A diagonal matrix of static size. More...

#include <dune/common/diagonalmatrix.hh>

Public Types
enum	{ blocklevel = 1 }
	We are at the leaf of the block recursion. More...

enum	{ rows = n, cols = n }
	export size More...

typedef K	value_type
	export the type representing the field More...

typedef value_type	field_type

typedef K	block_type
	export the type representing the components More...

typedef std::size_t	size_type
	The type used for the index access and size operations. More...

typedef DiagonalRowVector< K, n >	row_type
	Each row is implemented by a field vector. More...

typedef row_type	reference

typedef row_type	row_reference

typedef DiagonalRowVectorConst < K, n >	const_row_type

typedef const_row_type	const_reference

typedef const_row_type	const_row_reference

typedef ContainerWrapperIterator < const WrapperType, reference, reference >	Iterator
	Iterator class for sequential access. More...

typedef Iterator	iterator
	typedef for stl compliant access More...

typedef Iterator	RowIterator
	rename the iterators for easier access More...

typedef row_type::Iterator	ColIterator
	rename the iterators for easier access More...

typedef ContainerWrapperIterator < const WrapperType, const_reference, const_reference >	ConstIterator
	Iterator class for sequential access. More...

typedef ConstIterator	const_iterator
	typedef for stl compliant access More...

typedef ConstIterator	ConstRowIterator
	rename the iterators for easier access More...

typedef const_row_type::ConstIterator	ConstColIterator
	rename the iterators for easier access More...

Public Member Functions
size_type	size () const

	DiagonalMatrix ()
	Default constructor. More...

	DiagonalMatrix (const K &k)
	Constructor initializing the whole matrix with a scalar. More...

	DiagonalMatrix (const FieldVector< K, n > &diag)
	Constructor initializing the diagonal with a vector. More...

DiagonalMatrix &	operator= (const K &k)
	Assignment from a scalar. More...

bool	identical (const DiagonalMatrix< K, n > &other) const
	Check if matrix is the same object as the other matrix. More...

Iterator	begin ()
	begin iterator More...

Iterator	end ()
	end iterator More...

Iterator	beforeEnd ()

Iterator	beforeBegin ()

ConstIterator	begin () const
	begin iterator More...

ConstIterator	end () const
	end iterator More...

ConstIterator	beforeEnd () const

ConstIterator	beforeBegin () const

DiagonalMatrix &	operator+= (const DiagonalMatrix &y)
	vector space addition More...

DiagonalMatrix &	operator-= (const DiagonalMatrix &y)
	vector space subtraction More...

DiagonalMatrix &	operator+= (const K &k)
	vector space multiplication with scalar More...

DiagonalMatrix &	operator-= (const K &k)
	vector space division by scalar More...

DiagonalMatrix &	operator*= (const K &k)
	vector space multiplication with scalar More...

DiagonalMatrix &	operator/= (const K &k)
	vector space division by scalar More...

bool	operator== (const DiagonalMatrix &other) const
	comparison operator More...

bool	operator!= (const DiagonalMatrix &other) const
	incomparison operator More...

template<class X , class Y >
void	mv (const X &x, Y &y) const
	y = 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	umv (const X &x, Y &y) const
	y += A 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	umhv (const X &x, Y &y) const
	y += A^H 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	mmtv (const X &x, Y &y) const
	y -= A^T 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	usmv (const K &alpha, const X &x, Y &y) const
	y += alpha A x More...

template<class X , class Y >
void	usmtv (const K &alpha, const X &x, Y &y) const
	y += alpha A^T x More...

template<class X , class Y >
void	usmhv (const K &alpha, const X &x, Y &y) const
	y += alpha A^H x More...

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

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

template<class V >
void	solve (V &x, const V &b) const
	Solve system A x = b. More...

void	invert ()
	Compute inverse. More...

K	determinant () const
	calculates the determinant of this matrix More...

size_type	N () const
	number of blocks in row direction More...

size_type	M () const
	number of blocks in column direction More...

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

reference	operator[] (size_type i)
	Return reference object as row replacement. More...

const_reference	operator[] (size_type i) const
	Return const_reference object as row replacement. More...

const K &	diagonal (size_type i) const
	Get const reference to diagonal entry. More...

K &	diagonal (size_type i)
	Get reference to diagonal entry. More...

const FieldVector< K, n > &	diagonal () const
	Get const reference to diagonal vector. More...

FieldVector< K, n > &	diagonal ()
	Get reference to diagonal vector. More...

Friends
std::ostream &	operator<< (std::ostream &s, const DiagonalMatrix< K, n > &a)
	Sends the matrix to an output stream. More...

Detailed Description

template<class K, int n>
class Dune::DiagonalMatrix< K, n >

A diagonal matrix of static size.

This is meant to be a replacement of FieldMatrix for the case that it is a diagonal matrix.

Template Parameters

K	Type used for scalars
n	Matrix size

Member Typedef Documentation

template<class K, int n>

typedef K Dune::DiagonalMatrix< K, n >::block_type

export the type representing the components

template<class K, int n>

typedef row_type::Iterator Dune::DiagonalMatrix< K, n >::ColIterator

rename the iterators for easier access

template<class K, int n>

typedef ConstIterator Dune::DiagonalMatrix< K, n >::const_iterator

typedef for stl compliant access

template<class K, int n>

typedef const_row_type Dune::DiagonalMatrix< K, n >::const_reference

template<class K, int n>

typedef const_row_type Dune::DiagonalMatrix< K, n >::const_row_reference

template<class K, int n>

typedef DiagonalRowVectorConst<K,n> Dune::DiagonalMatrix< K, n >::const_row_type

template<class K, int n>

typedef const_row_type::ConstIterator Dune::DiagonalMatrix< K, n >::ConstColIterator

rename the iterators for easier access

template<class K, int n>

typedef ContainerWrapperIterator<const WrapperType, const_reference, const_reference> Dune::DiagonalMatrix< K, n >::ConstIterator

Iterator class for sequential access.

template<class K, int n>

typedef ConstIterator Dune::DiagonalMatrix< K, n >::ConstRowIterator

rename the iterators for easier access

template<class K, int n>

typedef value_type Dune::DiagonalMatrix< K, n >::field_type

template<class K, int n>

typedef ContainerWrapperIterator<const WrapperType, reference, reference> Dune::DiagonalMatrix< K, n >::Iterator

Iterator class for sequential access.

template<class K, int n>

typedef Iterator Dune::DiagonalMatrix< K, n >::iterator

typedef for stl compliant access

template<class K, int n>

typedef row_type Dune::DiagonalMatrix< K, n >::reference

template<class K, int n>

typedef row_type Dune::DiagonalMatrix< K, n >::row_reference

template<class K, int n>

typedef DiagonalRowVector<K,n> Dune::DiagonalMatrix< K, n >::row_type

Each row is implemented by a field vector.

template<class K, int n>

typedef Iterator Dune::DiagonalMatrix< K, n >::RowIterator

rename the iterators for easier access

template<class K, int n>

typedef std::size_t Dune::DiagonalMatrix< K, n >::size_type

The type used for the index access and size operations.

template<class K, int n>

typedef K Dune::DiagonalMatrix< K, n >::value_type

export the type representing the field

Member Enumeration Documentation

template<class K, int n>

anonymous enum

We are at the leaf of the block recursion.

Enumerator
blocklevel	The number of block levels we contain. This is 1.

template<class K, int n>

anonymous enum

export size

Enumerator
rows	The number of rows.
cols	The number of columns.

Constructor & Destructor Documentation

template<class K, int n>

Dune::DiagonalMatrix< K, n >::DiagonalMatrix ( )

inline

Default constructor.

template<class K, int n>

Dune::DiagonalMatrix< K, n >::DiagonalMatrix ( const K & k )

inline

Constructor initializing the whole matrix with a scalar.

template<class K, int n>

Dune::DiagonalMatrix< K, n >::DiagonalMatrix ( const FieldVector< K, n > & diag )

inline

Constructor initializing the diagonal with a vector.

Member Function Documentation

template<class K, int n>

Iterator Dune::DiagonalMatrix< K, n >::beforeBegin ( )

inline

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

template<class K, int n>

ConstIterator Dune::DiagonalMatrix< K, n >::beforeBegin ( ) const

inline

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

template<class K, int n>

Iterator Dune::DiagonalMatrix< K, n >::beforeEnd ( )

inline

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

template<class K, int n>

ConstIterator Dune::DiagonalMatrix< K, n >::beforeEnd ( ) const

inline

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

template<class K, int n>

Iterator Dune::DiagonalMatrix< K, n >::begin ( )

inline

begin iterator

template<class K, int n>

ConstIterator Dune::DiagonalMatrix< K, n >::begin ( ) const

inline

begin iterator

template<class K, int n>

K Dune::DiagonalMatrix< K, n >::determinant ( ) const

inline

calculates the determinant of this matrix

template<class K, int n>

const K& Dune::DiagonalMatrix< K, n >::diagonal ( size_type i ) const

inline

Get const reference to diagonal entry.

Referenced by Dune::DiagonalMatrix< K, n >::operator!=(), and Dune::DiagonalMatrix< K, n >::operator==().

template<class K, int n>

K& Dune::DiagonalMatrix< K, n >::diagonal ( size_type i )

inline

Get reference to diagonal entry.

template<class K, int n>

const FieldVector<K,n>& Dune::DiagonalMatrix< K, n >::diagonal ( ) const

inline

Get const reference to diagonal vector.

template<class K, int n>

FieldVector<K,n>& Dune::DiagonalMatrix< K, n >::diagonal ( )

inline

Get reference to diagonal vector.

template<class K, int n>

Iterator Dune::DiagonalMatrix< K, n >::end ( )

inline

end iterator

template<class K, int n>

ConstIterator Dune::DiagonalMatrix< K, n >::end ( ) const

inline

end iterator

template<class K, int n>

bool Dune::DiagonalMatrix< K, n >::exists	(	size_type	i,
		size_type	j
	)		const

inline

return true when (i,j) is in pattern

References DUNE_THROW.

template<class K, int n>

double Dune::DiagonalMatrix< K, n >::frobenius_norm ( ) const

inline

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

References Dune::DenseVector< V >::two_norm().

template<class K, int n>

double Dune::DiagonalMatrix< K, n >::frobenius_norm2 ( ) const

inline

square of frobenius norm, need for block recursion

References Dune::DenseVector< V >::two_norm2().

template<class K, int n>

bool Dune::DiagonalMatrix< K, n >::identical ( const DiagonalMatrix< K, n > & other ) const

inline

Check if matrix is the same object as the other matrix.

template<class K, int n>

double Dune::DiagonalMatrix< K, n >::infinity_norm ( ) const

inline

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

References Dune::DenseVector< V >::infinity_norm().

template<class K, int n>

double Dune::DiagonalMatrix< K, n >::infinity_norm_real ( ) const

inline

simplified infinity norm (uses Manhattan norm for complex values)

References Dune::DenseVector< V >::infinity_norm_real().

template<class K, int n>

void Dune::DiagonalMatrix< K, n >::invert ( )

inline

Compute inverse.

template<class K, int n>

size_type Dune::DiagonalMatrix< K, n >::M ( ) const

inline

number of blocks in column direction

Referenced by Dune::DiagonalMatrix< K, n >::mmhv(), Dune::DiagonalMatrix< K, n >::mmtv(), Dune::DiagonalMatrix< K, n >::mmv(), Dune::DiagonalMatrix< K, n >::mv(), Dune::DiagonalMatrix< K, n >::umhv(), Dune::DiagonalMatrix< K, n >::umtv(), Dune::DiagonalMatrix< K, n >::umv(), Dune::DiagonalMatrix< K, n >::usmhv(), Dune::DiagonalMatrix< K, n >::usmtv(), and Dune::DiagonalMatrix< K, n >::usmv().

template<class K, int n>

template<class X , class Y >

void Dune::DiagonalMatrix< K, n >::mmhv	(	const X &	x,
		Y &	y
	)		const

inline

y -= A^H x

References Dune::conjugateComplex(), DUNE_THROW, Dune::DiagonalMatrix< K, n >::M(), and Dune::DiagonalMatrix< K, n >::N().

template<class K, int n>

template<class X , class Y >

void Dune::DiagonalMatrix< K, n >::mmtv	(	const X &	x,
		Y &	y
	)		const

inline

y -= A^T x

References DUNE_THROW, Dune::DiagonalMatrix< K, n >::M(), and Dune::DiagonalMatrix< K, n >::N().

template<class K, int n>

template<class X , class Y >

void Dune::DiagonalMatrix< K, n >::mmv	(	const X &	x,
		Y &	y
	)		const

inline

y -= A x

References DUNE_THROW, Dune::DiagonalMatrix< K, n >::M(), and Dune::DiagonalMatrix< K, n >::N().

template<class K, int n>

template<class X , class Y >

void Dune::DiagonalMatrix< K, n >::mtv	(	const X &	x,
		Y &	y
	)		const

inline

y = A^T x

References Dune::DiagonalMatrix< K, n >::mv().

template<class K, int n>

template<class X , class Y >

void Dune::DiagonalMatrix< K, n >::mv	(	const X &	x,
		Y &	y
	)		const

inline

y = A x

References DUNE_THROW, Dune::DiagonalMatrix< K, n >::M(), and Dune::DiagonalMatrix< K, n >::N().

Referenced by Dune::DiagonalMatrix< K, n >::mtv().

template<class K, int n>

size_type Dune::DiagonalMatrix< K, n >::N ( ) const

inline

number of blocks in row direction

Referenced by Dune::DiagonalMatrix< K, n >::mmhv(), Dune::DiagonalMatrix< K, n >::mmtv(), Dune::DiagonalMatrix< K, n >::mmv(), Dune::DiagonalMatrix< K, n >::mv(), Dune::DiagonalMatrix< K, n >::umhv(), Dune::DiagonalMatrix< K, n >::umtv(), Dune::DiagonalMatrix< K, n >::umv(), Dune::DiagonalMatrix< K, n >::usmhv(), Dune::DiagonalMatrix< K, n >::usmtv(), and Dune::DiagonalMatrix< K, n >::usmv().

template<class K, int n>

bool Dune::DiagonalMatrix< K, n >::operator!= ( const DiagonalMatrix< K, n > & other ) const

inline

incomparison operator

References Dune::DiagonalMatrix< K, n >::diagonal().

template<class K, int n>

DiagonalMatrix& Dune::DiagonalMatrix< K, n >::operator*= ( const K & k )

inline

vector space multiplication with scalar

template<class K, int n>

DiagonalMatrix& Dune::DiagonalMatrix< K, n >::operator+= ( const DiagonalMatrix< K, n > & y )

inline

vector space addition

template<class K, int n>

DiagonalMatrix& Dune::DiagonalMatrix< K, n >::operator+= ( const K & k )

inline

vector space multiplication with scalar

template<class K, int n>

DiagonalMatrix& Dune::DiagonalMatrix< K, n >::operator-= ( const DiagonalMatrix< K, n > & y )

inline

vector space subtraction

template<class K, int n>

DiagonalMatrix& Dune::DiagonalMatrix< K, n >::operator-= ( const K & k )

inline

vector space division by scalar

template<class K, int n>

DiagonalMatrix& Dune::DiagonalMatrix< K, n >::operator/= ( const K & k )

inline

vector space division by scalar

template<class K, int n>

DiagonalMatrix& Dune::DiagonalMatrix< K, n >::operator= ( const K & k )

inline

Assignment from a scalar.

template<class K, int n>

bool Dune::DiagonalMatrix< K, n >::operator== ( const DiagonalMatrix< K, n > & other ) const

inline

comparison operator

References Dune::DiagonalMatrix< K, n >::diagonal().

template<class K, int n>

reference Dune::DiagonalMatrix< K, n >::operator[] ( size_type i )

inline

Return reference object as row replacement.

template<class K, int n>

const_reference Dune::DiagonalMatrix< K, n >::operator[] ( size_type i ) const

inline

Return const_reference object as row replacement.

template<class K, int n>

size_type Dune::DiagonalMatrix< K, n >::size ( ) const

inline

References Dune::DiagonalMatrix< K, n >::rows.

template<class K, int n>

template<class V >

void Dune::DiagonalMatrix< K, n >::solve	(	V &	x,
		const V &	b
	)		const

inline

Solve system A x = b.

template<class K, int n>

template<class X , class Y >

void Dune::DiagonalMatrix< K, n >::umhv	(	const X &	x,
		Y &	y
	)		const

inline

y += A^H x

References Dune::conjugateComplex(), DUNE_THROW, Dune::DiagonalMatrix< K, n >::M(), and Dune::DiagonalMatrix< K, n >::N().

template<class K, int n>

template<class X , class Y >

void Dune::DiagonalMatrix< K, n >::umtv	(	const X &	x,
		Y &	y
	)		const

inline

y += A^T x

References DUNE_THROW, Dune::DiagonalMatrix< K, n >::M(), and Dune::DiagonalMatrix< K, n >::N().

template<class K, int n>

template<class X , class Y >

void Dune::DiagonalMatrix< K, n >::umv	(	const X &	x,
		Y &	y
	)		const

inline

y += A x

References DUNE_THROW, Dune::DiagonalMatrix< K, n >::M(), and Dune::DiagonalMatrix< K, n >::N().

template<class K, int n>

template<class X , class Y >

void Dune::DiagonalMatrix< K, n >::usmhv	(	const K &	alpha,
		const X &	x,
		Y &	y
	)		const

inline

y += alpha A^H x

References Dune::conjugateComplex(), DUNE_THROW, Dune::DiagonalMatrix< K, n >::M(), and Dune::DiagonalMatrix< K, n >::N().

template<class K, int n>

template<class X , class Y >

void Dune::DiagonalMatrix< K, n >::usmtv	(	const K &	alpha,
		const X &	x,
		Y &	y
	)		const

inline

y += alpha A^T x

References DUNE_THROW, Dune::DiagonalMatrix< K, n >::M(), and Dune::DiagonalMatrix< K, n >::N().

template<class K, int n>

template<class X , class Y >

void Dune::DiagonalMatrix< K, n >::usmv	(	const K &	alpha,
		const X &	x,
		Y &	y
	)		const

inline

y += alpha A x

References DUNE_THROW, Dune::DiagonalMatrix< K, n >::M(), and Dune::DiagonalMatrix< K, n >::N().

Friends And Related Function Documentation

template<class K, int n>

std::ostream& operator<<	(	std::ostream &	s,
		const DiagonalMatrix< K, n > &	a
	)

friend

Sends the matrix to an output stream.

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

diagonalmatrix.hh

Public Types

Public Member Functions

Friends

Detailed Description

template<class K, int n> class Dune::DiagonalMatrix< K, n >

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

template<class K, int n>
class Dune::DiagonalMatrix< K, n >