SparseLUDecomposition< number > Class Template Reference
[Preconditioners]

Inheritance diagram for SparseLUDecomposition< number >:

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List of all members.

Classes

class  AdditionalData
class  ExcInvalidStrengthening

Public Member Functions

virtual ~SparseLUDecomposition ()
virtual void clear ()
template<typename somenumber >
void initialize (const SparseMatrix< somenumber > &matrix, const AdditionalData parameters)
void reinit (const SparsityPattern &sparsity)
template<typename somenumber >
void decompose (const SparseMatrix< somenumber > &matrix, const double strengthen_diagonal=0.)
virtual bool is_decomposed () const
bool empty () const
virtual unsigned int memory_consumption () const

Protected Member Functions

 SparseLUDecomposition ()
 SparseLUDecomposition (const SparsityPattern &sparsity)
template<typename somenumber >
void copy_from (const SparseMatrix< somenumber > &matrix)
virtual void strengthen_diagonal_impl ()
virtual number get_strengthen_diagonal (const number rowsum, const unsigned int row) const

Protected Attributes

bool decomposed
double strengthen_diagonal
std::vector< const unsigned int * > prebuilt_lower_bound

Private Member Functions

void prebuild_lower_bound ()

Private Attributes

SparsityPatternown_sparsity


Detailed Description

template<typename number>
class SparseLUDecomposition< number >

Abstract base class for sparse LU decompositions of a sparse matrix into another sparse matrix. This class can't be used by itself, but only as the base class of derived classes that actually implement particular decompositions such as SparseILU or SparseMIC.

The decomposition is stored as a sparse matrix which is why this class is derived from the SparseMatrix. Since it is not a matrix in the usual sense (the stored entries are not those of a matrix, but of two different matrix factors), the derivation is protected rather than public.

Fill-in

The sparse LU decompositions are frequently used with additional fill-in, i.e. the sparsity structure of the decomposition is denser than that of the matrix to be decomposed. The initialize() function of this class allows this fill-in as long as all entries present in the original matrix are present in the decomposition also, i.e. the sparsity pattern of the decomposition is a superset of the sparsity pattern in the original matrix.

Such fill-in can be accomplished by various ways, one of which is a copy-constructor of the SparsityPattern class which allows the addition of side-diagonals to a given sparsity structure.

Unified use of preconditioners

While objects of this class can not be used directly (this class is only a base class for others implementing actual decompositions), derived classes such as SparseILU and SparseMIC can be used in the usual form as preconditioners. For example, this works:

 SparseILU<double> ilu;
 ilu.initialize(matrix, SparseILU<double>::AdditionalData(...));

 somesolver.solve (A, x, f, ilu);

Through the AdditionalData object it is possible to specify additional parameters of the LU decomposition.

1/ The matrix diagonals can be strengthened by adding strengthen_diagonal times the sum of the absolute row entries of each row to the respective diagonal entries. By default no strengthening is performed.

2/ By default, each initialize() function call creates its own sparsity. For that, it copies the sparsity of matrix and adds a specific number of extra off diagonal entries specified by extra_off_diagonals.

3/ By setting use_previous_sparsity=true the sparsity is not recreated but the sparsity of the previous initialize() call is reused (recycled). This might be useful when several linear problems on the same sparsity need to solved, as for example several Newton iteration steps on the same triangulation. The default is false.

4/ It is possible to give a user defined sparsity to use_this_sparsity. Then, no sparsity is created but *use_this_sparsity is used to store the decomposed matrix. For restrictions on the sparsity see section `Fill-in' above).

State management

The state management simply requires the initialize() function to be called before the object is used as preconditioner.

Obsolete: In order to prevent users from applying decompositions before the decomposition itself has been built, and to introduce some optimization of common "sparse idioms", this class introduces a simple state management. A SparseLUdecomposition instance is considered not decomposed if the decompose method has not yet been invoked since the last time the underlying SparseMatrix had changed. The underlying sparse matrix is considered changed when one of this class reinit methods, constructors or destructors are invoked. The not-decomposed state is indicated by a false value returned by is_decomposed() method. It is illegal to apply this decomposition (vmult() method) in not decomposed state; in this case, the vmult() method throws an ExcInvalidState exception. This object turns into decomposed state immediately after its decompose() method is invoked. The decomposed state is indicated by true value returned by is_decomposed() method. It is legal to apply this decomposition (vmult() method) in decomposed state.

Particular implementations

It is enough to override the initialize() and vmult() methods to implement particular LU decompositions, like the true LU, or the Cholesky decomposition. Additionally, if that decomposition needs fine tuned diagonal strengthening on a per row basis, it may override the get_strengthen_diagonal() method. You should invoke the non-abstract base class method to employ the state management. Implementations may choose more restrictive definition of what is legal or illegal state; but they must conform to the is_decomposed() method specification above.

If an exception is thrown by method other than vmult(), this object may be left in an inconsistent state.

Author:
Stephen "Cheffo" Kolaroff, 2002, based on SparseILU implementation by Wolfgang Bangerth; unified interface: Ralf Hartmann, 2003

Constructor & Destructor Documentation

template<typename number>
SparseLUDecomposition< number >::SparseLUDecomposition (  )  [protected]

Constructor. Does nothing.

Call the initialize() function before using this object as preconditioner (vmult()).

template<typename number>
SparseLUDecomposition< number >::SparseLUDecomposition ( const SparsityPattern sparsity  )  [protected]

This method is deprecated, and left for backward compability. It will be removed in later versions.

template<typename number>
virtual SparseLUDecomposition< number >::~SparseLUDecomposition (  )  [virtual]

Destruction. Mark the destructor pure to ensure that this class isn't used directly, but only its derived classes.


Member Function Documentation

template<typename number>
virtual void SparseLUDecomposition< number >::clear (  )  [virtual]

Deletes all member variables. Leaves the class in the state that it had directly after calling the constructor

Reimplemented from SparseMatrix< number >.

Reimplemented in SparseMIC< number >.

template<typename number>
template<typename somenumber >
void SparseLUDecomposition< number >::initialize ( const SparseMatrix< somenumber > &  matrix,
const AdditionalData  parameters 
) [inline]

This function needs to be called before an object of this class is used as preconditioner.

For more detail about possible parameters, see the class documentation and the documentation of the SparseLUDecomposition::AdditionalData class.

According to the parameters, this function creates a new SparsityPattern or keeps the previous sparsity or takes the sparsity given by the user to data. Then, this function performs the LU decomposition.

After this function is called the preconditioner is ready to be used (using the vmult function of derived classes).

template<typename number>
void SparseLUDecomposition< number >::reinit ( const SparsityPattern sparsity  )  [virtual]

This method is deprecated, and left for backward compatibility. It will be removed in later versions.

Deprecated:

Reimplemented from SparseMatrix< number >.

Reimplemented in SparseMIC< number >.

template<typename number>
template<typename somenumber >
void SparseLUDecomposition< number >::decompose ( const SparseMatrix< somenumber > &  matrix,
const double  strengthen_diagonal = 0. 
) [inline]

This method is deprecated, and left for backward compability. It will be removed in later versions.

Deprecated:

Reimplemented in SparseILU< number >, and SparseMIC< number >.

template<typename number>
virtual bool SparseLUDecomposition< number >::is_decomposed (  )  const [virtual]

This method is deprecated, and left for backward compability. It will be removed in later versions.

Deprecated:

template<typename number>
bool SparseLUDecomposition< number >::empty (  )  const

Return whether the object is empty. It calls the inherited SparseMatrix::empty() function.

Reimplemented from SparseMatrix< number >.

template<typename number>
virtual unsigned int SparseLUDecomposition< number >::memory_consumption (  )  const [virtual]

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

Reimplemented from SparseMatrix< number >.

Reimplemented in SparseILU< number >, and SparseMIC< number >.

template<typename number>
template<typename somenumber >
void SparseLUDecomposition< number >::copy_from ( const SparseMatrix< somenumber > &  matrix  )  [inline, protected]

Copies the passed SparseMatrix onto this object. This object's sparsity pattern remains unchanged.

Reimplemented from SparseMatrix< number >.

template<typename number>
virtual void SparseLUDecomposition< number >::strengthen_diagonal_impl (  )  [protected, virtual]

Performs the strengthening loop. For each row calculates the sum of absolute values of its elements, determines the strengthening factor (through get_strengthen_diagonal()) sf and multiplies the diagonal entry with sf+1.

template<typename number>
virtual number SparseLUDecomposition< number >::get_strengthen_diagonal ( const number  rowsum,
const unsigned int  row 
) const [protected, virtual]

In the decomposition phase, computes a strengthening factor for the diagonal entry in row row with sum of absolute values of its elements rowsum.
Note: The default implementation in SparseLUDecomposition returns strengthen_diagonal's value.

template<typename number>
void SparseLUDecomposition< number >::prebuild_lower_bound (  )  [private]

Fills the prebuilt_lower_bound array.


Member Data Documentation

template<typename number>
bool SparseLUDecomposition< number >::decomposed [protected]

State flag. If not in decomposed state, it is illegal to apply the decomposition. This flag is cleared when the underlaying SparseMatrix SparsityPattern is changed, and set by decompose().

template<typename number>
double SparseLUDecomposition< number >::strengthen_diagonal [protected]

The default strenghtening value, returned by get_strengthen_diagonal().

template<typename number>
std::vector<const unsigned int*> SparseLUDecomposition< number >::prebuilt_lower_bound [protected]

For every row in the underlying SparsityPattern, this array contains a pointer to the row's first afterdiagonal entry. Becomes available after invocation of decompose().

template<typename number>
SparsityPattern* SparseLUDecomposition< number >::own_sparsity [private]

In general this pointer is zero except for the case that no SparsityPattern is given to this class. Then, a SparsityPattern is created and is passed down to the SparseMatrix base class.

Nevertheless, the SparseLUDecomposition needs to keep ownership of this sparsity. It keeps this pointer to it enabling it to delete this sparsity at destruction time.


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

deal.II documentation generated on Sat Aug 15 16:52:21 2009 by doxygen 1.5.9