
ExcDimensionMismatch (size(), is.size()));
compress ();
is.compress ();
return ranges == is.ranges;
}
inline
bool
IndexSet::operator != (const IndexSet &is) const
{
Assert (size() == is.size(),
ExcDimensionMismatch (size(), is.size()));
compress ();
is.compress ();
return ranges != is.ranges;
}
template <typename Vector>
void
IndexSet::fill_binary_vector (Vector &vector) const
{
Assert (vector.size() == size(),
ExcDimensionMismatch (vector.size(), size()));
compress();
// first fill all elements of the vector
// with zeroes.
std::fill (vector.begin(), vector.end(), 0);
// then write ones into the elements whose
// indices are contained in the index set
for (std::vector<Range>::iterator it = ranges.begin();
it != ranges.end();
++it)
for (types::global_dof_index i=it->begin; i<it->end; ++i)
vector[i] = 1;
}
template <class STREAM>
inline
void
IndexSet::print (STREAM &out) const
{
compress();
out << "{";
std::vector<Range>::const_iterator p;
for (p = ranges.begin(); p != ranges.end(); ++p)
{
if (p->end-p->begin==1)
out << p->begin;
else
out << "[" << p->begin << "," << p->end-1 << "]";
if (p !=--ranges.end())
out << ", ";
}
out << "}" << std::endl;
}
template <class Archive>
inline
void
IndexSet::Range::serialize (Archive &ar, const unsigned int)
{
ar &begin &end &nth_index_in_set;
}
template <class Archive>
inline
void
IndexSet::serialize (Archive &ar, const unsigned int)
{
ar &ranges &is_compressed &index_space_size &largest_range;
}
DEAL_II_NAMESPACE_CLOSE
#endif
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