A multiple of the identity matrix of static size. More...

#include <dune/istl/scaledidmatrix.hh>

Public Types
typedef K	field_type
	The type representing numbers.

typedef K	block_type
	The type representing matrix entries (which may be matrices themselves)

typedef std::size_t	size_type
	The type used for the indices and sizes.

typedef DiagonalRowVector< K, n >	row_type
	Type of a single matrix row.

typedef row_type	reference

typedef DiagonalRowVectorConst< K, n >	const_row_type
	Const type of a single row.

typedef const_row_type	const_reference

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

typedef Iterator	iterator
	typedef for stl compliant access

typedef Iterator	RowIterator
	rename the iterators for easier access

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

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

typedef ConstIterator	const_iterator
	typedef for stl compliant access

typedef ConstIterator	ConstRowIterator
	rename the iterators for easier access

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

Public Member Functions
	ScaledIdentityMatrix ()
	Default constructor.

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

ScaledIdentityMatrix &	operator= (const K &k)
	Assignment from scalar.

bool	identical (const ScaledIdentityMatrix< K, n > &other) const
	Check if matrix is identical to other matrix.

Iterator	begin ()
	begin iterator

Iterator	end ()
	end iterator

Iterator	beforeEnd ()

Iterator	beforeBegin ()

ConstIterator	begin () const
	begin iterator

ConstIterator	end () const
	end iterator

ConstIterator	beforeEnd () const

ConstIterator	beforeBegin () const

bool	operator== (const ScaledIdentityMatrix &other) const
	Test for equality.

bool	operator!= (const ScaledIdentityMatrix &other) const
	Test for inequality.

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

void	invert ()
	Compute inverse.

K	determinant () const
	Calculates the determinant of this matrix.

size_type	N () const
	number of blocks in row direction

size_type	M () const
	number of blocks in column direction

bool	exists (size_type i, size_type j) const
	Return true if (i,j) is in the matrix pattern, i.e., if i==j.

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

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

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

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

const K &	scalar () const
	Get const reference to the scalar diagonal value.

K &	scalar ()
	Get reference to the scalar diagonal value.

Matrix-vector products
template<class X , class Y >
void	mv (const X &x, Y &y) const
	y = A x

template<class X , class Y >
void	mtv (const X &x, Y &y) const
	y = A^T x

template<class X , class Y >
void	umv (const X &x, Y &y) const
	y += A x

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

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

template<class X , class Y >
void	mmv (const X &x, Y &y) const
	y -= A x

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

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

template<class X , class Y >
void	usmv (const K &alpha, const X &x, Y &y) const
	y += alpha A x

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

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

Norms
FieldTraits< field_type >::real_type	frobenius_norm () const
	The Frobenius norm.

FieldTraits< field_type >::real_type	frobenius_norm2 () const
	The square of the Frobenius norm.

FieldTraits< field_type >::real_type	infinity_norm () const
	The row sum norm.

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

Static Public Attributes
static constexpr std::integral_constant< size_type, n >	rows = {}
	The number of matrix rows.

static constexpr std::integral_constant< size_type, n >	cols = {}
	The number of matrix columns.

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

Vector space arithmetic
ScaledIdentityMatrix &	operator+= (const ScaledIdentityMatrix &y)
	Vector space addition.

ScaledIdentityMatrix &	operator-= (const ScaledIdentityMatrix &y)
	Vector space subtraction.

ScaledIdentityMatrix &	operator+= (const K &k)
	Addition of a scalar to the diagonal.

ScaledIdentityMatrix &	operator-= (const K &k)
	Subtraction of a scalar from the diagonal.

ScaledIdentityMatrix &	operator*= (const K &k)
	Vector space multiplication with scalar.

ScaledIdentityMatrix &	operator/= (const K &k)
	Vector space division by scalar.

template<class Scalar , std::enable_if_t< IsNumber< Scalar >::value, int > = 0>
auto	operator* (const ScaledIdentityMatrix &matrix, Scalar scalar)
	Vector space multiplication with scalar.

template<class Scalar , std::enable_if_t< IsNumber< Scalar >::value, int > = 0>
auto	operator* (Scalar scalar, const ScaledIdentityMatrix &matrix)
	Vector space multiplication with scalar.

template<class OtherScalar > requires requires(K k, OtherScalar otherScalar) { k + otherScalar; }
auto &	operator+= (FieldMatrix< OtherScalar, n, n > &fieldMatrix, const ScaledIdentityMatrix &matrix)
	Addition of ScaledIdentityMatrix to FieldMatrix.

template<class OtherScalar > requires requires(K k, OtherScalar otherScalar) { k + otherScalar; }
auto	operator+ (const FieldMatrix< OtherScalar, n, n > &fieldMatrix, const ScaledIdentityMatrix &matrix)
	Addition of ScaledIdentityMatrix to FieldMatrix.

template<class OtherScalar > requires requires(K k, OtherScalar otherScalar) { k + otherScalar; }
auto	operator+ (const ScaledIdentityMatrix &matrix, const FieldMatrix< OtherScalar, n, n > &fieldMatrix)
	Addition of FieldMatrix to ScaledIdentityMatrix.

template<class OtherScalar > requires requires(K k, OtherScalar otherScalar) { k + otherScalar; }
auto	operator+= (DiagonalMatrix< OtherScalar, n > &diagonalMatrix, const ScaledIdentityMatrix &matrix)
	Addition of ScaledIdentityMatrix to DiagonalMatrix.

template<class OtherScalar > requires requires(K k, OtherScalar otherScalar) { k + otherScalar; }
auto	operator+ (const DiagonalMatrix< OtherScalar, n > &diagonalMatrix, const ScaledIdentityMatrix &matrix)
	Addition of ScaledIdentityMatrix to DiagonalMatrix.

template<class OtherScalar > requires requires(K k, OtherScalar otherScalar) { k + otherScalar; }
auto	operator+ (const ScaledIdentityMatrix &matrix, const DiagonalMatrix< OtherScalar, n > &diagonalMatrix)
	Addition of DiagonalMatrix to ScaledIdentityMatrix.

Detailed Description

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

A multiple of the identity matrix of static size.

This class provides all operations specified by the dune-istl matrix API. The implementations exploit the fact that the matrix is a multiple of the identity.

Template Parameters

K	The number used for matrix entries
n	The number of matrix rows and columns

Warning: If m is an object of type ScaledIdentityMatrix, then code like
K entry = m[0][1];

will compile. However, the expression m[0][1] is not guaranteed to return 0. Rather, its behavior is undefined.

Member Typedef Documentation

◆ block_type

template<class K , int n>

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

The type representing matrix entries (which may be matrices themselves)

◆ ColIterator

template<class K , int n>

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

rename the iterators for easier access

◆ const_iterator

template<class K , int n>

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

typedef for stl compliant access

◆ const_reference

template<class K , int n>

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

◆ const_row_type

template<class K , int n>

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

Const type of a single row.

◆ ConstColIterator

template<class K , int n>

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

rename the iterators for easier access

◆ ConstIterator

template<class K , int n>

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

Iterator class for sequential access.

◆ ConstRowIterator

template<class K , int n>

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

rename the iterators for easier access

◆ field_type

template<class K , int n>

typedef K Dune::ScaledIdentityMatrix< K, n >::field_type

The type representing numbers.

◆ Iterator

template<class K , int n>

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

Iterator class for sequential access.

◆ iterator

template<class K , int n>

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

typedef for stl compliant access

◆ reference

template<class K , int n>

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

◆ row_type

template<class K , int n>

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

Type of a single matrix row.

Since the implementation does not store actual rows, this is a proxy type, which tries to behave like an array of matrix entries as much as possible.

Note: The type is really DiagonalRowVector. Implementing a dedicated ScaledIdentityMatrixRowVector would just be a copy of that.

◆ RowIterator

template<class K , int n>

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

rename the iterators for easier access

◆ size_type

template<class K , int n>

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

The type used for the indices and sizes.

Constructor & Destructor Documentation

◆ ScaledIdentityMatrix() [1/2]

template<class K , int n>

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

inline

Default constructor.

◆ ScaledIdentityMatrix() [2/2]

template<class K , int n>

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

inline

Constructor initializing the whole matrix with a scalar.

Member Function Documentation

◆ beforeBegin() [1/2]

template<class K , int n>

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

inline

begin iterator

◆ begin() [2/2]

template<class K , int n>

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

inline

begin iterator

◆ determinant()

template<class K , int n>

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

inline

Calculates the determinant of this matrix.

◆ diagonal() [1/2]

template<class K , int n>

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

inline

Get reference to diagonal entry.

◆ diagonal() [2/2]

template<class K , int n>

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

inline

Get const reference to diagonal entry.

◆ end() [1/2]

template<class K , int n>

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

inline

end iterator

◆ end() [2/2]

template<class K , int n>

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

inline

end iterator

◆ exists()

template<class K , int n>

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

inline

Return true if (i,j) is in the matrix pattern, i.e., if i==j.

◆ frobenius_norm()

template<class K , int n>

FieldTraits< field_type >::real_type Dune::ScaledIdentityMatrix< K, n >::frobenius_norm ( ) const

inline

The Frobenius norm.

◆ frobenius_norm2()

template<class K , int n>

FieldTraits< field_type >::real_type Dune::ScaledIdentityMatrix< K, n >::frobenius_norm2 ( ) const

inline

The square of the Frobenius norm.

◆ identical()

template<class K , int n>

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

inline

Check if matrix is identical to other matrix.

"Identical" means: Not just the same values, but the very same object.

◆ infinity_norm()

template<class K , int n>

FieldTraits< field_type >::real_type Dune::ScaledIdentityMatrix< K, n >::infinity_norm ( ) const

inline

The row sum norm.

For a multiple of the identity matrix, this is simply the absolute value of any diagonal matrix entry.

◆ infinity_norm_real()

template<class K , int n>

FieldTraits< field_type >::real_type Dune::ScaledIdentityMatrix< K, n >::infinity_norm_real ( ) const

inline

simplified infinity norm (uses Manhattan norm for complex values)

◆ invert()

template<class K , int n>

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

inline

Compute inverse.

◆ M()

template<class K , int n>

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

inline

number of blocks in column direction

◆ mmhv()

template<class K , int n>

template<class X , class Y >

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

inline

y = A x

◆ N()

template<class K , int n>

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

inline

number of blocks in row direction

◆ operator!=()

template<class K , int n>

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

inline

Test for inequality.

◆ operator*=()

template<class K , int n>

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

inline

Vector space multiplication with scalar.

◆ operator+=() [1/2]

template<class K , int n>

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

inline

Addition of a scalar to the diagonal.

Warning: This is not the same as adding a scalar to a FieldMatrix!

◆ operator+=() [2/2]

template<class K , int n>

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

inline

Vector space addition.

◆ operator-=() [1/2]

template<class K , int n>

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

inline

Subtraction of a scalar from the diagonal.

Warning: This is not the same as subtracting a scalar from a FieldMatrix!

◆ operator-=() [2/2]

template<class K , int n>

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

inline

Vector space subtraction.

◆ operator/=()

template<class K , int n>

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

inline

Vector space division by scalar.

◆ operator=()

template<class K , int n>

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

inline

Assignment from scalar.

◆ operator==()

template<class K , int n>

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

inline

Test for equality.

◆ operator[]() [1/2]

template<class K , int n>

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

inline

Return reference object as row replacement.

◆ operator[]() [2/2]

template<class K , int n>

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

inline

Return const_reference object as row replacement.

◆ scalar() [1/2]

template<class K , int n>

K & Dune::ScaledIdentityMatrix< K, n >::scalar ( )

inline

Get reference to the scalar diagonal value.

◆ scalar() [2/2]

template<class K , int n>

const K & Dune::ScaledIdentityMatrix< K, n >::scalar ( ) const

inline

Get const reference to the scalar diagonal value.

◆ solve()

template<class K , int n>

template<class V >

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

inline

Solve linear system A x = b.

Template Parameters

V	Vector data type

◆ umhv()

template<class K , int n>

template<class X , class Y >

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

inline

y += alpha A x

Friends And Related Symbol Documentation

◆ operator* [1/2]

template<class K , int n>

template<class Scalar , std::enable_if_t< IsNumber< Scalar >::value, int > = 0>

auto operator*	(	const ScaledIdentityMatrix< K, n > &	matrix,
		Scalar	scalar
	)

friend

Vector space multiplication with scalar.

◆ operator* [2/2]

template<class K , int n>

template<class Scalar , std::enable_if_t< IsNumber< Scalar >::value, int > = 0>

auto operator*	(	Scalar	scalar,
		const ScaledIdentityMatrix< K, n > &	matrix
	)

friend

Vector space multiplication with scalar.