Dune::DenseMatrix< M > Class Template Reference

A dense n x m matrix. More...

#include <dune/common/densematrix.hh>

Inheritance diagram for Dune::DenseMatrix< M >:

Public Types
enum	{ blocklevel = 1 }
	We are at the leaf of the block recursion. More...
typedef Traits::derived_type	derived_type
	type of derived matrix class More...
typedef Traits::value_type	value_type
	export the type representing the field More...
typedef Traits::value_type	field_type
	export the type representing the field More...
typedef Traits::value_type	block_type
	export the type representing the components More...
typedef Traits::size_type	size_type
	The type used for the index access and size operation. More...
typedef Traits::row_type	row_type
	The type used to represent a row (must fulfill the Dune::DenseVector interface) More...
typedef Traits::row_reference	row_reference
	The type used to represent a reference to a row (usually row_type &) More...
typedef Traits::const_row_reference	const_row_reference
	The type used to represent a reference to a constant row (usually const row_type &) More...
typedef DenseIterator < DenseMatrix, row_type >	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 DenseIterator< const DenseMatrix, const row_type >	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 row_type::ConstIterator	ConstColIterator
	rename the iterators for easier access More...

Public Member Functions
row_reference	operator[] (size_type i)
	random access More...
const_row_reference	operator[] (size_type i) const
size_type	size () const
	size method (number of rows) 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
template<class RHS >
DenseMatrix &	operator= (const RHS &rhs)
template<class Other >
DenseMatrix &	operator+= (const DenseMatrix< Other > &y)
	vector space addition More...
template<class Other >
DenseMatrix &	operator-= (const DenseMatrix< Other > &y)
	vector space subtraction More...
DenseMatrix &	operator*= (const field_type &k)
	vector space multiplication with scalar More...
DenseMatrix &	operator/= (const field_type &k)
	vector space division by scalar More...
template<class Other >
DenseMatrix &	axpy (const field_type &k, const DenseMatrix< Other > &y)
	vector space axpy operation (*this += k y) More...
template<class Other >
bool	operator== (const DenseMatrix< Other > &y) const
	Binary matrix comparison. More...
template<class Other >
bool	operator!= (const DenseMatrix< Other > &y) const
	Binary matrix incomparison. 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 field_type &alpha, const X &x, Y &y) const
	y += alpha A x More...
template<class X , class Y >
void	usmtv (const field_type &alpha, const X &x, Y &y) const
	y += alpha A^T x More...
template<class X , class Y >
void	usmhv (const field_type &alpha, const X &x, Y &y) const
	y += alpha A^H x More...
FieldTraits< value_type > ::real_type	frobenius_norm () const
	frobenius norm: sqrt(sum over squared values of entries) More...
FieldTraits< value_type > ::real_type	frobenius_norm2 () const
	square of frobenius norm, need for block recursion More...
FieldTraits< value_type > ::real_type	infinity_norm () const
	infinity norm (row sum norm, how to generalize for blocks?) More...
FieldTraits< value_type > ::real_type	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...
field_type	determinant () const
	calculates the determinant of this matrix More...
template<typename M2 >
MAT &	leftmultiply (const DenseMatrix< M2 > &M)
	Multiplies M from the left to this matrix. More...
template<typename M2 >
MAT &	rightmultiply (const DenseMatrix< M2 > &M)
	Multiplies M from the right to this matrix. More...
size_type	N () const
	number of rows More...
size_type	M () const
	number of columns More...
size_type	rows () const
	number of rows More...
size_type	cols () const
	number of columns More...
bool	exists (size_type i, size_type j) const
	return true when (i,j) is in pattern More...

Detailed Description

template<typename M>
class Dune::DenseMatrix< M >

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.

Template Parameters

MAT	type of the matrix implementation

Member Typedef Documentation

template<typename M>

typedef Traits::value_type Dune::DenseMatrix< M >::block_type

export the type representing the components

template<typename M>

typedef row_type::Iterator Dune::DenseMatrix< M >::ColIterator

rename the iterators for easier access

template<typename M>

typedef ConstIterator Dune::DenseMatrix< M >::const_iterator

typedef for stl compliant access

template<typename M>

typedef Traits::const_row_reference Dune::DenseMatrix< M >::const_row_reference

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

template<typename M>

typedef row_type::ConstIterator Dune::DenseMatrix< M >::ConstColIterator

rename the iterators for easier access

template<typename M>

typedef DenseIterator<const DenseMatrix,const row_type> Dune::DenseMatrix< M >::ConstIterator

Iterator class for sequential access.

template<typename M>

typedef ConstIterator Dune::DenseMatrix< M >::ConstRowIterator

rename the iterators for easier access

template<typename M>

typedef Traits::derived_type Dune::DenseMatrix< M >::derived_type

type of derived matrix class

template<typename M>

typedef Traits::value_type Dune::DenseMatrix< M >::field_type

export the type representing the field

template<typename M>

typedef DenseIterator<DenseMatrix,row_type> Dune::DenseMatrix< M >::Iterator

Iterator class for sequential access.

template<typename M>

typedef Iterator Dune::DenseMatrix< M >::iterator

typedef for stl compliant access

template<typename M>

typedef Traits::row_reference Dune::DenseMatrix< M >::row_reference

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

template<typename M>

typedef Traits::row_type Dune::DenseMatrix< M >::row_type

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

template<typename M>

typedef Iterator Dune::DenseMatrix< M >::RowIterator

rename the iterators for easier access

template<typename M>

typedef Traits::size_type Dune::DenseMatrix< M >::size_type

The type used for the index access and size operation.

template<typename M>

typedef Traits::value_type Dune::DenseMatrix< M >::value_type

export the type representing the field

Member Enumeration Documentation

template<typename M>

anonymous enum

We are at the leaf of the block recursion.

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

Member Function Documentation

template<typename M>

template<class Other >

DenseMatrix& Dune::DenseMatrix< M >::axpy ( const field_type &  k, const DenseMatrix< Other > &  y  )

inline

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

Referenced by Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::axpy().

template<typename M>

Iterator Dune::DenseMatrix< M >::beforeBegin ( )

inline

Returns

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

template<typename M>

ConstIterator Dune::DenseMatrix< M >::beforeBegin ( ) const

inline

Returns

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

template<typename M>

Iterator Dune::DenseMatrix< M >::beforeEnd ( )

inline

Returns

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

template<typename M>

ConstIterator Dune::DenseMatrix< M >::beforeEnd ( ) const

inline

Returns

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

template<typename M>

Iterator Dune::DenseMatrix< M >::begin ( )

inline

begin iterator

Referenced by Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::infinity_norm(), and Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::infinity_norm_real().

template<typename M>

ConstIterator Dune::DenseMatrix< M >::begin ( ) const

inline

begin iterator

template<typename M>

size_type Dune::DenseMatrix< M >::cols ( ) const

inline

number of columns

Referenced by Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::exists(), Dune::istl_assign_to_fmatrix(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::leftmultiply(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::M(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::mmhv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::mmtv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::mmv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::mtv(), Dune::DenseMatrixHelp::multAssign(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::mv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::rightmultiply(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::umhv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::umtv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::umv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::usmhv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::usmtv(), and Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::usmv().

template<typename M>

field_type Dune::DenseMatrix< M >::determinant

(

)

const

calculates the determinant of this matrix

template<typename M>

Iterator Dune::DenseMatrix< M >::end ( )

inline

end iterator

Referenced by Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::infinity_norm(), and Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::infinity_norm_real().

template<typename M>

ConstIterator Dune::DenseMatrix< M >::end ( ) const

inline

end iterator

template<typename M>

bool Dune::DenseMatrix< M >::exists ( size_type  i, size_type  j  ) const

inline

return true when (i,j) is in pattern

template<typename M>

FieldTraits<value_type>::real_type Dune::DenseMatrix< M >::frobenius_norm ( ) const

inline

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

template<typename M>

FieldTraits<value_type>::real_type Dune::DenseMatrix< M >::frobenius_norm2 ( ) const

inline

square of frobenius norm, need for block recursion

template<typename M>

FieldTraits<value_type>::real_type Dune::DenseMatrix< M >::infinity_norm ( ) const

inline

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

template<typename M>

FieldTraits<value_type>::real_type Dune::DenseMatrix< M >::infinity_norm_real ( ) const

inline

simplified infinity norm (uses Manhattan norm for complex values)

template<typename M>

void Dune::DenseMatrix< M >::invert

(

)

Compute inverse.

Exceptions

FMatrixError

if the matrix is singular

template<typename M>

template<typename M2 >

MAT& Dune::DenseMatrix< M >::leftmultiply ( const DenseMatrix< M2 > &  M )

inline

Multiplies M from the left to this matrix.

template<typename M>

size_type Dune::DenseMatrix< M >::M ( ) const

inline

number of columns

Referenced by Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::mmhv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::mmtv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::mmv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::mtv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::mv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::umhv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::umtv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::umv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::usmhv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::usmtv(), and Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::usmv().

template<typename M>

template<class X , class Y >

void Dune::DenseMatrix< M >::mmhv ( const X &  x, Y &  y  ) const

inline

y -= A^H x

template<typename M>

template<class X , class Y >

void Dune::DenseMatrix< M >::mmtv ( const X &  x, Y &  y  ) const

inline

y -= A^T x

template<typename M>

template<class X , class Y >

void Dune::DenseMatrix< M >::mmv ( const X &  x, Y &  y  ) const

inline

y -= A x

template<typename M>

template<class X , class Y >

void Dune::DenseMatrix< M >::mtv ( const X &  x, Y &  y  ) const

inline

y = A^T x

template<typename M>

template<class X , class Y >

void Dune::DenseMatrix< M >::mv ( const X &  x, Y &  y  ) const

inline

y = A x

template<typename M>

size_type Dune::DenseMatrix< M >::N ( ) const

inline

number of rows

Referenced by Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::mmhv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::mmtv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::mmv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::mtv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::mv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::umhv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::umtv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::umv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::usmhv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::usmtv(), and Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::usmv().

template<typename M>

template<class Other >

bool Dune::DenseMatrix< M >::operator!= ( const DenseMatrix< Other > &  y ) const

inline

Binary matrix incomparison.

template<typename M>

DenseMatrix& Dune::DenseMatrix< M >::operator*= ( const field_type &  k )

inline

vector space multiplication with scalar

template<typename M>

template<class Other >

DenseMatrix& Dune::DenseMatrix< M >::operator+= ( const DenseMatrix< Other > &  y )

inline

vector space addition

template<typename M>

template<class Other >

DenseMatrix& Dune::DenseMatrix< M >::operator-= ( const DenseMatrix< Other > &  y )

inline

vector space subtraction

template<typename M>

DenseMatrix& Dune::DenseMatrix< M >::operator/= ( const field_type &  k )

inline

vector space division by scalar

template<typename M>

template<class RHS >

DenseMatrix& Dune::DenseMatrix< M >::operator= ( const RHS &  rhs )

inline

template<typename M>

template<class Other >

bool Dune::DenseMatrix< M >::operator== ( const DenseMatrix< Other > &  y ) const

inline

Binary matrix comparison.

Referenced by Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::operator!=().

template<typename M>

row_reference Dune::DenseMatrix< M >::operator[] ( size_type  i )

inline

random access

template<typename M>

const_row_reference Dune::DenseMatrix< M >::operator[] ( size_type  i ) const

inline

template<typename M>

template<typename M2 >

MAT& Dune::DenseMatrix< M >::rightmultiply ( const DenseMatrix< M2 > &  M )

inline

Multiplies M from the right to this matrix.

template<typename M>

size_type Dune::DenseMatrix< M >::rows ( ) const

inline

number of rows

Referenced by Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::axpy(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::beforeEnd(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::end(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::exists(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::frobenius_norm(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::frobenius_norm2(), Dune::istl_assign_to_fmatrix(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::leftmultiply(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::mmhv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::mmtv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::mmv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::mtv(), Dune::DenseMatrixHelp::multAssign(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::mv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::N(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::operator*=(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::operator+=(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::operator-=(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::operator/=(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::operator==(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::rightmultiply(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::size(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::umhv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::umtv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::umv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::usmhv(), Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::usmtv(), and Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::usmv().

template<typename M>

size_type Dune::DenseMatrix< M >::size ( ) const

inline

size method (number of rows)

Referenced by Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::infinity_norm(), and Dune::DenseMatrix< FieldMatrix< T, ROWS, COLS > >::infinity_norm_real().

template<typename M>

template<class V >

void Dune::DenseMatrix< M >::solve	(	V &	x,
		const V &	b
	)		const

Solve system A x = b.

Exceptions

FMatrixError

if the matrix is singular

template<typename M>

template<class X , class Y >

void Dune::DenseMatrix< M >::umhv ( const X &  x, Y &  y  ) const

inline

y += A^H x

template<typename M>

template<class X , class Y >

void Dune::DenseMatrix< M >::umtv ( const X &  x, Y &  y  ) const

inline

y += A^T x

template<typename M>

template<class X , class Y >

void Dune::DenseMatrix< M >::umv ( const X &  x, Y &  y  ) const

inline

y += A x

template<typename M>

template<class X , class Y >

void Dune::DenseMatrix< M >::usmhv ( const field_type &  alpha, const X &  x, Y &  y  ) const

inline

y += alpha A^H x

template<typename M>

template<class X , class Y >

void Dune::DenseMatrix< M >::usmtv ( const field_type &  alpha, const X &  x, Y &  y  ) const

inline

y += alpha A^T x

template<typename M>

template<class X , class Y >

void Dune::DenseMatrix< M >::usmv ( const field_type &  alpha, const X &  x, Y &  y  ) const

inline

y += alpha A x

---

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

• densematrix.hh