BlockMatrixArray< number, BlockVectorType > Class Template Reference

#include <deal.II/lac/block_matrix_array.h>

Inheritance diagram for BlockMatrixArray< number, BlockVectorType >:

Classes
class	Entry

Public Types
using	size_type = types::global_dof_index

Public Member Functions
	BlockMatrixArray ()
	BlockMatrixArray (const unsigned int n_block_rows, const unsigned int n_block_cols)
void	initialize (const unsigned int n_block_rows, const unsigned int n_block_cols)
void	reinit (const unsigned int n_block_rows, const unsigned int n_block_cols)
template<typename MatrixType >
void	enter (const MatrixType &matrix, const unsigned int row, const unsigned int col, const number prefix=1., const bool transpose=false)
void	clear ()
unsigned int	n_block_rows () const
unsigned int	n_block_cols () const
void	vmult (BlockVectorType &dst, const BlockVectorType &src) const
void	vmult_add (BlockVectorType &dst, const BlockVectorType &src) const
void	Tvmult (BlockVectorType &dst, const BlockVectorType &src) const
void	Tvmult_add (BlockVectorType &dst, const BlockVectorType &src) const
number	matrix_scalar_product (const BlockVectorType &u, const BlockVectorType &v) const
number	matrix_norm_square (const BlockVectorType &u) const
template<class StreamType >
void	print_latex (StreamType &out) const
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)

Protected Attributes
std::vector< Entry >	entries

Private Attributes
unsigned int	block_rows
unsigned int	block_cols

Additional Inherited Members
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)

Detailed Description

template<typename number = double, typename BlockVectorType = BlockVector<number>>
class BlockMatrixArray< number, BlockVectorType >

Block matrix composed of different single matrices; these matrices may even be of different types.

Given a set of arbitrary matrices A_i, this class implements a block matrix with block entries of the form M_jk = s_jkA_i. Each A_i may be used several times with different prefix. The matrices are not copied into the BlockMatrixArray object, but rather a PointerMatrix referencing each of them will be stored along with factors and transposition flags.

Non-zero entries are registered by the function enter(), zero entries are not stored at all. Using enter() with the same location (i,j) several times will add the corresponding matrices in matrix-vector multiplications. These matrices will not be actually added, but the multiplications with them will be summed up.

Note

This mechanism makes it impossible to access single entries of BlockMatrixArray. In particular, (block) relaxation preconditioners based on PreconditionRelaxation or PreconditionBlock cannot be used with this class. If you need a preconditioner for a BlockMatrixArray object, use BlockTrianglePrecondition.

Requirements on MatrixType

The template argument MatrixType is a class providing the matrix- vector multiplication functions vmult(), Tvmult(), vmult_add() and Tvmult_add() used in this class, but with arguments of type Vector<number> instead of BlockVector<number>. Every matrix which can be used by PointerMatrix is allowed, in particular SparseMatrix is a possible entry type.

Example program

We document the relevant parts of examples/doxygen/block_matrix_array.cc.

Obviously, we have to include the header file containing the definition of BlockMatrixArray:

#include <deal.II/lac/block_matrix_array.h>

First, we set up some matrices to be entered into the blocks.

int main()
{
  FullMatrix<float> A(4, 4);
  FullMatrix<float> B1(4, 2);
  FullMatrix<float> B2(2, 4);
  FullMatrix<float> C(2, 2);
 
  A.fill(&Adata[0][0]);
  B1.fill(&B1data[0][0]);
  B2.fill(&B2data[0][0]);
  C.fill(&Cdata[0][0]);

Now, we are ready to build a 2x2 BlockMatrixArray.

  BlockMatrixArray<double> matrix(2, 2);

First, we enter the matrix A multiplied by 2 in the upper left block

  matrix.enter(A, 0, 0, 2.);

Now -1 times B1 in the upper right block.

  matrix.enter(B1, 0, 1, -1.);

We add the transpose of B2 to the upper right block and continue in a similar fashion. In the end, the block matrix structure is printed into an LaTeX table.

  matrix.enter(B2, 0, 1, 1., true);
  matrix.enter(B2, 1, 0, 1.);
  matrix.enter(B1, 1, 0, -1., true);
  matrix.enter(C, 1, 1);
  matrix.print_latex(deallog);

Now, we set up vectors to be multiplied with this matrix and do a multiplication.

 
  std::vector<unsigned int> block_sizes(2);
  block_sizes[0] = 4;
  block_sizes[1] = 2;
 
  BlockVector<double> result(block_sizes);
  BlockVector<double> x(block_sizes);
  BlockVector<double> y(block_sizes);
  for (unsigned int i = 0; i < result.size(); ++i)
    result(i) = i;
 
  matrix.vmult(y, result);

Finally, we solve a linear system with BlockMatrixArray, using no preconditioning and the conjugate gradient method.

 
  SolverControl        control(100, 1.e-10);
  PreconditionIdentity id;
 
  SolverCG<BlockVector<double>> cg(control);
  cg.solve(matrix, x, y, id);
  x.add(-1., result);
  deallog << "Error " << x.l2_norm() << std::endl;

The remaining code of this sample program concerns preconditioning and is described in the documentation of BlockTrianglePrecondition.

Deprecated:

This class has been superseded by BlockLinearOperator.

See also

Block (linear algebra)

Author

Guido Kanschat

Date

2000-2005, 2010

Definition at line 118 of file block_matrix_array.h.

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The documentation for this class was generated from the following files:

• deal.II/lac/block_matrix_array.h
• /build/deal.ii-Kzz1m0/deal.ii-9.1.1/source/lac/block_matrix_array.cc