Dense matrix. More...

#include <denseMatrix.hh>

Inheritance diagram for concepts::DenseMatrix< F >:

Collaboration diagram for concepts::DenseMatrix< F >:

Public Types
typedef Cmplxtype< F >::type	c_type
	Real type of data type.
typedef _Matrix_iterator< F, const F &, const F * >	const_iterator
typedef _Matrix_iterator< F, F &, F * >	iterator
typedef Realtype< F >::type	r_type
	Real type of data type.
typedef F	type
	Type of data, e.g. matrix entries.
typedef F	value_type
typedef F	value_type
Public Member Functions
void	add (const ElementMatrix< F > &A, uint offm=0, uint offn=0)
	Addition of another element matrix with possible offset.
template<class T >
void	addInto (Matrix< T > &dest, const T fact, const uint rowoffset=0, const uint coloffset=0) const
	allows to add a Real Matrix to a complex one.
void	addInto (Matrix< F > &dest, const F fact, const uint rowoffset=0, const uint coloffset=0) const
	This matrix is added into to the given matrix.
template<class T >
void	addIntoT (Matrix< T > &dest, const T fact, const uint rowoffset=0, const uint coloffset=0) const
	allows to add a Real Matrix to a complex one.
iterator	begin (uint r=0)
	Iterator over the elements, standing at position (r,0).
const_iterator	begin (uint r=0) const
	Constant iterator over the elements, standing at position (r,0)
uint	col () const
	Returns current column.
void	compress (const Real threshold=EPS)
	Compresses the matrix by dropping small entries.
	DenseMatrix (int m, int n, bool transpose=false)
	Constructor for an empty matrix.
	DenseMatrix (const Matrix< F > &m, bool t=false)
	Copy constructor.
	DenseMatrix (const Vector< F > &v, bool t=false)
	Transformation constructor from a vector of length n.
template<class G >
	DenseMatrix (const Space< G > &spcX, const Space< G > &spcY, BilinearForm< F, G > &bf)
	Constructor.
template<class G >
	DenseMatrix (const Space< G > &spc, BilinearForm< F, G > &bf)
	Constructor.
	DenseMatrix (const LiCo< F > &L)
	Constructor.
	DenseMatrix (const Compose< F > &L)
	Constructor.
template<class G >
	DenseMatrix (const Space< G > &spcX, const Space< G > &spcY)
	Constructor for an empty matrix.
	DenseMatrix (const DenseMatrix< F > &m)
	Copy constructor.
virtual const uint	dimX () const
	Returns the size of the image space of the operator (number of rows of the corresponding matrix)
virtual const uint	dimY () const
	Returns the size of the source space of the operator (number of columns of the corresponding matrix)
iterator	end ()
	Iterator, standing behind last element.
const_iterator	end () const
	Constant iterator, standing behind last element.
const Array< F > &	getData () const
	Returns the data array.
int	getIndex () const
bool	isTranspose () const
	Returns true if the matrix is transposed.
uint	m () const
	Returns the number of rows.
uint	n () const
	Returns the number of columns.
const uint	nofCols () const
	Number of columns.
const uint	nofRows () const
	Number of rows.
	operator const F * () const
	Returns a pointer to the data array.
	operator F * ()
	Returns a pointer to the data array.
virtual void	operator() (const Function< c_type > &fncY, Function< c_type > &fncX)
	Application operator for complex function `fncY`.
virtual F &	operator() (const uint i, const uint j)
	Returns and allows access to entry with indices `i` and `j`.
virtual void	operator() (const Function< r_type > &fncY, Function< F > &fncX)
	Computes `fncX` = A(`fncY`) where A is this matrix.
template<class H , class I >
void	operator() (const Vector< H > &fncY, Vector< I > &fncX)
virtual F	operator() (const uint i, const uint j) const
	Returns entry with indices `i` and `j`.
ElementMatrix< F > &	operator*= (const F n)
	Scaling operator.
virtual bool	operator== (const Matrix< F > &otherMat) const
void	resize (uint m, uint n)
	Sets a new size.
uint	row () const
	Returns current row.
void	setIndex (int i)
void	setTranspose (bool t)
uint	size () const
	Returns the number of entries in the matrix.
bool	storeMatlab (const std::string filename, std::string name="", bool append=false) const
	Stores the matrix in a Matlab matrix.
virtual void	transpMult (const Vector< c_type > &fncY, Vector< c_type > &fncX)
virtual void	transpMult (const Vector< r_type > &fncY, Vector< F > &fncX)
	Computes `fncX` = A^T `fncY` where A is this matrix.
bool	transpose ()
	Transposes the matrix.
void	zeros ()
	Fills the matrix with zeros.
Static Public Member Functions
template<class G >
static void	assembly (Matrix< F > &dest, const Space< G > &spc, BilinearForm< F, G > &bf, const Real threshold=0.0)
	Assembly operator for `dest` using the bilinear form `bf`.
template<class G >
static void	assembly (Matrix< F > &dest, BilinearForm< F, G > &bf, const ElementPairList< G > &pairs)
	Assembly operator for `dest` using the bilinear form `bf`.
template<class G >
static void	assembly (Matrix< F > &dest, const Space< G > &spcX, const Space< G > &spcY, BilinearForm< F, G > &bf, const Real threshold=0.0)
	Assembly operator for `dest` using the bilinear form `bf`.
Timing Interface
These functions are used to get timings from class internal computations. The values are stored in a user defined concepts::InOutParameters structure in different arrays (see `setTimings`). These arrays can be grouped into a table for easier postprocessing with concepts::ResultsTable table; table.addMap(concepts::ResultsTable::DOUBLE, "jacobian", output); table.addMap(concepts::ResultsTable::DOUBLE, "whole_sumfact", output); std::ofstream ofs("table.gnuplot"); ofs << std::setprecision(20); table.print<concepts::ResultsTable::GNUPLOT>(ofs);
static void	setTimings (InOutParameters *timings)
	Sets the class to store the timing values in.
static bool	timings ()
	Returns true if the class is able to do timings.
Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
Protected Attributes
Array< F >	data_
	Data.
uint	dimX_
	Dimension of image space and the source space.
uint	dimY_
uint	m_
	Number of rows.
uint	n_
	Number of columns.
bool	t_
	Transpose.

Detailed Description

template<class F>
class concepts::DenseMatrix< F >

Dense matrix.

The matrix has the size $m \times n$ where m is the dimension of the image space (spaceX) and n is the dimension of the source space (spaceY).

The matrix is setup and assembled in the constructor. It calls the bilinear form on every element of the space and uses the T matrices of the elements to assemble the element matrices into the global matrix.

There are quite a few solver which can be used to solve the system.

See also:: TMatrixBase; CG; GMRes

Definition at line 39 of file denseMatrix.hh.

Member Typedef Documentation

template<class F>

typedef Cmplxtype<F>::type concepts::DenseMatrix< F >::c_type

Real type of data type.

Reimplemented from concepts::Matrix< F >.

Definition at line 44 of file denseMatrix.hh.

template<class F>

typedef _Matrix_iterator<F, const F&, const F*> concepts::Matrix< F >::const_iterator [inherited]

Reimplemented in concepts::SparseMatrix< F >, concepts::SubMatrixN< F >, concepts::SparseMatrix< concepts::Real >, concepts::SparseMatrix< FX >, concepts::SparseMatrix< T >, concepts::SparseMatrix< Cmplx >, and concepts::SparseMatrix< Real >.

Definition at line 42 of file matrix.hh.

template<class F>

typedef _Matrix_iterator<F, F&, F*> concepts::Matrix< F >::iterator [inherited]

Reimplemented in concepts::SparseMatrix< F >, concepts::SubMatrixN< F >, concepts::SparseMatrix< concepts::Real >, concepts::SparseMatrix< FX >, concepts::SparseMatrix< T >, concepts::SparseMatrix< Cmplx >, and concepts::SparseMatrix< Real >.

Definition at line 41 of file matrix.hh.

template<class F>

typedef Realtype<F>::type concepts::DenseMatrix< F >::r_type

Real type of data type.

Reimplemented from concepts::Matrix< F >.

Definition at line 42 of file denseMatrix.hh.

template<class F>

typedef F concepts::Operator< F >::type [inherited]

Type of data, e.g. matrix entries.

Reimplemented in concepts::AfterIteration< F >, and concepts::SubMatrixN< F >.

Definition at line 43 of file compositions.hh.

template<class F>

typedef F concepts::Matrix< F >::value_type [inherited]

Definition at line 35 of file matrix.hh.

template<class F>

typedef F concepts::ElementMatrix< F >::value_type [inherited]

Reimplemented from concepts::ElementMatrixBase< F >.

Definition at line 195 of file element.hh.

Constructor & Destructor Documentation

template<class F>

template<class G >

concepts::DenseMatrix< F >::DenseMatrix	(	const Space< G > &	spcX,
		const Space< G > &	spcY,
		BilinearForm< F, G > &	bf
	)

Constructor.

Computes the global matrix by assembling the element matrices.

This constructor features a double loop over the elements of the image and the source space. On each combination, the bilinear form is called.

Using this constructor, if spcX != spcY or if you have local matrices which express the interaction of the two elements. You can force this constructor to execute the double loop in such a way that only for diagonal combinations of the elements in both space the integration and assembling is executed. Use single and set it to true.

In non-symmetric FEM (eg. DGFEM), one has to solve A^T u = f. This constructor computes A and not A^T.

Parameters:

spcX	Image space
spcY	Source space
bf	Bilinear form

template<class F>

template<class G >

concepts::DenseMatrix< F >::DenseMatrix	(	const Space< G > &	spc,
		BilinearForm< F, G > &	bf
	)

Constructor.

Computes the global matrix by assembling the element matrices.

This constructor features a single loop over the elements of the space. On each element, the bilinear form is called.

Use the constructor, if spcX == spcY and there is no special element interaction. This is the case for standard FEM.

Parameters:

spc	Image and source space
bf	Bilinear form

template<class F>

template<class G >

concepts::DenseMatrix< F >::DenseMatrix	(	const Space< G > &	spcX,
		const Space< G > &	spcY
	)

Constructor for an empty matrix.

Parameters:

spcX	Image space
spcY	Source space

template<class F>

concepts::DenseMatrix< F >::DenseMatrix	(	int	m,
		int	n,
		bool	transpose = `false`
	)		`[inline]`

Constructor for an empty matrix.

Parameters:

m	Number of rows
n	Number of columns
transpose	The matrix will be stored in transposed format

Definition at line 100 of file denseMatrix.hh.

template<class F>

concepts::DenseMatrix< F >::DenseMatrix ( const LiCo< F > & L )

Constructor.

Evaluates a linear combination and stores the result in the matrix.

template<class F>

concepts::DenseMatrix< F >::DenseMatrix ( const Compose< F > & L )

Constructor.

Evaluates a composition and stores the result in the matrix.

template<class F>

concepts::DenseMatrix< F >::DenseMatrix ( const DenseMatrix< F > & m )

Copy constructor.

template<class F>

concepts::DenseMatrix< F >::DenseMatrix	(	const Matrix< F > &	m,
		bool	t = `false`
	)

Copy constructor.

If t is set to true, the matrix is transposed during the copy process

template<class F>

concepts::DenseMatrix< F >::DenseMatrix	(	const Vector< F > &	v,
		bool	t = `false`
	)

Transformation constructor from a vector of length n.

If t is set to true, the matrix is a 1xn, otherwise nx1.

Member Function Documentation

template<class F>

void concepts::ElementMatrix< F >::add	(	const ElementMatrix< F > &	A,
		uint	offm = `0`,
		uint	offn = `0`
	)		`[inherited]`

Addition of another element matrix with possible offset.

template<class F>

template<class T >

void concepts::DenseMatrix< F >::addInto	(	Matrix< T > &	dest,
		const T	fact,
		const uint	rowoffset = `0`,
		const uint	coloffset = `0`
	)		const `[inline]`

allows to add a Real Matrix to a complex one.

Definition at line 157 of file denseMatrix.hh.

template<class F>

void concepts::DenseMatrix< F >::addInto	(	Matrix< F > &	dest,
		const F	fact,
		const uint	rowoffset = `0`,
		const uint	coloffset = `0`
	)		const

This matrix is added into to the given matrix.

Parameters:

dest	Matrix into which this matrix should be added.
fact	Factor by which this matrix should be multiplied.

template<class F>

template<class T >

void concepts::DenseMatrix< F >::addIntoT	(	Matrix< T > &	dest,
		const T	fact,
		const uint	rowoffset = `0`,
		const uint	coloffset = `0`
	)		const `[inline]`

allows to add a Real Matrix to a complex one.

Definition at line 173 of file denseMatrix.hh.

template<class F>

template<class G >

static void concepts::Matrix< F >::assembly	(	Matrix< F > &	dest,
		const Space< G > &	spc,
		BilinearForm< F, G > &	bf,
		const Real	threshold = `0.0`
	)		`[static, inherited]`

Assembly operator for dest using the bilinear form bf.

This assembly operator does not compute element matrices for two different elements. The elements are taken from the space spc.

Examples:: linearDG1d.cc.

template<class F>

template<class G >

static void concepts::Matrix< F >::assembly	(	Matrix< F > &	dest,
		const Space< G > &	spcX,
		const Space< G > &	spcY,
		BilinearForm< F, G > &	bf,
		const Real	threshold = `0.0`
	)		`[static, inherited]`

Assembly operator for dest using the bilinear form bf.

This assembly operator computes also the element matrices for two different elements (coming from spcX and spcY).

template<class F>

template<class G >

static void concepts::Matrix< F >::assembly	(	Matrix< F > &	dest,
		BilinearForm< F, G > &	bf,
		const ElementPairList< G > &	pairs
	)		`[static, inherited]`

Assembly operator for dest using the bilinear form bf.

This assembly operator uses the element pairs taken from pairs. For every two elements found in a ElementPair in pairs, the bilinear form is evaluated and the result assembled into dest.

template<class F>

iterator concepts::Matrix< F >::begin ( uint r = 0 ) [inline, inherited]

Iterator over the elements, standing at position (r,0).

Might be implemented differently for derived classes.

Reimplemented in concepts::SparseMatrix< F >, concepts::SubMatrixN< F >, concepts::SparseMatrix< concepts::Real >, concepts::SparseMatrix< FX >, concepts::SparseMatrix< T >, concepts::SparseMatrix< Cmplx >, and concepts::SparseMatrix< Real >.

Definition at line 55 of file matrix.hh.

template<class F>

const_iterator concepts::Matrix< F >::begin ( uint r = 0 ) const [inline, inherited]

Constant iterator over the elements, standing at position (r,0)

Might be implemented differently for derived classes.

Reimplemented in concepts::SparseMatrix< F >, concepts::SubMatrixN< F >, concepts::SparseMatrix< concepts::Real >, concepts::SparseMatrix< FX >, concepts::SparseMatrix< T >, concepts::SparseMatrix< Cmplx >, and concepts::SparseMatrix< Real >.

Definition at line 62 of file matrix.hh.

template<class F>

uint concepts::ElementMatrix< F >::col ( ) const [inline, inherited]

Returns current column.

Definition at line 262 of file element.hh.

template<class F>

void concepts::ElementMatrix< F >::compress ( const Real threshold = EPS ) [inherited]

Compresses the matrix by dropping small entries.

All matrix entries which are smaller than a certain threshold times the largest entry of the matrix are deleted from the matrix.

template<class F>

virtual const uint concepts::Operator< F >::dimX ( ) const [inline, virtual, inherited]

Returns the size of the image space of the operator (number of rows of the corresponding matrix)

Definition at line 87 of file compositions.hh.

template<class F>

virtual const uint concepts::Operator< F >::dimY ( ) const [inline, virtual, inherited]

Returns the size of the source space of the operator (number of columns of the corresponding matrix)

Definition at line 92 of file compositions.hh.

template<class F>

const_iterator concepts::Matrix< F >::end ( ) const [inline, inherited]

Constant iterator, standing behind last element.

Reimplemented in concepts::SparseMatrix< F >, concepts::SubMatrixN< F >, concepts::SparseMatrix< concepts::Real >, concepts::SparseMatrix< FX >, concepts::SparseMatrix< T >, concepts::SparseMatrix< Cmplx >, and concepts::SparseMatrix< Real >.

Definition at line 64 of file matrix.hh.

template<class F>

iterator concepts::Matrix< F >::end ( ) [inline, inherited]

Iterator, standing behind last element.

Definition at line 57 of file matrix.hh.

template<class F>

const Array<F>& concepts::ElementMatrixBase< F >::getData ( ) const [inline, inherited]

Returns the data array.

Definition at line 161 of file element.hh.

template<class F>

int concepts::ElementMatrix< F >::getIndex ( ) const [inline, inherited]

Deprecated:: : FIXME: what the heck is this even for?

Definition at line 242 of file element.hh.

template<class F>

virtual std::ostream& concepts::DenseMatrix< F >::info ( std::ostream & os ) const [protected, virtual]

Reimplemented from concepts::ElementMatrix< F >.

template<class F>

bool concepts::ElementMatrixBase< F >::isTranspose ( ) const [inline, inherited]

Returns true if the matrix is transposed.

Definition at line 164 of file element.hh.

template<class F>

uint concepts::ElementMatrixBase< F >::m ( ) const [inline, inherited]

Returns the number of rows.

Definition at line 140 of file element.hh.

template<class F>

uint concepts::ElementMatrixBase< F >::n ( ) const [inline, inherited]

Returns the number of columns.

Definition at line 142 of file element.hh.

template<class F>

const uint concepts::Matrix< F >::nofCols ( ) const [inline, inherited]

Number of columns.

Definition at line 49 of file matrix.hh.

template<class F>

const uint concepts::Matrix< F >::nofRows ( ) const [inline, inherited]

Number of rows.

Definition at line 47 of file matrix.hh.

template<class F>

concepts::ElementMatrixBase< F >::operator const F * ( ) const [inline, inherited]

Returns a pointer to the data array.

Definition at line 158 of file element.hh.

template<class F>

concepts::ElementMatrix< F >::operator F * ( ) [inline, inherited]

Returns a pointer to the data array.

Definition at line 251 of file element.hh.

template<class F>

virtual void concepts::DenseMatrix< F >::operator()	(	const Function< r_type > &	fncY,
		Function< F > &	fncX
	)		`[virtual]`

Computes fncX = A(fncY) where A is this matrix.

Implements concepts::Matrix< F >.

template<class F>

virtual void concepts::DenseMatrix< F >::operator()	(	const Function< c_type > &	fncY,
		Function< c_type > &	fncX
	)		`[virtual]`

Application operator for complex function fncY.

Computes fncX = A(fncY) where A is this operator. fncX becomes complex.

In derived classes its enough to implement the operator() for complex Operator's. If a real counterpart is not implemented, the function fncY is splitted into real and imaginary part and the application operator for real functions is called for each. Then the result is combined.

If in a derived class the operator() for complex Operator's is not implemented, a exception is thrown from here.

Implements concepts::Matrix< F >.

template<class F>

virtual F concepts::DenseMatrix< F >::operator()	(	const uint	i,
		const uint	j
	)		const `[inline, virtual]`

Returns entry with indices i and j.

Implements concepts::Matrix< F >.

Definition at line 140 of file denseMatrix.hh.

template<class F >

template<class H , class I >

void concepts::DenseMatrix< F >::operator()	(	const Vector< H > &	fncY,
		Vector< I > &	fncX
	)

Definition at line 192 of file denseMatrix.hh.

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template<class F>

virtual F& concepts::DenseMatrix< F >::operator()	(	const uint	i,
		const uint	j
	)		`[inline, virtual]`

Returns and allows access to entry with indices i and j.

Implements concepts::Matrix< F >.

Definition at line 144 of file denseMatrix.hh.

template<class F>

ElementMatrix<F>& concepts::ElementMatrix< F >::operator*= ( const F n ) [inline, inherited]

Scaling operator.

Definition at line 254 of file element.hh.

template<class F>

virtual bool concepts::Matrix< F >::operator== ( const Matrix< F > & otherMat ) const [inline, virtual, inherited]

Definition at line 103 of file matrix.hh.

template<class F>

void concepts::ElementMatrix< F >::resize	(	uint	m,
		uint	n
	)		`[inherited]`

Sets a new size.

template<class F>

uint concepts::ElementMatrix< F >::row ( ) const [inline, inherited]

Returns current row.

Definition at line 260 of file element.hh.

template<class F>

void concepts::ElementMatrix< F >::setIndex ( int i ) [inline, inherited]

Deprecated:: : FIXME: what the heck is this even for?

Definition at line 245 of file element.hh.

template<class F>

static void concepts::Matrix< F >::setTimings ( InOutParameters * timings ) [static, inherited]

Sets the class to store the timing values in.

Additionally, the timeCntr_ is reset to 0. This counter is used to fill in the values into the arrays listed below in subsequent calls. The following timings are taken and stored in timings:

evaluation of bilinear form in bilinear_form
application of T matrix in tmatrix_apply
assembling into global matrix in global_assembly

template<class F>

void concepts::ElementMatrix< F >::setTranspose ( bool t ) [inline, inherited]

Definition at line 239 of file element.hh.

template<class F>

uint concepts::ElementMatrixBase< F >::size ( ) const [inline, inherited]

Returns the number of entries in the matrix.

Definition at line 155 of file element.hh.

template<class F>

bool concepts::ElementMatrixBase< F >::storeMatlab	(	const std::string	filename,
		std::string	name = `""`,
		bool	append = `false`
	)		const `[inherited]`

Stores the matrix in a Matlab matrix.

Parameters:

filename	name of the matlab file, with ending '.m'
name	name of the variable, e.g. "A"
append	if false, create new file, otherwise append to it

Returns:: true if the writes was successfull

template<class F>

static bool concepts::Matrix< F >::timings ( ) [static, inherited]

Returns true if the class is able to do timings.

The ability to do timings depends on a compiler switch in matrix.cc file.

template<class F>

virtual void concepts::DenseMatrix< F >::transpMult	(	const Vector< r_type > &	fncY,
		Vector< F > &	fncX
	)		`[virtual]`

Computes fncX = A^T fncY where A is this matrix.

Implements concepts::Matrix< F >.

template<class F>

virtual void concepts::DenseMatrix< F >::transpMult	(	const Vector< c_type > &	fncY,
		Vector< c_type > &	fncX
	)		`[virtual]`

Implements concepts::Matrix< F >.

template<class F>

bool concepts::ElementMatrix< F >::transpose ( ) [inline, inherited]

Transposes the matrix.

Deprecated:: use isTranspose() and setTranspose()

Definition at line 237 of file element.hh.

template<class F>

void concepts::ElementMatrix< F >::zeros ( ) [inline, inherited]

Fills the matrix with zeros.

Definition at line 248 of file element.hh.

Member Data Documentation

template<class F>

Array<F> concepts::ElementMatrixBase< F >::data_ [protected, inherited]

Data.

Definition at line 176 of file element.hh.

template<class F>

uint concepts::Operator< F >::dimX_ [protected, inherited]

Dimension of image space and the source space.

Definition at line 96 of file compositions.hh.

template<class F>

uint concepts::Operator< F >::dimY_ [protected, inherited]

Definition at line 96 of file compositions.hh.

template<class F>

uint concepts::ElementMatrixBase< F >::m_ [protected, inherited]

Number of rows.

Definition at line 178 of file element.hh.

template<class F>

uint concepts::ElementMatrixBase< F >::n_ [protected, inherited]

Number of columns.

Definition at line 180 of file element.hh.

template<class F>

bool concepts::ElementMatrixBase< F >::t_ [protected, inherited]

Transpose.

Definition at line 182 of file element.hh.

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

operator/denseMatrix.hh

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

template<class F> class concepts::DenseMatrix< F >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<class F>
class concepts::DenseMatrix< F >