This class uses representation of subset of R^n inherited from template parameter. More...

#include <capd/dynset/C0HOSet.h>

Public Types
typedef BaseSetT	BaseSet

typedef BaseSet::BaseSet	C0BaseSet

typedef BaseSet::MatrixType	MatrixType

typedef BaseSet::VectorType	VectorType

typedef MatrixType::ScalarType	ScalarType

typedef MatrixType::size_type	size_type

typedef BaseSet::DynSysType	DynSysType

typedef BaseSet::SetType	SetType

typedef HOData< typename BaseSetT::Data >	Data

Public Member Functions
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 evalAt for two representations of this set: predictor and corrector. More...

VectorType	affineTransformation (const MatrixType &M, const VectorType &x) const

virtual ScalarType	evalAffineFunctional (const VectorType &gradient, const VectorType &u) const

template<class Solver >
void	move (Solver &solver)

std::string	show () const
	returns a set detailed information More...

void	move (DynSysType &)

std::string	name () const

virtual void	move (DynSysType &dynsys)=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::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)

virtual	operator VectorType () const=0

void	computeC0HORemainder (size_type p, size_type q)

void	computeC1HORemainder (size_type p, size_type q, MatrixType &jacRem)

void	computeC0HOCoefficients ()


	C0HOSet (const BaseSet &set)

	C0HOSet (const VectorType &x, ScalarType t=TypeTraits< ScalarType >::zero())

	C0HOSet (const VectorType &x, const VectorType &r0, ScalarType t=TypeTraits< ScalarType >::zero())

	C0HOSet (const VectorType &x, const MatrixType &C, const VectorType &r0, ScalarType t=TypeTraits< ScalarType >::zero())

	C0HOSet (const VectorType &x, const MatrixType &C, const VectorType &r0, const VectorType &r, ScalarType t=TypeTraits< ScalarType >::zero())

	C0HOSet (const VectorType &x, const MatrixType &C, const VectorType &r0, const MatrixType &B, const VectorType &r, ScalarType t=TypeTraits< ScalarType >::zero())


template<class Solver >
void	move (Solver &solver, C0HOSet &result) const

Static Public Member Functions
static const size_type	degree ()

Public Attributes
C0BaseSet	predictor

C0BaseSet	corrector

VectorType	psiPlus

VectorType	psiMinus

VectorType	pBound

VectorType	cBound

MatrixType	JPlus

MatrixType	JMinus

MatrixType	midJMinusInverse

MatrixType	T

Protected Member Functions
void	setLastEnclosure (const MatrixT::RowVectorType &enc)

Protected Attributes
ScalarType	m_currentTime

MatrixT::RowVectorType	m_currentSet

MatrixT::RowVectorType	m_lastEnclosure

Detailed Description

template<class BaseSetT>
class capd::dynset::C0HOSet< BaseSetT >

This class uses representation of subset of R^n inherited from template parameter.

The evaluation of the set by an ODE is realized by intersection of two methods: the Taylor method and the Hermite-Obreshkov method.

IMPORTANT: present implementation is valid for orders of the Taylor method less or equal 64, only. This is due to capacity of integer type used to store binomial coefficients. Minimal order should be at least 3.

Member Typedef Documentation

◆ BaseSet

template<class BaseSetT >

typedef BaseSetT capd::dynset::C0HOSet< BaseSetT >::BaseSet

◆ C0BaseSet

template<class BaseSetT >

typedef BaseSet::BaseSet capd::dynset::C0HOSet< BaseSetT >::C0BaseSet

◆ Data

template<class BaseSetT >

typedef HOData<typename BaseSetT::Data> capd::dynset::C0HOSet< BaseSetT >::Data

◆ DynSysType

template<class BaseSetT >

typedef BaseSet::DynSysType capd::dynset::C0HOSet< BaseSetT >::DynSysType

◆ MatrixType

template<class BaseSetT >

typedef BaseSet::MatrixType capd::dynset::C0HOSet< BaseSetT >::MatrixType

◆ ScalarType

template<class BaseSetT >

typedef MatrixType::ScalarType capd::dynset::C0HOSet< BaseSetT >::ScalarType

◆ SetType

template<class BaseSetT >

typedef BaseSet::SetType capd::dynset::C0HOSet< BaseSetT >::SetType

◆ size_type

template<class BaseSetT >

typedef MatrixType::size_type capd::dynset::C0HOSet< BaseSetT >::size_type

◆ VectorType

template<class BaseSetT >

typedef BaseSet::VectorType capd::dynset::C0HOSet< BaseSetT >::VectorType

Constructor & Destructor Documentation

◆ C0HOSet() [1/6]

template<class BaseSetT >

capd::dynset::C0HOSet< BaseSetT >::C0HOSet ( const BaseSet & set )

◆ C0HOSet() [2/6]

template<class BaseSetT >

capd::dynset::C0HOSet< BaseSetT >::C0HOSet	(	const VectorType &	x,
		ScalarType	t = `TypeTraits<ScalarType>::zero()`
	)

explicit

◆ C0HOSet() [3/6]

template<class BaseSetT >

capd::dynset::C0HOSet< BaseSetT >::C0HOSet	(	const VectorType &	x,
		const VectorType &	r0,
		ScalarType	t = `TypeTraits<ScalarType>::zero()`
	)

◆ C0HOSet() [4/6]

template<class BaseSetT >

capd::dynset::C0HOSet< BaseSetT >::C0HOSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0,
		ScalarType	t = `TypeTraits<ScalarType>::zero()`
	)

◆ C0HOSet() [5/6]

template<class BaseSetT >

capd::dynset::C0HOSet< BaseSetT >::C0HOSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0,
		const VectorType &	r,
		ScalarType	t = `TypeTraits<ScalarType>::zero()`
	)

◆ C0HOSet() [6/6]

template<class BaseSetT >

capd::dynset::C0HOSet< BaseSetT >::C0HOSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0,
		const MatrixType &	B,
		const VectorType &	r,
		ScalarType	t = `TypeTraits<ScalarType>::zero()`
	)

Member Function Documentation

◆ affineTransformation()

template<class BaseSetT >

VectorType capd::dynset::C0HOSet< BaseSetT >::affineTransformation	(	const MatrixType &	M,
		const VectorType &	x
	)		const

inline

◆ computeC0HOCoefficients()

void capd::dynset::HOData< BaseSetT::Data >::computeC0HOCoefficients ( )

inlineinherited

◆ computeC0HORemainder()

void capd::dynset::HOData< BaseSetT::Data >::computeC0HORemainder	(	size_type	p,
		size_type	q
	)

inlineinherited

◆ computeC1HORemainder()

void capd::dynset::HOData< BaseSetT::Data >::computeC1HORemainder	(	size_type	p,
		size_type	q,
		MatrixType &	jacRem
	)

inlineinherited

◆ degree()

static const size_type capd::dynset::C0Set< BaseSetT::MatrixType >::degree ( )

inlinestaticinherited

◆ evalAffineFunctional()

template<class BaseSetT >

virtual ScalarType capd::dynset::C0HOSet< BaseSetT >::evalAffineFunctional	(	const VectorType &	gradient,
		const VectorType &	u
	)		const

inlinevirtual

◆ evalAt()

template<class BaseSetT >

template<class Functional >

ScalarType capd::dynset::C0HOSet< BaseSetT >::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 evalAt for two representations of this set: predictor and corrector.

◆ getCurrentTime()

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

inlineinherited

◆ getLastEnclosure()

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

inlineinherited

◆ move() [1/4]

template<class BaseSetT >

void capd::dynset::C0HOSet< BaseSetT >::move ( DynSysType & )

inline

◆ move() [2/4]

virtual void capd::dynset::C0Set< BaseSetT::MatrixType >::move ( DynSysType & dynsys )

pure virtualinherited

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

◆ move() [3/4]

template<class BaseSetT >

template<class Solver >

void capd::dynset::C0HOSet< BaseSetT >::move ( Solver & solver )

inline

◆ move() [4/4]

template<class BaseSetT >

template<class Solver >

void capd::dynset::C0HOSet< BaseSetT >::move	(	Solver &	solver,
		C0HOSet< BaseSetT > &	result
	)		const

◆ name()

template<class BaseSetT >

std::string capd::dynset::C0HOSet< BaseSetT >::name ( ) const

inline

◆ 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 VectorType()

virtual capd::dynset::AbstractSet< MatrixT::RowVectorType >::operator VectorType ( ) const

pure virtualinherited

Implemented in capd::dynset::C11Rect2< MatrixT, QRPolicy >, capd::dynset::C1GraphicalSet< MatrixT, OutputClass >, capd::dynset::CnSet< MatrixT, DEGREE >, capd::dynset::CnSet< MatrixT, 0 >, capd::pdes::C0DoubletonSetGeometricTail< BaseT >, capd::pdes::C0DoubletonSetGeometricTail< capd::dynset::C1DoubletonSet< GeometricBound::MatrixType, Policies > >, and capd::pdes::C0HODoubletonSetGeometricTail< BaseSetT >.

◆ 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

◆ setLastEnclosure()

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

inlineprotectedinherited

◆ show()

template<class BaseSetT >

std::string capd::dynset::C0HOSet< BaseSetT >::show ( void ) const

inlinevirtual

returns a set detailed information

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

Member Data Documentation

◆ cBound

VectorType capd::dynset::HOData< BaseSetT::Data >::cBound

inherited

◆ corrector

template<class BaseSetT >

C0BaseSet capd::dynset::C0HOSet< BaseSetT >::corrector

◆ JMinus

MatrixType capd::dynset::HOData< BaseSetT::Data >::JMinus

inherited

◆ JPlus

MatrixType capd::dynset::HOData< BaseSetT::Data >::JPlus

inherited

◆ m_currentSet

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

protectedinherited

◆ m_currentTime

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

protectedinherited

◆ m_lastEnclosure

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

protectedinherited

◆ midJMinusInverse

MatrixType capd::dynset::HOData< BaseSetT::Data >::midJMinusInverse

inherited

◆ pBound

VectorType capd::dynset::HOData< BaseSetT::Data >::pBound

inherited

◆ predictor

template<class BaseSetT >

C0BaseSet capd::dynset::C0HOSet< BaseSetT >::predictor

◆ psiMinus

VectorType capd::dynset::HOData< BaseSetT::Data >::psiMinus

inherited

◆ psiPlus

VectorType capd::dynset::HOData< BaseSetT::Data >::psiPlus

inherited

◆ T

MatrixType capd::dynset::HOData< BaseSetT::Data >::T

inherited

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ BaseSet

◆ C0BaseSet

◆ Data

◆ DynSysType

◆ MatrixType

◆ ScalarType

◆ SetType

◆ size_type

◆ VectorType

Constructor & Destructor Documentation

◆ C0HOSet() [1/6]

◆ C0HOSet() [2/6]

◆ C0HOSet() [3/6]

◆ C0HOSet() [4/6]

◆ C0HOSet() [5/6]

◆ C0HOSet() [6/6]

Member Function Documentation

◆ affineTransformation()

◆ computeC0HOCoefficients()

◆ computeC0HORemainder()

◆ computeC1HORemainder()

◆ degree()

◆ evalAffineFunctional()

◆ evalAt()

◆ getCurrentTime()

◆ getLastEnclosure()

◆ move() [1/4]

◆ move() [2/4]

◆ move() [3/4]

◆ move() [4/4]

◆ name()

◆ operator MatrixT::RowVectorType()

◆ operator VectorType()

◆ refCurrentTime()

◆ setCurrentSet()

◆ setCurrentTime()

◆ setLastEnclosure()

◆ show()

Member Data Documentation

◆ cBound

◆ corrector

◆ JMinus

◆ JPlus

◆ m_currentSet

◆ m_currentTime

◆ m_lastEnclosure

◆ midJMinusInverse

◆ pBound

◆ predictor

◆ psiMinus

◆ psiPlus

◆ T