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// $Id: compressed_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_sparsity_pattern_h
#define __deal2__compressed_sparsity_pattern_h
#include <base/config.h>
#include <base/subscriptor.h>
#include <lac/exceptions.h>
#include <vector>
#include <algorithm>
DEAL_II_NAMESPACE_OPEN
template <typename number> class SparseMatrix;
//TODO[WB]: Unify implementation with the CompressedSetSparsityPattern since really all that's different is the Line structure in the two classes. We should have a templatized base class that simply gets the particular Line structure from a derived class.
/*! @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.
*
* <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
* CompressedSparsityPattern 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.
*
* <h3>Notes</h3>
*
* There are several, exchangeable variations of this class, see @ref Sparsity,
* section '"Dynamic" or "compressed" sparsity patterns' for more information.
*
* @author Wolfgang Bangerth, 2001
*/
class CompressedSparsityPattern : 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::vector<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.
*/
CompressedSparsityPattern ();
/**
* 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
* (CompressedSparsityPattern());</tt>,
* with @p v a vector of @p
* CompressedSparsityPattern objects.
*/
CompressedSparsityPattern (const CompressedSparsityPattern &);
/**
* Initialize a rectangular
* matrix with @p m rows and
* @p n columns.
*/
CompressedSparsityPattern (const unsigned int m,
const unsigned int n);
/**
* Initialize a square matrix of
* dimension @p n.
*/
CompressedSparsityPattern (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.
*/
CompressedSparsityPattern & operator = (const CompressedSparsityPattern &);
/**
* 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_unique_and_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;
/**
* Access to column number field.
* Return the column number of
* the @p indexth entry in @p row.
*/
unsigned int column_number (const unsigned int row,
const unsigned int index) 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;
/**
* Returns the end of the current 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;
/**
* Store some data for each row
* describing which entries of this row
* are nonzero. Data is organized as
* follows: if an entry is added to a
* row, it is first added to the #cache
* variable, irrespective of whether an
* entry with same column number has
* already been added. Only if the cache
* is full do we flush it by removing
* duplicates, removing entries that are
* already stored in the @p entries
* array, sorting everything, and merging
* the two arrays.
*
* The reasoning behind this scheme is
* that memory allocation is expensive,
* and we only want to do it when really
* necessary. Previously (in deal.II
* versions up to 5.0), we used to store
* the column indices inside a std::set,
* but this would allocate 20 bytes each
* time we added an entry. (A std::set
* based class has later been revived in
* form of the
* CompressedSetSparsityPattern class, as
* this turned out to be more efficient
* for hp finite element programs such as
* step-27). Using the
* present scheme, we only need to
* allocate memory once for every 8 added
* entries, and we waste a lot less
* memory by not using a balanced tree
* for storing column indices.
*
* Since some functions that are @p const
* need to access the data of this
* object, but need to flush caches
* before, the flush_cache() function is
* marked const, and the data members are
* marked @p mutable.
*
* A small testseries about the size of
* the cache showed that the run time of
* a small program just testing the
* compressed sparsity pattern element
* insertion routine ran for 3.6 seconds
* with a cache size of 8, and 4.2
* seconds with a cache size of 16. We
* deem even smaller cache sizes
* undesirable, since they lead to more
* memory allocations, while larger cache
* sizes lead to waste of memory. The
* original version of this class, with
* one std::set per row took 8.2 seconds
* on the same program.
*/
struct Line
{
private:
/**
* Size of the cache.
*/
static const unsigned int cache_size = 8;
public:
/**
* Storage for the column indices of
* this row, unless they are still in
* the cache. This array is always
* kept sorted.
*/
mutable std::vector<unsigned int> entries;
/**
* Cache of entries that have not yet
* been written to #entries;
*/
mutable unsigned int cache[cache_size];
/**
* Number of entries in the cache.
*/
mutable unsigned int cache_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,
const bool indices_are_sorted);
/**
* Flush the cache my merging it with
* the #entries array.
*/
void flush_cache () const;
};
/**
* Actual data: store for each
* row the set of nonzero
* entries.
*/
std::vector<Line> lines;
};
/*@}*/
/*---------------------- Inline functions -----------------------------------*/
inline
void
CompressedSparsityPattern::Line::add (const unsigned int j)
{
// first check whether this entry is
// already in the cache. if so, we can
// safely return
for (unsigned int i=0; i<cache_entries; ++i)
if (cache[i] == j)
return;
// if not, see whether there is still some
// space in the cache. if not, then flush
// the cache first
if (cache_entries == cache_size && cache_entries != 0)
flush_cache ();
cache[cache_entries] = j;
++cache_entries;
}
inline
unsigned int
CompressedSparsityPattern::n_rows () const
{
return rows;
}
inline
unsigned int
CompressedSparsityPattern::n_cols () const
{
return cols;
}
inline
void
CompressedSparsityPattern::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
CompressedSparsityPattern::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, indices_are_sorted);
}
inline
CompressedSparsityPattern::Line::Line ()
:
cache_entries (0)
{}
inline
unsigned int
CompressedSparsityPattern::row_length (const unsigned int row) const
{
Assert (row < n_rows(), ExcIndexRange (row, 0, n_rows()));
if (lines[row].cache_entries != 0)
lines[row].flush_cache ();
return lines[row].entries.size();
}
inline
unsigned int
CompressedSparsityPattern::column_number (const unsigned int row,
const unsigned int index) const
{
Assert (row < n_rows(), ExcIndexRange (row, 0, n_rows()));
Assert (index < lines[row].entries.size(),
ExcIndexRange (index, 0, lines[row].entries.size()));
if (lines[row].cache_entries != 0)
lines[row].flush_cache ();
return lines[row].entries[index];
}
inline
CompressedSparsityPattern::row_iterator
CompressedSparsityPattern::row_begin (const unsigned int row) const
{
Assert (row < n_rows(), ExcIndexRange (row, 0, n_rows()));
if (lines[row].cache_entries != 0)
lines[row].flush_cache ();
return lines[row].entries.begin();
}
inline
CompressedSparsityPattern::row_iterator
CompressedSparsityPattern::row_end (const unsigned int row) const
{
Assert (row < n_rows(), ExcIndexRange (row, 0, n_rows()));
return lines[row].entries.end();
}
inline
bool
CompressedSparsityPattern::stores_only_added_elements ()
{
return true;
}
DEAL_II_NAMESPACE_CLOSE
#endif
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