This class acts as an intermediate form of the SparsityPattern class. From the interface it mostly represents a SparsityPattern object that is kept compressed at all times. However, since the final sparsity pattern is not known while constructing it, keeping the pattern compressed at all times can only be achieved at the expense of either increased memory or run time consumption upon use. The main purpose of this class is to avoid some memory bottlenecks, so we chose to implement it memory conservative, but the chosen data format is too unsuited to be used for actual matrices. It is therefore necessary to first copy the data of this object over to an object of type SparsityPattern before using it in actual matrices.
Another viewpoint is that this class does not need up front allocation of a certain amount of memory, but grows as necessary. An extensive description of sparsity patterns can be found in the documentation of the Sparsity patterns module.
This class is an example of the "dynamic" type of Sparsity patterns. It is discussed in the step-27 and step-22 tutorial programs.
Since this class is intended as an intermediate replacement of the SparsityPattern class, it has mostly the same interface, with small changes where necessary. In particular, the add() function, and the functions inquiring properties of the sparsity pattern are the same.
Use this class as follows:
* CompressedSetSparsityPattern compressed_pattern (dof_handler.n_dofs()); * DoFTools::make_sparsity_pattern (dof_handler, * compressed_pattern); * constraints.condense (compressed_pattern); * * SparsityPattern sp; * sp.copy_from (compressed_pattern); *
See also step-11 and step-18 for usage patterns of the related CompressedSparsityPattern class, and step-27 of the current class.
There are several, exchangeable variations of this class, see Sparsity patterns, section '"Dynamic" or "compressed" sparsity patterns' for more information.
This class is a variation of the CompressedSparsityPattern class. Instead of using sorted vectors together with a caching algorithm for storing the column indices of nonzero entries, the std::set container is used. This solution might not be the fastest in all situations, but seems to work much better than the CompressedSparsityPattern in the context of hp-adaptivity (see for example step-27), or generally when there are many nonzero entries in each row of a matrix (see step-22). On the other hand, a benchmark where nonzero entries were randomly inserted into the sparsity pattern revealed that this class is slower by a factor 4-6 in this situation. Hence, currently the suggestion is to carefully analyze which of the CompressedSparsityPattern classes works best in a certain setting. An algorithm which performs equally well in all situations still has to be found.
typedef std::set<unsigned int>::const_iterator CompressedSetSparsityPattern::row_iterator |
An iterator that can be used to iterate over the elements of a single row. The result of dereferencing such an iterator is a column index.
CompressedSetSparsityPattern::CompressedSetSparsityPattern | ( | ) |
Initialize the matrix empty, that is with no memory allocated. This is useful if you want such objects as member variables in other classes. You can make the structure usable by calling the reinit() function.
CompressedSetSparsityPattern::CompressedSetSparsityPattern | ( | const CompressedSetSparsityPattern & | ) |
Copy constructor. This constructor is only allowed to be called if the matrix structure to be copied is empty. This is so in order to prevent involuntary copies of objects for temporaries, which can use large amounts of computing time. However, copy constructors are needed if yo want to use the STL data types on classes like this, e.g. to write such statements like v.push_back (CompressedSetSparsityPattern());
, with v
a vector of CompressedSetSparsityPattern
objects.
CompressedSetSparsityPattern::CompressedSetSparsityPattern | ( | const unsigned int | m, | |
const unsigned int | n | |||
) |
Initialize a rectangular matrix with m
rows and n
columns.
Initialize a square matrix of dimension n
.
CompressedSetSparsityPattern& CompressedSetSparsityPattern::operator= | ( | const CompressedSetSparsityPattern & | ) |
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.
Reimplemented from Subscriptor.
Reallocate memory and set up data structures for a new matrix with m
rows and n
columns, with at most max_entries_per_row() nonzero entries per row.
void CompressedSetSparsityPattern::compress | ( | ) |
Since this object is kept compressed at all times anway, this function does nothing, but is declared to make the interface of this class as much alike as that of the SparsityPattern class.
bool CompressedSetSparsityPattern::empty | ( | ) | 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.
Return the maximum number of entries per row. Note that this number may change as entries are added.
Check if a value at a certain position may be non-zero.
void CompressedSetSparsityPattern::symmetrize | ( | ) |
Make the sparsity pattern symmetric by adding the sparsity pattern of the transpose object.
This function throws an exception if the sparsity pattern does not represent a square matrix.
void CompressedSetSparsityPattern::print | ( | std::ostream & | out | ) | const |
Print the sparsity of the matrix. The output consists of one line per row of the format [i,j1,j2,j3,...]
. i is the row number and jn are the allocated columns in this row.
void CompressedSetSparsityPattern::print_gnuplot | ( | std::ostream & | out | ) | const |
Print the sparsity of the matrix in a format that gnuplot
understands and which can be used to plot the sparsity pattern in a graphical way. The format consists of pairs i j
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 (0,0)
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 plot
command.
Return number of rows of this matrix, which equals the dimension of the image space.
References rows.
Referenced by row_length().
Return number of columns of this matrix, which equals the dimension of the range space.
References cols.
CompressedSetSparsityPattern::row_iterator CompressedSetSparsityPattern::row_begin | ( | const unsigned int | row | ) | const [inline] |
Return an iterator that can loop over all entries in the given row. Dereferencing the iterator yields a column index.
References lines.
CompressedSetSparsityPattern::row_iterator CompressedSetSparsityPattern::row_end | ( | const unsigned int | row | ) | const [inline] |
End iterator for the given row.
References lines.
Compute the bandwidth of the matrix represented by this structure. The bandwidth is the maximum of for which the index pair
represents a nonzero entry of the matrix.
Return the number of nonzero elements allocated through this sparsity pattern.
bool CompressedSetSparsityPattern::stores_only_added_elements | ( | ) | [inline, static] |
Return whether this object stores only those entries that have been added explicitly, or if the sparsity pattern contains elements that have been added through other means (implicitly) while building it. For the current class, the result is always true.
This function mainly serves the purpose of describing the current class in cases where several kinds of sparsity patterns can be passed as template arguments.
unsigned int CompressedSetSparsityPattern::rows [private] |
Number of rows that this sparsity structure shall represent.
Referenced by add(), add_entries(), and n_rows().
unsigned int CompressedSetSparsityPattern::cols [private] |
std::vector<Line> CompressedSetSparsityPattern::lines [private] |
Actual data: store for each row the set of nonzero entries.
Referenced by add(), add_entries(), row_begin(), row_end(), and row_length().