Linear combination of two operators. More...

#include <compositions.hh>

Inheritance diagram for concepts::LiCo< F >:

Collaboration diagram for concepts::LiCo< F >:

Public Types
typedef Cmplxtype< F >::type	c_type
	Real type of data type.
typedef Realtype< F >::type	r_type
	Real type of data type.
typedef F	type
	Type of data, e.g. matrix entries.
Public Member Functions
bool	collapse (Matrix< F > &dest, const F fact=1.0) const
	Collapses the linear combination of matrices into one matrix.
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)
	LiCo (Operator< F > &A, Operator< F > &B, F a=1.0, F b=1.0)
	Constructor.
void	operator() (const Function< c_type > &fncY, Function< c_type > &fncX)
	Application operator for complex function `fncY`.
void	operator() (const Function< r_type > &fncY, Function< F > &fncX)
	Application operator.
Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.
Protected Attributes
uint	dimX_
	Dimension of image space and the source space.
uint	dimY_
Private Member Functions
template<class H , class I >
void	apply_ (const Function< H > &fncY, Function< I > &fncX)
Private Attributes
Operator< F > &	A_
	Operator A.
F	a_
	Scalar a.
F	b_
	Scalar b.
Operator< F > &	B_
	Operator B.

Detailed Description

template<class F>
class concepts::LiCo< F >

Linear combination of two operators.

The application operator evaluates a*A + b*B.

Test:

test::CompositionsTest

test::DeepCompositionsTest

Examples:: hpFEM3d-EV.cc, linearDG1d.cc, linearFEM1d-simple.cc, and linearFEM1d.cc.

Definition at line 351 of file compositions.hh.

Member Typedef Documentation

template<class F>

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

Real type of data type.

Reimplemented from concepts::Operator< F >.

Definition at line 356 of file compositions.hh.

template<class F>

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

Real type of data type.

Reimplemented from concepts::Operator< F >.

Definition at line 354 of file compositions.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.

Constructor & Destructor Documentation

template<class F>

concepts::LiCo< F >::LiCo	(	Operator< F > &	A,
		Operator< F > &	B,
		F	a = `1.0`,
		F	b = `1.0`
	)		`[inline]`

Constructor.

The operator consists of $a A + b B$ where $A$ and $B$ are two operators and $a$ and $b$ are scalars.

Parameters:

A	First operator
B	Second operator
a	Coefficient of $A$, defaults to 1
b	Coefficient of $B$, defaults to 1

Definition at line 366 of file compositions.hh.

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Member Function Documentation

template<class F >

template<class H , class I >

void concepts::LiCo< F >::apply_	(	const Function< H > &	fncY,
		Function< I > &	fncX
	)		`[inline, private]`

Definition at line 423 of file compositions.hh.

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template<class F>

bool concepts::LiCo< F >::collapse	(	Matrix< F > &	dest,
		const F	fact = `1.0`
	)		const

Collapses the linear combination of matrices into one matrix.

This only works in some rare combinations, test it out. This method calls addInto on each matrix which makes part of this linear combination or itself on a linear combination.

The method fails if it encounters something else than a LiCo, LiCoI or a matrix.

Returns:: True, if the operation was successful

Parameters:

dest	Matrix into which the operator should be collapsed. Should be zero on startup since the components are added into the matrix.
fact	Factor by which both components should be multiplied. Defaults to 1, ie. can be omitted.

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>

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

Returns information in an output stream.

Reimplemented from concepts::Operator< F >.

template<class F>

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

Application operator.

Calculates

$x=a \cdot Ay + b \cdot By = (aA + bB)y$

where $A$ and $B$ are the matrices and $a$ and $b$ their respective coefficients.

Parameters:

fncY	$y,$
fncX	$x,$

Reimplemented from concepts::Operator< F >.

Definition at line 380 of file compositions.hh.

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template<class F>

void concepts::LiCo< F >::operator()	(	const Function< c_type > &	fncY,
		Function< c_type > &	fncX
	)		`[inline, 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.

Reimplemented from concepts::Operator< F >.

Definition at line 384 of file compositions.hh.

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