Dune::DenseMatrix< MAT > Class Template Reference

A dense n x m matrix. More...

#include <dune/common/densematrix.hh>

Inherited by Dune::FieldMatrix< T, n, m >.

List of all members.

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
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 Traits::size_type	size_type
	The type used for the index access and size operation.
typedef Traits::row_type	row_type
	The type used to represent a row (must fulfill the Dune::DenseVector interface)
typedef Traits::row_reference	row_reference
	The type used to represent a reference to a row (usually row_type &)
typedef Traits::const_row_reference	const_row_reference
	The type used to represent a reference to a constant row (usually const row_type &)
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
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
Iterator	end ()
	end iterator
Iterator	beforeEnd ()
Iterator	beforeBegin ()
ConstIterator	begin () const
	begin iterator
ConstIterator	end () const
	end iterator
ConstIterator	beforeEnd () const
ConstIterator	beforeBegin () const
DenseMatrix &	operator= (const field_type &f)
template<typename T >
DenseMatrix &	operator= (const T &t)
template<class Other >
DenseMatrix &	operator+= (const DenseMatrix< Other > &y)
	vector space addition
template<class Other >
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
template<class Other >
DenseMatrix &	axpy (const field_type &k, const DenseMatrix< Other > &y)
	vector space axpy operation (*this += k y)
template<class Other >
bool	operator== (const DenseMatrix< Other > &y) const
	Binary matrix comparison.
template<class Other >
bool	operator!= (const DenseMatrix< Other > &y) const
	Binary matrix incomparison.
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 field_type &alpha, const X &x, Y &y) const
	y += alpha A x
template<class X , class Y >
void	usmtv (const field_type &alpha, const X &x, Y &y) const
	y += alpha A^T x
template<class X , class Y >
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)
template<class V >
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
template<typename M2 >
MAT &	leftmultiply (const DenseMatrix< M2 > &M)
	Multiplies M from the left to this matrix.
template<typename M2 >
MAT &	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<typename MAT>
class Dune::DenseMatrix< MAT >

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 MAT>

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

export the type representing the components

template<typename MAT>

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

rename the iterators for easier access

template<typename MAT>

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

typedef for stl compliant access

template<typename MAT>

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

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

Reimplemented in Dune::FieldMatrix< K, ROWS, COLS >, and Dune::FieldMatrix< T, n, m >.

template<typename MAT>

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

rename the iterators for easier access

template<typename MAT>

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

Iterator class for sequential access.

template<typename MAT>

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

rename the iterators for easier access

template<typename MAT>

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

type of derived matrix class

template<typename MAT>

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

export the type representing the field

template<typename MAT>

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

Iterator class for sequential access.

template<typename MAT>

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

typedef for stl compliant access

template<typename MAT>

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

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

Reimplemented in Dune::FieldMatrix< K, ROWS, COLS >, and Dune::FieldMatrix< T, n, m >.

template<typename MAT>

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

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

Reimplemented in Dune::FieldMatrix< K, ROWS, COLS >, Dune::FieldMatrix< T, n, m >, and Dune::DynamicMatrix< K >.

template<typename MAT>

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

rename the iterators for easier access

template<typename MAT>

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

The type used for the index access and size operation.

Reimplemented in Dune::FieldMatrix< K, ROWS, COLS >, Dune::FieldMatrix< T, n, m >, and Dune::DynamicMatrix< K >.

template<typename MAT>

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

export the type representing the field

Reimplemented in Dune::DynamicMatrix< K >.

---

Member Enumeration Documentation

template<typename MAT>

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 MAT>

template<class Other >

DenseMatrix& Dune::DenseMatrix< MAT >::axpy	(	const field_type &	k,
		const DenseMatrix< Other > &	y
	)		[inline]

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

Referenced by Dune::DenseMatrix< DynamicMatrix< K > >::axpy().

template<typename MAT>

Iterator Dune::DenseMatrix< MAT >::beforeBegin

(

)

[inline]

Returns:

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

template<typename MAT>

ConstIterator Dune::DenseMatrix< MAT >::beforeBegin

(

)

const [inline]

Returns:

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

template<typename MAT>

Iterator Dune::DenseMatrix< MAT >::beforeEnd

(

)

[inline]

Returns:

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

template<typename MAT>

ConstIterator Dune::DenseMatrix< MAT >::beforeEnd

(

)

const [inline]

Returns:

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

template<typename MAT>

Iterator Dune::DenseMatrix< MAT >::begin

(

)

[inline]

begin iterator

template<typename MAT>

ConstIterator Dune::DenseMatrix< MAT >::begin

(

)

const [inline]

begin iterator

template<typename MAT>

size_type Dune::DenseMatrix< MAT >::cols

(

)

const [inline]

number of columns

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

template<typename MAT>

field_type Dune::DenseMatrix< MAT >::determinant

(

)

const

calculates the determinant of this matrix

template<typename MAT>

Iterator Dune::DenseMatrix< MAT >::end

(

)

[inline]

end iterator

template<typename MAT>

ConstIterator Dune::DenseMatrix< MAT >::end

(

)

const [inline]

end iterator

template<typename MAT>

bool Dune::DenseMatrix< MAT >::exists	(	size_type	i,
		size_type	j
	)		const [inline]

return true when (i,j) is in pattern

template<typename MAT>

FieldTraits<value_type>::real_type Dune::DenseMatrix< MAT >::frobenius_norm

(

)

const [inline]

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

template<typename MAT>

FieldTraits<value_type>::real_type Dune::DenseMatrix< MAT >::frobenius_norm2

(

)

const [inline]

square of frobenius norm, need for block recursion

template<typename MAT>

FieldTraits<value_type>::real_type Dune::DenseMatrix< MAT >::infinity_norm

(

)

const [inline]

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

template<typename MAT>

FieldTraits<value_type>::real_type Dune::DenseMatrix< MAT >::infinity_norm_real

(

)

const [inline]

simplified infinity norm (uses Manhattan norm for complex values)

template<typename MAT>

void Dune::DenseMatrix< MAT >::invert

(

)

Compute inverse.

Exceptions:

FMatrixError

if the matrix is singular

template<typename MAT>

template<typename M2 >

MAT& Dune::DenseMatrix< MAT >::leftmultiply

(

const DenseMatrix< M2 > &

M

)

[inline]

Multiplies M from the left to this matrix.

template<typename MAT>

size_type Dune::DenseMatrix< MAT >::M

(

)

const [inline]

number of columns

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

template<typename MAT>

template<class X , class Y >

void Dune::DenseMatrix< MAT >::mmhv	(	const X &	x,
		Y &	y
	)		const [inline]

y -= A^H x

template<typename MAT>

template<class X , class Y >

void Dune::DenseMatrix< MAT >::mmtv	(	const X &	x,
		Y &	y
	)		const [inline]

y -= A^T x

template<typename MAT>

template<class X , class Y >

void Dune::DenseMatrix< MAT >::mmv	(	const X &	x,
		Y &	y
	)		const [inline]

y -= A x

template<typename MAT>

template<class X , class Y >

void Dune::DenseMatrix< MAT >::mtv	(	const X &	x,
		Y &	y
	)		const [inline]

y = A^T x

template<typename MAT>

template<class X , class Y >

void Dune::DenseMatrix< MAT >::mv	(	const X &	x,
		Y &	y
	)		const [inline]

y = A x

template<typename MAT>

size_type Dune::DenseMatrix< MAT >::N

(

)

const [inline]

number of rows

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

template<typename MAT>

template<class Other >

bool Dune::DenseMatrix< MAT >::operator!=

(

const DenseMatrix< Other > &

y

)

const [inline]

Binary matrix incomparison.

template<typename MAT>

DenseMatrix& Dune::DenseMatrix< MAT >::operator*=

(

const field_type &

k

)

[inline]

vector space multiplication with scalar

template<typename MAT>

template<class Other >

DenseMatrix& Dune::DenseMatrix< MAT >::operator+=

(

const DenseMatrix< Other > &

y

)

[inline]

vector space addition

template<typename MAT>

template<class Other >

DenseMatrix& Dune::DenseMatrix< MAT >::operator-=

(

const DenseMatrix< Other > &

y

)

[inline]

vector space subtraction

template<typename MAT>

DenseMatrix& Dune::DenseMatrix< MAT >::operator/=

(

const field_type &

k

)

[inline]

vector space division by scalar

template<typename MAT>

DenseMatrix& Dune::DenseMatrix< MAT >::operator=

(

const field_type &

f

)

[inline]

template<typename MAT>

template<typename T >

DenseMatrix& Dune::DenseMatrix< MAT >::operator=

(

const T &

t

)

[inline]

template<typename MAT>

template<class Other >

bool Dune::DenseMatrix< MAT >::operator==

(

const DenseMatrix< Other > &

y

)

const [inline]

Binary matrix comparison.

Referenced by Dune::DenseMatrix< DynamicMatrix< K > >::operator!=().

template<typename MAT>

row_reference Dune::DenseMatrix< MAT >::operator[]

(

size_type

i

)

[inline]

random access

template<typename MAT>

const_row_reference Dune::DenseMatrix< MAT >::operator[]

(

size_type

i

)

const [inline]

template<typename MAT>

template<typename M2 >

MAT& Dune::DenseMatrix< MAT >::rightmultiply

(

const DenseMatrix< M2 > &

M

)

[inline]

Multiplies M from the right to this matrix.

template<typename MAT>

size_type Dune::DenseMatrix< MAT >::rows

(

)

const [inline]

number of rows

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

template<typename MAT>

size_type Dune::DenseMatrix< MAT >::size

(

)

const [inline]

size method (number of rows)

template<typename MAT>

template<class V >

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

Solve system A x = b.

Exceptions:

FMatrixError

if the matrix is singular

template<typename MAT>

template<class X , class Y >

void Dune::DenseMatrix< MAT >::umhv	(	const X &	x,
		Y &	y
	)		const [inline]

y += A^H x

template<typename MAT>

template<class X , class Y >

void Dune::DenseMatrix< MAT >::umtv	(	const X &	x,
		Y &	y
	)		const [inline]

y += A^T x

template<typename MAT>

template<class X , class Y >

void Dune::DenseMatrix< MAT >::umv	(	const X &	x,
		Y &	y
	)		const [inline]

y += A x

template<typename MAT>

template<class X , class Y >

void Dune::DenseMatrix< MAT >::usmhv	(	const field_type &	alpha,
		const X &	x,
		Y &	y
	)		const [inline]

y += alpha A^H x

template<typename MAT>

template<class X , class Y >

void Dune::DenseMatrix< MAT >::usmtv	(	const field_type &	alpha,
		const X &	x,
		Y &	y
	)		const [inline]

y += alpha A^T x

template<typename MAT>

template<class X , class Y >

void Dune::DenseMatrix< MAT >::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