Reference documentation for deal.II version Git 03163e8c3d 20190423 18:40:00 0600

#include <deal.II/lac/sparsity_pattern.h>
Public Types  
using  size_type = SparsityPatternBase::size_type 
using  const_iterator = SparsityPatternBase::const_iterator 
using  iterator = SparsityPatternBase::iterator 
Public Types inherited from SparsityPatternBase  
using  size_type = types::global_dof_index 
using  const_iterator = SparsityPatternIterators::Iterator 
using  iterator = SparsityPatternIterators::Iterator 
Public Member Functions  
Construction and setup Constructors, destructor; functions  
initializing, copying and filling an object.  
SparsityPattern ()  
SparsityPattern (const SparsityPattern &)  
SparsityPattern (const size_type m, const size_type n, const unsigned int max_per_row)  
SparsityPattern (const size_type m, const size_type n, const std::vector< unsigned int > &row_lengths)  
SparsityPattern (const size_type m, const unsigned int max_per_row)  
SparsityPattern (const size_type m, const std::vector< unsigned int > &row_lengths)  
SparsityPattern (const SparsityPattern &original, const unsigned int max_per_row, const size_type extra_off_diagonals)  
~SparsityPattern () override=default  
SparsityPattern &  operator= (const SparsityPattern &) 
virtual void  reinit (const size_type m, const size_type n, const ArrayView< const unsigned int > &row_lengths) override 
void  compress () 
template<typename ForwardIterator >  
void  copy_from (const size_type n_rows, const size_type n_cols, const ForwardIterator begin, const ForwardIterator end) 
void  copy_from (const DynamicSparsityPattern &dsp) 
void  copy_from (const SparsityPattern &sp) 
template<typename number >  
void  copy_from (const FullMatrix< number > &matrix) 
template<typename ForwardIterator >  
void  add_entries (const size_type row, ForwardIterator begin, ForwardIterator end, const bool indices_are_sorted=false) 
Querying information  
bool  operator== (const SparsityPattern &) const 
bool  stores_only_added_elements () const 
std::size_t  memory_consumption () const 
Accessing entries  
size_type  operator() (const size_type i, const size_type j) const 
Input/Output  
void  block_write (std::ostream &out) const 
void  block_read (std::istream &in) 
template<class Archive >  
void  save (Archive &ar, const unsigned int version) const 
template<class Archive >  
void  load (Archive &ar, const unsigned int version) 
Public Member Functions inherited from SparsityPatternBase  
SparsityPatternBase ()  
~SparsityPatternBase () override=default  
void  reinit (const size_type m, const size_type n, const unsigned int max_per_row) 
void  reinit (const size_type m, const size_type n, const std::vector< unsigned int > &row_lengths) 
void  symmetrize () 
void  add (const size_type i, const size_type j) 
iterator  begin () const 
iterator  end () const 
iterator  begin (const size_type r) const 
iterator  end (const size_type r) const 
bool  operator== (const SparsityPatternBase &) const 
bool  empty () const 
bool  exists (const size_type i, const size_type j) const 
size_type  max_entries_per_row () const 
size_type  bandwidth () const 
std::size_t  n_nonzero_elements () const 
bool  is_compressed () const 
size_type  n_rows () const 
size_type  n_cols () const 
unsigned int  row_length (const size_type row) const 
std::size_t  memory_consumption () const 
size_type  column_number (const size_type row, const unsigned int index) const 
size_type  row_position (const size_type i, const size_type j) const 
std::pair< size_type, size_type >  matrix_position (const std::size_t global_index) const 
void  print (std::ostream &out) const 
void  print_gnuplot (std::ostream &out) const 
void  print_svg (std::ostream &out) const 
template<class Archive >  
void  save (Archive &ar, const unsigned int version) const 
template<class Archive >  
void  load (Archive &ar, const unsigned int version) 
Public Member Functions inherited from Subscriptor  
Subscriptor ()  
Subscriptor (const Subscriptor &)  
Subscriptor (Subscriptor &&) noexcept  
virtual  ~Subscriptor () 
Subscriptor &  operator= (const Subscriptor &) 
Subscriptor &  operator= (Subscriptor &&) noexcept 
void  subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const 
void  unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const 
unsigned int  n_subscriptions () const 
template<typename StreamType >  
void  list_subscribers (StreamType &stream) const 
void  list_subscribers () const 
template<class Archive >  
void  serialize (Archive &ar, const unsigned int version) 
Static Public Member Functions  
static ::ExceptionBase &  ExcIteratorRange (int arg1, int arg2) 
static ::ExceptionBase &  ExcInvalidNumberOfPartitions (int arg1) 
Static Public Member Functions inherited from SparsityPatternBase  
static ::ExceptionBase &  ExcNotCompressed () 
static ::ExceptionBase &  ExcNotEnoughSpace (int arg1, int arg2) 
static ::ExceptionBase &  ExcMatrixIsCompressed () 
Static Public Member Functions inherited from Subscriptor  
static ::ExceptionBase &  ExcInUse (int arg1, std::string arg2, std::string arg3) 
static ::ExceptionBase &  ExcNoSubscriber (std::string arg1, std::string arg2) 
Static Public Attributes  
static const size_type  invalid_entry = SparsityPatternBase::invalid_entry 
Static Public Attributes inherited from SparsityPatternBase  
static const size_type  invalid_entry = numbers::invalid_size_type 
Private Attributes  
bool  store_diagonal_first_in_row 
Friends  
template<typename number >  
class  SparseMatrix 
template<typename number >  
class  SparseLUDecomposition 
template<typename number >  
class  SparseILU 
template<typename number >  
class  ChunkSparseMatrix 
class  ChunkSparsityPattern 
class  DynamicSparsityPattern 
class  SparsityPatternIterators::Iterator 
class  SparsityPatternIterators::Accessor 
class  ChunkSparsityPatternIterators::Accessor 
Additional Inherited Members  
Protected Attributes inherited from SparsityPatternBase  
size_type  max_dim 
size_type  rows 
size_type  cols 
std::size_t  max_vec_len 
unsigned int  max_row_length 
std::unique_ptr< std::size_t[]>  rowstart 
std::unique_ptr< size_type[]>  colnums 
bool  compressed 
This class stores a sparsity pattern in the compressed row storage (CSR) format to store data, and is used as the basis for the SparseMatrix class.
The elements of a SparsityPattern, corresponding to the places where SparseMatrix objects can store nonzero entries, are stored rowbyrow. Within each row, elements are generally stored lefttoright 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).
Definition at line 857 of file sparsity_pattern.h.
Declare type for container size.
Definition at line 863 of file sparsity_pattern.h.
Typedef an iterator class that allows to walk over all nonzero elements of a sparsity pattern.
Definition at line 869 of file sparsity_pattern.h.
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 const_iterator
.
Definition at line 878 of file sparsity_pattern.h.
SparsityPattern::SparsityPattern  (  ) 
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.
Definition at line 51 of file sparsity_pattern.cc.
SparsityPattern::SparsityPattern  (  const SparsityPattern &  s  ) 
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 one wants to place a SparsityPattern in a container, e.g., to write such statements like v.push_back (SparsityPattern());
, with v
a std::vector of SparsityPattern objects.
Usually, it is sufficient to use the explicit keyword to disallow unwanted temporaries, but this does not work for std::vector
s. 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.
Definition at line 60 of file sparsity_pattern.cc.
SparsityPattern::SparsityPattern  (  const size_type  m, 
const size_type  n,  
const unsigned int  max_per_row  
) 
Initialize a rectangular pattern of size m x n
.
[in]  m  The number of rows. 
[in]  n  The number of columns. 
[in]  max_per_row  Maximum number of nonzero entries per row. 
Definition at line 76 of file sparsity_pattern.cc.
SparsityPattern::SparsityPattern  (  const size_type  m, 
const size_type  n,  
const std::vector< unsigned int > &  row_lengths  
) 
Initialize a rectangular pattern of size m x n
.
[in]  m  The number of rows. 
[in]  n  The number of columns. 
[in]  row_lengths  Possible number of nonzero entries for each row. This vector must have one entry for each row. 
Definition at line 87 of file sparsity_pattern.cc.
SparsityPattern::SparsityPattern  (  const size_type  m, 
const unsigned int  max_per_row  
) 
Initialize a quadratic pattern of dimension m
with at most max_per_row
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.
Definition at line 98 of file sparsity_pattern.cc.
SparsityPattern::SparsityPattern  (  const size_type  m, 
const std::vector< unsigned int > &  row_lengths  
) 
Initialize a quadratic pattern of size m x m
.
[in]  m  The number of rows and columns. 
[in]  row_lengths  Maximum number of nonzero entries for each row. This vector must have one entry for each row. 
Definition at line 107 of file sparsity_pattern.cc.
SparsityPattern::SparsityPattern  (  const SparsityPattern &  original, 
const unsigned int  max_per_row,  
const size_type  extra_off_diagonals  
) 
Make a copy with extra offdiagonals.
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 extra_off_diagonals
side diagonals is provided on both sides of the main diagonal.
max_per_row
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 original
as well as the new offdiagonal elements created by this constructor. You will usually want to give the same number as you gave for original
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 original
refers to a quadratic matrix structure. It must be compressed. The matrix structure is not compressed after this function finishes.
Definition at line 116 of file sparsity_pattern.cc.

overridedefault 
Destructor.
SparsityPattern & SparsityPattern::operator=  (  const SparsityPattern &  s  ) 
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.
Definition at line 196 of file sparsity_pattern.cc.

overridevirtual 
Reallocate memory for a matrix of size m
times n
. The number of entries for each row is taken from the ArrayView row_lengths
which has to give this number of each row \(i=0\ldots m1\).
Implements SparsityPatternBase.
Definition at line 227 of file sparsity_pattern.cc.
void SparsityPattern::compress  (  ) 
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.
Definition at line 336 of file sparsity_pattern.cc.
void SparsityPattern::copy_from  (  const size_type  n_rows, 
const size_type  n_cols,  
const ForwardIterator  begin,  
const ForwardIterator  end  
) 
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 std::vector
, std::list
, pointers into a Cstyle 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 operator*
or operator>
to one of these iterators) must be a container itself that provides functions begin
and end
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:
Note that this example works since the iterators dereferenced yield containers with functions begin
and end
(namely std::vector
s), and the inner iterators dereferenced yield unsigned integers as column indices. Note that we could have replaced each of the two std::vector
occurrences by std::list
, and the inner one by std::set
as well.
Another example would be as follows, where we initialize a whole matrix, not only a sparsity pattern:
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 std::vector
could be replaced by std::list
, and the inner std::map<unsigned int,double>
could be replaced by std::vector<std::pair<unsigned int,double> >
, or a list or set of such pairs, as they all return iterators that point to such pairs.
void SparsityPattern::copy_from  (  const DynamicSparsityPattern &  dsp  ) 
Copy data from a DynamicSparsityPattern. Previous content of this object is lost, and the sparsity pattern is in compressed mode afterwards.
Definition at line 490 of file sparsity_pattern.cc.
void SparsityPattern::copy_from  (  const SparsityPattern &  sp  ) 
Copy data from a SparsityPattern. Previous content of this object is lost, and the sparsity pattern is in compressed mode afterwards.
Definition at line 442 of file sparsity_pattern.cc.
void SparsityPattern::copy_from  (  const FullMatrix< number > &  matrix  ) 
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.
Definition at line 551 of file sparsity_pattern.cc.
void SparsityPattern::add_entries  (  const size_type  row, 
ForwardIterator  begin,  
ForwardIterator  end,  
const bool  indices_are_sorted = false 

) 
Add several nonzero entries to the specified matrix row. This function may only be called for noncompressed sparsity patterns.
If some of the entries already exist, nothing bad happens.
Definition at line 733 of file sparsity_pattern.cc.
bool SparsityPattern::operator==  (  const SparsityPattern &  )  const 
Test for equality of two SparsityPatterns.
bool SparsityPattern::stores_only_added_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 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.
std::size_t SparsityPattern::memory_consumption  (  )  const 
Determine an estimate for the memory consumption (in bytes) of this object. See MemoryConsumption.
Definition at line 1040 of file sparsity_pattern.cc.
SparsityPattern::size_type SparsityPattern::operator()  (  const size_type  i, 
const size_type  j  
)  const 
Return the index of the matrix element with row number i
and column number j
. 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 m
is the number of entries in row
, then the complexity of this function is log(m) if the sparsity pattern is compressed.
i
to find whether index j
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. Definition at line 666 of file sparsity_pattern.cc.
void SparsityPattern::block_write  (  std::ostream &  out  )  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 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.
Definition at line 969 of file sparsity_pattern.cc.
void SparsityPattern::block_read  (  std::istream &  in  ) 
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.
Definition at line 993 of file sparsity_pattern.cc.
void SparsityPattern::save  (  Archive &  ar, 
const unsigned int  version  
)  const 
Write the data of this object to a stream for the purpose of serialization
void SparsityPattern::load  (  Archive &  ar, 
const unsigned int  version  
) 
Read the data of this object from a stream for the purpose of serialization

friend 
Make all sparse matrices friends of this class.
Typedef for the sparse matrix type used.
Definition at line 1312 of file sparsity_pattern.h.

friend 
Also give access to internal details to the iterator/accessor classes.
Definition at line 1326 of file sparsity_pattern.h.

static 
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.
Definition at line 901 of file sparsity_pattern.h.

private 
Is special treatment of diagonals enabled?
Definition at line 1306 of file sparsity_pattern.h.