A dense n x m matrix. More...

#include <dune/common/fmatrix.hh>

Inheritance diagram for Dune::FieldMatrix< K, ROWS, COLS >:

Public Types
enum	{ rows = ROWS, cols = COLS }
	export size More...
typedef Base::size_type	size_type
	The type used for the index access and size operation.
typedef Base::row_type	row_type
	The type used to represent a row (must fulfill the Dune::DenseVector interface)
typedef Base::row_reference	row_reference
	The type used to represent a reference to a row (usually row_type &)
typedef Base::const_row_reference	const_row_reference
	The type used to represent a reference to a constant row (usually const row_type &)
enum
	We are at the leaf of the block recursion. More...
typedef Traits::derived_type	derived_type
	type of derived matrix class
typedef Traits::value_type	value_type
	export the type representing the field
typedef Traits::value_type	field_type
	export the type representing the field
typedef Traits::value_type	block_type
	export the type representing the components
typedef DenseIterator < DenseMatrix, row_type >	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 DenseIterator< const DenseMatrix, const row_type >	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 row_type::ConstIterator	ConstColIterator
	rename the iterators for easier access

Public Member Functions
	FieldMatrix ()
	Default constructor.
	FieldMatrix (const K &k)
	Constructor initializing the whole matrix with a scalar.
template<typename T >
	FieldMatrix (const T &t)
template<int l>
FieldMatrix< K, l, cols >	leftmultiplyany (const FieldMatrix< K, l, rows > &M) const
	Multiplies M from the left to this matrix, this matrix is not modified.
FieldMatrix &	rightmultiply (const FieldMatrix< K, cols, cols > &M)
	Multiplies M from the right to this matrix.
template<int l>
FieldMatrix< K, rows, l >	rightmultiplyany (const FieldMatrix< K, cols, l > &M) const
	Multiplies M from the right to this matrix, this matrix is not modified.
size_type	mat_rows () const
size_type	mat_cols () const
row_reference	mat_access (size_type i)
const_row_reference	mat_access (size_type i) const
row_reference	operator[] (size_type i)
	random access
const_row_reference	operator[] (size_type i) const
size_type	size () const
	size method (number of rows)
Iterator	begin ()
	begin iterator
ConstIterator	begin () const
	begin iterator
Iterator	end ()
	end iterator
ConstIterator	end () const
	end iterator
Iterator	beforeEnd ()
ConstIterator	beforeEnd () const
Iterator	beforeBegin ()
ConstIterator	beforeBegin () const
DenseMatrix &	operator+= (const DenseMatrix< Other > &y)
	vector space addition
DenseMatrix &	operator-= (const DenseMatrix< Other > &y)
	vector space subtraction
DenseMatrix &	operator*= (const field_type &k)
	vector space multiplication with scalar
DenseMatrix &	operator/= (const field_type &k)
	vector space division by scalar
DenseMatrix &	axpy (const field_type &k, const DenseMatrix< Other > &y)
	vector space axpy operation (*this += k y)
bool	operator== (const DenseMatrix< Other > &y) const
	Binary matrix comparison.
bool	operator!= (const DenseMatrix< Other > &y) const
	Binary matrix incomparison.
void	mv (const X &x, Y &y) const
	y = A x
void	mtv (const X &x, Y &y) const
	y = A^T x
void	umv (const X &x, Y &y) const
	y += A x
void	umtv (const X &x, Y &y) const
	y += A^T x
void	umhv (const X &x, Y &y) const
	y += A^H x
void	mmv (const X &x, Y &y) const
	y -= A x
void	mmtv (const X &x, Y &y) const
	y -= A^T x
void	mmhv (const X &x, Y &y) const
	y -= A^H x
void	usmv (const field_type &alpha, const X &x, Y &y) const
	y += alpha A x
void	usmtv (const field_type &alpha, const X &x, Y &y) const
	y += alpha A^T x
void	usmhv (const field_type &alpha, const X &x, Y &y) const
	y += alpha A^H x
FieldTraits< value_type > ::real_type	frobenius_norm () const
	frobenius norm: sqrt(sum over squared values of entries)
FieldTraits< value_type > ::real_type	frobenius_norm2 () const
	square of frobenius norm, need for block recursion
FieldTraits< value_type > ::real_type	infinity_norm () const
	infinity norm (row sum norm, how to generalize for blocks?)
FieldTraits< value_type > ::real_type	infinity_norm_real () const
	simplified infinity norm (uses Manhattan norm for complex values)
void	solve (V &x, const V &b) const
	Solve system A x = b.
void	invert ()
	Compute inverse.
field_type	determinant () const
	calculates the determinant of this matrix
FieldMatrix< K, ROWS, COLS > &	leftmultiply (const DenseMatrix< M2 > &M)
	Multiplies M from the left to this matrix.
FieldMatrix< K, ROWS, COLS > &	rightmultiply (const DenseMatrix< M2 > &M)
	Multiplies M from the right to this matrix.
size_type	N () const
	number of rows
size_type	M () const
	number of columns
size_type	rows () const
	number of rows
size_type	cols () const
	number of columns
bool	exists (size_type i, size_type j) const
	return true when (i,j) is in pattern

Detailed Description

template<class K, int ROWS, int COLS>
class Dune::FieldMatrix< K, ROWS, COLS >

A dense n x m matrix.

Matrices represent linear maps from a vector space V to a vector space W. This class represents such a linear map by storing a two-dimensional array of numbers of a given field type K. The number of rows and columns is given at compile time.

Member Typedef Documentation

typedef Traits::value_type Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::block_type

inherited

export the type representing the components

typedef row_type::Iterator Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::ColIterator

inherited

rename the iterators for easier access

typedef ConstIterator Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::const_iterator

inherited

typedef for stl compliant access

template<class K, int ROWS, int COLS>

typedef Base::const_row_reference Dune::FieldMatrix< K, ROWS, COLS >::const_row_reference

The type used to represent a reference to a constant row (usually const row_type &)

Reimplemented from Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >.

typedef row_type::ConstIterator Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::ConstColIterator

inherited

rename the iterators for easier access

typedef DenseIterator<const DenseMatrix,const row_type> Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::ConstIterator

inherited

Iterator class for sequential access.

typedef ConstIterator Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::ConstRowIterator

inherited

rename the iterators for easier access

typedef Traits::derived_type Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::derived_type

inherited

type of derived matrix class

typedef Traits::value_type Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::field_type

inherited

export the type representing the field

typedef DenseIterator<DenseMatrix,row_type> Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::Iterator

inherited

Iterator class for sequential access.

typedef Iterator Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::iterator

inherited

typedef for stl compliant access

template<class K, int ROWS, int COLS>

typedef Base::row_reference Dune::FieldMatrix< K, ROWS, COLS >::row_reference

The type used to represent a reference to a row (usually row_type &)

Reimplemented from Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >.

template<class K, int ROWS, int COLS>

typedef Base::row_type Dune::FieldMatrix< K, ROWS, COLS >::row_type

The type used to represent a row (must fulfill the Dune::DenseVector interface)

Reimplemented from Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >.

typedef Iterator Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::RowIterator

inherited

rename the iterators for easier access

template<class K, int ROWS, int COLS>

typedef Base::size_type Dune::FieldMatrix< K, ROWS, COLS >::size_type

The type used for the index access and size operation.

Reimplemented from Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >.

typedef Traits::value_type Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::value_type

inherited

export the type representing the field

Member Enumeration Documentation

template<class K, int ROWS, int COLS>

anonymous enum

export size

Enumerator:

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

anonymous enum

inherited

We are at the leaf of the block recursion.

Constructor & Destructor Documentation

template<class K, int ROWS, int COLS>

Dune::FieldMatrix< K, ROWS, COLS >::FieldMatrix ( )

inline

Default constructor.

template<class K, int ROWS, int COLS>

Dune::FieldMatrix< K, ROWS, COLS >::FieldMatrix ( const K & k )

inlineexplicit

Constructor initializing the whole matrix with a scalar.

template<class K, int ROWS, int COLS>

template<typename T >

Dune::FieldMatrix< K, ROWS, COLS >::FieldMatrix ( const T & t )

inlineexplicit

Member Function Documentation

DenseMatrix& Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::axpy	(	const field_type &	k,
		const DenseMatrix< Other > &	y
	)

inlineinherited

vector space axpy operation (*this += k y)

Iterator Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::beforeBegin ( )

inlineinherited

Returns:: an iterator that is positioned before the first entry of the vector.

ConstIterator Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::beforeBegin ( ) const

inlineinherited

Returns:: an iterator that is positioned before the first entry of the vector.

Iterator Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::beforeEnd ( )

inlineinherited

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

ConstIterator Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::beforeEnd ( ) const

inlineinherited

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

Iterator Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::begin ( )

inlineinherited

begin iterator

ConstIterator Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::begin ( ) const

inlineinherited

begin iterator

size_type Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::cols ( ) const

inlineinherited

number of columns

Referenced by Dune::FieldMatrix< T, n, m >::leftmultiplyany(), Dune::FieldMatrix< T, n, m >::rightmultiply(), and Dune::FieldMatrix< T, n, m >::rightmultiplyany().

field_type Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::determinant ( ) const

inherited

calculates the determinant of this matrix

Iterator Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::end ( )

inlineinherited

end iterator

ConstIterator Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::end ( ) const

inlineinherited

end iterator

bool Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::exists	(	size_type	i,
		size_type	j
	)		const

inlineinherited

return true when (i,j) is in pattern

FieldTraits<value_type>::real_type Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::frobenius_norm ( ) const

inlineinherited

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

FieldTraits<value_type>::real_type Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::frobenius_norm2 ( ) const

inlineinherited

square of frobenius norm, need for block recursion

FieldTraits<value_type>::real_type Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::infinity_norm ( ) const

inlineinherited

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

FieldTraits<value_type>::real_type Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::infinity_norm_real ( ) const

inlineinherited

simplified infinity norm (uses Manhattan norm for complex values)

void Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::invert ( )

inherited

Compute inverse.

Exceptions:

FMatrixError if the matrix is singular

FieldMatrix< K, ROWS, COLS > & Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::leftmultiply ( const DenseMatrix< M2 > & M )

inlineinherited

Multiplies M from the left to this matrix.

template<class K, int ROWS, int COLS>

template<int l>

FieldMatrix<K,l,cols> Dune::FieldMatrix< K, ROWS, COLS >::leftmultiplyany ( const FieldMatrix< K, l, rows > & M ) const

inline

Multiplies M from the left to this matrix, this matrix is not modified.

size_type Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::M ( ) const

inlineinherited

number of columns

template<class K, int ROWS, int COLS>

row_reference Dune::FieldMatrix< K, ROWS, COLS >::mat_access ( size_type i )

inline

template<class K, int ROWS, int COLS>

const_row_reference Dune::FieldMatrix< K, ROWS, COLS >::mat_access ( size_type i ) const

inline

template<class K, int ROWS, int COLS>

size_type Dune::FieldMatrix< K, ROWS, COLS >::mat_cols ( ) const

inline

template<class K, int ROWS, int COLS>

size_type Dune::FieldMatrix< K, ROWS, COLS >::mat_rows ( ) const

inline

void Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::mmhv	(	const X &	x,
		Y &	y
	)		const

inlineinherited

y -= A^H x

void Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::mmtv	(	const X &	x,
		Y &	y
	)		const

inlineinherited

y -= A^T x

void Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::mmv	(	const X &	x,
		Y &	y
	)		const

inlineinherited

y -= A x

void Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::mtv	(	const X &	x,
		Y &	y
	)		const

inlineinherited

y = A^T x

void Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::mv	(	const X &	x,
		Y &	y
	)		const

inlineinherited

y = A x

size_type Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::N ( ) const

inlineinherited

number of rows

bool Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::operator!= ( const DenseMatrix< Other > & y ) const

inlineinherited

Binary matrix incomparison.

DenseMatrix& Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::operator*= ( const field_type & k )

inlineinherited

vector space multiplication with scalar

DenseMatrix& Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::operator+= ( const DenseMatrix< Other > & y )

inlineinherited

vector space addition

DenseMatrix& Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::operator-= ( const DenseMatrix< Other > & y )

inlineinherited

vector space subtraction

DenseMatrix& Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::operator/= ( const field_type & k )

inlineinherited

vector space division by scalar

bool Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::operator== ( const DenseMatrix< Other > & y ) const

inlineinherited

Binary matrix comparison.

row_reference Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::operator[] ( size_type i )

inlineinherited

random access

const_row_reference Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::operator[] ( size_type i ) const

inlineinherited

template<class K, int ROWS, int COLS>

FieldMatrix& Dune::FieldMatrix< K, ROWS, COLS >::rightmultiply ( const FieldMatrix< K, cols, cols > & M )

inline

Multiplies M from the right to this matrix.

FieldMatrix< K, ROWS, COLS > & Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::rightmultiply ( const DenseMatrix< M2 > & M )

inlineinherited

Multiplies M from the right to this matrix.

template<class K, int ROWS, int COLS>

template<int l>

FieldMatrix<K,rows,l> Dune::FieldMatrix< K, ROWS, COLS >::rightmultiplyany ( const FieldMatrix< K, cols, l > & M ) const

inline

Multiplies M from the right to this matrix, this matrix is not modified.

size_type Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::rows ( ) const

inlineinherited

number of rows

Referenced by Dune::FieldMatrix< T, n, m >::FieldMatrix(), Dune::FieldMatrix< T, n, m >::leftmultiplyany(), Dune::FieldMatrix< T, n, m >::rightmultiply(), and Dune::FieldMatrix< T, n, m >::rightmultiplyany().

size_type Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::size ( ) const

inlineinherited

size method (number of rows)

void Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::solve	(	V &	x,
		const V &	b
	)		const

inherited

Solve system A x = b.

Exceptions:

FMatrixError if the matrix is singular

void Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::umhv	(	const X &	x,
		Y &	y
	)		const

inlineinherited

y += A^H x

void Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::umtv	(	const X &	x,
		Y &	y
	)		const

inlineinherited

y += A^T x

void Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::umv	(	const X &	x,
		Y &	y
	)		const

inlineinherited

y += A x

void Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::usmhv	(	const field_type &	alpha,
		const X &	x,
		Y &	y
	)		const

inlineinherited

y += alpha A^H x

void Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::usmtv	(	const field_type &	alpha,
		const X &	x,
		Y &	y
	)		const

inlineinherited

y += alpha A^T x

void Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::usmv	(	const field_type &	alpha,
		const X &	x,
		Y &	y
	)		const

inlineinherited

y += alpha A x

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

fmatrix.hh

Public Types

Public Member Functions

Detailed Description

template<class K, int ROWS, int COLS> class Dune::FieldMatrix< K, ROWS, COLS >

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

template<class K, int ROWS, int COLS>
class Dune::FieldMatrix< K, ROWS, COLS >