A dense n x m matrix. More...

#include <dune/common/fmatrix.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 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.

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

FieldMatrix &	operator= (const FieldMatrix &)=default
	copy assignment operator

template<typename T >
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

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

template<int l>
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>
FieldMatrix &	rightmultiply (const FieldMatrix< K, r, c > &M)
	Multiplies M from the right to this matrix.

template<int l>
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.

row_reference	operator[] (size_type i)
	random access

size_type	size () const
	size method (number of rows)

Iterator	begin ()
	begin iterator

ConstIterator	begin () const
	begin iterator

Iterator	end ()
	end iterator

ConstIterator	end () const
	end iterator

Iterator	beforeEnd ()

ConstIterator	beforeEnd () const

Iterator	beforeBegin ()

ConstIterator	beforeBegin () const

derived_type &	operator+= (const DenseMatrix< Other > &x)
	vector space addition

derived_type	operator- () const
	Matrix negation.

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

derived_type &	axpy (const field_type &a, const DenseMatrix< Other > &x)
	vector space axpy operation (*this += a x)

bool	operator== (const DenseMatrix< Other > &x) const
	Binary matrix comparison.

bool	operator!= (const DenseMatrix< Other > &x) const
	Binary matrix incomparison.

void	mv (const X &x, Y &y) const
	y = A x

void	mtv (const X &x, Y &y) const
	y = A^T x

void	umv (const X &x, Y &y) const
	y += A x

void	umtv (const X &x, Y &y) const
	y += A^T x

void	umhv (const X &x, Y &y) const
	y += A^H x

void	mmv (const X &x, Y &y) const
	y -= A x

void	mmtv (const X &x, Y &y) const
	y -= A^T x

void	mmhv (const X &x, Y &y) const
	y -= A^H x

void	usmv (const typename FieldTraits< Y >::field_type &alpha, const X &x, Y &y) const
	y += alpha A x

void	usmtv (const typename FieldTraits< Y >::field_type &alpha, const X &x, Y &y) const
	y += alpha A^T x

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

FieldTraits< vt >::real_type	infinity_norm () const
	infinity norm (row sum norm, how to generalize for blocks?)

FieldTraits< vt >::real_type	infinity_norm () const
	infinity norm (row sum norm, how to generalize for blocks?)

FieldTraits< vt >::real_type	infinity_norm_real () const
	simplified infinity norm (uses Manhattan norm for complex values)

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

bool	exists ([[maybe_unused]] size_type i,[[maybe_unused]] size_type j) const
	return true when (i,j) is in pattern

Static Public Attributes
constexpr static int	rows = ROWS
	The number of rows.

constexpr static int	cols = COLS
	The number of columns.

constexpr static 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
template<class OtherScalar >
auto	operator+ (const FieldMatrix &matrixA, const FieldMatrix< OtherScalar, ROWS, COLS > &matrixB)
	vector space addition – two-argument version

template<class OtherScalar >
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>
auto	operator* (const FieldMatrix &matrix, Scalar scalar)
	vector space multiplication with scalar

template<class Scalar , std::enable_if_t< IsNumber< Scalar >::value, int > = 0>
auto	operator* (Scalar scalar, const FieldMatrix &matrix)
	vector space multiplication with scalar

template<class Scalar , std::enable_if_t< IsNumber< Scalar >::value, int > = 0>
auto	operator/ (const FieldMatrix &matrix, Scalar scalar)
	vector space division by scalar

template<class OtherScalar , int otherCols>
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>
auto	operator* (const FieldMatrix &matrixA, const OtherMatrix &matrixB)
	Matrix-matrix multiplication. More...

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 &matrixB)
	Matrix-matrix multiplication. More...

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]

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

inlineinherited

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

inlineinherited

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

◆ beforeEnd() [1/2]

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

inlineinherited

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

inlineinherited

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 , 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* [2/2]

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).

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 Core Modules (2.9.0)

Public Types

Public Member Functions

Static Public Attributes

Static Protected Member Functions

Friends

Detailed Description

template<class K, int ROWS, int COLS>
class Dune::FieldMatrix< K, ROWS, COLS >

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]

Public Types

Public Member Functions

Static Public Attributes

Static Protected Member Functions

Friends

Detailed Description

template<class K, int ROWS, int COLS> class Dune::FieldMatrix< K, ROWS, COLS >

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]

template<class K, int ROWS, int COLS>
class Dune::FieldMatrix< K, ROWS, COLS >