Dune::DenseMatrix< MAT > Class Template Reference

A dense n x m matrix. More...

#include <dune/common/densematrix.hh>

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, row_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 std::remove_reference< row_reference >::type::Iterator	ColIterator
	rename the iterators for easier access
typedef DenseIterator< const DenseMatrix, const row_type, const_row_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 std::remove_reference< const_row_reference >::type::ConstIterator	ConstColIterator
	rename the iterators for easier access

Public Member Functions
row_reference	operator[] (size_type i)
	random access
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
template<class Other >
derived_type &	operator+= (const DenseMatrix< Other > &y)
	vector space addition
template<class Other >
derived_type &	operator-= (const DenseMatrix< Other > &y)
	vector space subtraction
derived_type &	operator*= (const field_type &k)
	vector space multiplication with scalar
derived_type &	operator/= (const field_type &k)
	vector space division by scalar
template<class Other >
derived_type &	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 typename FieldTraits< Y >::field_type &alpha, const X &x, Y &y) const
	y += alpha A x
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
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
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
template<typename vt = value_type, typename std::enable_if<!has_nan< vt >::value, int >::type = 0>
FieldTraits< vt >::real_type	infinity_norm () const
	infinity norm (row sum norm, how to generalize for blocks?)
template<typename vt = value_type, typename std::enable_if<!has_nan< vt >::value, int >::type = 0>
FieldTraits< vt >::real_type	infinity_norm_real () const
	simplified infinity norm (uses Manhattan norm for complex values)
template<typename vt = value_type, typename std::enable_if< has_nan< vt >::value, int >::type = 0>
FieldTraits< vt >::real_type	infinity_norm () const
	infinity norm (row sum norm, how to generalize for blocks?)
template<typename vt = value_type, typename std::enable_if< has_nan< vt >::value, int >::type = 0>
FieldTraits< vt >::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. More...
void	invert ()
	Compute inverse. More...
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 Enumeration Documentation

anonymous enum

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

beforeBegin() [1/2]

template<typename MAT >

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

inline

Returns

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

beforeBegin() [2/2]

template<typename MAT >

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

inline

Returns

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

beforeEnd() [1/2]

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.

References Dune::DenseMatrix< MAT >::rows().

beforeEnd() [2/2]

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

References Dune::DenseMatrix< MAT >::rows().

invert()

template<typename MAT >

void Dune::DenseMatrix< MAT >::invert

(

)

Compute inverse.

Exceptions

FMatrixError

if the matrix is singular

solve()

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

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

• dune/common/densematrix.hh