Schur complement. More...

#include <compositions.hh>

Inheritance diagram for concepts::SchurCompl< F >:

Public Types
typedef Cmplxtype< F >::type	c_type
	Real type of data type. More...

typedef Realtype< F >::type	r_type
	Real type of data type. More...

typedef F	type
	Type of data, e.g. matrix entries. More...

Public Member Functions
bool	collapse (Matrix< F > &dest, const F fact=1.0) const
	Collapses the linear combination of matrices into one matrix. More...

virtual const uint	dimX () const
	Returns the size of the image space of the operator (number of rows of the corresponding matrix) More...

virtual const uint	dimY () const
	Returns the size of the source space of the operator (number of columns of the corresponding matrix) More...

virtual void	operator() ()
	Application operator without argument. More...

void	operator() (const Function< c_type > &fncY, Function< c_type > &fncX)
	Application operator for complex function `fncY`. More...

void	operator() (const Function< r_type > &fncY, Function< F > &fncX)
	Application operator. More...

	SchurCompl (Operator< F > &A_II_inv, Operator< F > &A_IB, Operator< F > &A_BI, Operator< F > &A_BB)
	Constructor. More...

virtual void	show_messages ()

virtual	~SchurCompl ()

Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const

Protected Attributes
uint	dimX_
	Dimension of image space and the source space. More...

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. More...

F	a_
	Scalar a. More...

Operator< F > &	B_
	Operator B. More...

F	b_
	Scalar b. More...

Compose< F > *	C_
	Product of A_II^-1 * A_IB or A_BI * A_II^-1 * A_IB respectivly. More...

Compose< F > *	D_

Detailed Description

template<class F>
class concepts::SchurCompl< F >

Schur complement.

Calculates S = A_BB - A_BI * A_II^-1 * A_IB with given operators for A_BB, A_BI, A_II, AIB.

Author: Kersten Schmidt, 2005

Definition at line 457 of file compositions.hh.

Member Typedef Documentation

◆ c_type

template<class F >

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

inherited

Real type of data type.

Definition at line 369 of file compositions.hh.

◆ r_type

template<class F >

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

inherited

Real type of data type.

Definition at line 367 of file compositions.hh.

◆ type

template<class F >

typedef F concepts::Operator< F >::type

inherited

Type of data, e.g. matrix entries.

Definition at line 45 of file compositions.hh.

Constructor & Destructor Documentation

◆ SchurCompl()

template<class F >

concepts::SchurCompl< F >::SchurCompl	(	Operator< F > &	A_II_inv,
		Operator< F > &	A_IB,
		Operator< F > &	A_BI,
		Operator< F > &	A_BB
	)

Constructor.

Definition at line 471 of file compositions.hh.

◆ ~SchurCompl()

template<class F >

virtual concepts::SchurCompl< F >::~SchurCompl ( )

inlinevirtual

Definition at line 462 of file compositions.hh.

Member Function Documentation

◆ apply_()

template<class F >

template<class H , class I >

void concepts::LiCo< F >::apply_	(	const Function< H > &	fncY,
		Function< I > &	fncX
	)

inlineprivateinherited

Definition at line 436 of file compositions.hh.

◆ collapse()

template<class F >

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

inherited

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.

◆ dimX()

template<class F >

virtual const uint concepts::Operator< F >::dimX ( ) const

inlinevirtualinherited

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

Definition at line 93 of file compositions.hh.

◆ dimY()

template<class F >

virtual const uint concepts::Operator< F >::dimY ( ) const

inlinevirtualinherited

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

Definition at line 98 of file compositions.hh.

◆ info()

template<class F >

virtual std::ostream& concepts::LiCo< F >::info ( std::ostream & os ) const

protectedvirtualinherited

Reimplemented from concepts::Operator< F >.

◆ operator()() [1/3]

template<class F >

virtual void concepts::Operator< F >::operator() ( )

virtualinherited

Application operator without argument.

Reimplemented in concepts::VecOperator< F >, concepts::VecOperator< T >, concepts::VecOperator< F::d_type >, concepts::VecOperator< Cmplx >, concepts::VecOperator< Real >, and concepts::BelosSolver< T >.

◆ operator()() [2/3]

template<class F >

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

inlinevirtualinherited

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 397 of file compositions.hh.