A block-tridiagonal matrix. More...

#include <dune/istl/btdmatrix.hh>

Inheritance diagram for Dune::BTDMatrix< B, A >:

Public Types
enum	{ blocklevel = B::blocklevel+1 }
	increment block level counter More...

typedef B::field_type	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 A::size_type	size_type
	implement row_type with compressed vector More...

enum	{ blocklevel = B::blocklevel+1 }
	increment block level counter More...

enum	BuildMode { row_wise, random, unknown }
	we support two modes More...

typedef CompressedBlockVectorWindow< B, A >	row_type
	implement row_type with compressed vector 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
	BTDMatrix ()
	Default constructor. More...

	BTDMatrix (int size)

BTDMatrix &	operator= (const BTDMatrix &other)
	assignment More...

BTDMatrix &	operator= (const field_type &k)
	assignment from scalar More...

template<class V >
void	solve (V &x, const V &rhs) const
	Use the Thomas algorithm to solve the system Ax=b in O(n) time. More...

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...

ConstIterator	begin () const
	Get const iterator to first row. More...

Iterator	end ()
	Get iterator to one beyond last row. More...

ConstIterator	end () const
	Get const iterator to one beyond last row. More...

Iterator	beforeEnd ()

ConstIterator	beforeEnd () const

Iterator	beforeBegin ()

ConstIterator	beforeBegin () const

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...

CreateIterator	createbegin ()
	get initial create iterator More...

CreateIterator	createend ()
	get create iterator pointing to one after the last block 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...

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)
	Substract the entries of another matrix to 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 >
void	usmv (const field_type &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...

double	frobenius_norm2 () const
	square of frobenius norm, need for block recursion More...

double	frobenius_norm () const
	frobenius norm: sqrt(sum over squared values of entries) More...

double	infinity_norm () const
	infinity norm (row sum norm, how to generalize for blocks?) More...

double	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...

bool	exists (size_type i, size_type j) const
	return true if (i,j) is in pattern More...

Detailed Description

template<class B, class A = std::allocator>
class Dune::BTDMatrix< B, A >

A block-tridiagonal matrix.

Todo:: It would be safer and more efficient to have a real implementation of a block-tridiagonal matrix and not just subclassing from BCRSMatrix. But that's quite a lot of work for that little advantage.

Member Typedef Documentation

template<class B , class A = std::allocator>

typedef A Dune::BTDMatrix< B, A >::allocator_type

export the allocator type

template<class B , class A = std::allocator>

typedef B Dune::BTDMatrix< B, A >::block_type

export the type representing the components

template<class B, class A = std::allocator>

typedef row_type::Iterator Dune::BCRSMatrix< B, A >::ColIterator

inherited

Iterator for the entries of each row.

template<class B, class A = std::allocator>

typedef RealRowIterator<const row_type> Dune::BCRSMatrix< B, A >::const_iterator

inherited

The const iterator over the matrix rows.

template<class B, class A = std::allocator>

typedef row_type::ConstIterator Dune::BCRSMatrix< B, A >::ConstColIterator

inherited

Const iterator to the entries of a row.

template<class B, class A = std::allocator>

typedef RealRowIterator<const row_type> Dune::BCRSMatrix< B, A >::ConstIterator

inherited

template<class B, class A = std::allocator>

typedef ConstIterator Dune::BCRSMatrix< B, A >::ConstRowIterator

inherited

rename the const row iterator for easier access

template<class B , class A = std::allocator>

typedef B::field_type Dune::BTDMatrix< B, A >::field_type

export the type representing the field

template<class B, class A = std::allocator>

typedef RealRowIterator<row_type> Dune::BCRSMatrix< B, A >::iterator

inherited

The iterator over the (mutable matrix rows.

template<class B, class A = std::allocator>

typedef RealRowIterator<row_type> Dune::BCRSMatrix< B, A >::Iterator

inherited

template<class B, class A = std::allocator>

typedef CompressedBlockVectorWindow<B,A> Dune::BCRSMatrix< B, A >::row_type

inherited

implement row_type with compressed vector

template<class B, class A = std::allocator>

typedef Iterator Dune::BCRSMatrix< B, A >::RowIterator

inherited

rename the iterators for easier access

template<class B , class A = std::allocator>

typedef A::size_type Dune::BTDMatrix< B, A >::size_type

implement row_type with compressed vector

The type for the index access and the size

Member Enumeration Documentation

template<class B, class A = std::allocator>

anonymous enum

inherited

increment block level counter

Enumerator
blocklevel	The number of blocklevels the matrix contains.

template<class B , class A = std::allocator>

anonymous enum

increment block level counter

Enumerator
blocklevel

template<class B, class A = std::allocator>

enum Dune::BCRSMatrix::BuildMode

inherited

we support two modes

Enumerator

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 P1) but the size of a row and the indices of a row can not be defined in sequential order.

unknown

Build mode not set!

Constructor & Destructor Documentation

template<class B , class A = std::allocator>

Dune::BTDMatrix< B, A >::BTDMatrix ( )

inline

Default constructor.

template<class B , class A = std::allocator>

Dune::BTDMatrix< B, A >::BTDMatrix ( int size )

inlineexplicit

References Dune::BCRSMatrix< B, A >::addindex(), Dune::BCRSMatrix< B, A >::endindices(), Dune::BCRSMatrix< B, A >::endrowsizes(), and Dune::BCRSMatrix< B, A >::setrowsize().

Member Function Documentation

template<class B, class A = std::allocator>

BCRSMatrix& Dune::BCRSMatrix< B, A >::axpy	(	field_type	alpha,
		const BCRSMatrix< B, A > &	b
	)

inlineinherited

Add the scaled entries of another matrix to this one.

  Matrix axpy operation: *this += alpha * b

Parameters

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.

References Dune::BCRSMatrix< B, A >::begin(), Dune::BCRSMatrix< B, A >::end(), Dune::BCRSMatrix< B, A >::M(), and Dune::BCRSMatrix< B, A >::N().

template<class B, class A = std::allocator>

Iterator Dune::BCRSMatrix< B, A >::beforeBegin ( )

inlineinherited

Returns: an iterator that is positioned before the first row of the matrix.

template<class B, class A = std::allocator>

ConstIterator Dune::BCRSMatrix< B, A >::beforeBegin ( ) const

inlineinherited

Returns: an iterator that is positioned before the first row of the matrix.

template<class B, class A = std::allocator>

Iterator Dune::BCRSMatrix< B, A >::beforeEnd ( )

inlineinherited

Returns: an iterator that is positioned before the end iterator of the rows, i.e. at the last row.

template<class B, class A = std::allocator>

ConstIterator Dune::BCRSMatrix< B, A >::beforeEnd ( ) const

inlineinherited

Returns: an iterator that is positioned before the end iterator of the rows. i.e. at the last row.

template<class B, class A = std::allocator>

Iterator Dune::BCRSMatrix< B, A >::begin ( )

inlineinherited

Get iterator to first row.

template<class B, class A = std::allocator>

ConstIterator Dune::BCRSMatrix< B, A >::begin ( ) const

inlineinherited

Get const iterator to first row.

template<class B, class A = std::allocator>

CreateIterator Dune::BCRSMatrix< B, A >::createbegin ( )

inlineinherited

get initial create iterator

References Dune::BCRSMatrix< B, A >::CreateIterator.

Referenced by test_IO(), and test_Iter().

template<class B, class A = std::allocator>

CreateIterator Dune::BCRSMatrix< B, A >::createend ( )

inlineinherited

get create iterator pointing to one after the last block

References Dune::BCRSMatrix< B, A >::CreateIterator.

Referenced by test_IO(), and test_Iter().

template<class B, class A = std::allocator>

Iterator Dune::BCRSMatrix< B, A >::end ( )

inlineinherited

Get iterator to one beyond last row.

template<class B, class A = std::allocator>

ConstIterator Dune::BCRSMatrix< B, A >::end ( ) const

inlineinherited

Get const iterator to one beyond last row.

template<class B, class A = std::allocator>

bool Dune::BCRSMatrix< B, A >::exists	(	size_type	i,
		size_type	j
	)		const

inlineinherited

return true if (i,j) is in pattern

References Dune::BCRSMatrix< B, A >::end().

template<class B, class A = std::allocator>

double Dune::BCRSMatrix< B, A >::frobenius_norm ( ) const

inlineinherited

frobenius norm: sqrt(sum over squared values of entries)

References Dune::BCRSMatrix< B, A >::frobenius_norm2().

template<class B, class A = std::allocator>

double Dune::BCRSMatrix< B, A >::frobenius_norm2 ( ) const

inlineinherited

square of frobenius norm, need for block recursion

References Dune::BCRSMatrix< B, A >::begin(), and Dune::BCRSMatrix< B, A >::end().

Referenced by Dune::BCRSMatrix< B, A >::frobenius_norm().

template<class B, class A = std::allocator>

size_type Dune::BCRSMatrix< B, A >::getrowsize ( size_type i ) const

inlineinherited

get current number of indices in row i

References Dune::CompressedBlockVectorWindow< B, A >::getsize().

template<class B, class A = std::allocator>

void Dune::BCRSMatrix< B, A >::incrementrowsize	(	size_type	i,
		size_type	s = `1`
	)

inlineinherited

increment size of row i by s (1 by default)

References Dune::BCRSMatrix< B, A >::random, and Dune::CompressedBlockVectorWindow< B, A >::setsize().

template<class B, class A = std::allocator>

double Dune::BCRSMatrix< B, A >::infinity_norm ( ) const

inlineinherited

infinity norm (row sum norm, how to generalize for blocks?)

References Dune::BCRSMatrix< B, A >::begin(), and Dune::BCRSMatrix< B, A >::end().

template<class B, class A = std::allocator>

double Dune::BCRSMatrix< B, A >::infinity_norm_real ( ) const

inlineinherited

simplified infinity norm (uses Manhattan norm for complex values)

References Dune::BCRSMatrix< B, A >::begin(), and Dune::BCRSMatrix< B, A >::end().

template<class B, class A = std::allocator>

size_type Dune::BCRSMatrix< B, A >::M ( ) const

inlineinherited

number of columns (counted in blocks)

template<class B, class A = std::allocator>

template<class X , class Y >

void Dune::BCRSMatrix< B, A >::mmhv	(	const X &	x,
		Y &	y
	)		const

inlineinherited

y -= A^H x

References Dune::BCRSMatrix< B, A >::begin(), Dune::BCRSMatrix< B, A >::end(), Dune::BCRSMatrix< B, A >::M(), and Dune::BCRSMatrix< B, A >::N().

template<class B, class A = std::allocator>

template<class X , class Y >

void Dune::BCRSMatrix< B, A >::mmtv	(	const X &	x,
		Y &	y
	)		const

inlineinherited

y -= A^T x

References Dune::BCRSMatrix< B, A >::begin(), Dune::BCRSMatrix< B, A >::end(), Dune::BCRSMatrix< B, A >::M(), and Dune::BCRSMatrix< B, A >::N().

template<class B, class A = std::allocator>

template<class X , class Y >

void Dune::BCRSMatrix< B, A >::mmv	(	const X &	x,
		Y &	y
	)		const

inlineinherited

y -= A x

References Dune::BCRSMatrix< B, A >::begin(), Dune::BCRSMatrix< B, A >::end(), Dune::BCRSMatrix< B, A >::M(), and Dune::BCRSMatrix< B, A >::N().

Referenced by test_Iter().

template<class B, class A = std::allocator>

template<class X , class Y >

void Dune::BCRSMatrix< B, A >::mtv	(	const X &	x,
		Y &	y
	)		const

inlineinherited

y = A^T x

References Dune::BCRSMatrix< B, A >::M(), Dune::BCRSMatrix< B, A >::N(), and Dune::BCRSMatrix< B, A >::umtv().

template<class B, class A = std::allocator>

template<class X , class Y >

void Dune::BCRSMatrix< B, A >::mv	(	const X &	x,
		Y &	y
	)		const

inlineinherited

y = A x

References Dune::BCRSMatrix< B, A >::begin(), Dune::BCRSMatrix< B, A >::end(), Dune::BCRSMatrix< B, A >::M(), and Dune::BCRSMatrix< B, A >::N().

template<class B, class A = std::allocator>

size_type Dune::BCRSMatrix< B, A >::N ( ) const

inlineinherited

number of rows (counted in blocks)

template<class B, class A = std::allocator>

size_type Dune::BCRSMatrix< B, A >::nonzeroes ( ) const

inlineinherited

number of blocks that are stored (the number of blocks that possibly are nonzero)

template<class B, class A = std::allocator>

BCRSMatrix& Dune::BCRSMatrix< B, A >::operator*= ( const field_type & k )

inlineinherited

vector space multiplication with scalar

References Dune::BCRSMatrix< B, A >::begin(), and Dune::BCRSMatrix< B, A >::end().

template<class B, class A = std::allocator>

BCRSMatrix& Dune::BCRSMatrix< B, A >::operator+= ( const BCRSMatrix< B, A > & b )

inlineinherited

Add the entries of another matrix to this one.

Parameters

b	The matrix to add to this one. Its sparsity pattern has to be subset of the sparsity pattern of this matrix.

References Dune::BCRSMatrix< B, A >::begin(), Dune::BCRSMatrix< B, A >::end(), Dune::BCRSMatrix< B, A >::M(), and Dune::BCRSMatrix< B, A >::N().

template<class B, class A = std::allocator>

BCRSMatrix& Dune::BCRSMatrix< B, A >::operator-= ( const BCRSMatrix< B, A > & b )

inlineinherited

Substract the entries of another matrix to this one.

Parameters

b	The matrix to add to this one. Its sparsity pattern has to be subset of the sparsity pattern of this matrix.

References Dune::BCRSMatrix< B, A >::begin(), Dune::BCRSMatrix< B, A >::end(), Dune::BCRSMatrix< B, A >::M(), and Dune::BCRSMatrix< B, A >::N().

template<class B, class A = std::allocator>

BCRSMatrix& Dune::BCRSMatrix< B, A >::operator/= ( const field_type & k )

inlineinherited

vector space division by scalar

References Dune::BCRSMatrix< B, A >::begin(), and Dune::BCRSMatrix< B, A >::end().

template<class B , class A = std::allocator>

BTDMatrix& Dune::BTDMatrix< B, A >::operator= ( const BTDMatrix< B, A > & other )

inline

assignment

References Dune::BCRSMatrix< B, A >::operator=().

template<class B , class A = std::allocator>

BTDMatrix& Dune::BTDMatrix< B, A >::operator= ( const field_type & k )

inline

assignment from scalar

References Dune::BCRSMatrix< B, A >::operator=().

template<class B, class A = std::allocator>

row_type& Dune::BCRSMatrix< B, A >::operator[] ( size_type i )

inlineinherited

random access to the rows

template<class B, class A = std::allocator>

const row_type& Dune::BCRSMatrix< B, A >::operator[] ( size_type i ) const

inlineinherited

same for read only access

template<class B, class A = std::allocator>

void Dune::BCRSMatrix< B, A >::setBuildMode ( BuildMode bm )

inlineinherited

Sets the build mode of the matrix.

Parameters

bm	The build mode to use.

template<class B, class A = std::allocator>

void Dune::BCRSMatrix< B, A >::setSize	(	size_type	rows,
		size_type	columns,
		size_type	nnz = `0`
	)

inlineinherited

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.

Warning: After calling this methods on an already allocated (and probably setup matrix) results in all the structure and data being deleted. I.~e. one has to setup the matrix again.

Parameters

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).

template<class B , class A = std::allocator>

template<class V >