This class is an example of the "static" type of Sparsity patterns.
It uses the compressed row storage (CSR) format to store data.
ChunkSparsityPattern::ChunkSparsityPattern | ( | ) |
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::ChunkSparsityPattern | ( | const 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 v.push_back (ChunkSparsityPattern());
, with v
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::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.
ChunkSparsityPattern::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 rectangular matrix.
ChunkSparsityPattern::ChunkSparsityPattern | ( | const unsigned int | n, | |
const unsigned int | max_per_row, | |||
const unsigned int | chunk_size | |||
) |
Initialize a quadratic matrix of dimension n
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.
ChunkSparsityPattern::ChunkSparsityPattern | ( | const unsigned int | m, | |
const std::vector< unsigned int > & | row_lengths, | |||
const unsigned int | chunk_size, | |||
const bool | optimize_diagonal = true | |||
) |
Initialize a quadratic matrix.
ChunkSparsityPattern::~ChunkSparsityPattern | ( | ) |
Destructor.
ChunkSparsityPattern& ChunkSparsityPattern::operator= | ( | const 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.
void ChunkSparsityPattern::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 and set up data structures for a new matrix with m
rows and n
columns, with at most max_per_row
nonzero entries per row.
This function simply maps its operations to the other reinit
function.
void ChunkSparsityPattern::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 | |||
) |
Reallocate memory for a matrix of size m x n
. The number of entries for each row is taken from the array row_lengths
which has to give this number of each row i=1...m
.
If m*n==0
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 ChunkSparsityPattern::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 | |||
) |
Same as above, but with a VectorSlice argument instead.
void ChunkSparsityPattern::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 ChunkSparsityPattern objects they are initialized with to be compressed, to reduce memory requirements.
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_diagonal = true | |||
) | [inline] |
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 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 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:
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());
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:
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());
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 ChunkSparsityPattern::copy_from | ( | const CompressedSparsityPattern & | csp, | |
const unsigned int | chunk_size, | |||
const bool | optimize_diagonal = true | |||
) |
Copy data from an object of type CompressedSparsityPattern. Previous content of this object is lost, and the sparsity pattern is in compressed mode afterwards.
void ChunkSparsityPattern::copy_from | ( | const CompressedSetSparsityPattern & | csp, | |
const unsigned int | chunk_size, | |||
const bool | optimize_diagonal = true | |||
) |
Copy data from an object of type CompressedSetSparsityPattern. Previous content of this object is lost, and the sparsity pattern is in compressed mode afterwards.
void ChunkSparsityPattern::copy_from | ( | const FullMatrix< number > & | matrix, | |
const unsigned int | chunk_size, | |||
const bool | optimize_diagonal = true | |||
) | [inline] |
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.
bool ChunkSparsityPattern::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 chunk size given as argument when constructing this object.
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.
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 ChunkSparsityPattern::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 quadratic matrix.
Return number of rows of this matrix, which equals the dimension of the image space.
Return number of columns of this matrix, which equals the dimension of the range space.
Check if a value at a certain position may be non-zero.
Number of entries in a specific row.
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. Consequently, the maximum bandwidth a
matrix can have is
.
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.
bool ChunkSparsityPattern::is_compressed | ( | ) | const |
Return whether the structure is compressed or not.
bool ChunkSparsityPattern::optimize_diagonal | ( | ) | const |
Determine whether the matrix uses special convention for quadratic matrices.
A return value true
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 false
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 ChunkSparsityPattern::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 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 chunk_size==1
, 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.
void ChunkSparsityPattern::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 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 ChunkSparsityPattern::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.
void ChunkSparsityPattern::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 ChunkSparsityPattern::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.
Determine an estimate for the memory consumption (in bytes) of this object. See MemoryConsumption.
friend class ChunkSparseMatrix [friend] |
Make all the chunk sparse matrix kinds friends.
const unsigned int ChunkSparsityPattern::invalid_entry = SparsityPattern::invalid_entry [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.
unsigned int ChunkSparsityPattern::rows [private] |
Number of rows that this sparsity structure shall represent.
unsigned int ChunkSparsityPattern::cols [private] |
Number of columns that this sparsity structure shall represent.
unsigned int ChunkSparsityPattern::chunk_size [private] |
The size of chunks.
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.