The set is represented as doubleton: x + C*r0 + B*r; and is moved by the following method. More...

#include <capd/dynset/C0DoubletonSet.h>

Public Types
typedef MatrixT	MatrixType

typedef MatrixType::RowVectorType	VectorType

typedef MatrixType::ScalarType	ScalarType

typedef MatrixType::size_type	size_type

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

typedef capd::geomset::CenteredDoubletonSet< MatrixT >	BaseSet

typedef C0Set< MatrixT >::SetType	SetType

typedef C0Set< MatrixT >::DynSysType	DynSysType

typedef DoubletonData< MatrixT >	Data

typedef Policies	Policy

typedef BaseSet::ColumnVectorType	ColumnVectorType

typedef MatrixType::template rebind< typename ScalarType::BoundType >::other	RealMatrix

typedef VectorType::template rebind< typename ScalarType::BoundType >::other	RealVector

Public Member Functions
	C0DoubletonSet (const BaseSet &set, ScalarType t)

	C0DoubletonSet (const VectorType &x, ScalarType t=TypeTraits< ScalarType >::zero())

	C0DoubletonSet (const VectorType &x, const VectorType &r0, ScalarType t=TypeTraits< ScalarType >::zero())

	C0DoubletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0, ScalarType t=TypeTraits< ScalarType >::zero())

	C0DoubletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0, const VectorType &r, ScalarType t=TypeTraits< ScalarType >::zero())

	C0DoubletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0, const MatrixType &B, const VectorType &r, ScalarType t=TypeTraits< ScalarType >::zero())

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

void	move (DynSysType &dynsys, C0DoubletonSet &result) const
	computes image of the set after one step/iterate of the dynamical system and stores it in result 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...

std::string	show () const

std::string	name () const
	returns set's name 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

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

	operator VectorType () const

virtual VectorType	affineTransformation (const MatrixType &M, const VectorType &x0) const
	This method computes value of an affine map f at interval vector represented by this set. This set is represented as tripleton X=x+Cr0+intersection(Br,Qq). Then f(X) = M(X-x0) can be computed as M(x-x0) + (MC)r0 + intersection( MB)r, (MQ)*q ) More...

virtual ScalarType	evalAffineFunctional (const VectorType &gradient, const VectorType &x0) const
	This method computes value of an affine functional f at the vector represented by this set. This set is represented as doubleton X=x+Cr0+Br. Then f(X) = grad(X-x0) can be computed as grad(x-x0) + (gradC)r0 + (gradB)r. More...

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

size_type	dimension () const
	returns dimension of a set More...

const VectorType &	get_x () const

const ScalarType &	getElement_x (int i) const

void	set_x (const VectorType &x)

void	setElement_x (size_type i, const ScalarType &s)

const VectorType &	get_r () const

const ScalarType &	getElement_r (size_type i) const

void	set_r (const VectorType &r)

void	setElement_r (size_type i, const ScalarType &s)

const MatrixType &	get_B () const

const MatrixType &	get_invB () const

void	setToIdentity ()

const ScalarType &	getElement_B (size_type i, size_type j) const

VectorType	getRow_B (size_type i) const

ColumnVectorType	getColumn_B (size_type j) const

void	set_B (const MatrixType &B)

void	set_invB (const MatrixType &B)

void	setElement_B (size_type i, size_type j, const ScalarType &s)

template<typename VectorT >
void	setRow_B (size_type i, const VectorT &v)

template<typename VectorT >
void	setColumn_B (size_type j, const VectorT &v)

Static Public Member Functions
static void	move (const BaseSet &set, BaseSet &result, VectorType &bound, Data &data)
	this computes next representation of the set given computed one-step enclosure of the form y + jacPhi*deltaX + rem More...

const static size_type	degree ()

Public Attributes
MatrixType	m_C
	C is a coordinate system of the 'Lipschitz' part. More...

VectorType	m_r0
	r0 is a interval set in given coordinate system that represents 'Lipschitz' part More...

VectorType	m_x
	x is a center of the set More...

MatrixType	m_B
	B is a coordinate system. More...

MatrixType	m_invB

VectorType	m_r
	r is a interval set in given coordinate system More...

VectorType	x

VectorType	deltaX

VectorType	y

VectorType	deltaY

VectorType	rem

VectorType	enc

MatrixType	jacPhi

MatrixType	deltaC

MatrixType	B

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<typename MatrixT, typename Policies>
class capd::dynset::C0DoubletonSet< MatrixT, Policies >

The set is represented as doubleton: x + C*r0 + B*r; and is moved by the following method.

internal representation : C*r0 - basic 'Lipschitz part' B*r - depending on the QRPolicy

Member Typedef Documentation

◆ BaseSet

template<typename MatrixT , typename Policies >

typedef capd::geomset::CenteredDoubletonSet<MatrixT> capd::dynset::C0DoubletonSet< MatrixT, Policies >::BaseSet

◆ ColumnVectorType

template<typename MatrixT >

typedef BaseSet::ColumnVectorType capd::geomset::CenteredDoubletonSet< MatrixT >::ColumnVectorType

inherited

◆ Data

template<typename MatrixT , typename Policies >

typedef DoubletonData<MatrixT> capd::dynset::C0DoubletonSet< MatrixT, Policies >::Data

◆ DynSysType

template<typename MatrixT , typename Policies >

typedef C0Set<MatrixT>::DynSysType capd::dynset::C0DoubletonSet< MatrixT, Policies >::DynSysType

◆ MatrixType

template<typename MatrixT , typename Policies >

typedef MatrixT capd::dynset::C0DoubletonSet< MatrixT, Policies >::MatrixType

◆ NormType

template<typename MatrixT , typename Policies >

typedef capd::vectalg::Norm<VectorType,MatrixType> capd::dynset::C0DoubletonSet< MatrixT, Policies >::NormType

◆ Policy

template<typename MatrixT , typename Policies >

typedef Policies capd::dynset::C0DoubletonSet< MatrixT, Policies >::Policy

◆ RealMatrix

template<typename MatrixT >

typedef MatrixType::template rebind<typename ScalarType::BoundType>::other capd::geomset::AffineSet< MatrixT >::RealMatrix

inherited

◆ RealVector

template<typename MatrixT >

typedef VectorType::template rebind<typename ScalarType::BoundType>::other capd::geomset::AffineSet< MatrixT >::RealVector

inherited

◆ ScalarType

template<typename MatrixT , typename Policies >

typedef MatrixType::ScalarType capd::dynset::C0DoubletonSet< MatrixT, Policies >::ScalarType

◆ SetType

template<typename MatrixT , typename Policies >

typedef C0Set<MatrixT>::SetType capd::dynset::C0DoubletonSet< MatrixT, Policies >::SetType

◆ size_type

template<typename MatrixT , typename Policies >

typedef MatrixType::size_type capd::dynset::C0DoubletonSet< MatrixT, Policies >::size_type

◆ VectorType

template<typename MatrixT , typename Policies >

typedef MatrixType::RowVectorType capd::dynset::C0DoubletonSet< MatrixT, Policies >::VectorType

Constructor & Destructor Documentation

◆ C0DoubletonSet() [1/6]

template<typename MatrixType , typename Policies >

capd::dynset::C0DoubletonSet< MatrixType, Policies >::C0DoubletonSet	(	const BaseSet &	set,
		ScalarType	t
	)

◆ C0DoubletonSet() [2/6]

template<typename MatrixType , typename Policies >

capd::dynset::C0DoubletonSet< MatrixType, Policies >::C0DoubletonSet	(	const VectorType &	x,
		ScalarType	t = `TypeTraits<ScalarType>::zero()`
	)

◆ C0DoubletonSet() [3/6]

template<typename MatrixType , typename Policies >

capd::dynset::C0DoubletonSet< MatrixType, Policies >::C0DoubletonSet	(	const VectorType &	x,
		const VectorType &	r0,
		ScalarType	t = `TypeTraits<ScalarType>::zero()`
	)

◆ C0DoubletonSet() [4/6]

template<typename MatrixType , typename Policies >

capd::dynset::C0DoubletonSet< MatrixType, Policies >::C0DoubletonSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0,
		ScalarType	t = `TypeTraits<ScalarType>::zero()`
	)

◆ C0DoubletonSet() [5/6]

template<typename MatrixType , typename Policies >

capd::dynset::C0DoubletonSet< MatrixType, Policies >::C0DoubletonSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0,
		const VectorType &	r,
		ScalarType	t = `TypeTraits<ScalarType>::zero()`
	)

◆ C0DoubletonSet() [6/6]

template<typename MatrixType , typename Policies >

capd::dynset::C0DoubletonSet< MatrixType, Policies >::C0DoubletonSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0,
		const MatrixType &	B,
		const VectorType &	r,
		ScalarType	t = `TypeTraits<ScalarType>::zero()`
	)

Member Function Documentation

◆ degree()

template<typename MatrixT >

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

inlinestaticinherited

◆ dimension()

template<typename MatrixT >

size_type capd::geomset::AffineSet< MatrixT >::dimension ( ) const

inlineinherited

returns dimension of a set

◆ evalAt()

template<typename MatrixT , typename Policies >

template<class Functional >

ScalarType capd::dynset::C0DoubletonSet< MatrixT, Policies >::evalAt ( const Functional & f ) const

inline

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

◆ get_B()

template<typename MatrixT >

const MatrixType& capd::geomset::AffineSet< MatrixT >::get_B ( ) const

inlineinherited

◆ get_invB()

template<typename MatrixT >

const MatrixType& capd::geomset::AffineSet< MatrixT >::get_invB ( ) const

inlineinherited

◆ get_r()

template<typename MatrixT >

const VectorType& capd::geomset::AffineSet< MatrixT >::get_r ( ) const

inlineinherited

◆ get_x()

template<typename MatrixT >

const VectorType& capd::geomset::AffineSet< MatrixT >::get_x ( ) const

inlineinherited

◆ getColumn_B()

template<typename MatrixT >

ColumnVectorType capd::geomset::AffineSet< MatrixT >::getColumn_B ( size_type j ) const

inlineinherited

◆ getCurrentTime()

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

inlineinherited

◆ getElement_B()

template<typename MatrixT >

const ScalarType& capd::geomset::AffineSet< MatrixT >::getElement_B	(	size_type	i,
		size_type	j
	)		const

inlineinherited

◆ getElement_r()

template<typename MatrixT >

const ScalarType& capd::geomset::AffineSet< MatrixT >::getElement_r ( size_type i ) const

inlineinherited

◆ getElement_x()

template<typename MatrixT >

const ScalarType& capd::geomset::AffineSet< MatrixT >::getElement_x ( int i ) const

inlineinherited

◆ getLastEnclosure()

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

inlineinherited

◆ getRow_B()

template<typename MatrixT >

VectorType capd::geomset::AffineSet< MatrixT >::getRow_B ( size_type i ) const

inlineinherited

◆ move() [1/3]

template<typename MatrixType , typename Policies >

void capd::dynset::C0DoubletonSet< MatrixType, Policies >::move	(	const BaseSet &	set,
		BaseSet &	result,
		VectorType &	bound,
		Data &	data
	)

static

this computes next representation of the set given computed one-step enclosure of the form y + jacPhi*deltaX + rem

◆ move() [2/3]

template<typename MatrixType , typename Policies >

void capd::dynset::C0DoubletonSet< MatrixType, Policies >::move ( DynSysType & dynsys )

virtual

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

Implements capd::dynset::C0Set< MatrixT >.

◆ move() [3/3]

template<typename MatrixType , typename Policies >

void capd::dynset::C0DoubletonSet< MatrixType, Policies >::move	(	DynSysType &	dynsys,
		C0DoubletonSet< MatrixT, Policies > &	result
	)		const

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

◆ name()

template<typename MatrixT , typename Policies >

std::string capd::dynset::C0DoubletonSet< MatrixT, Policies >::name ( ) const

inlinevirtual

returns set's name

Reimplemented from capd::geomset::CenteredDoubletonSet< MatrixT >.

Reimplemented in capd::dynset::C0HODoubletonSet< MatrixT, Policies >.

◆ 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() [1/2]

template<typename MatrixT >

capd::geomset::DoubletonSet< MatrixT >::operator VectorType ( ) const

inherited

◆ operator VectorType() [2/2]

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

pure virtualinherited

Implemented in capd::dynset::CnSet< MatrixT, 0 >.

◆ refCurrentTime()

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

inlineinherited

◆ set_B()

template<typename MatrixT >

void capd::geomset::AffineSet< MatrixT >::set_B ( const MatrixType & B )

inlineinherited

◆ set_invB()

template<typename MatrixT >

void capd::geomset::AffineSet< MatrixT >::set_invB ( const MatrixType & B )

inlineinherited

◆ set_r()

template<typename MatrixT >

void capd::geomset::AffineSet< MatrixT >::set_r ( const VectorType & r )

inlineinherited

◆ set_x()

template<typename MatrixT >

void capd::geomset::AffineSet< MatrixT >::set_x ( const VectorType & x )

inlineinherited

◆ setColumn_B()

template<typename MatrixT >

template<typename VectorT >

void capd::geomset::AffineSet< MatrixT >::setColumn_B	(	size_type	j,
		const VectorT &	v
	)

inlineinherited

◆ setCurrentSet()

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

inlineinherited

◆ setCurrentTime()

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

inlineinherited

◆ setElement_B()

template<typename MatrixT >

void capd::geomset::AffineSet< MatrixT >::setElement_B	(	size_type	i,
		size_type	j,
		const ScalarType &	s
	)

inlineinherited

◆ setElement_r()

template<typename MatrixT >

void capd::geomset::AffineSet< MatrixT >::setElement_r	(	size_type	i,
		const ScalarType &	s
	)

inlineinherited

◆ setElement_x()

template<typename MatrixT >

void capd::geomset::AffineSet< MatrixT >::setElement_x	(	size_type	i,
		const ScalarType &	s
	)

inlineinherited

◆ setLastEnclosure()

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

inlineprotectedinherited

◆ setRow_B()

template<typename MatrixT >

template<typename VectorT >

void capd::geomset::AffineSet< MatrixT >::setRow_B	(	size_type	i,
		const VectorT &	v
	)

inlineinherited

◆ setToIdentity()

template<typename MatrixT >

void capd::geomset::AffineSet< MatrixT >::setToIdentity ( )

inlineinherited

◆ show() [1/2]

template<typename MatrixType , typename Policies >

std::string capd::dynset::C0DoubletonSet< MatrixType, Policies >::show

◆ show() [2/2]

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

pure virtualinherited

returns a set detailed information

Implemented in capd::dynset::C2DoubletonSet< MatrixT, Policies >, capd::dynset::C1GraphicalSet< MatrixT, OutputClass >, capd::dynset::C0BallSet< MatrixT >, capd::dynset::C11Rect2< MatrixT, QRPolicy >, capd::dynset::C0FlowballSet< MatrixT >, capd::dynset::C1DoubletonSet< MatrixT, C11Rect2Policies >, and capd::dynset::C0DoubletonSet< MatrixT, capd::C0Rect2Policies >.

Member Data Documentation

◆ m_B

template<typename MatrixT >

MatrixType capd::geomset::AffineSet< MatrixT >::m_B

inherited

B is a coordinate system.

◆ m_C

template<typename MatrixT >

MatrixType capd::geomset::DoubletonSet< MatrixT >::m_C

inherited

C is a coordinate system of the 'Lipschitz' part.

◆ m_currentSet

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

protectedinherited

◆ m_currentTime

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

protectedinherited

◆ m_invB

template<typename MatrixT >

MatrixType capd::geomset::AffineSet< MatrixT >::m_invB

inherited

◆ m_lastEnclosure

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

protectedinherited

◆ m_r

template<typename MatrixT >

VectorType capd::geomset::AffineSet< MatrixT >::m_r

inherited

r is a interval set in given coordinate system

◆ m_r0

template<typename MatrixT >

VectorType capd::geomset::DoubletonSet< MatrixT >::m_r0

inherited

r0 is a interval set in given coordinate system that represents 'Lipschitz' part

◆ m_x

template<typename MatrixT >

VectorType capd::geomset::AffineSet< MatrixT >::m_x

inherited

x is a center of the set

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Detailed Description

template<typename MatrixT, typename Policies> class capd::dynset::C0DoubletonSet< MatrixT, Policies >

Member Typedef Documentation

◆ BaseSet

◆ ColumnVectorType

◆ Data

◆ DynSysType

◆ MatrixType

◆ NormType

◆ Policy

◆ RealMatrix

◆ RealVector

◆ ScalarType

◆ SetType

◆ size_type

◆ VectorType

Constructor & Destructor Documentation

◆ C0DoubletonSet() [1/6]

◆ C0DoubletonSet() [2/6]

◆ C0DoubletonSet() [3/6]

◆ C0DoubletonSet() [4/6]

◆ C0DoubletonSet() [5/6]

◆ C0DoubletonSet() [6/6]

Member Function Documentation

◆ degree()

◆ dimension()

◆ evalAt()

◆ get_B()

◆ get_invB()

◆ get_r()

◆ get_x()

◆ getColumn_B()

◆ getCurrentTime()

◆ getElement_B()

◆ getElement_r()

◆ getElement_x()

◆ getLastEnclosure()

◆ getRow_B()

◆ move() [1/3]

◆ move() [2/3]

◆ move() [3/3]

◆ name()

◆ operator MatrixT::RowVectorType()

◆ operator VectorType() [1/2]

◆ operator VectorType() [2/2]

◆ refCurrentTime()

◆ set_B()

◆ set_invB()

◆ set_r()

◆ set_x()

◆ setColumn_B()

◆ setCurrentSet()

◆ setCurrentTime()

◆ setElement_B()

◆ setElement_r()

◆ setElement_x()

◆ setLastEnclosure()

◆ setRow_B()

◆ setToIdentity()

◆ show() [1/2]

◆ show() [2/2]

Member Data Documentation

◆ m_B

◆ m_C

◆ m_currentSet

◆ m_currentTime

◆ m_invB

◆ m_lastEnclosure

◆ m_r

◆ m_r0

◆ m_x

template<typename MatrixT, typename Policies>
class capd::dynset::C0DoubletonSet< MatrixT, Policies >