A dense n x m matrix. More...

#include <dune/common/fmatrix.hh>

Public Types
using	size_type = typename Base::size_type
	The type used for the index access and size operation.

using	value_type = typename Base::value_type
	The type of the elements stored in the matrix.

using	reference = value_type &
	The type used for references to the matrix entries.

using	const_reference = const value_type &
	The type used for const references to the matrix entries.

using	row_type = typename Base::row_type
	The type the rows of the matrix are represented by.

using	row_reference = typename Base::row_reference
	The type used for references to the rows of the matrix.

using	const_row_reference = typename Base::const_row_reference
	The type used for const references to the rows of the matrix.

typedef Traits::derived_type	derived_type
	type of derived matrix class

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
template<class OtherK , int otherRows, int otherCols> requires (otherRows != ROWS \|\| otherCols != COLS)
constexpr FieldMatrix &	operator= (const FieldMatrix< OtherK, otherRows, otherCols > &)=delete
	Delete assignment from FieldMatrix of different shape.

constexpr FieldMatrix< K, COLS, ROWS >	transposed () const
	Return transposed of the matrix as FieldMatrix.

constexpr row_reference	operator[] (size_type i)
	random access

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. More...

void	invert (bool doPivoting=true)
	Compute inverse. More...

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.

FieldMatrix< K, ROWS, COLS > &	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

constexpr bool	exists (size_type i, size_type j) const
	return true when (i,j) is in pattern

Constructors
constexpr	FieldMatrix () noexcept(std::is_nothrow_default_constructible_v< K >)
	Default constructor, making value-initialized matrix with all components set to zero.

constexpr	FieldMatrix (std::initializer_list< Dune::FieldVector< K, cols > > const &l)
	Constructor initializing the matrix from a nested list of values.

template<class OtherK , int otherRows, int otherCols> requires (otherRows != ROWS \|\| otherCols != COLS)
constexpr	FieldMatrix (const FieldMatrix< OtherK, otherRows, otherCols > &)=delete
	Delete assignment from FieldMatrix of different shape.

template<class OtherMatrix > requires (HasDenseMatrixAssigner<FieldMatrix, OtherMatrix>::value)
constexpr	FieldMatrix (const OtherMatrix &rhs)
	copy constructor from assignable type OtherMatrix

Element access
constexpr row_reference	mat_access (size_type i)

constexpr const_row_reference	mat_access (size_type i) const

constexpr	operator const_reference () const noexcept
	Conversion operator.

constexpr	operator reference () noexcept
	Conversion operator.

Static Public Member Functions
Capacity
static constexpr size_type	mat_rows ()

static constexpr size_type	mat_cols ()

Static Public Attributes
static constexpr std::integral_constant< int, ROWS >	rows = {}
	The number of rows.

static constexpr std::integral_constant< 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 More...

Friends
Comparison operators
template<Concept::Number S> requires (ROWS*COLS == 1)
constexpr bool	operator== (const FieldMatrix &a, const S &b) noexcept
	comparing FieldMatrix<1,1> with scalar for equality

template<Concept::Number S> requires (ROWS*COLS == 1)
constexpr bool	operator== (const S &a, const FieldMatrix &b) noexcept
	comparing FieldMatrix<1,1> with scalar for equality

template<class OtherK > requires (Std::three_way_comparable_with<K,OtherK>)
constexpr auto	operator<=> (const FieldMatrix &a, const FieldMatrix< OtherK, ROWS, COLS > &b) noexcept
	three-way comparison of FieldMatrix

template<Concept::Number S> requires (ROWS*COLS == 1)
constexpr auto	operator<=> (const FieldMatrix &a, const S &b) noexcept
	three-way comparison of FieldMatrix<1,1> with scalar

template<Concept::Number S> requires (ROWS*COLS == 1)
constexpr auto	operator<=> (const S &a, const FieldMatrix &b) noexcept
	three-way comparison of FieldMatrix<1,1> with scalar

Vector space operations
template<class OtherK >
constexpr auto	operator+ (const FieldMatrix &matrixA, const FieldMatrix< OtherK, ROWS, COLS > &matrixB)
	vector space addition

template<Concept::Number S> requires (ROWS*COLS == 1)
constexpr auto	operator+ (const FieldMatrix &a, const S &b) noexcept
	Binary addition, when using FieldVector<K,1,1> like K.

template<Concept::Number S> requires (ROWS*COLS == 1)
constexpr auto	operator+ (const S &a, const FieldMatrix &b) noexcept
	Binary addition, when using FieldMatrix<K,1,1> like K.

template<class OtherK >
constexpr auto	operator- (const FieldMatrix &matrixA, const FieldMatrix< OtherK, ROWS, COLS > &matrixB)
	vector space subtraction

template<Concept::Number S> requires (ROWS*COLS == 1)
constexpr auto	operator- (const FieldMatrix &a, const S &b) noexcept
	Binary subtraction, when using FieldMatrix<K,1,1> like K.

template<Concept::Number S> requires (ROWS*COLS == 1)
constexpr auto	operator- (const S &a, const FieldMatrix &b) noexcept
	Binary subtraction, when using FieldMatrix<K,1,1> like K.

template<Concept::Number S>
constexpr auto	operator* (const FieldMatrix &matrix, const S &scalar)
	vector space multiplication with scalar

template<Concept::Number S>
constexpr auto	operator* (const S &scalar, const FieldMatrix &matrix)
	vector space multiplication with scalar

template<Concept::Number S>
constexpr auto	operator/ (const FieldMatrix &matrix, const S &scalar)
	vector space division by scalar

template<Concept::Number S> requires (ROWS*COLS == 1)
constexpr FieldMatrix	operator/ (const S &a, const FieldMatrix &b) noexcept
	Binary division, when using FieldMatrix<K,1,1> like K.

template<Concept::Number S> requires (ROWS*COLS == 1)
constexpr FieldMatrix &	operator+= (const S &scalar)
	add scalar

template<Concept::Number S> requires (ROWS*COLS == 1)
constexpr FieldMatrix &	operator-= (const S &scalar)
	subtract scalar

template<Concept::Number S> requires (ROWS*COLS == 1)
constexpr FieldMatrix &	*operator=** (const S &scalar)
	multiplication with scalar

template<Concept::Number S> requires (ROWS*COLS == 1)
constexpr FieldMatrix &	operator/= (const S &scalar)
	division by scalar

Matrix-matrix multiplication
template<class OtherK , int otherCols>
constexpr auto	operator* (const FieldMatrix &matrixA, const FieldMatrix< OtherK, COLS, otherCols > &matrixB)
	Matrix-matrix multiplication of FieldMatrix types.

template<class OtherMatrix > requires (Impl::IsStaticSizeMatrix_v<OtherMatrix> and not Impl::IsFieldMatrix_v<OtherMatrix>)
constexpr auto	operator* (const FieldMatrix &matrixA, const OtherMatrix &matrixB)
	Matrix-matrix multiplication of FieldMatrix with other matrix type. More...

template<class OtherMatrix > requires (Impl::IsStaticSizeMatrix_v<OtherMatrix> and not Impl::IsFieldMatrix_v<OtherMatrix>)
constexpr auto	operator* (const OtherMatrix &matrixA, const FieldMatrix &matrixB)
	Matrix-matrix multiplication. More...

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.

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.

Examples: recipe-integration.cc.

Member Function Documentation

◆ beforeBegin() [1/2]

constexpr 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]

constexpr 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]

constexpr 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]

constexpr 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

◆ invert()

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

inherited

Compute inverse.

Exceptions

FMatrixError if the matrix is singular

◆ luDecomposition()

static 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.

◆ 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

Friends And Related Function Documentation

◆ operator* [1/2]

template<class K , int ROWS, int COLS>

template<class OtherMatrix >
requires (Impl::IsStaticSizeMatrix_v<OtherMatrix> and not Impl::IsFieldMatrix_v<OtherMatrix>)

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

friend

Matrix-matrix multiplication of FieldMatrix with other matrix type.

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* [2/2]

template<class K , int ROWS, int COLS>

template<class OtherMatrix >
requires (Impl::IsStaticSizeMatrix_v<OtherMatrix> and not Impl::IsFieldMatrix_v<OtherMatrix>)

constexpr 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).

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

dune/common/densematrix.hh
dune/common/fmatrix.hh

DUNE Distributed and Unified Numerics Environment

DUNE PDELab (unstable)

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Static Protected Member Functions

Friends

Vector space operations

Matrix-matrix multiplication

Detailed Description

Member Function Documentation

◆ beforeBegin() [1/2]

◆ beforeBegin() [2/2]

◆ beforeEnd() [1/2]

◆ beforeEnd() [2/2]

◆ invert()

◆ luDecomposition()

◆ solve()

Friends And Related Function Documentation

◆ operator* [1/2]

◆ operator* [2/2]