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

#include <capd/pdes/C0HODoubletonSetGeometricTail.h>

Public Types
typedef capd::pdes::GeometricBound	VectorType

typedef BaseSetT::MatrixType	MatrixType

typedef MatrixType::RowVectorType	FiniteVectorType

typedef MatrixType::ScalarType	ScalarType

typedef MatrixType::size_type	size_type

typedef capd::vectalg::Norm< VectorType, MatrixType >	NormType

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

typedef capd::dynset::C0Set< MatrixType >::SetType	SetType

typedef capd::pdes::PdeSolver< VectorType >	DynSysType

typedef BaseSet::Data	Data

typedef BaseSet::BaseSet	C0BaseSet

Public Member Functions
	C0HODoubletonSetGeometricTail (const VectorType &x, ScalarType t=TypeTraits< ScalarType >::zero())

	C0HODoubletonSetGeometricTail (const VectorType &x, const FiniteVectorType &r0, ScalarType t=TypeTraits< ScalarType >::zero())

	C0HODoubletonSetGeometricTail (const VectorType &x, const MatrixType &C, const FiniteVectorType &r0, ScalarType t=TypeTraits< ScalarType >::zero())

void	move (DynSysType &dynsys)
	computes image of the set after one step/iterate of the dynamical system More...

template<class Functional >
ScalarType	evalAt (const Functional &f) const
	This method computes value of functor f at interval vector represented by this set. More...

	operator VectorType () const

std::string	name () const

const VectorType &	getCurrentSeries () const

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)

virtual void	move (DynSysType &dynsys)=0
	computes image of the set after one step/iterate of the dynamical system More...

std::string	show () const

virtual std::string	show () const=0
	returns a set detailed information More...

const ScalarType	getCurrentTime () const

ScalarType &	refCurrentTime ()

void	setCurrentTime (const ScalarType &t)

const BaseSetT::MatrixType ::RowVectorType &	getLastEnclosure () const

virtual	operator BaseSetT::MatrixType ::RowVectorType () const
	returns an enclosure of the set in the canonical coordinates More...

void	setCurrentSet (const BaseSetT::MatrixType ::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 ()


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


void	move (DynSysType &dynsys, C0HODoubletonSetGeometricTail &result) const
	computes image of the set after one step/iterate of the dynamical system and stores it in result More...


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

Static Public Member Functions
const static size_type	degree ()

Public Attributes
VectorType	m_currentSeries

VectorType	m_enc

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 BaseSetT::MatrixType ::RowVectorType &enc)

Protected Attributes
ScalarType	m_currentTime

BaseSetT::MatrixType ::RowVectorType	m_currentSet

BaseSetT::MatrixType ::RowVectorType	m_lastEnclosure

Detailed Description

template<class BaseSetT>
class capd::pdes::C0HODoubletonSetGeometricTail< 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 capd::dynset::C0HOSet<BaseSetT> capd::pdes::C0HODoubletonSetGeometricTail< BaseSetT >::BaseSet

◆ C0BaseSet

template<class BaseSetT >

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

inherited

◆ Data

template<class BaseSetT >

typedef BaseSet::Data capd::pdes::C0HODoubletonSetGeometricTail< BaseSetT >::Data

◆ DynSysType

template<class BaseSetT >

typedef capd::pdes::PdeSolver<VectorType> capd::pdes::C0HODoubletonSetGeometricTail< BaseSetT >::DynSysType

◆ FiniteVectorType

template<class BaseSetT >

typedef MatrixType::RowVectorType capd::pdes::C0HODoubletonSetGeometricTail< BaseSetT >::FiniteVectorType

◆ MatrixType

template<class BaseSetT >

typedef BaseSetT::MatrixType capd::pdes::C0HODoubletonSetGeometricTail< BaseSetT >::MatrixType

◆ NormType

template<class BaseSetT >

typedef capd::vectalg::Norm<VectorType,MatrixType> capd::pdes::C0HODoubletonSetGeometricTail< BaseSetT >::NormType

◆ ScalarType

template<class BaseSetT >

typedef MatrixType::ScalarType capd::pdes::C0HODoubletonSetGeometricTail< BaseSetT >::ScalarType

◆ SetType

template<class BaseSetT >

typedef capd::dynset::C0Set<MatrixType>::SetType capd::pdes::C0HODoubletonSetGeometricTail< BaseSetT >::SetType

◆ size_type

template<class BaseSetT >

typedef MatrixType::size_type capd::pdes::C0HODoubletonSetGeometricTail< BaseSetT >::size_type

◆ VectorType

template<class BaseSetT >

typedef capd::pdes::GeometricBound capd::pdes::C0HODoubletonSetGeometricTail< BaseSetT >::VectorType

Constructor & Destructor Documentation

◆ C0HODoubletonSetGeometricTail() [1/3]

template<class BaseSetT >

capd::pdes::C0HODoubletonSetGeometricTail< BaseSetT >::C0HODoubletonSetGeometricTail	(	const VectorType &	x,
		ScalarType	t = `TypeTraits<ScalarType>::zero()`
	)

inline

◆ C0HODoubletonSetGeometricTail() [2/3]

template<class BaseSetT >

capd::pdes::C0HODoubletonSetGeometricTail< BaseSetT >::C0HODoubletonSetGeometricTail	(	const VectorType &	x,
		const FiniteVectorType &	r0,
		ScalarType	t = `TypeTraits<ScalarType>::zero()`
	)

inline

◆ C0HODoubletonSetGeometricTail() [3/3]

template<class BaseSetT >

capd::pdes::C0HODoubletonSetGeometricTail< BaseSetT >::C0HODoubletonSetGeometricTail	(	const VectorType &	x,
		const MatrixType &	C,
		const FiniteVectorType &	r0,
		ScalarType	t = `TypeTraits<ScalarType>::zero()`
	)

inline

Member Function Documentation

◆ affineTransformation()

template<class BaseSetT >

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

inlineinherited

◆ 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()

const static 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

inlinevirtualinherited

◆ evalAt()

template<class BaseSetT >

template<class Functional >

ScalarType capd::pdes::C0HODoubletonSetGeometricTail< BaseSetT >::evalAt ( const Functional & f ) const

inline

This method computes value of functor f at interval vector represented by this set.

◆ getCurrentSeries()

template<class BaseSetT >

const VectorType& capd::pdes::C0HODoubletonSetGeometricTail< BaseSetT >::getCurrentSeries ( ) const

inline

◆ getCurrentTime()

const ScalarType capd::diffAlgebra::TimeRange< BaseSetT::MatrixType ::ScalarType >::getCurrentTime ( ) const

inlineinherited

◆ getLastEnclosure()

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

inlineinherited

◆ move() [1/5]

template<class BaseSetT >

void capd::pdes::C0HODoubletonSetGeometricTail< BaseSetT >::move ( DynSysType & dynsys )

inline

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

◆ move() [2/5]

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() [3/5]

template<typename Policies >

void capd::pdes::C0HODoubletonSetGeometricTail< Policies >::move	(	DynSysType &	dynsys,
		C0HODoubletonSetGeometricTail< BaseSetT > &	result
	)		const

computes image of the set after one step/iterate of the dynamical system and stores it in result

◆ move() [4/5]

template<class BaseSetT >

template<class Solver >

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

inlineinherited

◆ move() [5/5]

template<class BaseSetT >

template<class Solver >

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

inherited

◆ name()

template<class BaseSetT >

std::string capd::pdes::C0HODoubletonSetGeometricTail< BaseSetT >::name ( ) const

inline

◆ operator BaseSetT::MatrixType ::RowVectorType()

virtual capd::dynset::C0EnclosureHolder< BaseSetT::MatrixType ::RowVectorType >::operator BaseSetT::MatrixType ::RowVectorType ( ) const

inlinevirtualinherited

returns an enclosure of the set in the canonical coordinates

◆ operator VectorType() [1/2]

template<class BaseSetT >

capd::pdes::C0HODoubletonSetGeometricTail< BaseSetT >::operator VectorType ( ) const

inline

◆ operator VectorType() [2/2]

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

pure virtualinherited

◆ refCurrentTime()

ScalarType& capd::diffAlgebra::TimeRange< BaseSetT::MatrixType ::ScalarType >::refCurrentTime ( )

inlineinherited

◆ setCurrentSet()

void capd::dynset::C0EnclosureHolder< BaseSetT::MatrixType ::RowVectorType >::setCurrentSet ( const VectorT & x )

inlineinherited

◆ setCurrentTime()

void capd::diffAlgebra::TimeRange< BaseSetT::MatrixType ::ScalarType >::setCurrentTime ( const ScalarType & t )

inlineinherited

◆ setLastEnclosure()

void capd::dynset::C0EnclosureHolder< BaseSetT::MatrixType ::RowVectorType >::setLastEnclosure ( const VectorT & enc )

inlineprotectedinherited

◆ show() [1/2]

template<class BaseSetT >

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

inlineinherited

◆ show() [2/2]

virtual std::string capd::dynset::AbstractSet< BaseSetT::MatrixType ::RowVectorType >::show ( ) const

pure virtualinherited

returns a set detailed information

Member Data Documentation

◆ cBound

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

inherited

◆ corrector

template<class BaseSetT >

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

inherited

◆ JMinus

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

inherited

◆ JPlus

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

inherited

◆ m_currentSeries

template<class BaseSetT >

VectorType capd::pdes::C0HODoubletonSetGeometricTail< BaseSetT >::m_currentSeries

◆ m_currentSet

BaseSetT::MatrixType ::RowVectorType capd::dynset::C0EnclosureHolder< BaseSetT::MatrixType ::RowVectorType >::m_currentSet

protectedinherited

◆ m_currentTime

ScalarType capd::diffAlgebra::TimeRange< BaseSetT::MatrixType ::ScalarType >::m_currentTime

protectedinherited

◆ m_enc

template<class BaseSetT >

VectorType capd::pdes::C0HODoubletonSetGeometricTail< BaseSetT >::m_enc

◆ m_lastEnclosure

BaseSetT::MatrixType ::RowVectorType capd::dynset::C0EnclosureHolder< BaseSetT::MatrixType ::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

inherited

◆ 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

template<class BaseSetT> class capd::pdes::C0HODoubletonSetGeometricTail< BaseSetT >

Member Typedef Documentation

◆ BaseSet

◆ C0BaseSet

◆ Data

◆ DynSysType

◆ FiniteVectorType

◆ MatrixType

◆ NormType

◆ ScalarType

◆ SetType

◆ size_type

◆ VectorType

Constructor & Destructor Documentation

◆ C0HODoubletonSetGeometricTail() [1/3]

◆ C0HODoubletonSetGeometricTail() [2/3]

◆ C0HODoubletonSetGeometricTail() [3/3]

Member Function Documentation

◆ affineTransformation()

◆ computeC0HOCoefficients()

◆ computeC0HORemainder()

◆ computeC1HORemainder()

◆ degree()

◆ evalAffineFunctional()

◆ evalAt()

◆ getCurrentSeries()

◆ getCurrentTime()

◆ getLastEnclosure()

◆ move() [1/5]

◆ move() [2/5]

◆ move() [3/5]

◆ move() [4/5]

◆ move() [5/5]

◆ name()

◆ operator BaseSetT::MatrixType ::RowVectorType()

◆ operator VectorType() [1/2]

◆ operator VectorType() [2/2]

◆ refCurrentTime()

◆ setCurrentSet()

◆ setCurrentTime()

◆ setLastEnclosure()

◆ show() [1/2]

◆ show() [2/2]

Member Data Documentation

◆ cBound

◆ corrector

◆ JMinus

◆ JPlus

◆ m_currentSeries

◆ m_currentSet

◆ m_currentTime

◆ m_enc

◆ m_lastEnclosure

◆ midJMinusInverse

◆ pBound

◆ predictor

◆ psiMinus

◆ psiPlus

◆ T

template<class BaseSetT>
class capd::pdes::C0HODoubletonSetGeometricTail< BaseSetT >