CAPD DynSys Library 5.2.0
Public Types | Public Member Functions | Static Public Member Functions | Protected Member Functions | Protected Attributes | List of all members
capd::dynset::C11Rect2< MatrixT, QRPolicy > Class Template Referenceabstract
Dynset

$C^1$ doubleton set with reorganization moved by QR decomposition (3rd method). More...

#include <capd/dynset/C11Rect2.h>

Public Types

typedef MatrixT MatrixType
 
typedef MatrixType::RowVectorType VectorType
 
typedef MatrixType::ScalarType ScalarType
 
typedef MatrixType::size_type size_type
 
typedef C1Set SetType
 defines class of given set (C0, C1, C2, ...) More...
 
typedef capd::dynsys::C1DynSys< MatrixType > DynSysType
 defines minimal regularity of the dynamical system More...
 

Public Member Functions

 C11Rect2 (const VectorType &x, double s_factor=20)
 
 C11Rect2 (const VectorType &x, const VectorType &r0, double sizeFactor=20)
 
 C11Rect2 (const VectorType &x, const MatrixType &C, const VectorType &r0, double sizeFactor=20)
 
virtual ~C11Rect2 ()
 
void move (capd::dynsys::C1DynSys< MatrixType > &c1dynsys)
 
void move (capd::dynsys::C1DynSys< MatrixType > &c1dynsys, C11Rect2 &result) const
 
std::string show (void) const
 returns a set detailed information More...
 
double setFactor (double sFactor)
 
void disableSwapping ()
 
double getFactor ()
 
 operator VectorType () const
 
 operator MatrixType () const
 
C11Rect2 & operator= (const VectorType &v)
 
template<class Functional >
ScalarType evalAt (const Functional &f) const
 This method computes value of functor f at interval vector represented by this set. It computes the value as an intersection of two intervals: More...
 
virtual void move (DynSysType &c1dynsys)=0
 computes image of the set after one step/iterate of the dynamical system More...
 
const ScalarType getCurrentTime () const
 
ScalarType & refCurrentTime ()
 
void setCurrentTime (const ScalarType &t)
 
const MatrixT & getLastMatrixEnclosure () const
 
virtual operator MatrixT () const
 returns an enclosure of derivative in the canonical coordinates More...
 
const MatrixT::RowVectorType & getLastEnclosure () const
 
virtual operator MatrixT::RowVectorType () const
 returns an enclosure of the set in the canonical coordinates More...
 
void setCurrentSet (const MatrixT::RowVectorType &x)
 

Static Public Member Functions

static const size_type degree ()
 

Protected Member Functions

void setLastMatrixEnclosure (const MatrixT &M)
 
void setLastEnclosure (const MatrixT::RowVectorType &enc)
 

Protected Attributes

VectorType m_x
 
VectorType m_r
 
VectorType m_r0
 
MatrixType m_B
 
MatrixType m_C
 
MatrixType m_D
 
MatrixType m_Bjac
 
MatrixType m_R
 
MatrixType m_Cjac
 
MatrixType m_R0
 
double m_sizeFactor
 
ScalarType m_currentTime
 
MatrixT m_currentMatrix
 
MatrixT m_lastMatrixEnclosure
 
MatrixT::RowVectorType m_currentSet
 
MatrixT::RowVectorType m_lastEnclosure
 

Detailed Description

template<typename MatrixT, typename QRPolicy = FullQRWithPivoting>
class capd::dynset::C11Rect2< MatrixT, QRPolicy >

$C^1$ doubleton set with reorganization moved by QR decomposition (3rd method).

C^1-Lohner algorithm. Derivative of the flow moved via QR decomposition (third method) the set part - QR decomposition (3-rd method)

Member Typedef Documentation

◆ DynSysType

template<typename MatrixT >
typedef capd::dynsys::C1DynSys<MatrixType> capd::dynset::C1Set< MatrixT >::DynSysType
inherited

defines minimal regularity of the dynamical system

◆ MatrixType

template<typename MatrixT , typename QRPolicy = FullQRWithPivoting>
typedef MatrixT capd::dynset::C11Rect2< MatrixT, QRPolicy >::MatrixType

◆ ScalarType

template<typename MatrixT , typename QRPolicy = FullQRWithPivoting>
typedef MatrixType::ScalarType capd::dynset::C11Rect2< MatrixT, QRPolicy >::ScalarType

◆ SetType

template<typename MatrixT >
typedef C1Set capd::dynset::C1Set< MatrixT >::SetType
inherited

defines class of given set (C0, C1, C2, ...)

◆ size_type

template<typename MatrixT , typename QRPolicy = FullQRWithPivoting>
typedef MatrixType::size_type capd::dynset::C11Rect2< MatrixT, QRPolicy >::size_type

◆ VectorType

template<typename MatrixT , typename QRPolicy = FullQRWithPivoting>
typedef MatrixType::RowVectorType capd::dynset::C11Rect2< MatrixT, QRPolicy >::VectorType

Constructor & Destructor Documentation

◆ C11Rect2() [1/3]

template<typename MatrixType , typename QRPolicy >
capd::dynset::C11Rect2< MatrixType, QRPolicy >::C11Rect2 ( const VectorType &  x,
double  s_factor = 20 
)

◆ C11Rect2() [2/3]

template<typename MatrixType , typename QRPolicy >
capd::dynset::C11Rect2< MatrixType, QRPolicy >::C11Rect2 ( const VectorType &  x,
const VectorType &  r0,
double  sizeFactor = 20 
)

◆ C11Rect2() [3/3]

template<typename MatrixType , typename QRPolicy >
capd::dynset::C11Rect2< MatrixType, QRPolicy >::C11Rect2 ( const VectorType &  x,
const MatrixType &  C,
const VectorType &  r0,
double  sizeFactor = 20 
)

◆ ~C11Rect2()

template<typename MatrixT , typename QRPolicy = FullQRWithPivoting>
virtual capd::dynset::C11Rect2< MatrixT, QRPolicy >::~C11Rect2 ( )
inlinevirtual

Member Function Documentation

◆ degree()

template<typename MatrixT >
static const size_type capd::dynset::C1Set< MatrixT >::degree ( )
inlinestaticinherited

◆ disableSwapping()

template<typename MatrixType , typename QRPolicy >
void capd::dynset::C11Rect2< MatrixType, QRPolicy >::disableSwapping
inline

◆ evalAt()

template<typename MatrixT , typename QRPolicy = FullQRWithPivoting>
template<class Functional >
ScalarType capd::dynset::C11Rect2< MatrixT, QRPolicy >::evalAt ( const Functional &  f) const
inline

This method computes value of functor f at interval vector represented by this set. It computes the value as an intersection of two intervals:

  1. f(set)
  2. f(center(set)) + Df(set)*(set-center(set)) This set is represented as doubleton X=x+C*r0+B*r. The above reduces to f(x) + (Df(X)*C)*r0 + (Df(X)*B)*r

◆ getCurrentTime()

const ScalarType capd::diffAlgebra::TimeRange< MatrixT::ScalarType >::getCurrentTime ( ) const
inlineinherited

◆ getFactor()

template<typename MatrixType , typename QRPolicy >
double capd::dynset::C11Rect2< MatrixType, QRPolicy >::getFactor
inline

◆ getLastEnclosure()

const MatrixT::RowVectorType & capd::dynset::C0EnclosureHolder< MatrixT::RowVectorType >::getLastEnclosure ( ) const
inlineinherited

◆ getLastMatrixEnclosure()

template<class MatrixT >
const MatrixT & capd::dynset::C1EnclosureHolder< MatrixT >::getLastMatrixEnclosure ( ) const
inlineinherited

◆ move() [1/3]

template<typename MatrixType , typename QRPolicy >
void capd::dynset::C11Rect2< MatrixType, QRPolicy >::move ( capd::dynsys::C1DynSys< MatrixType > &  c1dynsys)
inline

◆ move() [2/3]

template<typename MatrixType , typename QRPolicy >
void capd::dynset::C11Rect2< MatrixType, QRPolicy >::move ( capd::dynsys::C1DynSys< MatrixType > &  c1dynsys,
C11Rect2< MatrixT, QRPolicy > &  result 
) const

◆ move() [3/3]

template<typename MatrixT >
virtual void capd::dynset::C1Set< MatrixT >::move ( DynSysType &  c1dynsys)
pure virtualinherited

computes image of the set after one step/iterate of the dynamical system

Implemented in capd::dynset::C1AffineSet< MatrixT, Policies >, capd::dynset::C1DoubletonSet< MatrixT, Policies >, capd::dynset::C1DoubletonSet< MatrixT, C11Rect2Policies >, and capd::dynset::C1DoubletonSet< GeometricBound::MatrixType, Policies >.

◆ operator MatrixT()

template<class MatrixT >
virtual capd::dynset::C1EnclosureHolder< MatrixT >::operator MatrixT ( ) const
inlinevirtualinherited

returns an enclosure of derivative in the canonical coordinates

◆ operator MatrixT::RowVectorType()

virtual capd::dynset::C0EnclosureHolder< MatrixT::RowVectorType >::operator MatrixT::RowVectorType ( ) const
inlinevirtualinherited

returns an enclosure of the set in the canonical coordinates

◆ operator MatrixType()

template<typename MatrixT , typename QRPolicy = FullQRWithPivoting>
capd::dynset::C11Rect2< MatrixT, QRPolicy >::operator MatrixType ( ) const

◆ operator VectorType()

template<typename MatrixT , typename QRPolicy = FullQRWithPivoting>
capd::dynset::C11Rect2< MatrixT, QRPolicy >::operator VectorType ( ) const
virtual

Implements capd::dynset::AbstractSet< MatrixT::RowVectorType >.

◆ operator=()

template<typename MatrixType , typename QRPolicy >
C11Rect2< MatrixType, QRPolicy > & capd::dynset::C11Rect2< MatrixType, QRPolicy >::operator= ( const VectorType &  v)

◆ refCurrentTime()

ScalarType & capd::diffAlgebra::TimeRange< MatrixT::ScalarType >::refCurrentTime ( )
inlineinherited

◆ setCurrentSet()

void capd::dynset::C0EnclosureHolder< MatrixT::RowVectorType >::setCurrentSet ( const MatrixT::RowVectorType &  x)
inlineinherited

◆ setCurrentTime()

void capd::diffAlgebra::TimeRange< MatrixT::ScalarType >::setCurrentTime ( const ScalarType &  t)
inlineinherited

◆ setFactor()

template<typename MatrixType , typename QRPolicy >
double capd::dynset::C11Rect2< MatrixType, QRPolicy >::setFactor ( double  sFactor)
inline

◆ setLastEnclosure()

void capd::dynset::C0EnclosureHolder< MatrixT::RowVectorType >::setLastEnclosure ( const MatrixT::RowVectorType &  enc)
inlineprotectedinherited

◆ setLastMatrixEnclosure()

template<class MatrixT >
void capd::dynset::C1EnclosureHolder< MatrixT >::setLastMatrixEnclosure ( const MatrixT &  M)
inlineprotectedinherited

◆ show()

template<typename MatrixType , typename QRPolicy >
std::string capd::dynset::C11Rect2< MatrixType, QRPolicy >::show ( void  ) const
virtual

returns a set detailed information

Implements capd::dynset::AbstractSet< MatrixT::RowVectorType >.

Member Data Documentation

◆ m_B

template<typename MatrixT , typename QRPolicy = FullQRWithPivoting>
MatrixType capd::dynset::C11Rect2< MatrixT, QRPolicy >::m_B
protected

◆ m_Bjac

template<typename MatrixT , typename QRPolicy = FullQRWithPivoting>
MatrixType capd::dynset::C11Rect2< MatrixT, QRPolicy >::m_Bjac
protected

◆ m_C

template<typename MatrixT , typename QRPolicy = FullQRWithPivoting>
MatrixType capd::dynset::C11Rect2< MatrixT, QRPolicy >::m_C
protected

◆ m_Cjac

template<typename MatrixT , typename QRPolicy = FullQRWithPivoting>
MatrixType capd::dynset::C11Rect2< MatrixT, QRPolicy >::m_Cjac
protected

◆ m_currentMatrix

template<class MatrixT >
MatrixT capd::dynset::C1EnclosureHolder< MatrixT >::m_currentMatrix
protectedinherited

◆ m_currentSet

MatrixT::RowVectorType capd::dynset::C0EnclosureHolder< MatrixT::RowVectorType >::m_currentSet
protectedinherited

◆ m_currentTime

ScalarType capd::diffAlgebra::TimeRange< MatrixT::ScalarType >::m_currentTime
protectedinherited

◆ m_D

template<typename MatrixT , typename QRPolicy = FullQRWithPivoting>
MatrixType capd::dynset::C11Rect2< MatrixT, QRPolicy >::m_D
protected

◆ m_lastEnclosure

MatrixT::RowVectorType capd::dynset::C0EnclosureHolder< MatrixT::RowVectorType >::m_lastEnclosure
protectedinherited

◆ m_lastMatrixEnclosure

template<class MatrixT >
MatrixT capd::dynset::C1EnclosureHolder< MatrixT >::m_lastMatrixEnclosure
protectedinherited

◆ m_r

template<typename MatrixT , typename QRPolicy = FullQRWithPivoting>
VectorType capd::dynset::C11Rect2< MatrixT, QRPolicy >::m_r
protected

◆ m_R

template<typename MatrixT , typename QRPolicy = FullQRWithPivoting>
MatrixType capd::dynset::C11Rect2< MatrixT, QRPolicy >::m_R
protected

◆ m_r0

template<typename MatrixT , typename QRPolicy = FullQRWithPivoting>
VectorType capd::dynset::C11Rect2< MatrixT, QRPolicy >::m_r0
protected

◆ m_R0

template<typename MatrixT , typename QRPolicy = FullQRWithPivoting>
MatrixType capd::dynset::C11Rect2< MatrixT, QRPolicy >::m_R0
protected

◆ m_sizeFactor

template<typename MatrixT , typename QRPolicy = FullQRWithPivoting>
double capd::dynset::C11Rect2< MatrixT, QRPolicy >::m_sizeFactor
protected

◆ m_x

template<typename MatrixT , typename QRPolicy = FullQRWithPivoting>
VectorType capd::dynset::C11Rect2< MatrixT, QRPolicy >::m_x
protected