dune-istl 2.9.0
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A sparse block matrix with compressed row storage. More...
#include <dune/istl/bcrsmatrix.hh>
Classes | |
class | CreateIterator |
Iterator class for sequential creation of blocks More... | |
class | RealRowIterator |
Iterator access to matrix rows More... | |
Public Types | |
enum | BuildStage { notbuilt =0 , notAllocated =0 , building =1 , rowSizesBuilt =2 , built =3 } |
enum | BuildMode { row_wise , random , implicit , unknown } |
we support two modes More... | |
using | field_type = typename Imp::BlockTraits< B >::field_type |
export the type representing the field More... | |
typedef B | block_type |
export the type representing the components More... | |
typedef A | allocator_type |
export the allocator type More... | |
typedef Imp::CompressedBlockVectorWindow< B, A > | row_type |
implement row_type with compressed vector More... | |
typedef A::size_type | size_type |
The type for the index access and the size. More... | |
typedef ::Dune::CompressionStatistics< size_type > | CompressionStatistics |
The type for the statistics object returned by compress() More... | |
typedef RealRowIterator< row_type > | iterator |
The iterator over the (mutable matrix rows. More... | |
typedef RealRowIterator< row_type > | Iterator |
typedef Iterator | RowIterator |
rename the iterators for easier access More... | |
typedef row_type::Iterator | ColIterator |
Iterator for the entries of each row. More... | |
typedef RealRowIterator< const row_type > | const_iterator |
The const iterator over the matrix rows. More... | |
typedef RealRowIterator< const row_type > | ConstIterator |
typedef ConstIterator | ConstRowIterator |
rename the const row iterator for easier access More... | |
typedef row_type::ConstIterator | ConstColIterator |
Const iterator to the entries of a row. More... | |
Public Member Functions | |
row_type & | operator[] (size_type i) |
random access to the rows More... | |
const row_type & | operator[] (size_type i) const |
same for read only access More... | |
Iterator | begin () |
Get iterator to first row. More... | |
Iterator | end () |
Get iterator to one beyond last row. More... | |
Iterator | beforeEnd () |
Iterator | beforeBegin () |
ConstIterator | begin () const |
Get const iterator to first row. More... | |
ConstIterator | end () const |
Get const iterator to one beyond last row. More... | |
ConstIterator | beforeEnd () const |
ConstIterator | beforeBegin () const |
BCRSMatrix () | |
an empty matrix More... | |
BCRSMatrix (size_type _n, size_type _m, size_type _nnz, BuildMode bm) | |
matrix with known number of nonzeroes More... | |
BCRSMatrix (size_type _n, size_type _m, BuildMode bm) | |
matrix with unknown number of nonzeroes More... | |
BCRSMatrix (size_type _n, size_type _m, size_type _avg, double compressionBufferSize, BuildMode bm) | |
construct matrix with a known average number of entries per row More... | |
BCRSMatrix (const BCRSMatrix &Mat) | |
copy constructor More... | |
~BCRSMatrix () | |
destructor More... | |
void | setBuildMode (BuildMode bm) |
Sets the build mode of the matrix. More... | |
void | setSize (size_type rows, size_type columns, size_type nnz=0) |
Set the size of the matrix. More... | |
void | setImplicitBuildModeParameters (size_type _avg, double compressionBufferSize) |
Set parameters needed for creation in implicit build mode. More... | |
BCRSMatrix & | operator= (const BCRSMatrix &Mat) |
assignment More... | |
BCRSMatrix & | operator= (const field_type &k) |
Assignment from a scalar. More... | |
CreateIterator | createbegin () |
get initial create iterator More... | |
CreateIterator | createend () |
get create iterator pointing to one after the last block More... | |
void | setrowsize (size_type i, size_type s) |
Set number of indices in row i to s. More... | |
size_type | getrowsize (size_type i) const |
get current number of indices in row i More... | |
void | incrementrowsize (size_type i, size_type s=1) |
increment size of row i by s (1 by default) More... | |
void | endrowsizes () |
indicate that size of all rows is defined More... | |
void | addindex (size_type row, size_type col) |
add index (row,col) to the matrix More... | |
template<typename It > | |
void | setIndices (size_type row, It begin, It end) |
Set all column indices for row from the given iterator range. More... | |
void | endindices () |
indicate that all indices are defined, check consistency More... | |
B & | entry (size_type row, size_type col) |
Returns reference to entry (row,col) of the matrix. More... | |
CompressionStatistics | compress () |
Finishes the buildstage in implicit mode. More... | |
BCRSMatrix & | operator*= (const field_type &k) |
vector space multiplication with scalar More... | |
BCRSMatrix & | operator/= (const field_type &k) |
vector space division by scalar More... | |
BCRSMatrix & | operator+= (const BCRSMatrix &b) |
Add the entries of another matrix to this one. More... | |
BCRSMatrix & | operator-= (const BCRSMatrix &b) |
Subtract the entries of another matrix from this one. More... | |
BCRSMatrix & | axpy (field_type alpha, const BCRSMatrix &b) |
Add the scaled entries of another matrix to this one. More... | |
template<class X , class Y > | |
void | mv (const X &x, Y &y) const |
y = A x More... | |
template<class X , class Y > | |
void | umv (const X &x, Y &y) const |
y += A x More... | |
template<class X , class Y > | |
void | mmv (const X &x, Y &y) const |
y -= A x More... | |
template<class X , class Y , class F > | |
void | usmv (F &&alpha, const X &x, Y &y) const |
y += alpha A x More... | |
template<class X , class Y > | |
void | mtv (const X &x, Y &y) const |
y = A^T x More... | |
template<class X , class Y > | |
void | umtv (const X &x, Y &y) const |
y += A^T x More... | |
template<class X , class Y > | |
void | mmtv (const X &x, Y &y) const |
y -= A^T x More... | |
template<class X , class Y > | |
void | usmtv (const field_type &alpha, const X &x, Y &y) const |
y += alpha A^T x More... | |
template<class X , class Y > | |
void | umhv (const X &x, Y &y) const |
y += A^H x More... | |
template<class X , class Y > | |
void | mmhv (const X &x, Y &y) const |
y -= A^H x More... | |
template<class X , class Y > | |
void | usmhv (const field_type &alpha, const X &x, Y &y) const |
y += alpha A^H x More... | |
FieldTraits< field_type >::real_type | frobenius_norm2 () const |
square of frobenius norm, need for block recursion More... | |
FieldTraits< field_type >::real_type | frobenius_norm () const |
frobenius norm: sqrt(sum over squared values of entries) More... | |
template<typename ft = field_type, typename std::enable_if<!HasNaN< ft >::value, int >::type = 0> | |
FieldTraits< ft >::real_type | infinity_norm () const |
infinity norm (row sum norm, how to generalize for blocks?) More... | |
template<typename ft = field_type, typename std::enable_if<!HasNaN< ft >::value, int >::type = 0> | |
FieldTraits< ft >::real_type | infinity_norm_real () const |
simplified infinity norm (uses Manhattan norm for complex values) More... | |
template<typename ft = field_type, typename std::enable_if< HasNaN< ft >::value, int >::type = 0> | |
FieldTraits< ft >::real_type | infinity_norm () const |
infinity norm (row sum norm, how to generalize for blocks?) More... | |
template<typename ft = field_type, typename std::enable_if< HasNaN< ft >::value, int >::type = 0> | |
FieldTraits< ft >::real_type | infinity_norm_real () const |
simplified infinity norm (uses Manhattan norm for complex values) More... | |
size_type | N () const |
number of rows (counted in blocks) More... | |
size_type | M () const |
number of columns (counted in blocks) More... | |
size_type | nonzeroes () const |
number of blocks that are stored (the number of blocks that possibly are nonzero) More... | |
BuildStage | buildStage () const |
The current build stage of the matrix. More... | |
BuildMode | buildMode () const |
The currently selected build mode of the matrix. More... | |
bool | exists (size_type i, size_type j) const |
return true if (i,j) is in pattern More... | |
Static Public Attributes | |
static constexpr unsigned int | blocklevel = blockLevel<B>()+1 |
increment block level counter More... | |
Protected Types | |
typedef std::map< std::pair< size_type, size_type >, B > | OverflowType |
Protected Member Functions | |
void | setWindowPointers (ConstRowIterator row) |
void | setColumnPointers (ConstRowIterator row) |
Copy row sizes from iterator range starting at row and set column index pointers for all rows. More... | |
void | setDataPointers () |
Set data pointers for all rows. More... | |
void | copyWindowStructure (const BCRSMatrix &Mat) |
Copy the window structure from another matrix. More... | |
void | deallocate (bool deallocateRows=true) |
deallocate memory of the matrix. More... | |
void | allocate (size_type rows, size_type columns, size_type allocationSize, bool allocateRows, bool allocate_data) |
Allocate memory for the matrix structure. More... | |
void | allocateData () |
void | implicit_allocate (size_type _n, size_type _m) |
organizes allocation implicit mode calculates correct array size to be allocated and sets the the window pointers to their correct positions for insertion. internally uses allocate() for the real allocation. More... | |
Protected Attributes | |
BuildMode | build_mode |
BuildStage | ready |
std::allocator_traits< A >::template rebind_alloc< B > | allocator_ |
std::allocator_traits< A >::template rebind_alloc< row_type > | rowAllocator_ |
std::allocator_traits< A >::template rebind_alloc< size_type > | sizeAllocator_ |
size_type | n |
size_type | m |
size_type | nnz_ |
size_type | allocationSize_ |
row_type * | r |
B * | a |
std::shared_ptr< size_type > | j_ |
size_type | avg |
double | compressionBufferSize_ |
OverflowType | overflow |
A sparse block matrix with compressed row storage.
Implements a block compressed row storage scheme. The block type B can be any type implementing the matrix interface.
Different ways to build up a compressed row storage matrix are supported:
Error checking: no error checking is provided normally. Setting the compile time switch DUNE_ISTL_WITH_CHECKING enables error checking.
Details:
Rows are built up in sequential order. Size of the row and the column indices are defined. A row can be used as soon as it is initialized. With respect to memory there are two variants of this scheme: (a) number of non-zeroes known in advance (application finite difference schemes), (b) number of non-zeroes not known in advance (application: Sparse LU, ILU(n)).
For general finite element implementations the number of rows n is known, the number of non-zeroes might also be known (e.g. #edges + #nodes for P2) but the size of a row and the indices of a row can not be defined in sequential order.
With the 'random scheme` described above, the sparsity pattern has to be determined and stored before the matrix is assembled. This requires a dedicated iteration over the grid elements, which can be costly in terms of time. Also, additional memory is needed to store the pattern before it can be given to the 'random' build mode.
On the other hand, often one has good a priori knowledge about the number of entries a row contains on average. The implicit
mode tries to make use of that knowledge, and allows the setup of matrix pattern and numerical values together.
Constructing and filling a BCRSMatrix with the 'implicit' mode is performed in two steps: In a setup phase, matrix entries with numerical values can be inserted into the matrix. Then, a compression algorithm is called which defragments and optimizes the memory layout. After this compression step, the matrix is ready to be used, and no further nonzero entries can be added.
To use this mode, either construct a matrix object via
or default-construct the matrix and then call
The parameter _avg
specifies the expected number of (block) entries per matrix row.
When the BCRSMatrix object is first constructed with the 'implicit' build mode, two areas for matrix entry storage are allocated:
1) A large continuous chunk of memory that can hold the expected number of entries. In addition, this chunk contains an extra part of memory called the 'compression buffer', located before the memory for the matrix itself. The size of this buffer will be _avg * _n * compressionBufferSize
.
2) An associative container indexed by -pairs, which will hold surplus matrix entries during the setup phase (the 'overflow area'). Its content is merged into the main memory during compression.
You can then start filling your matrix by calling entry(size_type row, size_type col), which returns the corresponding matrix entry, creating it on the fly if it does not exist yet. The matrix pattern is hence created implicitly by simply accessing nonzero entries during the initial matrix assembly. Note that new entries are not zero-initialized, though, and hence the first operation on each entry has to be an assignment.
If a row contains more non-zero entries than what was specified in the _avg parameter, the surplus entries are stored in the 'overflow area' during the initial setup phase. After all indices are added, call compress() to trigger the compression step that optimizes the matrix and integrates any entries from the overflow area into the standard BCRS storage. This compression step builds up the final memory layout row by row. It will fail with an exception if the compression buffer is not large enough, which would lead to compressed rows overwriting uncompressed ones. More precisely, if denotes the number of non-zeros in the
-th row, then the compression algorithm will succeed if the maximal number of non-zeros in the
-th row is
for all , where
is the total size of the compression buffer determined by the parameters explained above.
The data of the matrix is now located at the beginning of the allocated area, and covers what used to be the compression buffer. In exchange, there is now unused space at the end of the large allocated piece of memory. This will go unused and cannot be freed during the lifetime of the matrix, but it has no negative impact on run-time performance. No matrix entries may be added after the compression step.
The compress() method returns a value of type Dune::CompressionStatistics, which you can inspect to tune the construction parameters _avg
and compressionBufferSize
.
Use of copy constructor, assignment operator and matrix vector arithmetics are not supported until the matrix is fully built.
The following sample code constructs a matrix, with an expected number of two entries per matrix row. The compression buffer size is set to 0.4. Hence the main chunk of allocated memory will be able to hold
10 * 2
entries in the matrix rows, and 10 * 2 * 0.4
entries in the compression buffer. In total that's 28 entries.
Internally the index array now looks like this:
The second row denotes the beginnings of the matrix rows. The eight 'x' on the left are the compression buffer. The overflow area contains the entries (1,5,0.0), (3,8,0.0), (5,8,0.0), (7,8,0.0), and (9,8,0.0). These are entries of rows 1, 3, 5, 7, and 9, which have three entries each, even though only two were anticipated.
Internally the index array now looks like this:
The compression buffer on the left is gone now, and the matrix has a real CRS layout. The 'x' on the right will be unused for the rest of the matrix' lifetime.
typedef A Dune::BCRSMatrix< B, A >::allocator_type |
export the allocator type
typedef B Dune::BCRSMatrix< B, A >::block_type |
export the type representing the components
typedef row_type::Iterator Dune::BCRSMatrix< B, A >::ColIterator |
Iterator for the entries of each row.
typedef ::Dune::CompressionStatistics<size_type> Dune::BCRSMatrix< B, A >::CompressionStatistics |
The type for the statistics object returned by compress()
typedef RealRowIterator<const row_type> Dune::BCRSMatrix< B, A >::const_iterator |
The const iterator over the matrix rows.
typedef row_type::ConstIterator Dune::BCRSMatrix< B, A >::ConstColIterator |
Const iterator to the entries of a row.
typedef RealRowIterator<const row_type> Dune::BCRSMatrix< B, A >::ConstIterator |
typedef ConstIterator Dune::BCRSMatrix< B, A >::ConstRowIterator |
rename the const row iterator for easier access
using Dune::BCRSMatrix< B, A >::field_type = typename Imp::BlockTraits<B>::field_type |
export the type representing the field
typedef RealRowIterator<row_type> Dune::BCRSMatrix< B, A >::iterator |
The iterator over the (mutable matrix rows.
typedef RealRowIterator<row_type> Dune::BCRSMatrix< B, A >::Iterator |
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typedef Imp::CompressedBlockVectorWindow<B,A> Dune::BCRSMatrix< B, A >::row_type |
implement row_type with compressed vector
typedef Iterator Dune::BCRSMatrix< B, A >::RowIterator |
rename the iterators for easier access
typedef A::size_type Dune::BCRSMatrix< B, A >::size_type |
The type for the index access and the size.
enum Dune::BCRSMatrix::BuildMode |
we support two modes
Enumerator | |
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row_wise | Build in a row-wise manner. Rows are built up in sequential order. Size of the row and the column indices are defined. A row can be used as soon as it is initialized. With respect to memory there are two variants of this scheme: (a) number of non-zeroes known in advance (application finite difference schemes), (b) number of non-zeroes not known in advance (application: Sparse LU, ILU(n)). |
random | Build entries randomly. For general finite element implementations the number of rows n is known, the number of non-zeroes might also be known (e.g. #edges + #nodes for P2) but the size of a row and the indices of a row cannot be defined in sequential order. |
implicit | Build entries randomly with an educated guess for the number of entries per row. Allows random order generation as in random mode, but row sizes do not need to be given first. Instead an average number of non-zeroes per row is passed to the constructor. Matrix setup is finished with compress(), full data access during build stage is possible. |
unknown | Build mode not set! |
enum Dune::BCRSMatrix::BuildStage |
Enumerator | |
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notbuilt | Matrix is not built at all, no memory has been allocated, build mode and size can still be set. |
notAllocated | Matrix is not built at all, no memory has been allocated, build mode and size can still be set. |
building | Matrix is currently being built, some memory has been allocated, build mode and size are fixed. |
rowSizesBuilt | The row sizes of the matrix are known. Only used in random mode. |
built | The matrix structure is fully built. |
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an empty matrix
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matrix with known number of nonzeroes
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matrix with unknown number of nonzeroes
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construct matrix with a known average number of entries per row
Constructs a matrix in implicit buildmode.
_n | number of rows of the matrix |
_m | number of columns of the matrix |
_avg | expected average number of entries per row |
compressionBufferSize | fraction of _n*_avg which is expected to be needed for elements that exceed _avg entries per row. |
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copy constructor
Does a deep copy as expected.
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destructor
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add index (row,col) to the matrix
This method can only be used when building the BCRSMatrix in random mode.
addindex adds a new column entry to the row. If this column entry already exists, nothing is done.
Don't call addindex after the setup phase is finished (after endindices is called).
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Allocate memory for the matrix structure.
Sets the number of rows and columns of the matrix and allocates the memory needed for the storage of the matrix entries.
row | The number of rows the matrix should contain. |
columns | the number of columns the matrix should contain. |
allocationSize | The number of nonzero entries the matrix should hold (if omitted defaults to 0). |
allocateRow | Whether we have to allocate the row pointers, too. (Defaults to true) |
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Add the scaled entries of another matrix to this one.
Matrix axpy operation: *this += alpha * b
alpha | Scaling factor. |
b | The matrix to add to this one. Its sparsity pattern has to be subset of the sparsity pattern of this matrix. |
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Get iterator to first row.
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Get const iterator to first row.
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The currently selected build mode of the matrix.
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The current build stage of the matrix.
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Finishes the buildstage in implicit mode.
Performs compression of index and data arrays with linear complexity in the number of nonzeroes.
After calling this method, the matrix is in the built state and no more entries can be added.
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Copy the window structure from another matrix.
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get initial create iterator
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get create iterator pointing to one after the last block
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deallocate memory of the matrix.
deallocateRows | Whether we have to deallocate the row pointers, too. If false they will not be touched. (Defaults to true). |
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Get iterator to one beyond last row.
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Get const iterator to one beyond last row.
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indicate that all indices are defined, check consistency
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indicate that size of all rows is defined
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Returns reference to entry (row,col) of the matrix.
This method can only be used when the matrix is in implicit building mode.
A reference to entry (row, col) of the matrix is returned. If entry (row, col) is accessed for the first time, it is created on the fly.
This method can only be used while building the matrix, after compression operator[] gives a much better performance.
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return true if (i,j) is in pattern
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frobenius norm: sqrt(sum over squared values of entries)
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square of frobenius norm, need for block recursion
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get current number of indices in row i
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organizes allocation implicit mode calculates correct array size to be allocated and sets the the window pointers to their correct positions for insertion. internally uses allocate() for the real allocation.
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increment size of row i by s (1 by default)
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infinity norm (row sum norm, how to generalize for blocks?)
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infinity norm (row sum norm, how to generalize for blocks?)
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simplified infinity norm (uses Manhattan norm for complex values)
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simplified infinity norm (uses Manhattan norm for complex values)
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number of columns (counted in blocks)
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y -= A^H x
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y -= A^T x
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y -= A x
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y = A^T x
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y = A x
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number of rows (counted in blocks)
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number of blocks that are stored (the number of blocks that possibly are nonzero)
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vector space multiplication with scalar
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Add the entries of another matrix to this one.
b | The matrix to add to this one. Its sparsity pattern has to be subset of the sparsity pattern of this matrix. |
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Subtract the entries of another matrix from this one.
b | The matrix to subtract from this one. Its sparsity pattern has to be subset of the sparsity pattern of this matrix. |
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vector space division by scalar
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assignment
Frees and reallocates space. Both sparsity pattern and values are set from Mat.
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Assignment from a scalar.
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random access to the rows
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same for read only access
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Sets the build mode of the matrix.
bm | The build mode to use. |
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Copy row sizes from iterator range starting at row and set column index pointers for all rows.
This method does not modify the data pointers, as those are set only after building the pattern (to allow for a delayed allocation).
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Set data pointers for all rows.
This method assumes that column pointers and row sizes have been correctly set up by a prior call to setColumnPointers().
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Set parameters needed for creation in implicit build mode.
Use this method before setSize() to define storage behaviour of a matrix in implicit build mode
_avg | expected average number of entries per row |
compressionBufferSize | fraction of _n*_avg which is expected to be needed for elements that exceed _avg entries per row. |
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Set all column indices for row from the given iterator range.
The iterator range has to be of the same length as the previously set row size. The entries in the iterator range do not have to be in any particular order, but must not contain duplicate values.
Calling this method overwrites any previously set column indices!
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Set number of indices in row i to s.
The number s may actually be larger than the true number of nonzero entries in row i. In that case, the extra memory goes wasted. You will receive run-time warnings about this, sent to the Dune::dwarn stream.
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Set the size of the matrix.
Sets the number of rows and columns of the matrix and allocates the memory needed for the storage of the matrix entries.
rows | The number of rows the matrix should contain. |
columns | the number of columns the matrix should contain. |
nnz | The number of nonzero entries the matrix should hold (if omitted defaults to 0). Must be omitted in implicit mode. |
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y += A^H x
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y += A^T x
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y += A x
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y += alpha A^H x
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y += alpha A^T x
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y += alpha A x
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increment block level counter
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