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//
// Copyright (C) 2002 - 2016 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#ifndef dealii__sparse_decomposition_h
#define dealii__sparse_decomposition_h
#include <deal.II/base/config.h>
#include <deal.II/lac/sparse_matrix.h>
#include <cmath>
DEAL_II_NAMESPACE_OPEN
/*! @addtogroup Preconditioners
*@{
*/
/**
* Abstract base class for incomplete decompositions of a sparse matrix into
* sparse factors. 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 the two factors of
* the original matrix), the derivation is <tt>protected</tt> rather than
* <tt>public</tt>.
*
*
* <h3>Fill-in</h3>
*
* Sparse 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 via the AdditionalData object 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 the copy-
* constructor of the SparsityPattern class that allows the addition of side-
* diagonals to a given sparsity structure.
*
*
* <h3>Unified use of preconditioners</h3>
*
* 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:
* @code
* SparseILU<double> ilu;
* ilu.initialize(matrix, SparseILU<double>::AdditionalData(...));
*
* somesolver.solve (A, x, f, ilu);
* @endcode
*
* Through the AdditionalData object it is possible to specify additional
* parameters of the LU decomposition.
*
* 1/ The matrix diagonal can be strengthened by adding
* <code>strengthen_diagonal</code> 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 <code>matrix</code> and adds a specific
* number of extra off diagonal entries specified by
* <code>extra_off_diagonals</code>.
*
* 3/ By setting <code>use_previous_sparsity=true</code> 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 <code>false</code>.
*
* 4/ It is possible to give a user defined sparsity to
* <code>use_this_sparsity</code>. Then, no sparsity is created but
* <code>*use_this_sparsity</code> is used to store the decomposed matrix. For
* restrictions on the sparsity see section `Fill-in' above).
*
*
* <h3>Particular implementations</h3>
*
* 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.
*
* @author Stephen "Cheffo" Kolaroff, 2002, based on SparseILU implementation
* by Wolfgang Bangerth; unified interface: Ralf Hartmann, 2003; extension for
* full compatibility with LinearOperator class: Jean-Paul Pelteret, 2015
*/
template <typename number>
class SparseLUDecomposition : protected SparseMatrix<number>,
public virtual Subscriptor
{
protected:
/**
* Constructor. Does nothing.
*
* Call the initialize() function before using this object as preconditioner
* (vmult()).
*/
SparseLUDecomposition ();
public:
/**
* Declare type for container size.
*/
typedef typename SparseMatrix<number>::size_type size_type;
/**
* Destruction. Mark the destructor pure to ensure that this class isn't
* used directly, but only its derived classes.
*/
virtual ~SparseLUDecomposition () = 0;
/**
* Deletes all member variables. Leaves the class in the state that it had
* directly after calling the constructor
*/
virtual void clear();
/**
* Parameters for SparseDecomposition.
*/
class AdditionalData
{
public:
/**
* Constructor. For the parameters' description, see below.
*/
AdditionalData (const double strengthen_diagonal=0,
const unsigned int extra_off_diagonals=0,
const bool use_previous_sparsity=false,
const SparsityPattern *use_this_sparsity=0);
/**
* <code>strengthen_diag</code> times the sum of absolute row entries is
* added to the diagonal entries.
*
* Per default, this value is zero, i.e. the diagonal is not strengthened.
*/
double strengthen_diagonal;
/**
* By default, the <code>initialize(matrix, data)</code> function creates
* its own sparsity. This sparsity has the same SparsityPattern as
* <code>matrix</code> with some extra off diagonals the number of which
* is specified by <code>extra_off_diagonals</code>.
*
* The user can give a SparsityPattern to <code>use_this_sparsity</code>.
* Then this sparsity is used and the <code>extra_off_diagonals</code>
* argument is ignored.
*/
unsigned int extra_off_diagonals;
/**
* If this flag is true the initialize() function uses the same sparsity
* that was used during the previous initialize() call.
*
* 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.
*/
bool use_previous_sparsity;
/**
* When a SparsityPattern is given to this argument, the initialize()
* function calls <code>reinit(*use_this_sparsity)</code> causing this
* sparsity to be used.
*
* Note that the sparsity structures of <code>*use_this_sparsity</code>
* and the matrix passed to the initialize function need not be equal.
* Fill-in is allowed, as well as filtering out some elements in the
* matrix.
*/
const SparsityPattern *use_this_sparsity;
};
/**
* 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 <code>parameters</code>, this function creates a new
* SparsityPattern or keeps the previous sparsity or takes the sparsity
* given by the user to <code>data</code>. Then, this function performs the
* LU decomposition.
*
* After this function is called the preconditioner is ready to be used
* (using the <code>vmult</code> function of derived classes).
*/
template <typename somenumber>
void initialize (const SparseMatrix<somenumber> &matrix,
const AdditionalData parameters);
/**
* Return whether the object is empty. It calls the inherited
* SparseMatrix::empty() function.
*/
bool empty () const;
/**
* Return the dimension of the codomain (or range) space. It calls the
* inherited SparseMatrix::m() function. To remember: the matrix is of
* dimension $m \times n$.
*/
size_type m () const;
/**
* Return the dimension of the domain space. It calls the inherited
* SparseMatrix::n() function. To remember: the matrix is of dimension $m
* \times n$.
*/
size_type n () const;
/**
* Adding Matrix-vector multiplication. Add <i>M*src</i> on <i>dst</i> with
* <i>M</i> being this matrix.
*
* Source and destination must not be the same vector.
*
*/
template <class OutVector, class InVector>
void vmult_add (OutVector &dst,
const InVector &src) const;
/**
* Adding Matrix-vector multiplication. Add <i>M<sup>T</sup>*src</i> to
* <i>dst</i> with <i>M</i> being this matrix. This function does the same
* as vmult_add() but takes the transposed matrix.
*
* Source and destination must not be the same vector.
*/
template <class OutVector, class InVector>
void Tvmult_add (OutVector &dst,
const InVector &src) const;
/**
* Determine an estimate for the memory consumption (in bytes) of this
* object.
*/
virtual std::size_t memory_consumption () const;
/**
* @addtogroup Exceptions
* @{
*/
/**
* Exception
*/
DeclException1 (ExcInvalidStrengthening,
double,
<< "The strengthening parameter " << arg1
<< " is not greater or equal than zero!");
//@}
protected:
/**
* Copies the passed SparseMatrix onto this object. This object's sparsity
* pattern remains unchanged.
*/
template<typename somenumber>
void copy_from (const SparseMatrix<somenumber> &matrix);
/**
* 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 <code>sf+1</code>.
*/
virtual void strengthen_diagonal_impl ();
/**
* In the decomposition phase, computes a strengthening factor for the
* diagonal entry in row <code>row</code> with sum of absolute values of its
* elements <code>rowsum</code>.
*
* @note The default implementation in SparseLUDecomposition returns
* <code>strengthen_diagonal</code>'s value.
*/
virtual number get_strengthen_diagonal(const number rowsum, const size_type row) const;
/**
* The default strengthening value, returned by get_strengthen_diagonal().
*/
double strengthen_diagonal;
/**
* 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().
*/
std::vector<const size_type *> prebuilt_lower_bound;
/**
* Fills the #prebuilt_lower_bound array.
*/
void prebuild_lower_bound ();
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.
*/
SparsityPattern *own_sparsity;
};
/*@}*/
//---------------------------------------------------------------------------
#ifndef DOXYGEN
template <typename number>
inline number
SparseLUDecomposition<number>::
get_strengthen_diagonal(const number /*rowsum*/,
const size_type /*row*/) const
{
return strengthen_diagonal;
}
template <typename number>
inline bool
SparseLUDecomposition<number>::empty () const
{
return SparseMatrix<number>::empty();
}
template <typename number>
inline typename SparseLUDecomposition<number>::size_type
SparseLUDecomposition<number>::m () const
{
return SparseMatrix<number>::m();
}
template <typename number>
inline typename SparseLUDecomposition<number>::size_type
SparseLUDecomposition<number>::n () const
{
return SparseMatrix<number>::n();
}
// Note: This function is required for full compatibility with
// the LinearOperator class. ::MatrixInterfaceWithVmultAdd
// picks up the vmult_add function in the protected SparseMatrix
// base class.
template <typename number>
template <class OutVector, class InVector>
inline void
SparseLUDecomposition<number>::vmult_add (OutVector &dst,
const InVector &src) const
{
OutVector tmp;
tmp.reinit(dst);
this->vmult(tmp, src);
dst += tmp;
}
// Note: This function is required for full compatibility with
// the LinearOperator class. ::MatrixInterfaceWithVmultAdd
// picks up the vmult_add function in the protected SparseMatrix
// base class.
template <typename number>
template <class OutVector, class InVector>
inline void
SparseLUDecomposition<number>::Tvmult_add (OutVector &dst,
const InVector &src) const
{
OutVector tmp;
tmp.reinit(dst);
this->Tvmult(tmp, src);
dst += tmp;
}
//---------------------------------------------------------------------------
template <typename number>
SparseLUDecomposition<number>::AdditionalData::AdditionalData (
const double strengthen_diag,
const unsigned int extra_off_diag,
const bool use_prev_sparsity,
const SparsityPattern *use_this_spars):
strengthen_diagonal(strengthen_diag),
extra_off_diagonals(extra_off_diag),
use_previous_sparsity(use_prev_sparsity),
use_this_sparsity(use_this_spars)
{}
#endif // DOXYGEN
DEAL_II_NAMESPACE_CLOSE
#endif // dealii__sparse_decomposition_h
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