A diagonal matrix of static size. More...

#include <dune/common/diagonalmatrix.hh>

Public Types
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
constexpr	DiagonalMatrix ()=default
	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 (std::initializer_list< K > const &l)
	Construct diagonal matrix from an initializer list. More...

template<class OtherK >
	DiagonalMatrix (const DiagonalMatrix< OtherK, n > &other)
	Converting constructor. More...

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

template<class OtherK >
DiagonalMatrix &	operator= (const DiagonalMatrix< OtherK, n > &other)
	Converting assignment operator. More...

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

DiagonalMatrix< K, n >	transposed () const
	Return transposed of the matrix as DiagonalMatrix. 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 typename FieldTraits< Y >::field_type &alpha, const X &x, Y &y) const
	y += alpha A x More...

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

template<class X , class Y >
void	usmhv (const typename FieldTraits< Y >::field_type &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...

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...

Static Public Member Functions
static constexpr size_type	size ()

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

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

Static Public Attributes
static constexpr int	blocklevel = 1
	The number of block levels we contain. This is the leaf, that is, 1. More...

static constexpr int	rows = n
	The number of rows. More...

static constexpr int	cols = n
	The number of columns. More...

Friends
template<class , int >
class	DiagonalMatrix

template<class OtherScalar >
auto	operator* (const DiagonalMatrix &matrixA, const DiagonalMatrix< OtherScalar, n > &matrixB)
	Matrix-matrix multiplication. More...

template<class OtherMatrix , std::enable_if_t<(Impl::IsDenseMatrix< OtherMatrix >::value), int > = 0, std::enable_if_t<(not Impl::IsFieldMatrix< OtherMatrix >::value), int > = 0>
auto	operator* (const DiagonalMatrix &matrixA, const OtherMatrix &matrixB)
	Multiply a diagonal matrix with a dense matrix. More...

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

◆ block_type

template<class K, int n>

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

export the type representing the components

◆ ColIterator

template<class K, int n>

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

rename the iterators for easier access

◆ const_iterator

template<class K, int n>

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

typedef for stl compliant access

◆ const_reference

template<class K, int n>

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

◆ const_row_reference

template<class K, int n>

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

◆ const_row_type

template<class K, int n>

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

◆ ConstColIterator

template<class K, int n>

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

rename the iterators for easier access

◆ ConstIterator

template<class K, int n>

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

Iterator class for sequential access.

◆ ConstRowIterator

template<class K, int n>

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

rename the iterators for easier access

◆ field_type

template<class K, int n>

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

◆ Iterator

template<class K, int n>

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

Iterator class for sequential access.

◆ iterator

template<class K, int n>

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

typedef for stl compliant access

◆ reference

template<class K, int n>

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

◆ row_reference

template<class K, int n>

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

◆ row_type

template<class K, int n>

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

Each row is implemented by a field vector.

◆ RowIterator

template<class K, int n>

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

rename the iterators for easier access

◆ size_type

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.

◆ value_type

template<class K, int n>

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

export the type representing the field

Constructor & Destructor Documentation

◆ DiagonalMatrix() [1/5]

template<class K, int n>

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

default

Default constructor.

◆ DiagonalMatrix() [2/5]

template<class K, int n>

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

inline

Constructor initializing the whole matrix with a scalar.

◆ DiagonalMatrix() [3/5]

template<class K, int n>

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

inline

Constructor initializing the diagonal with a vector.

◆ DiagonalMatrix() [4/5]

template<class K, int n>

Dune::DiagonalMatrix< K, n >::DiagonalMatrix ( std::initializer_list< K > const & l )

inline

Construct diagonal matrix from an initializer list.

The elements of the list are copied into the diagonal elements of the matrix. If the initializer list is shorter than the matrix diagonal (which has n elements), the remaining matrix diagonal elements are left uninitialized. If the initializer list is longer, than only the first n elements will be copied into the matrix diagonal.

◆ DiagonalMatrix() [5/5]

template<class K, int n>

template<class OtherK >

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

inline

Converting constructor.

Member Function Documentation

◆ beforeBegin() [1/2]

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.

◆ beforeBegin() [2/2]

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.

◆ beforeEnd() [1/2]

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.

◆ beforeEnd() [2/2]

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.

◆ begin() [1/2]

template<class K, int n>

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

inline

begin iterator

◆ begin() [2/2]

template<class K, int n>

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

inline

begin iterator

◆ determinant()

template<class K, int n>

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

inline

calculates the determinant of this matrix

◆ diagonal() [1/4]

template<class K, int n>

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

inline

Get const reference to diagonal entry.

◆ diagonal() [2/4]

template<class K, int n>

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

inline

Get reference to diagonal entry.

◆ diagonal() [3/4]

template<class K, int n>

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

inline

Get const reference to diagonal vector.

◆ diagonal() [4/4]

template<class K, int n>

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

inline

Get reference to diagonal vector.

◆ end() [1/2]

template<class K, int n>

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

inline

end iterator

◆ end() [2/2]

template<class K, int n>

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

inline

end iterator

◆ exists()

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

◆ frobenius_norm()

template<class K, int n>

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

inline

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

◆ frobenius_norm2()

template<class K, int n>

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

inline

square of frobenius norm, need for block recursion

◆ identical()

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.

◆ infinity_norm()

template<class K, int n>

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

inline

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

◆ infinity_norm_real()

template<class K, int n>

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

inline

simplified infinity norm (uses Manhattan norm for complex values)

◆ invert()

template<class K, int n>

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

inline

Compute inverse.

◆ M()

template<class K, int n>

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

inlinestatic

number of blocks in column direction

◆ mmhv()

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

◆ mmtv()

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

◆ mmv()

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

◆ mtv()

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

◆ 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

◆ N()

template<class K, int n>

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

inlinestatic

number of blocks in row direction

◆ operator!=()

template<class K, int n>

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

inline

incomparison operator

◆ operator*=()

template<class K, int n>

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

inline

vector space multiplication with scalar

◆ operator+=() [1/2]

template<class K, int n>

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

inline

vector space addition

◆ operator+=() [2/2]

template<class K, int n>

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

inline

vector space multiplication with scalar

◆ operator-=() [1/2]

template<class K, int n>

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

inline

vector space subtraction

◆ operator-=() [2/2]

template<class K, int n>

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

inline

vector space division by scalar

◆ operator/=()

template<class K, int n>

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

inline

vector space division by scalar

◆ operator=() [1/2]

template<class K, int n>

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

inline

Assignment from a scalar.

◆ operator=() [2/2]

template<class K, int n>

template<class OtherK >

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

inline

Converting assignment operator.

◆ operator==()

template<class K, int n>

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

inline

comparison operator

◆ operator[]() [1/2]

template<class K, int n>

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

inline

Return reference object as row replacement.

◆ operator[]() [2/2]

template<class K, int n>

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

inline

Return const_reference object as row replacement.

◆ size()

template<class K, int n>

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

inlinestatic

◆ solve()

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.

◆ transposed()

template<class K, int n>

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

inline

Return transposed of the matrix as DiagonalMatrix.

◆ umhv()

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

◆ umtv()

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

◆ umv()

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

◆ usmhv()

template<class K, int n>

template<class X , class Y >

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

inline

y += alpha A^H x

◆ usmtv()

template<class K, int n>

template<class X , class Y >

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

inline

y += alpha A^T x

◆ usmv()

template<class K, int n>

template<class X , class Y >

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

inline

y += alpha A x

Friends And Related Function Documentation

◆ DiagonalMatrix

template<class K, int n>

template<class , int >

friend class DiagonalMatrix

friend

◆ operator* [1/2]

template<class K, int n>

template<class OtherScalar >

auto operator*	(	const DiagonalMatrix< K, n > &	matrixA,
		const DiagonalMatrix< OtherScalar, n > &	matrixB
	)

friend

Matrix-matrix multiplication.

◆ operator* [2/2]

template<class K, int n>

template<class OtherMatrix , std::enable_if_t<(Impl::IsDenseMatrix< OtherMatrix >::value), int > = 0, std::enable_if_t<(not Impl::IsFieldMatrix< OtherMatrix >::value), int > = 0>

auto operator*	(	const DiagonalMatrix< K, n > &	matrixA,
		const OtherMatrix &	matrixB
	)

friend

Multiply a diagonal matrix with a dense matrix.

The result of this multiplication is either a FieldMatrix if the matrixB is a matrix with static size, or a DynamicMatrix. This overload is deactivated for matrixB being a FieldMatrix since this is already covered by the corresponding overload of the operator* in the FieldMatrix class.

◆ operator<<

template<class K, int n>

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

friend

Sends the matrix to an output stream.

Member Data Documentation

◆ blocklevel

template<class K, int n>

constexpr int Dune::DiagonalMatrix< K, n >::blocklevel = 1

static

The number of block levels we contain. This is the leaf, that is, 1.

◆ cols

template<class K, int n>

constexpr int Dune::DiagonalMatrix< K, n >::cols = n

static

The number of columns.

◆ rows

template<class K, int n>

constexpr int Dune::DiagonalMatrix< K, n >::rows = n

static

The number of rows.

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

diagonalmatrix.hh

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Friends

Detailed Description

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

Member Typedef Documentation

◆ block_type

◆ ColIterator

◆ const_iterator

◆ const_reference

◆ const_row_reference

◆ const_row_type

◆ ConstColIterator

◆ ConstIterator

◆ ConstRowIterator

◆ field_type

◆ Iterator

◆ iterator

◆ reference

◆ row_reference

◆ row_type

◆ RowIterator

◆ size_type

◆ value_type

Constructor & Destructor Documentation

◆ DiagonalMatrix() [1/5]

◆ DiagonalMatrix() [2/5]

◆ DiagonalMatrix() [3/5]

◆ DiagonalMatrix() [4/5]

◆ DiagonalMatrix() [5/5]

Member Function Documentation

◆ beforeBegin() [1/2]

◆ beforeBegin() [2/2]

◆ beforeEnd() [1/2]

◆ beforeEnd() [2/2]

◆ begin() [1/2]

◆ begin() [2/2]

◆ determinant()

◆ diagonal() [1/4]

◆ diagonal() [2/4]

◆ diagonal() [3/4]

◆ diagonal() [4/4]

◆ end() [1/2]

◆ end() [2/2]

◆ exists()

◆ frobenius_norm()

◆ frobenius_norm2()

◆ identical()

◆ infinity_norm()

◆ infinity_norm_real()

◆ invert()

◆ M()

◆ mmhv()

◆ mmtv()

◆ mmv()

◆ mtv()

◆ mv()

◆ N()

◆ operator!=()

◆ operator*=()

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator/=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ size()

◆ solve()

◆ transposed()

◆ umhv()

◆ umtv()

◆ umv()

◆ usmhv()

◆ usmtv()

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