Dune::Fufem::SymmetricMatrix< T, N > Class Template Reference

A class implementing a symmetric matrix with compile-time size. More...

#include <dune/fufem/symmetricmatrix.hh>

Public Types
using	field_type = T
	The type used for scalars.
using	Data = Dune::FieldVector< T, N *(N+1)/2 >

Public Member Functions
	SymmetricMatrix ()
	Default constructor, creates uninitialized matrix.
template<class Iterator >
	SymmetricMatrix (Iterator it)
	Construct from raw memory.
SymmetricMatrix< T, N > &	operator= (const T &s)
SymmetricMatrix< T, N > &	operator*= (const T &s)
void	setEntry (int i, int j, const T &entry)
	Random write access to components.
T	operator() (int i, int j) const
	Matrix style random read access to components.
T	energyScalarProduct (const FieldVector< T, N > &v1, const FieldVector< T, N > &v2) const
void	axpy (const T &a, const SymmetricMatrix< T, N > &other)
T	frobenius_norm2 () const
	Compute the Frobenius norm of the matrix.
T	frobenius_norm () const
	Compute the Frobenius norm of the matrix.
const Data &	data () const
Data &	data ()

Static Public Member Functions
static constexpr SymmetricMatrix< T, N >	identityMatrix ()
	Construct identityMatrix.
static constexpr Data	traceMap ()
	return the trace map in vector representation the returned vector is such that <data,a> = trace(A) where A.data = a
static constexpr size_t	dataSize ()
	Number of scalars needed for compressed vector storage of the symmetric matrix.

Detailed Description

template<class T, int N>
class Dune::Fufem::SymmetricMatrix< T, N >

A class implementing a symmetric matrix with compile-time size.

A \( dim\times dim \) matrix is stored internally as a Dune::FieldVector<double, dim*(dim+1)/2> The components are assumed to be \( [ E(1,1),\ E(2,1),\ E(2,2),\ E(3,1),\ E(3,2),\ E(3,3) ]\) and analogous for other dimensions

Template Parameters

dim	number of lines/columns of the matrix

Member Typedef Documentation

Data

template<class T , int N>

using Dune::Fufem::SymmetricMatrix< T, N >::Data = Dune::FieldVector<T,N*(N+1)/2>

field_type

template<class T , int N>

using Dune::Fufem::SymmetricMatrix< T, N >::field_type = T

The type used for scalars.

Constructor & Destructor Documentation

SymmetricMatrix() [1/2]

template<class T , int N>

Dune::Fufem::SymmetricMatrix< T, N >::SymmetricMatrix ( )

inline

Default constructor, creates uninitialized matrix.

SymmetricMatrix() [2/2]

template<class T , int N>

template<class Iterator >

Dune::Fufem::SymmetricMatrix< T, N >::SymmetricMatrix ( Iterator  it )

inline

Construct from raw memory.

Member Function Documentation

axpy()

template<class T , int N>

void Dune::Fufem::SymmetricMatrix< T, N >::axpy ( const T &  a, const SymmetricMatrix< T, N > &  other  )

inline

data() [1/2]

template<class T , int N>

Data & Dune::Fufem::SymmetricMatrix< T, N >::data ( )

inline

data() [2/2]

template<class T , int N>

const Data & Dune::Fufem::SymmetricMatrix< T, N >::data ( ) const

inline

dataSize()

template<class T , int N>

static constexpr size_t Dune::Fufem::SymmetricMatrix< T, N >::dataSize ( )

inlinestaticconstexpr

Number of scalars needed for compressed vector storage of the symmetric matrix.

energyScalarProduct()

template<class T , int N>

T Dune::Fufem::SymmetricMatrix< T, N >::energyScalarProduct ( const FieldVector< T, N > &  v1, const FieldVector< T, N > &  v2  ) const

inline

frobenius_norm()

template<class T , int N>

T Dune::Fufem::SymmetricMatrix< T, N >::frobenius_norm ( ) const

inline

Compute the Frobenius norm of the matrix.

frobenius_norm2()

template<class T , int N>

T Dune::Fufem::SymmetricMatrix< T, N >::frobenius_norm2 ( ) const

inline

Compute the Frobenius norm of the matrix.

We have a guaranteed isometric mapping between the Frobenius norm of the matrix and the two-norm of the data vector!

identityMatrix()

template<class T , int N>

static constexpr SymmetricMatrix< T, N > Dune::Fufem::SymmetricMatrix< T, N >::identityMatrix ( )

inlinestaticconstexpr

Construct identityMatrix.

operator()()

template<class T , int N>

T Dune::Fufem::SymmetricMatrix< T, N >::operator() ( int  i, int  j  ) const

inline

Matrix style random read access to components.

Parameters

i	line index
j	column index The off-diagonal entries are scaled by 1/sqrt(2) to ensure isometry

operator*=()

template<class T , int N>

SymmetricMatrix< T, N > & Dune::Fufem::SymmetricMatrix< T, N >::operator*= ( const T &  s )

inline

operator=()

template<class T , int N>

SymmetricMatrix< T, N > & Dune::Fufem::SymmetricMatrix< T, N >::operator= ( const T &  s )

inline

setEntry()

template<class T , int N>

void Dune::Fufem::SymmetricMatrix< T, N >::setEntry ( int  i, int  j, const T &  entry  )

inline

Random write access to components.

Parameters

i	line index
j	column index
entry	The value to store as matrix entry The off-diagonal entries are scaled by sqrt(2) to ensure isometry

Note

: You need to know what you are doing: Modifying an off-diagonal entry modifies two entries in the matrix!

traceMap()

template<class T , int N>

static constexpr Data Dune::Fufem::SymmetricMatrix< T, N >::traceMap ( )

inlinestaticconstexpr

return the trace map in vector representation the returned vector is such that <data,a> = trace(A) where A.data = a

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

• symmetricmatrix.hh