Linear combination of two operators. More...

#include <compositions.hh>

Inheritance diagram for concepts::LiCo< F >:
concepts::Operator< F > 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...
 
 LiCo (Operator< F > &A, Operator< F > &B, F a=1.0, F b=1.0)
 Constructor. 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...
 
virtual void show_messages ()
 

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...
 
a_
 Scalar a. More...
 
Operator< F > & B_
 Operator B. More...
 
b_
 Scalar b. More...
 

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
linearDG1d.cc, linearFEM1d-simple.cc, and linearFEM1d.cc.

Definition at line 364 of file compositions.hh.

Member Typedef Documentation

◆ c_type

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

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

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

◆ LiCo()

template<class F >
concepts::LiCo< F >::LiCo ( Operator< F > &  A,
Operator< F > &  B,
a = 1.0,
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
AFirst operator
BSecond operator
aCoefficient of $A$, defaults to 1
bCoefficient of $B$, defaults to 1

Definition at line 379 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 
)
inlineprivate

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

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
destMatrix into which the operator should be collapsed. Should be zero on startup since the components are added into the matrix.
factFactor 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
protectedvirtual

Reimplemented from concepts::Operator< F >.

◆ operator()() [1/3]

template<class F >
virtual void concepts::Operator< F >::operator() ( )
virtualinherited

◆ operator()() [2/3]

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

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.

◆ operator()() [3/3]

template<class F >
void concepts::LiCo< F >::operator() ( const Function< r_type > &  fncY,
Function< F > &  fncX 
)
inlinevirtual

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 393 of file compositions.hh.

◆ show_messages()

template<class F >
virtual void concepts::Operator< F >::show_messages ( )
inlinevirtualinherited

Reimplemented in concepts::Newton< F >, concepts::MumpsOverlap< F >, and concepts::Mumps< F >.

Definition at line 100 of file compositions.hh.

Member Data Documentation

◆ A_

template<class F >
Operator<F>& concepts::LiCo< F >::A_
private

Operator A.

Definition at line 422 of file compositions.hh.

◆ a_

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

Scalar a.

Definition at line 426 of file compositions.hh.

◆ B_

template<class F >
Operator<F>& concepts::LiCo< F >::B_
private

Operator B.

Definition at line 424 of file compositions.hh.

◆ b_

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

Scalar b.

Definition at line 428 of file compositions.hh.

◆ dimX_

template<class F >
uint concepts::Operator< F >::dimX_
protectedinherited

Dimension of image space and the source space.

Definition at line 104 of file compositions.hh.

◆ dimY_

template<class F >
uint concepts::Operator< F >::dimY_
protectedinherited

Definition at line 104 of file compositions.hh.


The documentation for this class was generated from the following file:
Page URL: http://wiki.math.ethz.ch/bin/view/Concepts/WebHome
21 August 2020
© 2020 Eidgenössische Technische Hochschule Zürich