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// $Id: chunk_sparsity_pattern.h 20212 2009-12-08 16:02:22Z kronbichler $
// Version: $Name$
//
// Copyright (C) 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__chunk_sparsity_pattern_h
#define __deal2__chunk_sparsity_pattern_h
#include <base/config.h>
#include <base/exceptions.h>
#include <base/subscriptor.h>
#include <base/vector_slice.h>
#include <lac/sparsity_pattern.h>
#include <vector>
#include <iostream>
DEAL_II_NAMESPACE_OPEN
template <typename> class ChunkSparseMatrix;
/*! @addtogroup Sparsity
*@{
*/
/**
* Structure representing the sparsity pattern of a sparse matrix.
*
* This class is an example of the "static" type of @ref Sparsity.
*
* It uses the compressed row storage (CSR) format to store data.
*
* @author Wolfgang Bangerth, 2008
*/
class ChunkSparsityPattern : public Subscriptor
{
public:
/**
* Define a value which is used
* to indicate that a certain
* value in the colnums array
* is unused, i.e. does not
* represent a certain column
* number index.
*
* Indices with this invalid
* value are used to insert new
* entries to the sparsity
* pattern using the add() member
* function, and are removed when
* calling compress().
*
* You should not assume that the
* variable declared here has a
* certain value. The
* initialization is given here
* only to enable the compiler to
* perform some optimizations,
* but the actual value of the
* variable may change over time.
*/
static const unsigned int invalid_entry = SparsityPattern::invalid_entry;
/**
* 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.
*/
ChunkSparsityPattern ();
/**
* 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
* (ChunkSparsityPattern());</tt>,
* with <tt>v</tt> a vector of
* ChunkSparsityPattern objects.
*
* Usually, it is sufficient to
* use the explicit keyword to
* disallow unwanted temporaries,
* but for the STL vectors, this
* does not work. Since copying a
* structure like this is not
* useful anyway because multiple
* matrices can use the same
* sparsity structure, copies are
* only allowed for empty
* objects, as described above.
*/
ChunkSparsityPattern (const ChunkSparsityPattern &);
/**
* Initialize a rectangular
* matrix.
*
* @arg m number of rows
* @arg n number of columns
* @arg max_per_row maximum
* number of nonzero entries per row
*
* @arg optimize_diagonal store
* diagonal entries first in row;
* see optimize_diagonal(). This
* takes effect for quadratic
* matrices only.
*/
ChunkSparsityPattern (const unsigned int m,
const unsigned int n,
const unsigned int max_chunks_per_row,
const unsigned int chunk_size,
const bool optimize_diagonal = true);
/**
* Initialize a rectangular
* matrix.
*
* @arg m number of rows
* @arg n number of columns
*
* @arg row_lengths possible
* number of nonzero entries for
* each row. This vector must
* have one entry for each row.
*
* @arg optimize_diagonal store
* diagonal entries first in row;
* see optimize_diagonal(). This
* takes effect for quadratic
* matrices only.
*/
ChunkSparsityPattern (const unsigned int m,
const unsigned int n,
const std::vector<unsigned int>& row_lengths,
const unsigned int chunk_size,
const bool optimize_diagonal = true);
/**
* Initialize a quadratic matrix
* of dimension <tt>n</tt> with
* at most <tt>max_per_row</tt>
* nonzero entries per row.
*
* This constructor automatically
* enables optimized storage of
* diagonal elements. To avoid
* this, use the constructor
* taking row and column numbers
* separately.
*/
ChunkSparsityPattern (const unsigned int n,
const unsigned int max_per_row,
const unsigned int chunk_size);
/**
* Initialize a quadratic matrix.
*
* @arg m number of rows and columns
*
* @arg row_lengths possible
* number of nonzero entries for
* each row. This vector must
* have one entry for each row.
*
* @arg optimize_diagonal store
* diagonal entries first in row;
* see optimize_diagonal().
*/
ChunkSparsityPattern (const unsigned int m,
const std::vector<unsigned int>& row_lengths,
const unsigned int chunk_size,
const bool optimize_diagonal = true);
/**
* Destructor.
*/
~ChunkSparsityPattern ();
/**
* 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.
*/
ChunkSparsityPattern & operator = (const ChunkSparsityPattern &);
/**
* Reallocate memory and set up data
* structures for a new matrix with
* <tt>m </tt>rows and <tt>n</tt> columns,
* with at most <tt>max_per_row</tt>
* nonzero entries per row.
*
* This function simply maps its
* operations to the other
* <tt>reinit</tt> function.
*/
void reinit (const unsigned int m,
const unsigned int n,
const unsigned int max_per_row,
const unsigned int chunk_size,
const bool optimize_diagonal = true);
/**
* Reallocate memory for a matrix
* of size <tt>m x n</tt>. The
* number of entries for each row
* is taken from the array
* <tt>row_lengths</tt> which has to
* give this number of each row
* <tt>i=1...m</tt>.
*
* If <tt>m*n==0</tt> all memory is freed,
* resulting in a total reinitialization
* of the object. If it is nonzero, new
* memory is only allocated if the new
* size extends the old one. This is done
* to save time and to avoid fragmentation
* of the heap.
*
* If the number of rows equals
* the number of columns and the
* last parameter is true,
* diagonal elements are stored
* first in each row to allow
* optimized access in relaxation
* methods of SparseMatrix.
*/
void reinit (const unsigned int m,
const unsigned int n,
const std::vector<unsigned int> &row_lengths,
const unsigned int chunk_size,
const bool optimize_diagonal = true);
/**
* Same as above, but with a
* VectorSlice argument instead.
*/
void reinit (const unsigned int m,
const unsigned int n,
const VectorSlice<const std::vector<unsigned int> > &row_lengths,
const unsigned int chunk_size,
const bool optimize_diagonal = true);
/**
* This function compresses the sparsity
* structure that this object represents.
* It does so by eliminating unused
* entries and sorting the remaining ones
* to allow faster access by usage of
* binary search algorithms. A special
* sorting scheme is used for the
* diagonal entry of quadratic matrices,
* which is always the first entry of
* each row.
*
* The memory which is no more
* needed is released.
*
* SparseMatrix objects require the
* ChunkSparsityPattern objects they are
* initialized with to be compressed, to
* reduce memory requirements.
*/
void compress ();
/**
* This function can be used as a
* replacement for reinit(),
* subsequent calls to add() and
* a final call to close() if you
* know exactly in advance the
* entries that will form the
* matrix sparsity pattern.
*
* The first two parameters
* determine the size of the
* matrix. For the two last ones,
* note that a sparse matrix can
* be described by a sequence of
* rows, each of which is
* represented by a sequence of
* pairs of column indices and
* values. In the present
* context, the begin() and
* end() parameters designate
* iterators (of forward iterator
* type) into a container, one
* representing one row. The
* distance between begin()
* and end() should therefore
* be equal to
* n_rows(). These iterators
* may be iterators of
* <tt>std::vector</tt>,
* <tt>std::list</tt>, pointers into a
* C-style array, or any other
* iterator satisfying the
* requirements of a forward
* iterator. The objects pointed
* to by these iterators
* (i.e. what we get after
* applying <tt>operator*</tt> or
* <tt>operator-></tt> to one of these
* iterators) must be a container
* itself that provides functions
* <tt>begin</tt> and <tt>end</tt>
* designating a range of
* iterators that describe the
* contents of one
* line. Dereferencing these
* inner iterators must either
* yield a pair of an unsigned
* integer as column index and a
* value of arbitrary type (such
* a type would be used if we
* wanted to describe a sparse
* matrix with one such object),
* or simply an unsigned integer
* (of we only wanted to describe
* a sparsity pattern). The
* function is able to determine
* itself whether an unsigned
* integer or a pair is what we
* get after dereferencing the
* inner iterators, through some
* template magic.
*
* While the order of the outer
* iterators denotes the
* different rows of the matrix,
* the order of the inner
* iterator denoting the columns
* does not matter, as they are
* sorted internal to this
* function anyway.
*
* Since that all sounds very
* complicated, consider the
* following example code, which
* may be used to fill a sparsity
* pattern:
* @code
* std::vector<std::vector<unsigned int> > column_indices (n_rows);
* for (unsigned int row=0; row<n_rows; ++row)
* // generate necessary columns in this row
* fill_row (column_indices[row]);
*
* sparsity.copy_from (n_rows, n_cols,
* column_indices.begin(),
* column_indices.end());
* @endcode
*
* Note that this example works
* since the iterators
* dereferenced yield containers
* with functions <tt>begin</tt> and
* <tt>end</tt> (namely
* <tt>std::vector</tt>s), and the
* inner iterators dereferenced
* yield unsigned integers as
* column indices. Note that we
* could have replaced each of
* the two <tt>std::vector</tt>
* occurrences by <tt>std::list</tt>,
* and the inner one by
* <tt>std::set</tt> as well.
*
* Another example would be as
* follows, where we initialize a
* whole matrix, not only a
* sparsity pattern:
* @code
* std::vector<std::map<unsigned int,double> > entries (n_rows);
* for (unsigned int row=0; row<n_rows; ++row)
* // generate necessary pairs of columns
* // and corresponding values in this row
* fill_row (entries[row]);
*
* sparsity.copy_from (n_rows, n_cols,
* column_indices.begin(),
* column_indices.end());
* matrix.reinit (sparsity);
* matrix.copy_from (column_indices.begin(),
* column_indices.end());
* @endcode
*
* This example works because
* dereferencing iterators of the
* inner type yields a pair of
* unsigned integers and a value,
* the first of which we take as
* column index. As previously,
* the outer <tt>std::vector</tt>
* could be replaced by
* <tt>std::list</tt>, and the inner
* <tt>std::map<unsigned int,double></tt>
* could be replaced by
* <tt>std::vector<std::pair<unsigned int,double> ></tt>,
* or a list or set of such
* pairs, as they all return
* iterators that point to such
* pairs.
*/
template <typename ForwardIterator>
void copy_from (const unsigned int n_rows,
const unsigned int n_cols,
const ForwardIterator begin,
const ForwardIterator end,
const unsigned int chunk_size,
const bool optimize_diagonal = true);
/**
* Copy data from an object of type
* CompressedSparsityPattern,
* CompressedSetSparsityPattern or
* CompressedSimpleSparsityPattern.
* Previous content of this object is
* lost, and the sparsity pattern is in
* compressed mode afterwards.
*/
template <typename SparsityType>
void copy_from (const SparsityType &csp,
const unsigned int chunk_size,
const bool optimize_diagonal = true);
/**
* Take a full matrix and use its
* nonzero entries to generate a
* sparse matrix entry pattern
* for this object.
*
* Previous content of this
* object is lost, and the
* sparsity pattern is in
* compressed mode afterwards.
*/
template <typename number>
void copy_from (const FullMatrix<number> &matrix,
const unsigned int chunk_size,
const bool optimize_diagonal = true);
/**
* 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 chunk size given as
* argument when constructing this
* object.
*/
unsigned int get_chunk_size () const;
/**
* Return the maximum number of entries per
* row. Before compression, this equals the
* number given to the constructor, while
* after compression, it equals the maximum
* number of entries actually allocated by
* the user.
*/
unsigned int max_entries_per_row () const;
/**
* Add a nonzero entry to the matrix.
* This function may only be called
* for non-compressed sparsity patterns.
*
* If the entry already exists, nothing
* bad happens.
*/
void add (const unsigned int i,
const unsigned int j);
/**
* 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
* quadratic matrix.
*/
void symmetrize ();
/**
* Return number of rows of this
* matrix, which equals the dimension
* of the image space.
*/
inline unsigned int n_rows () const;
/**
* Return number of columns of this
* matrix, which equals the dimension
* of the range space.
*/
inline unsigned int n_cols () const;
/**
* Check if a value at a certain
* position may be non-zero.
*/
bool exists (const unsigned int i,
const unsigned int j) const;
/**
* Number of entries in a specific row.
*/
unsigned int row_length (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. Consequently, the maximum
* bandwidth a $n\times m$ matrix can
* have is $\max\{n-1,m-1\}$.
*/
unsigned int bandwidth () const;
/**
* Return the number of nonzero elements of
* this matrix. Actually, it returns the
* number of entries in the sparsity
* pattern; if any of the entries should
* happen to be zero, it is counted
* anyway.
*
* This function may only be called if the
* matrix struct is compressed. It does not
* make too much sense otherwise anyway.
*/
unsigned int n_nonzero_elements () const;
/**
* Return whether the structure is
* compressed or not.
*/
bool is_compressed () const;
/**
* Determine whether the matrix
* uses special convention for
* quadratic matrices.
*
* A return value <tt>true</tt> means
* that diagonal elements are stored
* first in each row. A number of
* functions in this class and the
* library in general, for example
* relaxation methods like Jacobi() and
* SOR(), require this to make their
* operations more efficient, since they
* need to quickly access the diagonal
* elements and do not have to search for
* them if they are the first element of
* each row. A side effect of this scheme
* is that each row contains at least one
* element, even if the row is empty
* (i.e. the diagonal element exists, but
* has value zero).
*
* A return value <tt>false</tt> means
* that diagonal elements are stored
* anywhere in the row, or not at all. In
* particular, a row or even the whole
* matrix may be empty. This can be used
* if you have block matrices where the
* off-diagonal blocks are quadratic but
* are never used for operations like the
* ones mentioned above. In this case,
* some memory can be saved by not using
* the diagonal storage optimization.
*/
bool optimize_diagonal () 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 false because we store
* entire chunks, not individual
* elements, and adding one entry to the
* sparsity pattern requires also adding
* all the other elements of a chunk. The
* only exception is if
* <code>chunk_size==1</code>, the
* sparsity pattern is nonsymmetric or
* optimize_diag has been set to false.
*
* 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.
*/
bool stores_only_added_elements () const;
/**
* Write the data of this object
* en bloc to a file. This is
* done in a binary mode, so the
* output is neither readable by
* humans nor (probably) by other
* computers using a different
* operating system of number
* format.
*
* The purpose of this function
* is that you can swap out
* matrices and sparsity pattern
* if you are short of memory,
* want to communicate between
* different programs, or allow
* objects to be persistent
* across different runs of the
* program.
*/
void block_write (std::ostream &out) const;
/**
* Read data that has previously
* been written by block_write()
* from a file. This is done
* using the inverse operations
* to the above function, so it
* is reasonably fast because the
* bitstream is not interpreted
* except for a few numbers up
* front.
*
* The object is resized on this
* operation, and all previous
* contents are lost.
*
* A primitive form of error
* checking is performed which
* will recognize the bluntest
* attempts to interpret some
* data as a vector stored
* bitwise to a file, but not
* more.
*/
void block_read (std::istream &in);
/**
* 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 <tt>gnuplot</tt> 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
* <tt>plot</tt> command.
*/
void print_gnuplot (std::ostream &out) const;
/**
* Determine an estimate for the
* memory consumption (in bytes)
* of this object. See
* MemoryConsumption.
*/
unsigned int memory_consumption () const;
/** @addtogroup Exceptions
* @{ */
/**
* Exception
*/
DeclException1 (ExcInvalidNumber,
int,
<< "The provided number is invalid here: " << arg1);
/**
* Exception
*/
DeclException2 (ExcInvalidIndex,
int, int,
<< "The given index " << arg1
<< " should be less than " << arg2 << ".");
/**
* Exception
*/
DeclException2 (ExcNotEnoughSpace,
int, int,
<< "Upon entering a new entry to row " << arg1
<< ": there was no free entry any more. " << std::endl
<< "(Maximum number of entries for this row: "
<< arg2 << "; maybe the matrix is already compressed?)");
/**
* Exception
*/
DeclException0 (ExcNotCompressed);
/**
* Exception
*/
DeclException0 (ExcMatrixIsCompressed);
/**
* Exception
*/
DeclException0 (ExcEmptyObject);
/**
* Exception
*/
DeclException0 (ExcInvalidConstructorCall);
/**
* This exception is thrown if
* the matrix does not follow the
* convention of storing diagonal
* elements first in row. Refer
* to
* SparityPattern::optimize_diagonal()
* for more information.
*/
DeclException0 (ExcDiagonalNotOptimized);
/**
* Exception
*/
DeclException2 (ExcIteratorRange,
int, int,
<< "The iterators denote a range of " << arg1
<< " elements, but the given number of rows was " << arg2);
/**
* Exception
*/
DeclException0 (ExcMETISNotInstalled);
/**
* Exception
*/
DeclException1 (ExcInvalidNumberOfPartitions,
int,
<< "The number of partitions you gave is " << arg1
<< ", but must be greater than zero.");
/**
* Exception
*/
DeclException2 (ExcInvalidArraySize,
int, int,
<< "The array has size " << arg1 << " but should have size "
<< arg2);
//@}
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;
/**
* The size of chunks.
*/
unsigned int chunk_size;
/**
* The reduced sparsity pattern. We store
* only which chunks exist, with each
* chunk a block in the matrix of size
* chunk_size by chunk_size.
*/
SparsityPattern sparsity_pattern;
/**
* Make all the chunk sparse matrix kinds
* friends.
*/
template <typename> friend class ChunkSparseMatrix;
};
/*@}*/
/*---------------------- Inline functions -----------------------------------*/
#ifndef DOXYGEN
inline
unsigned int
ChunkSparsityPattern::n_rows () const
{
return rows;
}
inline
unsigned int
ChunkSparsityPattern::n_cols () const
{
return cols;
}
inline
unsigned int
ChunkSparsityPattern::get_chunk_size () const
{
return chunk_size;
}
inline
bool
ChunkSparsityPattern::is_compressed () const
{
return sparsity_pattern.compressed;
}
inline
bool
ChunkSparsityPattern::optimize_diagonal () const
{
return sparsity_pattern.diagonal_optimized;
}
template <typename ForwardIterator>
void
ChunkSparsityPattern::copy_from (const unsigned int n_rows,
const unsigned int n_cols,
const ForwardIterator begin,
const ForwardIterator end,
const unsigned int chunk_size,
const bool optimize_diag)
{
Assert (static_cast<unsigned int>(std::distance (begin, end)) == n_rows,
ExcIteratorRange (std::distance (begin, end), n_rows));
// first determine row lengths for
// each row. if the matrix is
// quadratic, then we might have to
// add an additional entry for the
// diagonal, if that is not yet
// present. as we have to call
// compress anyway later on, don't
// bother to check whether that
// diagonal entry is in a certain
// row or not
const bool is_square = optimize_diag && (n_rows == n_cols);
std::vector<unsigned int> row_lengths;
row_lengths.reserve(n_rows);
for (ForwardIterator i=begin; i!=end; ++i)
row_lengths.push_back (std::distance (i->begin(), i->end())
+
(is_square ? 1 : 0));
reinit (n_rows, n_cols, row_lengths, chunk_size, is_square);
// now enter all the elements into
// the matrix
unsigned int row = 0;
typedef typename std::iterator_traits<ForwardIterator>::value_type::const_iterator inner_iterator;
for (ForwardIterator i=begin; i!=end; ++i, ++row)
{
const inner_iterator end_of_row = i->end();
for (inner_iterator j=i->begin(); j!=end_of_row; ++j)
{
const unsigned int col
= internal::SparsityPatternTools::get_column_index_from_iterator(*j);
Assert (col < n_cols, ExcInvalidIndex(col,n_cols));
add (row, col);
}
}
// finally compress
// everything. this also sorts the
// entries within each row
compress ();
}
#endif // DOXYGEN
DEAL_II_NAMESPACE_CLOSE
#endif
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