A block-tridiagonal matrix. More...

#include <dune/istl/btdmatrix.hh>

Public Types
enum
	increment block level counter

typedef B::field_type	field_type
	export the type representing the field

typedef B	block_type
	export the type representing the components

typedef A	allocator_type
	export the allocator type

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

enum
	increment block level counter

enum	BuildMode
	we support two modes

typedef CompressedBlockVectorWindow< B, std::allocator< B > >	row_type
	implement row_type with compressed vector

typedef ::Dune::CompressionStatistics< size_type >	CompressionStatistics
	The type for the statistics object returned by compress()

typedef RealRowIterator< row_type >	iterator
	The iterator over the (mutable matrix rows.

typedef Iterator	RowIterator
	rename the iterators for easier access

typedef row_type::Iterator	ColIterator
	Iterator for the entries of each row.

typedef RealRowIterator< const row_type >	const_iterator
	The const iterator over the matrix rows.

typedef ConstIterator	ConstRowIterator
	rename the const row iterator for easier access

typedef row_type::ConstIterator	ConstColIterator
	Const iterator to the entries of a row.

Public Member Functions
	BTDMatrix ()
	Default constructor.

BTDMatrix &	operator= (const BTDMatrix &other)
	assignment

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

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

const row_type &	operator[] (size_type i) const
	same for read only access

Iterator	begin ()
	Get iterator to first row.

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

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

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

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...

void	setImplicitBuildModeParameters (size_type _avg, double _overflow)
	Set parameters needed for creation in implicit build mode. More...

CreateIterator	createbegin ()
	get initial create iterator

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

size_type	getrowsize (size_type i) const
	get current number of indices in row i

void	incrementrowsize (size_type i, size_type s=1)
	increment size of row i by s (1 by default)

void	setIndices (size_type row, It begin, It end)
	Set all column indices for row from the given iterator range. More...

B &	entry (size_type row, size_type col)
	Returns reference to entry (row,col) of the matrix. More...

CompressionStatistics	compress ()
	Finishes the buildstage in implicit mode. More...

BCRSMatrix &	*operator=** (const field_type &k)
	vector space multiplication with scalar

BCRSMatrix &	operator/= (const field_type &k)
	vector space division by scalar

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...

void	mv (const X &x, Y &y) const
	y = A x

void	umv (const X &x, Y &y) const
	y += A x

void	mmv (const X &x, Y &y) const
	y -= A x

void	usmv (const field_type &alpha, const X &x, Y &y) const
	y += alpha A x

void	mtv (const X &x, Y &y) const
	y = A^T x

void	umtv (const X &x, Y &y) const
	y += A^T x

void	mmtv (const X &x, Y &y) const
	y -= A^T x

void	usmtv (const field_type &alpha, const X &x, Y &y) const
	y += alpha A^T x

void	umhv (const X &x, Y &y) const
	y += A^H x

void	mmhv (const X &x, Y &y) const
	y -= A^H x

void	usmhv (const field_type &alpha, const X &x, Y &y) const
	y += alpha A^H x

FieldTraits< field_type >::real_type	frobenius_norm2 () const
	square of frobenius norm, need for block recursion

FieldTraits< field_type >::real_type	frobenius_norm () const
	frobenius norm: sqrt(sum over squared values of entries)

FieldTraits< field_type >::real_type	infinity_norm () const
	infinity norm (row sum norm, how to generalize for blocks?)

FieldTraits< field_type >::real_type	infinity_norm_real () const
	simplified infinity norm (uses Manhattan norm for complex values)

size_type	N () const
	number of rows (counted in blocks)

size_type	M () const
	number of columns (counted in blocks)

size_type	nonzeroes () const
	number of blocks that are stored (the number of blocks that possibly are nonzero)

BuildStage	buildStage () const
	The current build stage of the matrix.

BuildMode	buildMode () const
	The currently selected build mode of the matrix.

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

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

◆ size_type

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 Function Documentation

◆ axpy()

BCRSMatrix & Dune::BCRSMatrix< B, std::allocator< B > >::axpy	(	field_type	alpha,
		const BCRSMatrix< B, std::allocator< B > > &	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.

◆ beforeBegin() [1/2]

Iterator Dune::BCRSMatrix< B, std::allocator >::beforeBegin ( )

inlineinherited

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

◆ beforeBegin() [2/2]

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

inlineinherited

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

◆ beforeEnd() [1/2]

Iterator Dune::BCRSMatrix< B, std::allocator >::beforeEnd ( )

inlineinherited

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

◆ beforeEnd() [2/2]

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

inlineinherited

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

◆ compress()

CompressionStatistics Dune::BCRSMatrix< B, std::allocator >::compress ( )

inlineinherited

Finishes the buildstage in implicit mode.

Performs compression of index and data arrays with linear complexity in the number of nonzeroes.

After calling this method, the matrix is in the built state and no more entries can be added.

Returns: An object with some statistics about the compression for future optimization.

◆ entry()

B & Dune::BCRSMatrix< B, std::allocator< B > >::entry	(	size_type	row,
		size_type	col
	)

inlineinherited

Returns reference to entry (row,col) of the matrix.

This method can only be used when the matrix is in implicit building mode.

A reference to entry (row, col) of the matrix is returned. If entry (row, col) is accessed for the first time, it is created on the fly.

This method can only be used while building the matrix, after compression operator[] gives a much better performance.

◆ operator+=()

BCRSMatrix & Dune::BCRSMatrix< B, std::allocator >::operator+= ( const BCRSMatrix< B, std::allocator > & 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.

◆ operator-=()

BCRSMatrix & Dune::BCRSMatrix< B, std::allocator >::operator-= ( const BCRSMatrix< B, std::allocator > & 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.

◆ setBuildMode()

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

inlineinherited

Sets the build mode of the matrix.

Parameters

bm	The build mode to use.

◆ setImplicitBuildModeParameters()

void Dune::BCRSMatrix< B, std::allocator< B > >::setImplicitBuildModeParameters	(	size_type	_avg,
		double	_overflow
	)

inlineinherited

Set parameters needed for creation in implicit build mode.

Use this method before setSize() to define storage behaviour of a matrix in implicit build mode

Parameters

_avg	expected average number of entries per row
_overflowsize	fraction of _n*_avg which is expected to be needed for elements that exceed _avg entries per row.

◆ setIndices()

void Dune::BCRSMatrix< B, std::allocator< B > >::setIndices	(	size_type	row,
		It	begin,
		It	end
	)

inlineinherited

Set all column indices for row from the given iterator range.

The iterator range has to be of the same length as the previously set row size. The entries in the iterator range do not have to be in any particular order, but must not contain duplicate values.

Calling this method overwrites any previously set column indices!

◆ setSize()

void Dune::BCRSMatrix< B, std::allocator< B > >::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). Must be omitted in implicit mode.

◆ solve()

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

template<class V >

void Dune::BTDMatrix< B, A >::solve	(	V &	x,
		const V &	rhs
	)		const

inline

Use the Thomas algorithm to solve the system Ax=b in O(n) time.

Exceptions

ISTLError if the matrix is singular

References Dune::BCRSMatrix< B, std::allocator >::N().

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

dune/istl/btdmatrix.hh

DUNE Distributed and Unified Numerics Environment

Dune Core Modules (2.3.1)

Public Types

Public Member Functions

Detailed Description

Member Typedef Documentation

◆ size_type

Member Function Documentation

◆ axpy()

◆ beforeBegin() [1/2]

◆ beforeBegin() [2/2]

◆ beforeEnd() [1/2]

◆ beforeEnd() [2/2]

◆ compress()

◆ entry()

◆ operator+=()

◆ operator-=()

◆ setBuildMode()

◆ setImplicitBuildModeParameters()

◆ setIndices()

◆ setSize()

◆ solve()