Classes | Public Member Functions | Static Public Member Functions | Protected Member Functions | Protected Attributes | Private Types

PreconditionBlock< MATRIX, inverse_type > Class Template Reference
[Preconditioners and Relaxation Operators]

Inheritance diagram for PreconditionBlock< MATRIX, inverse_type >:
Inheritance graph
[legend]

List of all members.

Classes

class  AdditionalData

Public Member Functions

 PreconditionBlock (bool store_diagonals=false)
 ~PreconditionBlock ()
void initialize (const MATRIX &A, const AdditionalData parameters)
void clear ()
bool empty () const
value_type el (unsigned int i, unsigned int j) const
void invert_diagblocks ()
template<typename number2 >
void forward_step (Vector< number2 > &dst, const Vector< number2 > &prev, const Vector< number2 > &src, const bool transpose_diagonal) const
template<typename number2 >
void backward_step (Vector< number2 > &dst, const Vector< number2 > &prev, const Vector< number2 > &src, const bool transpose_diagonal) const
unsigned int block_size () const
unsigned int n_blocks () const
std::size_t memory_consumption () const

Static Public Member Functions

::ExceptionBaseExcWrongBlockSize (int arg1, int arg2) throw (errortext << "The blocksize " << arg1 << " and the size of the matrix " << arg2 << " do not match." )
::ExceptionBaseExcInverseMatricesAlreadyExist ()

Protected Member Functions

void initialize (const MATRIX &A, const std::vector< unsigned int > &permutation, const std::vector< unsigned int > &inverse_permutation, const AdditionalData parameters)
void set_permutation (const std::vector< unsigned int > &permutation, const std::vector< unsigned int > &inverse_permutation)
void invert_permuted_diagblocks (const std::vector< unsigned int > &permutation, const std::vector< unsigned int > &inverse_permutation)

Protected Attributes

unsigned int blocksize
SmartPointer< const MATRIX,
PreconditionBlock< MATRIX,
inverse_type > > 
A
double relaxation
std::vector< unsigned int > permutation
std::vector< unsigned int > inverse_permutation

Private Types

typedef MATRIX::value_type number
typedef inverse_type value_type

Detailed Description

template<class MATRIX, typename inverse_type = typename MATRIX::value_type>
class PreconditionBlock< MATRIX, inverse_type >

Base class for actual block preconditioners. This class assumes the MATRIX consisting of invertible blocks of blocksize on the diagonal and provides the inversion of the diagonal blocks of the matrix. NOT only block diagonal matrices are allowed but all matrices of arbitrary structure with the minimal property of having invertible blocks on the diagonal! Still the matrix must have access to single matrix entries. therefore, BlockMatrixArray is not a possible matrix class.

This block matrix structure is given e.g. for the DG method for the transport equation. For a downstream numbering the matrices even have got a block lower left matrix structure, i.e. the matrices are empty above the diagonal blocks.

For all matrices that are empty above and below the diagonal blocks (i.e. for all block diagonal matrices) the BlockJacobi preconditioner is a direct solver. For all matrices that are empty only above the diagonal blocks (e.g. the matrices one gets by the DG method with downstream numbering) BlockSOR is a direct solver.

This first implementation of the PreconditionBlock assumes the matrix has blocks each of the same block size. Varying block sizes within the matrix must still be implemented if needed.

The first template parameter denotes the type of number representation in the sparse matrix, the second denotes the type of number representation in which the inverted diagonal block matrices are stored within this class by invert_diagblocks(). If you don't want to use the block inversion as an exact solver, but rather as a preconditioner, you may probably want to store the inverted blocks with less accuracy than the original matrix; for example, number==double, inverse_type=float might be a viable choice.

See also:
Block (linear algebra)
Author:
Ralf Hartmann, Guido Kanschat
Date:
1999, 2000, 2010

Definition at line 75 of file precondition_block.h.


Member Typedef Documentation

template<class MATRIX , typename inverse_type = typename MATRIX::value_type>
typedef MATRIX::value_type PreconditionBlock< MATRIX, inverse_type >::number [private]
template<class MATRIX , typename inverse_type = typename MATRIX::value_type>
typedef inverse_type PreconditionBlock< MATRIX, inverse_type >::value_type [private]

Value type for inverse matrices.

Definition at line 88 of file precondition_block.h.


Constructor & Destructor Documentation

template<class MATRIX , typename inverse_type = typename MATRIX::value_type>
PreconditionBlock< MATRIX, inverse_type >::PreconditionBlock ( bool  store_diagonals = false )

Constructor.

template<class MATRIX , typename inverse_type = typename MATRIX::value_type>
PreconditionBlock< MATRIX, inverse_type >::~PreconditionBlock (  )

Destructor.


Member Function Documentation

template<class MATRIX , typename inverse_type = typename MATRIX::value_type>
void PreconditionBlock< MATRIX, inverse_type >::initialize ( const MATRIX A,
const AdditionalData  parameters 
)

Initialize matrix and block size. We store the matrix and the block size in the preconditioner object. In a second step, the inverses of the diagonal blocks may be computed.

Additionally, a relaxation parameter for derived classes may be provided.

template<class MATRIX , typename inverse_type = typename MATRIX::value_type>
void PreconditionBlock< MATRIX, inverse_type >::initialize ( const MATRIX A,
const std::vector< unsigned int > &  permutation,
const std::vector< unsigned int > &  inverse_permutation,
const AdditionalData  parameters 
) [protected]

Initialize matrix and block size for permuted preconditioning. Additionally to the parameters of the other initalize() function, we hand over two index vectors with the permutation and its inverse. For the meaning of these vectors see PreconditionBlockSOR.

In a second step, the inverses of the diagonal blocks may be computed. Make sure you use invert_permuted_diagblocks() to yield consistent data.

Additionally, a relaxation parameter for derived classes may be provided.

template<class MATRIX , typename inverse_type = typename MATRIX::value_type>
void PreconditionBlock< MATRIX, inverse_type >::set_permutation ( const std::vector< unsigned int > &  permutation,
const std::vector< unsigned int > &  inverse_permutation 
) [protected]

Set either the permutation of rows or the permutation of blocks, depending on the size of the vector.

If the size of the permutation vectors is equal to the dimension of the linear system, it is assumed that rows are permuted individually. In this case, set_permutation() must be called before initialize(), since the diagonal blocks are built from the permuted entries of the matrix.

If the size of the permutation vector is not equal to the dimension of the system, the diagonal blocks are computed from the unpermuted entries. Instead, the relaxation methods step() and Tstep() are executed applying the blocks in the order given by the permutation vector. They will throw an exception if length of this vector is not equal to the number of blocks.

Note:
Permutation of blocks can only be applied to the relaxation operators step() and Tstep(), not to the preconditioning operators vmult() and Tvmult().
It is safe to call set_permutation() before initialize(), while the other order is only admissible for block permutation.
template<class MATRIX , typename inverse_type = typename MATRIX::value_type>
void PreconditionBlock< MATRIX, inverse_type >::invert_permuted_diagblocks ( const std::vector< unsigned int > &  permutation,
const std::vector< unsigned int > &  inverse_permutation 
) [protected]

Replacement of invert_diagblocks() for permuted preconditioning.

template<class MATRIX , typename inverse_type = typename MATRIX::value_type>
void PreconditionBlock< MATRIX, inverse_type >::clear (  )

Deletes the inverse diagonal block matrices if existent, sets the blocksize to 0, hence leaves the class in the state that it had directly after calling the constructor.

Reimplemented from PreconditionBlockBase< inverse_type >.

template<class MATRIX , typename inverse_type = typename MATRIX::value_type>
bool PreconditionBlock< MATRIX, inverse_type >::empty (  ) const

Checks whether the object is empty.

Reimplemented from PreconditionBlockBase< inverse_type >.

template<class MATRIX , typename inverse_type = typename MATRIX::value_type>
value_type PreconditionBlock< MATRIX, inverse_type >::el ( unsigned int  i,
unsigned int  j 
) const

Read-only access to entries. This function is only possible if the inverse diagonal blocks are stored.

Reimplemented from PreconditionBlockBase< inverse_type >.

template<class MATRIX , typename inverse_type = typename MATRIX::value_type>
void PreconditionBlock< MATRIX, inverse_type >::invert_diagblocks (  )

Stores the inverse of the diagonal blocks in inverse. This costs some additional memory - for DG methods about 1/3 (for double inverses) or 1/6 (for float inverses) of that used for the matrix - but it makes the preconditioning much faster.

It is not allowed to call this function twice (will produce an error) before a call of clear(...) because at the second time there already exist the inverse matrices.

After this function is called, the lock on the matrix given through the use_matrix function is released, i.e. you may overwrite of delete it. You may want to do this in case you use this matrix to precondition another matrix.

template<class MATRIX , typename inverse_type = typename MATRIX::value_type>
template<typename number2 >
void PreconditionBlock< MATRIX, inverse_type >::forward_step ( Vector< number2 > &  dst,
const Vector< number2 > &  prev,
const Vector< number2 > &  src,
const bool  transpose_diagonal 
) const

Perform one block relaxation step in forward numbering.

Depending on the arguments dst and pref, this performs an SOR step (both reference the same vector) of a Jacobi step (botha different vectors). For the Jacobi step, the calling function must copy dst to pref after this.

Note:
If a permutation is set, it is automatically honored by this function.
template<class MATRIX , typename inverse_type = typename MATRIX::value_type>
template<typename number2 >
void PreconditionBlock< MATRIX, inverse_type >::backward_step ( Vector< number2 > &  dst,
const Vector< number2 > &  prev,
const Vector< number2 > &  src,
const bool  transpose_diagonal 
) const

Perform one block relaxation step in backward numbering.

Depending on the arguments dst and pref, this performs an SOR step (both reference the same vector) of a Jacobi step (botha different vectors). For the Jacobi step, the calling function must copy dst to pref after this.

Note:
If a permutation is set, it is automatically honored by this function.
template<class MATRIX , typename inverse_type = typename MATRIX::value_type>
unsigned int PreconditionBlock< MATRIX, inverse_type >::block_size (  ) const

Return the size of the blocks.

template<class MATRIX , typename inverse_type = typename MATRIX::value_type>
unsigned int PreconditionBlock< MATRIX, inverse_type >::n_blocks (  ) const
Deprecated:
Use size() instead.

The number of blocks of the matrix.

template<class MATRIX , typename inverse_type = typename MATRIX::value_type>
std::size_t PreconditionBlock< MATRIX, inverse_type >::memory_consumption (  ) const

Determine an estimate for the memory consumption (in bytes) of this object.

Reimplemented from PreconditionBlockBase< inverse_type >.


Member Data Documentation

template<class MATRIX , typename inverse_type = typename MATRIX::value_type>
unsigned int PreconditionBlock< MATRIX, inverse_type >::blocksize [protected]

Size of the blocks. Each diagonal block is assumed to be of the same size.

Definition at line 410 of file precondition_block.h.

template<class MATRIX , typename inverse_type = typename MATRIX::value_type>
SmartPointer<const MATRIX,PreconditionBlock<MATRIX,inverse_type> > PreconditionBlock< MATRIX, inverse_type >::A [protected]

Pointer to the matrix. Make sure that the matrix exists as long as this class needs it, i.e. until calling invert_diagblocks, or (if the inverse matrices should not be stored) until the last call of the preconditoining vmult function of the derived classes.

Definition at line 424 of file precondition_block.h.

template<class MATRIX , typename inverse_type = typename MATRIX::value_type>
double PreconditionBlock< MATRIX, inverse_type >::relaxation [protected]

Relaxation parameter to be used by derived classes.

Definition at line 429 of file precondition_block.h.

template<class MATRIX , typename inverse_type = typename MATRIX::value_type>
std::vector<unsigned int> PreconditionBlock< MATRIX, inverse_type >::permutation [protected]

The permutation vector

Definition at line 434 of file precondition_block.h.

template<class MATRIX , typename inverse_type = typename MATRIX::value_type>
std::vector<unsigned int> PreconditionBlock< MATRIX, inverse_type >::inverse_permutation [protected]

The inverse permutation vector

Definition at line 439 of file precondition_block.h.


The documentation for this class was generated from the following file:
 All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Friends Defines

deal.II documentation generated on Fri Feb 3 2012 06:04:10 by doxygen 1.7.2