dune-common  2.3.1
Public Types | Public Member Functions | List of all members
Dune::FieldMatrix< K, ROWS, COLS > Class Template Reference

A dense n x m matrix. More...

#include <dune/common/fmatrix.hh>

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

Public Types

enum  { rows = ROWS, cols = COLS }
 export size More...
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
enum  
 We are at the leaf of the block recursion. More...
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
Iterator
 Iterator class for sequential access.
typedef Iterator iterator
 typedef for stl compliant access
typedef Iterator RowIterator
 rename the iterators for easier access
typedef row_type::Iterator ColIterator
 rename the iterators for easier access
typedef DenseIterator< const
DenseMatrix, const row_type
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 row_type::ConstIterator ConstColIterator
 rename the iterators for easier access

Public Member Functions

 FieldMatrix ()
 Default constructor.
template<class Other >
 FieldMatrix (const Other &other)
 Constructor initializing the whole matrix with a scalar.
template<int l>
FieldMatrix< K, l, colsleftmultiplyany (const FieldMatrix< K, l, rows > &M) const
 Multiplies M from the left to this matrix, this matrix is not modified.
FieldMatrixrightmultiply (const FieldMatrix< K, cols, cols > &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.
DUNE_CONSTEXPR size_type mat_rows () const
DUNE_CONSTEXPR size_type mat_cols () const
row_reference mat_access (size_type i)
const_row_reference mat_access (size_type i) const
row_reference operator[] (size_type i)
 random access
const_row_reference operator[] (size_type i) const
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
DenseMatrixoperator+= (const DenseMatrix< Other > &y)
 vector space addition
DenseMatrixoperator-= (const DenseMatrix< Other > &y)
 vector space subtraction
DenseMatrixoperator*= (const field_type &k)
 vector space multiplication with scalar
DenseMatrixoperator/= (const field_type &k)
 vector space division by scalar
DenseMatrixaxpy (const field_type &k, const DenseMatrix< Other > &y)
 vector space axpy operation (*this += k y)
bool operator== (const DenseMatrix< Other > &y) const
 Binary matrix comparison.
bool operator!= (const DenseMatrix< Other > &y) 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 field_type &alpha, const X &x, Y &y) const
 y += alpha A x
void usmtv (const field_type &alpha, const X &x, Y &y) const
 y += alpha A^T x
void usmhv (const 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< value_type >
::real_type 
infinity_norm () const
 infinity norm (row sum norm, how to generalize for blocks?)
FieldTraits< value_type >
::real_type 
infinity_norm_real () const
 simplified infinity norm (uses Manhattan norm for complex values)
void solve (V &x, const V &b) const
 Solve system A x = b.
void invert ()
 Compute inverse.
field_type determinant () 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.
size_type N () const
 number of rows
size_type M () const
 number of columns
size_type rows () const
 number of rows
size_type cols () const
 number of columns
bool exists (size_type i, size_type j) const
 return true when (i,j) is in pattern

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

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

export the type representing the components

typedef row_type::Iterator Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::ColIterator
inherited

rename the iterators for easier access

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

typedef for stl compliant access

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

rename the iterators for easier access

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

Iterator class for sequential access.

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

rename the iterators for easier access

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

type of derived matrix class

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

export the type representing the field

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

Iterator class for sequential access.

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

typedef for stl compliant access

template<class K, int ROWS, int COLS>
typedef Base::row_reference Dune::FieldMatrix< K, ROWS, COLS >::row_reference
template<class K, int ROWS, int COLS>
typedef Base::row_type Dune::FieldMatrix< K, ROWS, COLS >::row_type
typedef Iterator Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::RowIterator
inherited

rename the iterators for easier access

template<class K, int ROWS, int COLS>
typedef Base::size_type Dune::FieldMatrix< K, ROWS, COLS >::size_type
typedef Traits::value_type Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::value_type
inherited

export the type representing the field

Member Enumeration Documentation

template<class K, int ROWS, int COLS>
anonymous enum

export size

Enumerator:
rows 

The number of rows.

cols 

The number of columns.

anonymous enum
inherited

We are at the leaf of the block recursion.

Constructor & Destructor Documentation

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

Default constructor.

template<class K, int ROWS, int COLS>
template<class Other >
Dune::FieldMatrix< K, ROWS, COLS >::FieldMatrix ( const Other &  other)
inline

Constructor initializing the whole matrix with a scalar.

Member Function Documentation

DenseMatrix& Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::axpy ( const field_type k,
const DenseMatrix< Other > &  y 
)
inlineinherited

vector space axpy operation (*this += k y)

Iterator Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::beforeBegin ( )
inlineinherited
Returns
an iterator that is positioned before the first entry of the vector.
ConstIterator Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::beforeBegin ( ) const
inlineinherited
Returns
an iterator that is positioned before the first entry of the vector.
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.
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
Iterator Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::begin ( )
inlineinherited

begin iterator

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

begin iterator

size_type Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::cols ( ) const
inlineinherited
field_type Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::determinant ( ) const
inherited

calculates the determinant of this matrix

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

end iterator

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

end iterator

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

return true when (i,j) is in pattern

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

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

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

square of frobenius norm, need for block recursion

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

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

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

simplified infinity norm (uses Manhattan norm for complex values)

void Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::invert ( )
inherited

Compute inverse.

Exceptions
FMatrixErrorif the matrix is singular
FieldMatrix< K, ROWS, COLS > & Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::leftmultiply ( const DenseMatrix< M2 > &  M)
inlineinherited

Multiplies M from the left to this matrix.

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
inline

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

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

number of columns

template<class K, int ROWS, int COLS>
row_reference Dune::FieldMatrix< K, ROWS, COLS >::mat_access ( size_type  i)
inline
template<class K, int ROWS, int COLS>
const_row_reference Dune::FieldMatrix< K, ROWS, COLS >::mat_access ( size_type  i) const
inline
template<class K, int ROWS, int COLS>
DUNE_CONSTEXPR size_type Dune::FieldMatrix< K, ROWS, COLS >::mat_cols ( ) const
inline
template<class K, int ROWS, int COLS>
DUNE_CONSTEXPR size_type Dune::FieldMatrix< K, ROWS, COLS >::mat_rows ( ) const
inline
void Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::mmhv ( const X &  x,
Y &  y 
) const
inlineinherited

y -= A^H x

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

y -= A^T x

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

y -= A x

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

y = A^T x

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

y = A x

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

number of rows

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

Binary matrix incomparison.

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

vector space multiplication with scalar

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

vector space addition

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

vector space subtraction

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

vector space division by scalar

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

Binary matrix comparison.

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

random access

const_row_reference Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::operator[] ( size_type  i) const
inlineinherited
template<class K, int ROWS, int COLS>
FieldMatrix& Dune::FieldMatrix< K, ROWS, COLS >::rightmultiply ( const FieldMatrix< K, cols, cols > &  M)
inline

Multiplies M from the right to this matrix.

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

Multiplies M from the right to this matrix.

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
inline

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

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

size method (number of rows)

void Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::solve ( V &  x,
const V &  b 
) const
inherited

Solve system A x = b.

Exceptions
FMatrixErrorif the matrix is singular
void Dune::DenseMatrix< FieldMatrix< K, ROWS, COLS > >::umhv ( const X &  x,
Y &  y 
) const
inlineinherited

y += A^H x

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

y += A^T x

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

y += A x

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

y += alpha A^H x

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

y += alpha A^T x

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

y += alpha A x


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