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// $Id: compressed_set_sparsity_pattern.h 20602 2010-02-13 17:44:17Z bangerth $
// Version: $Name$
//
// Copyright (C) 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008 by the deal.II authors
//
// This file is subject to QPL and may not be distributed
// without copyright and license information. Please refer
// to the file deal.II/doc/license.html for the text and
// further information on this license.
//
//---------------------------------------------------------------------------
#ifndef __deal2__compressed_set_sparsity_pattern_h
#define __deal2__compressed_set_sparsity_pattern_h
#include <base/config.h>
#include <base/subscriptor.h>
#include <lac/exceptions.h>
#include <vector>
#include <algorithm>
#include <set>
DEAL_II_NAMESPACE_OPEN
template <typename number> class SparseMatrix;
/*! @addtogroup Sparsity
*@{
*/
/**
* This class acts as an intermediate form of the
* SparsityPattern class. From the interface it mostly
* represents a SparsityPattern object that is kept compressed
* at all times. However, since the final sparsity pattern is not
* known while constructing it, keeping the pattern compressed at all
* times can only be achieved at the expense of either increased
* memory or run time consumption upon use. The main purpose of this
* class is to avoid some memory bottlenecks, so we chose to implement
* it memory conservative, but the chosen data format is too unsuited
* to be used for actual matrices. It is therefore necessary to first
* copy the data of this object over to an object of type
* SparsityPattern before using it in actual matrices.
*
* Another viewpoint is that this class does not need up front allocation of a
* certain amount of memory, but grows as necessary. An extensive description
* of sparsity patterns can be found in the documentation of the @ref Sparsity
* module.
*
* This class is an example of the "dynamic" type of @ref Sparsity. It
* is discussed in the step-27 and @ref step_22
* "step-22" tutorial programs.
*
* <h3>Interface</h3>
*
* Since this class is intended as an intermediate replacement of the
* SparsityPattern class, it has mostly the same interface, with
* small changes where necessary. In particular, the add()
* function, and the functions inquiring properties of the sparsity
* pattern are the same.
*
*
* <h3>Usage</h3>
*
* Use this class as follows:
* @verbatim
* CompressedSetSparsityPattern compressed_pattern (dof_handler.n_dofs());
* DoFTools::make_sparsity_pattern (dof_handler,
* compressed_pattern);
* constraints.condense (compressed_pattern);
*
* SparsityPattern sp;
* sp.copy_from (compressed_pattern);
* @endverbatim
*
* See also step-11 and step-18 for usage
* patterns of the related CompressedSparsityPattern class, and
* step-27 of the current class.
*
* <h3>Notes</h3>
*
* There are several, exchangeable variations of this class, see @ref Sparsity,
* section '"Dynamic" or "compressed" sparsity patterns' for more information.
*
* This class is a variation of the CompressedSparsityPattern class.
* Instead of using sorted vectors together with a caching algorithm
* for storing the column indices of nonzero entries, the std::set
* container is used. This solution might not be the fastest in all
* situations, but seems to work much better than the
* CompressedSparsityPattern in the context of hp-adaptivity (see for
* example step-27), or generally when there are many
* nonzero entries in each row of a matrix (see @ref step_22
* "step-22"). On the other hand, a benchmark where nonzero entries
* were randomly inserted into the sparsity pattern revealed that this
* class is slower by a factor 4-6 in this situation. Hence, currently
* the suggestion is to carefully analyze which of the
* CompressedSparsityPattern classes works best in a certain
* setting. An algorithm which performs equally well in all situations
* still has to be found.
*
*
* @author Oliver Kayser-Herold, 2007
*/
class CompressedSetSparsityPattern : public Subscriptor
{
public:
/**
* An iterator that can be used to
* iterate over the elements of a single
* row. The result of dereferencing such
* an iterator is a column index.
*/
typedef std::set<unsigned int>::const_iterator row_iterator;
/**
* 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.
*/
CompressedSetSparsityPattern ();
/**
* 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 yo
* want to use the STL data types on
* classes like this, e.g. to write such
* statements like <tt>v.push_back
* (CompressedSetSparsityPattern());</tt>,
* with @p v a vector of @p
* CompressedSetSparsityPattern objects.
*/
CompressedSetSparsityPattern (const CompressedSetSparsityPattern &);
/**
* Initialize a rectangular
* matrix with @p m rows and
* @p n columns.
*/
CompressedSetSparsityPattern (const unsigned int m,
const unsigned int n);
/**
* Initialize a square matrix of
* dimension @p n.
*/
CompressedSetSparsityPattern (const unsigned int n);
/**
* 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.
*/
CompressedSetSparsityPattern & operator = (const CompressedSetSparsityPattern &);
/**
* Reallocate memory and set up
* data structures for a new
* matrix with @p m rows and
* @p n columns, with at most
* max_entries_per_row() nonzero
* entries per row.
*/
void reinit (const unsigned int m,
const unsigned int n);
/**
* Since this object is kept
* compressed at all times anway,
* this function does nothing,
* but is declared to make the
* interface of this class as
* much alike as that of the
* SparsityPattern class.
*/
void compress ();
/**
* Return whether the object is
* empty. It is empty if no
* memory is allocated, which is
* the same as that both
* dimensions are zero.
*/
bool empty () const;
/**
* Return the maximum number of
* entries per row. Note that
* this number may change as
* entries are added.
*/
unsigned int max_entries_per_row () const;
/**
* Add a nonzero entry to the
* matrix. If the entry already
* exists, nothing bad happens.
*/
void add (const unsigned int i,
const unsigned int j);
/**
* Add several nonzero entries to the
* specified row of the matrix. If the
* entries already exist, nothing bad
* happens.
*/
template <typename ForwardIterator>
void add_entries (const unsigned int row,
ForwardIterator begin,
ForwardIterator end,
const bool indices_are_sorted = false);
/**
* Check if a value at a certain
* position may be non-zero.
*/
bool exists (const unsigned int i,
const unsigned int j) const;
/**
* 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.
*/
void symmetrize ();
/**
* Print the sparsity of the
* matrix. The output consists of
* one line per row of the format
* <tt>[i,j1,j2,j3,...]</tt>. <i>i</i>
* is the row number and
* <i>jn</i> are the allocated
* columns in this row.
*/
void print (std::ostream &out) const;
/**
* Print the sparsity of the matrix in a
* format that @p gnuplot understands and
* which can be used to plot the sparsity
* pattern in a graphical way. The format
* consists of pairs <tt>i j</tt> 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
* <tt>(0,0)</tt> 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
* @p plot command.
*/
void print_gnuplot (std::ostream &out) const;
/**
* Return number of rows of this
* matrix, which equals the dimension
* of the image space.
*/
unsigned int n_rows () const;
/**
* Return number of columns of this
* matrix, which equals the dimension
* of the range space.
*/
unsigned int n_cols () const;
/**
* Number of entries in a specific row.
*/
unsigned int row_length (const unsigned int row) const;
/**
* Return an iterator that can loop over
* all entries in the given
* row. Dereferencing the iterator yields
* a column index.
*/
row_iterator row_begin (const unsigned int row) const;
/**
* End iterator for the given row.
*/
row_iterator row_end (const unsigned int row) 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.
*/
unsigned int bandwidth () const;
/**
* Return the number of nonzero elements
* allocated through this sparsity
* pattern.
*/
unsigned int n_nonzero_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 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.
*/
static
bool stores_only_added_elements ();
private:
/**
* Number of rows that this sparsity
* structure shall represent.
*/
unsigned int rows;
/**
* Number of columns that this sparsity
* structure shall represent.
*/
unsigned int cols;
/**
* For each row of the matrix, store the
* allocated non-zero entries as a
* std::set of column indices. For a
* discussion of storage schemes see the
* CompressedSparsityPattern::Line class.
*/
struct Line
{
std::set<unsigned int> entries;
/**
* Constructor.
*/
Line ();
/**
* Add the given column number to
* this line.
*/
void add (const unsigned int col_num);
/**
* Add the columns specified by the
* iterator range to this line.
*/
template <typename ForwardIterator>
void add_entries (ForwardIterator begin,
ForwardIterator end);
};
/**
* Actual data: store for each
* row the set of nonzero
* entries.
*/
std::vector<Line> lines;
};
/*@}*/
/*---------------------- Inline functions -----------------------------------*/
inline
CompressedSetSparsityPattern::Line::Line ()
{}
inline
void
CompressedSetSparsityPattern::Line::add (const unsigned int j)
{
entries.insert (j);
}
template <typename ForwardIterator>
inline
void
CompressedSetSparsityPattern::Line::add_entries (ForwardIterator begin,
ForwardIterator end)
{
entries.insert (begin, end);
}
inline
unsigned int
CompressedSetSparsityPattern::n_rows () const
{
return rows;
}
inline
unsigned int
CompressedSetSparsityPattern::n_cols () const
{
return cols;
}
inline
void
CompressedSetSparsityPattern::add (const unsigned int i,
const unsigned int j)
{
Assert (i<rows, ExcIndexRange(i, 0, rows));
Assert (j<cols, ExcIndexRange(j, 0, cols));
lines[i].add (j);
}
template <typename ForwardIterator>
inline
void
CompressedSetSparsityPattern::add_entries (const unsigned int row,
ForwardIterator begin,
ForwardIterator end,
const bool /*indices_are_sorted*/)
{
Assert (row < rows, ExcIndexRange (row, 0, rows));
lines[row].add_entries (begin, end);
}
inline
unsigned int
CompressedSetSparsityPattern::row_length (const unsigned int row) const
{
Assert (row < n_rows(), ExcIndexRange (row, 0, n_rows()));
return lines[row].entries.size();
}
inline
CompressedSetSparsityPattern::row_iterator
CompressedSetSparsityPattern::row_begin (const unsigned int row) const
{
return (lines[row].entries.begin ());
}
inline
CompressedSetSparsityPattern::row_iterator
CompressedSetSparsityPattern::row_end (const unsigned int row) const
{
return (lines[row].entries.end ());
}
inline
bool
CompressedSetSparsityPattern::stores_only_added_elements ()
{
return true;
}
DEAL_II_NAMESPACE_CLOSE
#endif
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