A dense n x m matrix. More...

#include <dune/common/fmatrix.hh>

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

Public Types
typedef Base::size_type	size_type
typedef Base::row_type	row_type
typedef Base::row_reference	row_reference
typedef Base::const_row_reference	const_row_reference
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, 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
constexpr	FieldMatrix ()=default
	Default constructor.
constexpr	FieldMatrix (std::initializer_list< Dune::FieldVector< K, cols > > const &l)
	Constructor initializing the matrix from a list of vector.
	FieldMatrix (const FieldMatrix &)=default
	copy constructor
template<class T, typename = std::enable_if_t<HasDenseMatrixAssigner<FieldMatrix, T>::value>>
constexpr	FieldMatrix (T const &rhs)
	copy constructor from assignable type T
constexpr FieldMatrix &	operator= (const FieldMatrix &)=default
	copy assignment operator
template<typename T>
constexpr FieldMatrix &	operator= (const FieldMatrix< T, ROWS, COLS > &x)
	copy assignment from FieldMatrix over a different field
template<typename T, int rows, int cols>
FieldMatrix &	operator= (FieldMatrix< T, rows, cols > const &)=delete
	no copy assignment from FieldMatrix of different size
constexpr FieldMatrix< K, COLS, ROWS >	transposed () const
	Return transposed of the matrix as FieldMatrix.
template<int l>
constexpr 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.
template<int r, int c>
constexpr FieldMatrix &	rightmultiply (const FieldMatrix< K, r, c > &M)
	Multiplies M from the right to this matrix.
template<int l>
constexpr 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.
constexpr row_reference	mat_access (size_type i)
constexpr const_row_reference	mat_access (size_type i) const
constexpr derived_type &	operator= (const RHS &rhs)
FieldMatrix< K, ROWS, COLS > &	rightmultiply (const DenseMatrix< M2 > &M)
	Multiplies M from the right to this matrix.
constexpr row_reference	operator[] (size_type i)
	random access
constexpr const_row_reference	operator[] (size_type i) const
constexpr size_type	size () const
	size method (number of rows)
constexpr Iterator	begin ()
	begin iterator
constexpr ConstIterator	begin () const
	begin iterator
constexpr Iterator	end ()
	end iterator
constexpr ConstIterator	end () const
	end iterator
constexpr Iterator	beforeEnd ()
constexpr ConstIterator	beforeEnd () const
constexpr Iterator	beforeBegin ()
constexpr ConstIterator	beforeBegin () const
constexpr derived_type &	operator+= (const DenseMatrix< Other > &x)
	vector space addition
constexpr derived_type	operator- () const
	Matrix negation.
constexpr derived_type &	operator-= (const DenseMatrix< Other > &x)
	vector space subtraction
constexpr derived_type &	operator*= (const field_type &k)
	vector space multiplication with scalar
constexpr derived_type &	operator/= (const field_type &k)
	vector space division by scalar
constexpr derived_type &	axpy (const field_type &a, const DenseMatrix< Other > &x)
	vector space axpy operation (*this += a x)
constexpr bool	operator== (const DenseMatrix< Other > &x) const
	Binary matrix comparison.
constexpr bool	operator!= (const DenseMatrix< Other > &x) const
	Binary matrix incomparison.
constexpr void	mv (const X &x, Y &y) const
	y = A x
constexpr void	mtv (const X &x, Y &y) const
	y = A^T x
constexpr void	umv (const X &x, Y &y) const
	y += A x
constexpr void	umtv (const X &x, Y &y) const
	y += A^T x
constexpr void	umhv (const X &x, Y &y) const
	y += A^H x
constexpr void	mmv (const X &x, Y &y) const
	y -= A x
constexpr void	mmtv (const X &x, Y &y) const
	y -= A^T x
constexpr void	mmhv (const X &x, Y &y) const
	y -= A^H x
constexpr void	usmv (const typename FieldTraits< Y >::field_type &alpha, const X &x, Y &y) const
	y += alpha A x
constexpr void	usmtv (const typename FieldTraits< Y >::field_type &alpha, const X &x, Y &y) const
	y += alpha A^T x
constexpr void	usmhv (const typename FieldTraits< Y >::field_type &alpha, const X &x, Y &y) const
	y += alpha A^H x
constexpr FieldTraits< value_type >::real_type	frobenius_norm () const
	frobenius norm: sqrt(sum over squared values of entries)
constexpr FieldTraits< value_type >::real_type	frobenius_norm2 () const
	square of frobenius norm, need for block recursion
constexpr FieldTraits< vt >::real_type	infinity_norm () const
	infinity norm (row sum norm, how to generalize for blocks?)
constexpr FieldTraits< vt >::real_type	infinity_norm () const
	infinity norm (row sum norm, how to generalize for blocks?)
constexpr FieldTraits< vt >::real_type	infinity_norm_real () const
	simplified infinity norm (uses Manhattan norm for complex values)
constexpr FieldTraits< vt >::real_type	infinity_norm_real () const
	simplified infinity norm (uses Manhattan norm for complex values)
void	solve (V1 &x, const V2 &b, bool doPivoting=true) const
	Solve system A x = b.
void	invert (bool doPivoting=true)
	Compute inverse.
field_type	determinant (bool doPivoting=true) const
	calculates the determinant of this matrix
FieldMatrix< K, ROWS, COLS > &	leftmultiply (const DenseMatrix< M2 > &M)
	Multiplies M from the left 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
constexpr bool	exists (size_type i, size_type j) const
	return true when (i,j) is in pattern

Static Public Member Functions
static constexpr size_type	mat_rows ()
static constexpr size_type	mat_cols ()

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

Static Protected Member Functions
static void	luDecomposition (DenseMatrix< FieldMatrix< K, ROWS, COLS > > &A, Func func, Mask &nonsingularLanes, bool throwEarly, bool doPivoting)
	do an LU-Decomposition on matrix A

Friends
template<class, int, int>
class	FieldMatrix
template<class OtherScalar>
constexpr auto	operator+ (const FieldMatrix &matrixA, const FieldMatrix< OtherScalar, ROWS, COLS > &matrixB)
	vector space addition – two-argument version
template<class OtherScalar>
constexpr auto	operator- (const FieldMatrix &matrixA, const FieldMatrix< OtherScalar, ROWS, COLS > &matrixB)
	vector space subtraction – two-argument version
template<class Scalar, std::enable_if_t< IsNumber< Scalar >::value, int > = 0>
constexpr auto	operator* (const FieldMatrix &matrix, Scalar scalar)
	vector space multiplication with scalar
template<class Scalar, std::enable_if_t< IsNumber< Scalar >::value, int > = 0>
constexpr auto	operator* (Scalar scalar, const FieldMatrix &matrix)
	vector space multiplication with scalar
template<class Scalar, std::enable_if_t< IsNumber< Scalar >::value, int > = 0>
constexpr auto	operator/ (const FieldMatrix &matrix, Scalar scalar)
	vector space division by scalar
template<class OtherScalar, int otherCols>
constexpr auto	operator* (const FieldMatrix &matrixA, const FieldMatrix< OtherScalar, COLS, otherCols > &matrixB)
	Matrix-matrix multiplication.
template<class OtherMatrix, std::enable_if_t< Impl::IsStaticSizeMatrix_v< OtherMatrix > and not Impl::IsFieldMatrix_v< OtherMatrix >, int > = 0>
constexpr auto	operator* (const FieldMatrix &matrixA, const OtherMatrix &matrixB)
	Matrix-matrix multiplication.
template<class OtherMatrix, std::enable_if_t< Impl::IsStaticSizeMatrix_v< OtherMatrix > and not Impl::IsFieldMatrix_v< OtherMatrix >, int > = 0>
constexpr auto	operator* (const OtherMatrix &matrixA, const FieldMatrix &matrixB)
	Matrix-matrix multiplication.

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

◆ block_type

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

inherited

export the type representing the components

◆ ColIterator

typedef std::remove_reference<row_reference>::type::Iterator Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::ColIterator

inherited

rename the iterators for easier access

◆ const_iterator

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

inherited

typedef for stl compliant access

◆ const_row_reference

template<class K, int ROWS, int COLS>

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

◆ ConstColIterator

typedef std::remove_reference<const_row_reference>::type::ConstIterator Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::ConstColIterator

inherited

rename the iterators for easier access

◆ ConstIterator

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

inherited

Iterator class for sequential access.

◆ ConstRowIterator

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

inherited

rename the iterators for easier access

◆ derived_type

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

inherited

type of derived matrix class

◆ field_type

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

inherited

export the type representing the field

◆ Iterator

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

inherited

Iterator class for sequential access.

◆ iterator

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

inherited

typedef for stl compliant access

◆ row_reference

template<class K, int ROWS, int COLS>

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

◆ row_type

template<class K, int ROWS, int COLS>

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

◆ RowIterator

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

inherited

rename the iterators for easier access

◆ size_type

template<class K, int ROWS, int COLS>

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

◆ value_type

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

inherited

export the type representing the field

Constructor & Destructor Documentation

◆ FieldMatrix() [1/4]

template<class K, int ROWS, int COLS>

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

constexprdefault

Default constructor.

◆ FieldMatrix() [2/4]

template<class K, int ROWS, int COLS>

Dune::FieldMatrix< K, ROWS, COLS >::FieldMatrix ( std::initializer_list< Dune::FieldVector< K, cols > > const & l )

inlineconstexpr

Constructor initializing the matrix from a list of vector.

◆ FieldMatrix() [3/4]

template<class K, int ROWS, int COLS>

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

default

copy constructor

◆ FieldMatrix() [4/4]

template<class K, int ROWS, int COLS>

template<class T, typename = std::enable_if_t<HasDenseMatrixAssigner<FieldMatrix, T>::value>>

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

inlineconstexpr

copy constructor from assignable type T

Member Function Documentation

◆ axpy()

derived_type & Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::axpy	(	const field_type &	a,
		const DenseMatrix< Other > &	x )

inlineconstexprinherited

vector space axpy operation (*this += a x)

◆ beforeBegin() [1/2]

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

inlineconstexprinherited

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

◆ beforeBegin() [2/2]

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

inlineconstexprinherited

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

◆ beforeEnd() [1/2]

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

inlineconstexprinherited

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

◆ beforeEnd() [2/2]

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

inlineconstexprinherited

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

◆ begin() [1/2]

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

inlineconstexprinherited

begin iterator

◆ begin() [2/2]

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

inlineconstexprinherited

begin iterator

◆ cols()

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

inlineconstexprinherited

number of columns

◆ determinant()

field_type Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::determinant ( bool doPivoting = true ) const

inherited

calculates the determinant of this matrix

◆ end() [1/2]

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

inlineconstexprinherited

end iterator

◆ end() [2/2]

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

inlineconstexprinherited

end iterator

◆ exists()

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

inlineconstexprinherited

return true when (i,j) is in pattern

◆ frobenius_norm()

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

inlineconstexprinherited

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

◆ frobenius_norm2()

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

inlineconstexprinherited

square of frobenius norm, need for block recursion

◆ infinity_norm() [1/2]

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

inlineconstexprinherited

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

◆ infinity_norm() [2/2]

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

inlineconstexprinherited

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

◆ infinity_norm_real() [1/2]

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

inlineconstexprinherited

simplified infinity norm (uses Manhattan norm for complex values)

◆ infinity_norm_real() [2/2]

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

inlineconstexprinherited

simplified infinity norm (uses Manhattan norm for complex values)

◆ invert()

void Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::invert ( bool doPivoting = true )

inherited

Compute inverse.

Exceptions

FMatrixError if the matrix is singular

◆ leftmultiply()

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

inlineinherited

Multiplies M from the left to this matrix.

◆ leftmultiplyany()

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

inlineconstexpr

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

◆ luDecomposition()

void Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::luDecomposition	(	DenseMatrix< FieldMatrix< K, ROWS, COLS > > &	A,
		Func	func,
		Mask &	nonsingularLanes,
		bool	throwEarly,
		bool	doPivoting )

staticprotectedinherited

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.

◆ M()

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

inlineconstexprinherited

number of columns

◆ mat_access() [1/2]

template<class K, int ROWS, int COLS>

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

inlineconstexpr

◆ mat_access() [2/2]

template<class K, int ROWS, int COLS>

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

inlineconstexpr

◆ mat_cols()

template<class K, int ROWS, int COLS>

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

inlinestaticconstexpr

◆ mat_rows()

template<class K, int ROWS, int COLS>

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

inlinestaticconstexpr

◆ mmhv()

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

inlineconstexprinherited

y -= A^H x

◆ mmtv()

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

inlineconstexprinherited

y -= A^T x

◆ mmv()

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

inlineconstexprinherited

y -= A x

◆ mtv()

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

inlineconstexprinherited

y = A^T x

◆ mv()

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

inlineconstexprinherited

y = A x

◆ N()

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

inlineconstexprinherited

number of rows

◆ operator!=()

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

inlineconstexprinherited

Binary matrix incomparison.

◆ operator*=()

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

inlineconstexprinherited

vector space multiplication with scalar

◆ operator+=()

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

inlineconstexprinherited

vector space addition

◆ operator-()

derived_type Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::operator- ( ) const

inlineconstexprinherited

Matrix negation.

◆ operator-=()

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

inlineconstexprinherited

vector space subtraction

◆ operator/=()

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

inlineconstexprinherited

vector space division by scalar

◆ operator=() [1/4]

template<class K, int ROWS, int COLS>

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

constexprdefault

copy assignment operator

◆ operator=() [2/4]

template<class K, int ROWS, int COLS>

template<typename T>

FieldMatrix & Dune::FieldMatrix< K, ROWS, COLS >::operator= ( const FieldMatrix< T, ROWS, COLS > & x )

inlineconstexpr

copy assignment from FieldMatrix over a different field

◆ operator=() [3/4]

template<class K, int ROWS, int COLS>

derived_type & Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::operator= ( const RHS & rhs )

inlineconstexpr

◆ operator=() [4/4]

template<class K, int ROWS, int COLS>

template<typename T, int rows, int cols>

FieldMatrix & Dune::FieldMatrix< K, ROWS, COLS >::operator= ( FieldMatrix< T, rows, cols > const & )

delete

no copy assignment from FieldMatrix of different size

◆ operator==()

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

inlineconstexprinherited

Binary matrix comparison.

◆ operator[]() [1/2]

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

inlineconstexprinherited

random access

◆ operator[]() [2/2]

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

inlineconstexprinherited

◆ rightmultiply() [1/2]

template<class K, int ROWS, int COLS>

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

inline

Multiplies M from the right to this matrix.

◆ rightmultiply() [2/2]

template<class K, int ROWS, int COLS>

template<int r, int c>

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

inlineconstexpr

Multiplies M from the right to this matrix.

◆ rightmultiplyany()

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

inlineconstexpr

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

◆ rows()

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

inlineconstexprinherited

number of rows

◆ size()

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

inlineconstexprinherited

size method (number of rows)

◆ solve()

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

inherited

Solve system A x = b.

Exceptions

FMatrixError if the matrix is singular

◆ transposed()

template<class K, int ROWS, int COLS>

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

inlineconstexpr

Return transposed of the matrix as FieldMatrix.

◆ umhv()

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

inlineconstexprinherited

y += A^H x

◆ umtv()

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

inlineconstexprinherited

y += A^T x

◆ umv()

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

inlineconstexprinherited

y += A x

◆ usmhv()

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

inlineconstexprinherited

y += alpha A^H x

◆ usmtv()

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

inlineconstexprinherited

y += alpha A^T x

◆ usmv()

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

inlineconstexprinherited

y += alpha A x

◆ FieldMatrix

template<class K, int ROWS, int COLS>

template<class, int, int>

friend class FieldMatrix

friend

◆ operator* [1/5]

template<class K, int ROWS, int COLS>

template<class Scalar, std::enable_if_t< IsNumber< Scalar >::value, int > = 0>

auto operator*	(	const FieldMatrix< K, ROWS, COLS > &	matrix,
		Scalar	scalar )

friend

vector space multiplication with scalar

◆ operator* [2/5]

template<class K, int ROWS, int COLS>

template<class OtherScalar, int otherCols>

auto operator*	(	const FieldMatrix< K, ROWS, COLS > &	matrixA,
		const FieldMatrix< OtherScalar, COLS, otherCols > &	matrixB )

friend

Matrix-matrix multiplication.

◆ operator* [3/5]

template<class K, int ROWS, int COLS>

template<class OtherMatrix, std::enable_if_t< Impl::IsStaticSizeMatrix_v< OtherMatrix > and not Impl::IsFieldMatrix_v< OtherMatrix >, int > = 0>

auto operator*	(	const FieldMatrix< K, ROWS, COLS > &	matrixA,
		const OtherMatrix &	matrixB )

friend

Matrix-matrix multiplication.

This implements multiplication of a FieldMatrix with another matrix of type OtherMatrix. The latter has to provide OtherMatrix::field_type, OtherMatrix::cols, and OtherMatrix::mtv(x,y).

◆ operator* [4/5]

template<class K, int ROWS, int COLS>

template<class OtherMatrix, std::enable_if_t< Impl::IsStaticSizeMatrix_v< OtherMatrix > and not Impl::IsFieldMatrix_v< OtherMatrix >, int > = 0>

auto operator*	(	const OtherMatrix &	matrixA,
		const FieldMatrix< K, ROWS, COLS > &	matrixB )

friend

Matrix-matrix multiplication.

This implements multiplication of another matrix of type OtherMatrix with a FieldMatrix. The former has to provide OtherMatrix::field_type, OtherMatrix::rows, and OtherMatrix::mv(x,y).

◆ operator* [5/5]

template<class K, int ROWS, int COLS>

template<class Scalar, std::enable_if_t< IsNumber< Scalar >::value, int > = 0>

auto operator*	(	Scalar	scalar,
		const FieldMatrix< K, ROWS, COLS > &	matrix )

friend

vector space multiplication with scalar

◆ operator+

template<class K, int ROWS, int COLS>

template<class OtherScalar>

auto operator+	(	const FieldMatrix< K, ROWS, COLS > &	matrixA,
		const FieldMatrix< OtherScalar, ROWS, COLS > &	matrixB )

friend

vector space addition – two-argument version

◆ operator-

template<class K, int ROWS, int COLS>

template<class OtherScalar>

auto operator-	(	const FieldMatrix< K, ROWS, COLS > &	matrixA,
		const FieldMatrix< OtherScalar, ROWS, COLS > &	matrixB )

friend

vector space subtraction – two-argument version

◆ operator/

template<class K, int ROWS, int COLS>

template<class Scalar, std::enable_if_t< IsNumber< Scalar >::value, int > = 0>

auto operator/	(	const FieldMatrix< K, ROWS, COLS > &	matrix,
		Scalar	scalar )

friend

vector space division by scalar

Member Data Documentation

◆ blocklevel

int Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::blocklevel

staticconstexprinherited

The number of block levels we contain. This is the leaf, that is, 1.

◆ cols

template<class K, int ROWS, int COLS>

int Dune::FieldMatrix< K, ROWS, COLS >::cols = COLS

staticconstexpr

The number of columns.

◆ rows

template<class K, int ROWS, int COLS>

int Dune::FieldMatrix< K, ROWS, COLS >::rows = ROWS

staticconstexpr

The number of rows.

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

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Static Protected Member Functions

Friends

Detailed Description

Member Typedef Documentation

◆ block_type

◆ ColIterator

◆ const_iterator

◆ const_row_reference

◆ ConstColIterator

◆ ConstIterator

◆ ConstRowIterator

◆ derived_type

◆ field_type

◆ Iterator

◆ iterator

◆ row_reference

◆ row_type

◆ RowIterator

◆ size_type

◆ value_type

Constructor & Destructor Documentation

◆ FieldMatrix() [1/4]

◆ FieldMatrix() [2/4]

◆ FieldMatrix() [3/4]

◆ FieldMatrix() [4/4]

Member Function Documentation

◆ axpy()

◆ beforeBegin() [1/2]

◆ beforeBegin() [2/2]

◆ beforeEnd() [1/2]

◆ beforeEnd() [2/2]

◆ begin() [1/2]

◆ begin() [2/2]

◆ cols()

◆ determinant()

◆ end() [1/2]

◆ end() [2/2]

◆ exists()

◆ frobenius_norm()

◆ frobenius_norm2()

◆ infinity_norm() [1/2]

◆ infinity_norm() [2/2]

◆ infinity_norm_real() [1/2]

◆ infinity_norm_real() [2/2]

◆ invert()

◆ leftmultiply()

◆ leftmultiplyany()

◆ luDecomposition()

◆ M()

◆ mat_access() [1/2]

◆ mat_access() [2/2]

◆ mat_cols()

◆ mat_rows()

◆ mmhv()

◆ mmtv()

◆ mmv()

◆ mtv()

◆ mv()

◆ N()

◆ operator!=()

◆ operator*=()

◆ operator+=()

◆ operator-()

◆ operator-=()

◆ operator/=()

◆ operator=() [1/4]

◆ operator=() [2/4]

◆ operator=() [3/4]

◆ operator=() [4/4]

◆ operator==()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ rightmultiply() [1/2]

◆ rightmultiply() [2/2]

◆ rightmultiplyany()

◆ rows()