Dune::DenseMatrix< MAT > Class Template Reference

A dense n x m matrix. More...

#include <dune/common/densematrix.hh>

Public Types
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 > &x)
	vector space addition
derived_type	operator- () const
	Matrix negation.
template<class Other >
derived_type &	operator-= (const DenseMatrix< Other > &x)
	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 &a, const DenseMatrix< Other > &x)
	vector space axpy operation (*this += a x)
template<class Other >
bool	operator== (const DenseMatrix< Other > &x) const
	Binary matrix comparison.
template<class Other >
bool	operator!= (const DenseMatrix< Other > &x) 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<!HasNaN< 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<!HasNaN< 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< HasNaN< 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< HasNaN< vt >::value, int >::type = 0>
FieldTraits< vt >::real_type	infinity_norm_real () const
	simplified infinity norm (uses Manhattan norm for complex values)
template<class V1 , class V2 >
void	solve (V1 &x, const V2 &b, bool doPivoting=true) const
	Solve system A x = b. More...
void	invert (bool doPivoting=true)
	Compute inverse. More...
field_type	determinant (bool doPivoting=true) 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.
constexpr size_type	N () const
	number of rows
constexpr size_type	M () const
	number of columns
constexpr size_type	rows () const
	number of rows
constexpr size_type	cols () const
	number of columns
bool	exists (size_type i, size_type j) const
	return true when (i,j) is in pattern

Static Public Attributes
static constexpr int	blocklevel = 1
	The number of block levels we contain. This is the leaf, that is, 1.

Static Protected Member Functions
template<class Func , class Mask >
static void	luDecomposition (DenseMatrix< MAT > &A, Func func, Mask &nonsingularLanes, bool throwEarly, bool doPivoting)
	do an LU-Decomposition on matrix A More...

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 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

(

bool

doPivoting = true

)

Compute inverse.

Exceptions

FMatrixError

if the matrix is singular

Referenced by Dune::Fem::LocalMassMatrixImplementation< DiscreteFunctionSpace, VolumeQuadrature, refElemScaling >::leftMultiplyInverseDgOrthoNormalBasis(), and Dune::Fem::LocalMassMatrixImplementation< DiscreteFunctionSpace, VolumeQuadrature, refElemScaling >::rightMultiplyInverseDgOrthoNormalBasis().

luDecomposition()

template<typename MAT >

template<class Func , class Mask >

static void Dune::DenseMatrix< MAT >::luDecomposition ( DenseMatrix< MAT > &  A, Func  func, Mask &  nonsingularLanes, bool  throwEarly, bool  doPivoting  )

staticprotected

do an LU-Decomposition on matrix A

Parameters

A	The matrix to decompose, and to store the result in.
func	Functor used for swapping lanes and to conduct the elimination. Depending on the functor, luDecomposition() can be used for solving, for inverting, or to compute the determinant.
nonsingularLanes	SimdMask of lanes that are nonsingular.
throwEarly	Whether to throw an FMatrixError immediately as soon as one lane is discovered to be singular. If false, do not throw, instead continue until finished or all lanes are singular, and exit via return in both cases.
doPivoting	Enable pivoting.

There are two modes of operation:

• Terminate as soon as one lane is discovered to be singular. Early termination is done by throwing an FMatrixError. On entry, Simd::allTrue(nonsingularLanes) and throwEarly==true should hold. After early termination, the contents of A should be considered bogus, and nonsingularLanes has the lane(s) that triggered the early termination unset. There may be more singular lanes than the one reported in nonsingularLanes, which just haven't been discovered yet; so the value of nonsingularLanes is mostly useful for diagnostics.
• Terminate only when all lanes are discovered to be singular. Use this when you want to apply special postprocessing in singular lines (e.g. setting the determinant of singular lanes to 0 in determinant()). On entry, nonsingularLanes may have any value and throwEarly==false should hold. The function will not throw an exception if some lanes are discovered to be singular, instead it will continue running until all lanes are singular or until finished, and terminate only via normal return. On exit, nonsingularLanes contains the map of lanes that are valid in A.

solve()

template<typename MAT >

template<class V1 , class V2 >

void Dune::DenseMatrix< MAT >::solve	(	V1 &	x,
		const V2 &	b,
		bool	doPivoting = true
	)		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