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// $Id: sparsity_pattern.h 31227 2013-10-14 13:23:43Z bangerth $
//
// Copyright (C) 2000 - 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__sparsity_pattern_h
#define __deal2__sparsity_pattern_h
#include <deal.II/base/config.h>
#include <deal.II/base/exceptions.h>
#include <deal.II/base/subscriptor.h>
#include <boost/serialization/array.hpp>
#include <boost/serialization/split_member.hpp>
#include <vector>
#include <iostream>
DEAL_II_NAMESPACE_OPEN
class SparsityPattern;
class ChunkSparsityPattern;
template <typename number> class FullMatrix;
template <typename number> class SparseMatrix;
template <typename number> class SparseLUDecomposition;
template <typename number> class SparseILU;
template <class VECTOR> class VectorSlice;
class CompressedSparsityPattern;
class CompressedSetSparsityPattern;
class CompressedSimpleSparsityPattern;
namespace ChunkSparsityPatternIterators
{
class Accessor;
}
/*! @addtogroup Sparsity
*@{
*/
namespace internals
{
namespace SparsityPatternTools
{
/**
* Declare type for container size.
*/
typedef types::global_dof_index size_type;
/**
* Helper function to get the column index from a dereferenced iterator in
* the copy_from() function, if the inner iterator type points to plain
* unsigned integers.
*/
size_type
get_column_index_from_iterator (const size_type i);
/**
* Helper function to get the column index from a dereferenced iterator in
* the copy_from() function, if the inner iterator type points to pairs of
* unsigned integers and some other value.
*/
template <typename value>
size_type
get_column_index_from_iterator (const std::pair<size_type, value> &i);
/**
* Likewise, but sometimes needed for certain types of containers that
* make the first element of the pair constant (such as
* <tt>std::map</tt>).
*/
template <typename value>
size_type
get_column_index_from_iterator (const std::pair<const size_type, value> &i);
}
}
/**
* Iterators on sparsity patterns
*/
namespace SparsityPatternIterators
{
// forward declaration
class Iterator;
/**
* Declare type for container size.
*/
typedef types::global_dof_index size_type;
/**
* Accessor class for iterators into sparsity patterns. This class is
* also the base class for both const and non-const accessor classes
* into sparse matrices.
*
* Note that this class only allows read access to elements, providing their
* row and column number (or alternatively the index within the complete
* sparsity pattern). It does not allow modifying the sparsity pattern
* itself.
*
* @author Wolfgang Bangerth
* @date 2004
*/
class Accessor
{
public:
/**
* Constructor.
*
* @deprecated This constructor is deprecated. Use the other constructor
* with a global index instead.
*/
Accessor (const SparsityPattern *matrix,
const size_type row,
const size_type index) DEAL_II_DEPRECATED;
/**
* Constructor.
*/
Accessor (const SparsityPattern *matrix,
const std::size_t index_within_sparsity);
/**
* Constructor. Construct the end accessor for the given sparsity pattern.
*/
Accessor (const SparsityPattern *matrix);
/**
* Row number of the element represented by this object. This function can
* only be called for entries for which is_valid_entry() is true.
*/
size_type row () const;
/**
* Index within the current row of the element represented by this object. This function
* can only be called for entries for which is_valid_entry() is true.
*/
size_type index () const;
/**
* Column number of the element represented by this object. This function
* can only be called for entries for which is_valid_entry() is true.
*/
size_type column () const;
/**
* Return whether the sparsity pattern entry pointed to by this iterator
* is valid or not. Note that after compressing the sparsity pattern, all
* entries are valid. However, before compression, the sparsity pattern
* allocated some memory to be used while still adding new nonzero
* entries; if you create iterators in this phase of the sparsity
* pattern's lifetime, you will iterate over elements that are not
* valid. If this is so, then this function will return false.
*/
bool is_valid_entry () const;
/**
* Comparison. True, if both iterators point to the same matrix position.
*/
bool operator == (const Accessor &) const;
/**
* Comparison operator. Result is true if either the first row number is
* smaller or if the row numbers are equal and the first index is smaller.
*
* This function is only valid if both iterators point into the same
* sparsity pattern.
*/
bool operator < (const Accessor &) const;
protected:
/**
* The sparsity pattern we operate on accessed.
*/
const SparsityPattern *sparsity_pattern;
/**
* Index in global sparsity pattern. This index represents the location
* the iterator/accessor points to within the array of the SparsityPattern
* class that stores the column numbers. It is also the index within the
* values array of a sparse matrix that stores the corresponding value of
* this site.
*/
std::size_t index_within_sparsity;
/**
* Move the accessor to the next nonzero entry in the matrix.
*/
void advance ();
/**
* Grant access to iterator class.
*/
friend class Iterator;
/**
* Grant access to accessor class of ChunkSparsityPattern.
*/
friend class ChunkSparsityPatternIterators::Accessor;
};
/**
* STL conforming iterator walking over the elements of a sparsity pattern.
*
* The typical use for these iterators is to iterate over the elements of
* a sparsity pattern (or, since they also serve as the basis for iterating
* over the elements of an associated matrix, over the elements of a sparse matrix)
* or over the elements of individual rows. Note that there is no guarantee
* that the elements of a row are actually traversed in an order in which
* columns monotonically increase. See the documentation of the
* SparsityPattern class for more information.
*
* @note This class operates directly on the internal data structures of the
* SparsityPattern class. As a consequence, some operations are cheap and
* some are not. In particular, it is cheap to access the column index of
* the sparsity pattern entry pointed to. On the other hand, it is expensive
* to access the row index (this requires $O(\log(N))$ operations for a
* matrix with $N$ row). As a consequence, when you design algorithms that
* use these iterators, it is common practice to not loop over <i>all</i>
* elements of a sparsity pattern at once, but to have an outer loop over
* all rows and within this loop iterate over the elements of this row.
* This way, you only ever need to dereference the iterator to obtain
* the column indices whereas the (expensive) lookup of the row index
* can be avoided by using the loop index instead.
*/
class Iterator
{
public:
/**
* Constructor. Create an iterator into the sparsity pattern @p sp for the
* given row and the index within it.
*
* @deprecated This constructor is deprecated. Use the other constructor
* with a global index instead.
*/
Iterator (const SparsityPattern *sp,
const size_type row,
const size_type index) DEAL_II_DEPRECATED;
/**
* Constructor. Create an iterator into the sparsity pattern @p sp for the
* given global index (i.e., the index of the given element counting from
* the zeroth row).
*/
Iterator (const SparsityPattern *sp,
const std::size_t index_within_sparsity);
/**
* Prefix increment.
*/
Iterator &operator++ ();
/**
* Postfix increment.
*/
Iterator operator++ (int);
/**
* Dereferencing operator.
*/
const Accessor &operator* () const;
/**
* Dereferencing operator.
*/
const Accessor *operator-> () const;
/**
* Comparison. True, if both iterators point to the same matrix position.
*/
bool operator == (const Iterator &) const;
/**
* Inverse of <tt>==</tt>.
*/
bool operator != (const Iterator &) const;
/**
* Comparison operator. Result is true if either the first row number is
* smaller or if the row numbers are equal and the first index is smaller.
*
* This function is only valid if both iterators point into the same
* matrix.
*/
bool operator < (const Iterator &) const;
/**
* Return the distance between the current iterator and the argument.
* The distance is given by how many times one has to apply operator++
* to the current iterator to get the argument (for a positive return
* value), or operator-- (for a negative return value).
*/
int operator - (const Iterator &p) const;
private:
/**
* Store an object of the accessor class.
*/
Accessor accessor;
};
}
/**
* 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.
*
* The elements of a SparsityPattern, corresponding to the places where
* SparseMatrix objects can store nonzero entries, are stored row-by-row.
* Within each row, elements are generally stored left-to-right in increasing
* column index order; the exception to this rule is that if the matrix
* is square (n_rows() == n_columns()), then the diagonal entry is stored
* as the first element in each row to make operations like applying a
* Jacobi or SSOR preconditioner faster. As a consequence, if you traverse
* the elements of a row of a SparsityPattern with the help of iterators into
* this object (using SparsityPattern::begin and SparsityPattern::end) you
* will find that the elements are not sorted by column index within each row
* whenever the matrix is square (the first item will be the diagonal, followed
* by the other entries sorted by column index).
*
* @note While this class forms the basis upon which SparseMatrix
* objects base their storage format, and thus plays a central role in
* setting up linear systems, it is rarely set up directly due to the
* way it stores its information. Rather, one typically goes through
* an intermediate format first, see for example the step-2 tutorial
* program as well as the documentation module @ref Sparsity.
*
* @author Wolfgang Bangerth, Guido Kanschat and others
*/
class SparsityPattern : public Subscriptor
{
public:
/**
* Declare type for container size.
*/
typedef types::global_dof_index size_type;
/**
* Typedef an iterator class that allows to walk over all nonzero elements
* of a sparsity pattern.
*/
typedef
SparsityPatternIterators::Iterator
const_iterator;
/**
* Typedef an iterator class that allows to walk over the nonzero elements
* of a row of a sparsity pattern.
*
* @deprecated This typedef is deprecated. Use proper iterators instead.
*/
typedef
const size_type *row_iterator;
/**
* Typedef an iterator class that allows to walk over all nonzero elements
* of a sparsity pattern.
*
* Since the iterator does not allow to modify the sparsity pattern, this
* type is the same as that for @p const_iterator.
*/
typedef
SparsityPatternIterators::Iterator
iterator;
/**
* 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 size_type invalid_entry = numbers::invalid_size_type;
/**
* @name Construction and setup
* Constructors, destructor; functions initializing, copying and filling an object.
*/
// @{
/**
* 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.
*/
SparsityPattern ();
/**
* 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 (SparsityPattern());</tt>, with
* <tt>v</tt> a vector of SparsityPattern 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.
*/
SparsityPattern (const SparsityPattern &);
/**
* 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 This parameter is ignored.
*
* @deprecated Use the constructor without the last argument since
* it is ignored.
*/
SparsityPattern (const size_type m,
const size_type n,
const unsigned int max_per_row,
const bool optimize_diagonal) DEAL_II_DEPRECATED;
/**
* 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
*/
SparsityPattern (const size_type m,
const size_type n,
const unsigned int max_per_row);
/**
* 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 This argument is ignored.
*
* @deprecated Use the constructor without the last argument since
* it is ignored.
*/
SparsityPattern (const size_type m,
const size_type n,
const std::vector<unsigned int> &row_lengths,
const bool optimize_diagonal) DEAL_II_DEPRECATED;
/**
* 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.
*/
SparsityPattern (const size_type m,
const size_type n,
const std::vector<unsigned int> &row_lengths);
/**
* 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.
*/
SparsityPattern (const size_type n,
const unsigned int max_per_row);
/**
* 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 This argument is ignored.
*
* @deprecated Use the constructor without the last argument since
* it is ignored.
*/
SparsityPattern (const size_type m,
const std::vector<unsigned int> &row_lengths,
const bool optimize_diagonal) DEAL_II_DEPRECATED;
/**
* 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.
*/
SparsityPattern (const size_type m,
const std::vector<unsigned int> &row_lengths);
/**
* Make a copy with extra off-diagonals.
*
* This constructs objects intended for the application of the ILU(n)-method
* or other incomplete decompositions. Therefore, additional to the
* original entry structure, space for <tt>extra_off_diagonals</tt>
* side-diagonals is provided on both sides of the main diagonal.
*
* <tt>max_per_row</tt> is the maximum number of nonzero elements per row
* which this structure is to hold. It is assumed that this number is
* sufficiently large to accommodate both the elements in <tt>original</tt>
* as well as the new off-diagonal elements created by this constructor. You
* will usually want to give the same number as you gave for
* <tt>original</tt> plus the number of side diagonals times two. You may
* however give a larger value if you wish to add further nonzero entries
* for the decomposition based on other criteria than their being on
* side-diagonals.
*
* This function requires that <tt>original</tt> refers to a quadratic
* matrix structure. It must be compressed. The matrix structure is not
* compressed after this function finishes.
*/
SparsityPattern (const SparsityPattern &original,
const unsigned int max_per_row,
const size_type extra_off_diagonals);
/**
* Destructor.
*/
~SparsityPattern ();
/**
* 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.
*/
SparsityPattern &operator = (const SparsityPattern &);
/**
* 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.
*
* @deprecated The last argument of this function is ignored. Use the
* version of this function without the last argument.
*/
void reinit (const size_type m,
const size_type n,
const unsigned int max_per_row,
const bool optimize_diagonal) DEAL_II_DEPRECATED;
/**
* 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 size_type m,
const size_type n,
const unsigned int max_per_row);
/**
* 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.
*
* @deprecated The last argument of this function is ignored. Use the
* version of this function without the last argument.
*/
void reinit (const size_type m,
const size_type n,
const std::vector<unsigned int> &row_lengths,
const bool optimize_diagonal) DEAL_II_DEPRECATED;
/**
* 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 size_type m,
const size_type n,
const std::vector<unsigned int> &row_lengths);
/**
* Same as above, but with a VectorSlice argument instead.
*
* @deprecated The last argument of this function is ignored. Use the
* version of this function without the last argument.
*/
void reinit (const size_type m,
const size_type n,
const VectorSlice<const std::vector<unsigned int> > &row_lengths,
const bool optimize_diagonal) DEAL_II_DEPRECATED;
/**
* Same as above, but with a VectorSlice argument instead.
*/
void reinit (const size_type m,
const size_type n,
const VectorSlice<const std::vector<unsigned int> > &row_lengths);
/**
* 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 SparsityPattern 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.
*
* @deprecated The last argument of this function is ignored. Use the
* version of this function without the last argument.
*/
template <typename ForwardIterator>
void copy_from (const size_type n_rows,
const size_type n_cols,
const ForwardIterator begin,
const ForwardIterator end,
const bool optimize_diagonal) DEAL_II_DEPRECATED;
/**
* 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 size_type n_rows,
const size_type n_cols,
const ForwardIterator begin,
const ForwardIterator end);
/**
* 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.
*
* @deprecated The last argument of this function is ignored. Use the
* version of this function without the last argument.
*/
template <typename CompressedSparsityType>
void copy_from (const CompressedSparsityType &csp,
const bool optimize_diagonal) DEAL_II_DEPRECATED;
/**
* Copy data from an object of type CompressedSparsityPattern,
* CompressedSetSparsityPattern or CompressedSimpleSparsityPattern. Although
* not a compressed sparsity pattern, this function is also instantiated
* if the argument is of type SparsityPattern (i.e., the current class).
* Previous content of this object is lost, and the sparsity pattern is in
* compressed mode afterwards.
*/
template <typename CompressedSparsityType>
void copy_from (const CompressedSparsityType &csp);
/**
* 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.
*
* @deprecated The last argument of this function is ignored. Use the
* version of this function without the last argument.
*/
template <typename number>
void copy_from (const FullMatrix<number> &matrix,
const bool optimize_diagonal) DEAL_II_DEPRECATED;
/**
* 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);
/**
* 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 ();
/**
* 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 size_type i,
const size_type j);
/**
* Add several nonzero entries to the specified matrix row. This function
* may only be called for non-compressed sparsity patterns.
*
* If some of the entries already exist, nothing bad happens.
*/
template <typename ForwardIterator>
void add_entries (const size_type row,
ForwardIterator begin,
ForwardIterator end,
const bool indices_are_sorted = false);
// @}
/**
* @name Iterators
*/
// @{
/**
* STL-like iterator with the first entry of the matrix. The resulting
* iterator can be used to walk over all nonzero entries of the sparsity
* pattern.
*
* Note the discussion in the general documentation of this class about
* the order in which elements are accessed.
*/
iterator begin () const;
/**
* Final iterator.
*/
iterator end () const;
/**
* STL-like iterator with the first entry of row <tt>r</tt>.
*
* Note that if the given row is empty, i.e. does not contain any nonzero
* entries, then the iterator returned by this function equals
* <tt>end(r)</tt>. Note also that the iterator may not be dereferencable in
* that case.
*
* Note also the discussion in the general documentation of this class about
* the order in which elements are accessed.
*/
iterator begin (const size_type r) const;
/**
* Final iterator of row <tt>r</tt>. It points to the first element past the
* end of line @p r, or past the end of the entire sparsity pattern.
*
* Note that the end iterator is not necessarily dereferencable. This is in
* particular the case if it is the end iterator for the last row of a
* matrix.
*/
iterator end (const size_type r) const;
/**
* STL-like iterator with the first entry of row <tt>r</tt>.
*
* Note that if the given row is empty, i.e. does not contain any nonzero
* entries, then the iterator returned by this function equals
* <tt>end(r)</tt>. Note also that the iterator may not be dereferencable in
* that case.
*
* @deprecated Use the iterators provided by the begin() and end()
* functions instead.
*/
row_iterator row_begin (const size_type r) const DEAL_II_DEPRECATED;
/**
* Final iterator of row <tt>r</tt>. It points to the first element past the
* end of line @p r, or past the end of the entire sparsity pattern.
*
* Note that the end iterator is not necessarily dereferencable. This is in
* particular the case if it is the end iterator for the last row of a
* matrix.
*
* @deprecated Use the iterators provided by the begin() and end()
* functions instead.
*/
row_iterator row_end (const size_type r) const DEAL_II_DEPRECATED;
// @}
/**
* @name Querying information
*/
// @{
/**
* Test for equality of two SparsityPatterns.
*/
bool operator == (const SparsityPattern &) const;
/**
* 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. 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.
*/
size_type max_entries_per_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 $\max\{n-1,m-1\}$.
*/
size_type 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.
*/
size_type n_nonzero_elements () const;
/**
* Return whether the structure is compressed or not.
*/
bool is_compressed () const;
/**
* Return number of rows of this matrix, which equals the dimension of the
* image space.
*/
size_type n_rows () const;
/**
* Return number of columns of this matrix, which equals the dimension of
* the range space.
*/
size_type n_cols () const;
/**
* Number of entries in a specific row.
*/
unsigned int row_length (const size_type row) const;
/**
* Determine whether the matrix uses the special convention for quadratic
* matrices that the diagonal entries are stored first in each row.
*
* @deprecated The function always returns true if the matrix is
* square and false if it is not.
*/
bool optimize_diagonal () const DEAL_II_DEPRECATED;
/**
* 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 if and only if it is square because it then
* unconditionally stores the diagonal entries whether they have been added
* explicitly or not.
*
* 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;
/**
* Determine an estimate for the memory consumption (in bytes) of this
* object. See MemoryConsumption.
*/
std::size_t memory_consumption () const;
// @}
/**
* @name Accessing entries
*/
// @{
/**
* Return the index of the matrix element with row number <tt>i</tt> and
* column number <tt>j</tt>. If the matrix element is not a nonzero one,
* return SparsityPattern::invalid_entry.
*
* This function is usually called by the SparseMatrix::operator()(). It may
* only be called for compressed sparsity patterns, since in this case
* searching whether the entry exists can be done quite fast with a binary
* sort algorithm because the column numbers are sorted.
*
* If <tt>m</tt> is the number of entries in <tt>row</tt>, then the
* complexity of this function is <i>log(m)</i> if the sparsity pattern is
* compressed.
*
* @note This function is not cheap since it has to search through all
* of the elements of the given row <tt>i</tt> to find whether index
* <tt>j</tt> exists. Thus, it is more expensive than necessary in cases
* where you want to loop over all of the nonzero elements of this
* sparsity pattern (or of a sparse matrix associated with it) or of a
* single row. In such cases, it is more efficient to use iterators over
* the elements of the sparsity pattern or of the sparse matrix.
*/
size_type operator() (const size_type i,
const size_type j) const;
/**
* This is the inverse operation to operator()(): given a global index, find
* out row and column of the matrix entry to which it belongs. The returned
* value is the pair composed of row and column index.
*
* This function may only be called if the sparsity pattern is closed. The
* global index must then be between zero and n_nonzero_elements().
*
* If <tt>N</tt> is the number of rows of this matrix, then the complexity
* of this function is <i>log(N)</i>.
*/
std::pair<size_type, size_type>
matrix_position (const size_type global_index) const;
/**
* Check if a value at a certain position may be non-zero.
*/
bool exists (const size_type i,
const size_type j) const;
/**
* The index of a global matrix entry in its row.
*
* This function is analogous to operator(), but it computes the index not
* with respect to the total field, but only with respect to the row
* <tt>j</tt>.
*/
size_type row_position(const size_type i,
const size_type j) const;
/**
* Access to column number field. Return the column number of the
* <tt>index</tt>th entry in <tt>row</tt>. Note that if diagonal elements
* are optimized, the first element in each row is the diagonal element,
* i.e. <tt>column_number(row,0)==row</tt>.
*
* If the sparsity pattern is already compressed, then (except for the
* diagonal element), the entries are sorted by columns,
* i.e. <tt>column_number(row,i)</tt> <tt><</tt>
* <tt>column_number(row,i+1)</tt>.
*/
size_type column_number (const size_type row,
const unsigned int index) const;
// @}
/**
* @name Input/Output
*/
// @{
/**
* 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 or 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;
/**
* Write the data of this object to a stream for the purpose of
* serialization
*/
template <class Archive>
void save (Archive &ar, const unsigned int version) const;
/**
* Read the data of this object from a stream for the purpose of
* serialization
*/
template <class Archive>
void load (Archive &ar, const unsigned int version);
// @}
/**
* @name Deprecated functions
*/
// @{
/**
* @deprecated This function is deprecated. Use SparsityTools::partition
* instead.
*
* Use the METIS partitioner to generate a partitioning of the degrees of
* freedom represented by this sparsity pattern. In effect, we view this
* sparsity pattern as a graph of connections between various degrees of
* freedom, where each nonzero entry in the sparsity pattern corresponds to
* an edge between two nodes in the connection graph. The goal is then to
* decompose this graph into groups of nodes so that a minimal number of
* edges are cut by the boundaries between node groups. This partitioning is
* done by METIS. Note that METIS can only partition symmetric sparsity
* patterns, and that of course the sparsity pattern has to be square. We do
* not check for symmetry of the sparsity pattern, since this is an
* expensive operation, but rather leave this as the responsibility of
* caller of this function.
*
* After calling this function, the output array will have values between
* zero and @p n_partitions-1 for each node (i.e. row or column of the
* matrix).
*
* This function will generate an error if METIS is not installed unless @p
* n_partitions is one. I.e., you can write a program so that it runs in the
* single-processor single-partition case without METIS installed, and only
* requires METIS when multiple partitions are required.
*
* Note that the sparsity pattern itself is not changed by calling this
* function. However, you will likely use the information generated by
* calling this function to renumber degrees of freedom, after which you
* will of course have to regenerate the sparsity pattern.
*
* This function will rarely be called separately, since in finite element
* methods you will want to partition the mesh, not the matrix. This can be
* done by calling @p GridTools::partition_triangulation.
*/
void partition (const unsigned int n_partitions,
std::vector<unsigned int> &partition_indices) const DEAL_II_DEPRECATED;
/**
* @deprecated This is kind of an expert mode. Get access to the rowstart
* array, but read-only.
*
* Use of this function is highly deprecated. Use @p row_length and @p
* column_number instead. Also, using iterators may get you most of the
* information you may want.
*
* Though the return value is declared <tt>const</tt>, you should be aware
* that it may change if you call any nonconstant function of objects which
* operate on it.
*
* You should use this interface very carefully and only if you are
* absolutely sure to know what you do. You should also note that the
* structure of these arrays may change over time. If you change the layout
* yourself, you should also rename this function to avoid programs relying
* on outdated information!
*/
const std::size_t *get_rowstart_indices () const DEAL_II_DEPRECATED;
/**
* @deprecated. Use @p row_length and @p column_number instead. Also, using
* iterators may get you most of the information you may want.
*
* This is kind of an expert mode: get access to the colnums array, but
* readonly.
*
* Though the return value is declared <tt>const</tt>, you should be aware
* that it may change if you call any nonconstant function of objects which
* operate on it.
*
* You should use this interface very carefully and only if you are
* absolutely sure to know what you do. You should also note that the
* structure of these arrays may change over time. If you change the layout
* yourself, you should also rename this function to avoid programs relying
* on outdated information!
*/
const size_type *get_column_numbers () const DEAL_II_DEPRECATED;
BOOST_SERIALIZATION_SPLIT_MEMBER()
/** @addtogroup Exceptions
* @name Exceptions
* @{ */
/**
* You tried to add an element to a row, but there was no space left.
*/
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?)");
/**
* The operation is only allowed after the SparsityPattern has been set up
* and compress() was called.
*/
DeclException0 (ExcNotCompressed);
/**
* This operation changes the structure of the SparsityPattern and is not
* possible after compress() has been called.
*/
DeclException0 (ExcMatrixIsCompressed);
/**
* 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
*/
DeclException1 (ExcInvalidNumberOfPartitions,
int,
<< "The number of partitions you gave is " << arg1
<< ", but must be greater than zero.");
//@}
private:
/**
* Maximum number of rows that can be stored in the #rowstart array. Since
* reallocation of that array only happens if the present one is too small,
* but never when the size of this matrix structure shrinks, #max_dim might
* be larger than #rows and in this case #rowstart has more elements than
* are used.
*/
size_type max_dim;
/**
* Number of rows that this sparsity structure shall represent.
*/
size_type rows;
/**
* Number of columns that this sparsity structure shall represent.
*/
size_type cols;
/**
* Size of the actually allocated array #colnums. Here, the same applies as
* for the #rowstart array, i.e. it may be larger than the actually used
* part of the array.
*/
size_type max_vec_len;
/**
* Maximum number of elements per row. This is set to the value given to the
* reinit() function (or to the constructor), or to the maximum row length
* computed from the vectors in case the more flexible constructors or
* reinit versions are called. Its value is more or less meaningless after
* compress() has been called.
*/
unsigned int max_row_length;
/**
* Array which hold for each row which is the first element in #colnums
* belonging to that row. Note that the size of the array is one larger than
* the number of rows, because the last element is used for
* <tt>row</tt>=#rows, i.e. the row past the last used one. The value of
* #rowstart[#rows]} equals the index of the element past the end in
* #colnums; this way, we are able to write loops like <tt>for
* (i=rowstart[k]; i<rowstart[k+1]; ++i)</tt> also for the last row.
*
* Note that the actual size of the allocated memory may be larger than the
* region that is used. The actual number of elements that was allocated is
* stored in #max_dim.
*/
std::size_t *rowstart;
/**
* Array of column numbers. In this array, we store for each non-zero
* element its column number. The column numbers for the elements in row
* <i>r</i> are stored within the index range
* #rowstart[<i>r</i>]...#rowstart[<i>r+1</i>]. Therefore to find out
* whether a given element (<i>r,c</i>) exists, we have to check whether the
* column number <i>c</i> exists in the above-mentioned range within this
* array. If it exists, say at position <i>p</i> within this array, the
* value of the respective element in the sparse matrix will also be at
* position <i>p</i> of the values array of that class.
*
* At the beginning, all elements of this array are set to @p -1 indicating
* invalid (unused) column numbers (diagonal elements are preset if
* optimized storage is requested, though). Now, if nonzero elements are
* added, one column number in the row's respective range after the other is
* set to the column number of the added element. When compress is called,
* unused elements (indicated by column numbers @p -1) are eliminated by
* copying the column number of subsequent rows and the column numbers
* within each row (with possible exception of the diagonal element) are
* sorted, such that finding whether an element exists and determining its
* position can be done by a binary search.
*/
size_type *colnums;
/**
* Store whether the compress() function was called for this object.
*/
bool compressed;
/**
* Is special treatment of diagonals enabled?
*/
bool store_diagonal_first_in_row;
/**
* Make all sparse matrices friends of this class.
*/
template <typename number> friend class SparseMatrix;
template <typename number> friend class SparseLUDecomposition;
template <typename number> friend class SparseILU;
template <typename number> friend class ChunkSparseMatrix;
friend class ChunkSparsityPattern;
/**
* Also give access to internal details to the iterator/accessor
* classes.
*/
friend class SparsityPatternIterators::Iterator;
friend class SparsityPatternIterators::Accessor;
friend class ChunkSparsityPatternIterators::Accessor;
};
/*@}*/
/*---------------------- Inline functions -----------------------------------*/
#ifndef DOXYGEN
namespace SparsityPatternIterators
{
inline
Accessor::
Accessor (const SparsityPattern *sparsity_pattern,
const size_type r,
const size_type i)
:
sparsity_pattern(sparsity_pattern),
index_within_sparsity(sparsity_pattern->rowstart[r]+i)
{}
inline
Accessor::
Accessor (const SparsityPattern *sparsity_pattern,
const std::size_t i)
:
sparsity_pattern(sparsity_pattern),
index_within_sparsity(i)
{}
inline
Accessor::
Accessor (const SparsityPattern *sparsity_pattern)
:
sparsity_pattern(sparsity_pattern),
index_within_sparsity(sparsity_pattern->rowstart[sparsity_pattern->rows])
{}
inline
bool
Accessor::is_valid_entry () const
{
return (index_within_sparsity < sparsity_pattern->rowstart[sparsity_pattern->rows]
&&
sparsity_pattern->colnums[index_within_sparsity]
!= SparsityPattern::invalid_entry);
}
inline
size_type
Accessor::row() const
{
Assert (is_valid_entry() == true, ExcInvalidIterator());
const std::size_t *insert_point =
std::upper_bound(sparsity_pattern->rowstart,
sparsity_pattern->rowstart + sparsity_pattern->rows + 1,
index_within_sparsity);
return insert_point - sparsity_pattern->rowstart - 1;
}
inline
size_type
Accessor::column() const
{
Assert (is_valid_entry() == true, ExcInvalidIterator());
return (sparsity_pattern->colnums[index_within_sparsity]);
}
inline
size_type
Accessor::index() const
{
Assert (is_valid_entry() == true, ExcInvalidIterator());
return index_within_sparsity - sparsity_pattern->rowstart[row()];
}
inline
bool
Accessor::operator == (const Accessor &other) const
{
return (sparsity_pattern == other.sparsity_pattern &&
index_within_sparsity == other.index_within_sparsity);
}
inline
bool
Accessor::operator < (const Accessor &other) const
{
Assert (sparsity_pattern == other.sparsity_pattern,
ExcInternalError());
return index_within_sparsity < other.index_within_sparsity;
}
inline
void
Accessor::advance ()
{
Assert (index_within_sparsity < sparsity_pattern->rowstart[sparsity_pattern->rows],
ExcIteratorPastEnd());
++index_within_sparsity;
}
inline
Iterator::Iterator (const SparsityPattern *sparsity_pattern,
const size_type r,
const size_type i)
:
accessor(sparsity_pattern, sparsity_pattern->rowstart[r]+i)
{}
inline
Iterator::Iterator (const SparsityPattern *sparsity_pattern,
const std::size_t i)
:
accessor(sparsity_pattern, i)
{}
inline
Iterator &
Iterator::operator++ ()
{
accessor.advance ();
return *this;
}
inline
Iterator
Iterator::operator++ (int)
{
const Iterator iter = *this;
accessor.advance ();
return iter;
}
inline
const Accessor &
Iterator::operator* () const
{
return accessor;
}
inline
const Accessor *
Iterator::operator-> () const
{
return &accessor;
}
inline
bool
Iterator::operator == (const Iterator &other) const
{
return (accessor == other.accessor);
}
inline
bool
Iterator::operator != (const Iterator &other) const
{
return ! (*this == other);
}
inline
bool
Iterator::operator < (const Iterator &other) const
{
return accessor < other.accessor;
}
inline
int
Iterator::operator - (const Iterator &other) const
{
Assert (accessor.sparsity_pattern == other.accessor.sparsity_pattern,
ExcInternalError());
return (*this)->index_within_sparsity - other->index_within_sparsity;
}
}
inline
SparsityPattern::iterator
SparsityPattern::begin () const
{
return iterator(this, rowstart[0]);
}
inline
SparsityPattern::iterator
SparsityPattern::end () const
{
return iterator(this, rowstart[rows]);
}
inline
SparsityPattern::iterator
SparsityPattern::begin (const size_type r) const
{
Assert (r<n_rows(), ExcIndexRangeType<size_type>(r,0,n_rows()));
return iterator(this, rowstart[r]);
}
inline
SparsityPattern::iterator
SparsityPattern::end (const size_type r) const
{
Assert (r<n_rows(), ExcIndexRangeType<size_type>(r,0,n_rows()));
return iterator(this, rowstart[r+1]);
}
inline
SparsityPattern::row_iterator
SparsityPattern::row_begin (const size_type r) const
{
Assert (r<n_rows(), ExcIndexRangeType<size_type>(r,0,n_rows()));
return &colnums[rowstart[r]];
}
inline
SparsityPattern::row_iterator
SparsityPattern::row_end (const size_type r) const
{
Assert (r<n_rows(), ExcIndexRangeType<size_type>(r,0,n_rows()));
return &colnums[rowstart[r+1]];
}
inline
SparsityPattern::size_type
SparsityPattern::n_rows () const
{
return rows;
}
inline
SparsityPattern::size_type
SparsityPattern::n_cols () const
{
return cols;
}
inline
bool
SparsityPattern::is_compressed () const
{
return compressed;
}
inline
bool
SparsityPattern::optimize_diagonal () const
{
return store_diagonal_first_in_row;
}
inline
bool
SparsityPattern::stores_only_added_elements () const
{
return (store_diagonal_first_in_row == false);
}
inline
const std::size_t *
SparsityPattern::get_rowstart_indices () const
{
return rowstart;
}
inline
const SparsityPattern::size_type *
SparsityPattern::get_column_numbers () const
{
return colnums;
}
inline
unsigned int
SparsityPattern::row_length (const size_type row) const
{
Assert(row<rows, ExcIndexRangeType<size_type>(row,0,rows));
return rowstart[row+1]-rowstart[row];
}
inline
SparsityPattern::size_type
SparsityPattern::column_number (const size_type row,
const unsigned int index) const
{
Assert(row<rows, ExcIndexRangeType<size_type>(row,0,rows));
Assert(index<row_length(row), ExcIndexRange(index,0,row_length(row)));
return colnums[rowstart[row]+index];
}
inline
SparsityPattern::size_type
SparsityPattern::n_nonzero_elements () const
{
Assert ((rowstart!=0) && (colnums!=0), ExcEmptyObject());
Assert (compressed, ExcNotCompressed());
return rowstart[rows]-rowstart[0];
}
template <class Archive>
inline
void
SparsityPattern::save (Archive &ar, const unsigned int) const
{
// forward to serialization function in the base class.
ar &static_cast<const Subscriptor &>(*this);
ar &max_dim &rows &cols &max_vec_len &max_row_length &compressed &store_diagonal_first_in_row;
ar &boost::serialization::make_array(rowstart, max_dim + 1);
ar &boost::serialization::make_array(colnums, max_vec_len);
}
template <class Archive>
inline
void
SparsityPattern::load (Archive &ar, const unsigned int)
{
// forward to serialization function in the base class.
ar &static_cast<Subscriptor &>(*this);
ar &max_dim &rows &cols &max_vec_len &max_row_length &compressed &store_diagonal_first_in_row;
rowstart = new std::size_t [max_dim + 1];
colnums = new size_type [max_vec_len];
ar &boost::serialization::make_array(rowstart, max_dim + 1);
ar &boost::serialization::make_array(colnums, max_vec_len);
}
inline
bool
SparsityPattern::operator == (const SparsityPattern &sp2) const
{
// it isn't quite necessary to compare *all* member variables. by only
// comparing the essential ones, we can say that two sparsity patterns are
// equal even if one is compressed and the other is not (in which case some
// of the member variables are not yet set correctly)
if (rows != sp2.rows ||
cols != sp2.cols ||
compressed != sp2.compressed ||
store_diagonal_first_in_row != sp2.store_diagonal_first_in_row)
return false;
for (size_type i = 0; i < rows+1; ++i)
if (rowstart[i] != sp2.rowstart[i])
return false;
for (size_type i = 0; i < rowstart[rows]; ++i)
if (colnums[i] != sp2.colnums[i])
return false;
return true;
}
namespace internal
{
namespace SparsityPatternTools
{
/**
* Declare type for container size.
*/
typedef types::global_dof_index size_type;
inline
size_type
get_column_index_from_iterator (const size_type i)
{
return i;
}
template <typename value>
inline
size_type
get_column_index_from_iterator (const std::pair<size_type, value> &i)
{
return i.first;
}
template <typename value>
inline
size_type
get_column_index_from_iterator (const std::pair<const size_type, value> &i)
{
return i.first;
}
}
}
template <typename ForwardIterator>
void
SparsityPattern::copy_from (const size_type n_rows,
const size_type n_cols,
const ForwardIterator begin,
const ForwardIterator end,
const bool)
{
copy_from (n_rows, n_cols, begin, end);
}
template <typename ForwardIterator>
void
SparsityPattern::copy_from (const size_type n_rows,
const size_type n_cols,
const ForwardIterator begin,
const ForwardIterator end)
{
Assert (static_cast<size_type>(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 = (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);
// now enter all the elements into the matrix. note that if the matrix is
// quadratic, then we already have the diagonal element preallocated
//
// for use in the inner loop, we define a typedef to the type of the inner
// iterators
size_type row = 0;
typedef typename std::iterator_traits<ForwardIterator>::value_type::const_iterator inner_iterator;
for (ForwardIterator i=begin; i!=end; ++i, ++row)
{
size_type *cols = &colnums[rowstart[row]] + (is_square ? 1 : 0);
const inner_iterator end_of_row = i->end();
for (inner_iterator j=i->begin(); j!=end_of_row; ++j)
{
const size_type col
= internal::SparsityPatternTools::get_column_index_from_iterator(*j);
Assert (col < n_cols, ExcIndexRange(col,0,n_cols));
if ((col!=row) || !is_square)
*cols++ = col;
}
}
// finally compress everything. this also sorts the entries within each row
compress ();
}
#endif // DOXYGEN
DEAL_II_NAMESPACE_CLOSE
#endif
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