Dune::FieldMatrix< K, ROWS, COLS > Class Template Reference

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.
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>>
	FieldMatrix (T const &rhs)
	copy constructor from assignable type T
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 (size_type i, size_type j) const
	return true when (i,j) is in pattern

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 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

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

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