The C1 set is represented as doubleton: x + C*r0 + B*r;. More...

#include <capd/dynset/C1DoubletonSet.h>

Public Types
typedef MatrixT	MatrixType

typedef MatrixType::RowVectorType	VectorType

typedef MatrixType::ScalarType	ScalarType

typedef MatrixType::size_type	size_type

typedef C1Set< MatrixT >	SetType

typedef C1Set< MatrixT >::DynSysType	DynSysType

typedef capd::geomset::CenteredDoubletonSet< MatrixT >	C0BaseSet

typedef capd::geomset::MatrixDoubletonSet< MatrixT >	C1BaseSet

typedef C1DoubletonData< MatrixT >	Data

typedef Policies	Policy

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

typedef BaseSet::ColumnVectorType	ColumnVectorType

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

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

typedef MatrixAffineSet< MatrixT >	BaseSet

typedef BaseSet::ColumnVectorType	ColumnVectorType

typedef BaseSet::NormType	NormType

Public Member Functions
	C1DoubletonSet (const VectorType &x, ScalarType t=TypeTraits< ScalarType >::zero())

	C1DoubletonSet (const VectorType &x, const VectorType &r0, ScalarType t=TypeTraits< ScalarType >::zero())

	C1DoubletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0, ScalarType t=TypeTraits< ScalarType >::zero())

	C1DoubletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0, const VectorType &r, ScalarType t=TypeTraits< ScalarType >::zero())

	C1DoubletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0, const MatrixType &B, const VectorType &r, ScalarType t=TypeTraits< ScalarType >::zero())

	C1DoubletonSet (const C0BaseSet &c0part, const C1BaseSet &c1part, 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, C1DoubletonSet &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
	returns a set detailed information More...

virtual std::string	name () const
	returns set's name More...

const MatrixType &	get_R0 () const

const ScalarType &	getElement_R0 (size_type i, size_type j) const

VectorType	getRow_R0 (size_type i) const

ColumnVectorType	getColumn_R0 (size_type j) const

const MatrixType &	get_Cjac () const

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

VectorType	getRow_Cjac (size_type i) const

ColumnVectorType	getColumn_Cjac (size_type j) const

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)

virtual	operator VectorType () const=0

	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...

const VectorType &	get_r0 () const
	returns r0 More...

const ScalarType &	getElement_r0 (size_type i) const
	returns i-th coordinate of r0 More...

void	set_r0 (const VectorType &r)
	sets r0 More...

void	setElement_r0 (size_type i, const ScalarType &s)
	sets i-th coordinate of r0 More...

const MatrixType &	get_C () const
	returns matrix C More...

const ScalarType &	getElement_C (size_type i, size_type j) const
	returns element C[i][j] More...

VectorType	getRow_C (size_type i) const
	returns i-th row of C More...

ColumnVectorType	getColumn_C (size_type j) const
	returns j-th column of C More...

void	set_C (const MatrixType &B)
	sets matrix C:= B More...

void	setElement_C (size_type i, size_type j, const ScalarType &s)
	sets C[i][j] := s More...

template<typename VectorT >
void	setRow_C (size_type i, const VectorT &v)
	sets i-th row of C to v More...

template<typename VectorT >
void	setColumn_C (size_type j, const VectorT &v)
	sets j-th columne of C to v 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)

	operator MatrixType () const

void	setToIdentity (size_type dim)

void	setToIdentity ()
	sets the set to identity More...

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

virtual MatrixType	affineMatrixTransformation (const MatrixType &) const
	returns image of the set after affine transformation More...

const MatrixType &	get_R0 () const

const ScalarType &	getElement_R0 (size_type i, size_type j) const

VectorType	getRow_R0 (size_type i) const

ColumnVectorType	getColumn_R0 (size_type j) const

void	set_R0 (const MatrixType &R0)

void	setElement_R0 (size_type i, size_type j, const ScalarType &s)

template<typename VectorT >
void	setRow_R0 (size_type i, const VectorT &v)

template<typename VectorT >
void	setColumn_R0 (size_type j, const VectorT &v)

const MatrixType &	get_Cjac () const

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

VectorType	getRow_Cjac (size_type i) const

ColumnVectorType	getColumn_Cjac (size_type j) const

void	set_Cjac (const MatrixType &C)

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

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

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

const MatrixType &	get_D () const

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

VectorType	getRow_D (size_type i) const

ColumnVectorType	getColumn_D (size_type j) const

void	set_D (const MatrixType &Bjac)

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

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

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

const MatrixType &	get_R () const

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

VectorType	getRow_R (size_type i) const

ColumnVectorType	getColumn_R (size_type j) const

void	set_R (const MatrixType &Bjac)

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

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

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

const MatrixType &	get_invBjac () const

const MatrixType &	get_Bjac () const

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

VectorType	getRow_Bjac (size_type i) const

ColumnVectorType	getColumn_Bjac (size_type j) const

void	set_Bjac (const MatrixType &Bjac)

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

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

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

Static Public Member Functions
static void	move (const C1BaseSet &set, C1BaseSet &result, MatrixType &bound, Data &data)
	this computes next representation of the set given computed one-step enclosure of the form y + jacPhi*deltaX + rem More...

static const size_type	degree ()

Public Attributes
MatrixType	m_R0
	r0 is a interval set in given coordinate system that represents 'Lipschitz' part More...

MatrixType	m_Cjac
	C is a coordinate system of the 'Lipschitz' part. More...

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...

MatrixType	m_D
	D is a center of the set. More...

MatrixType	m_Bjac
	Bjac is a coordinate system. More...

MatrixType	m_R
	R is a interval set in given coordinate system. More...

MatrixType	m_invBjac

MatrixType	jacRem

MatrixType	jacEnc

VectorType	x

VectorType	deltaX

VectorType	y

VectorType	deltaY

VectorType	rem

VectorType	enc

MatrixType	jacPhi

MatrixType	deltaC

MatrixType	B

Protected Member Functions
void	setLastMatrixEnclosure (const MatrixT &M)

void	setLastEnclosure (const MatrixT::RowVectorType &enc)

Protected Attributes
ScalarType	m_currentTime

MatrixT	m_currentMatrix

MatrixT	m_lastMatrixEnclosure

MatrixT::RowVectorType	m_currentSet

MatrixT::RowVectorType	m_lastEnclosure

Detailed Description

template<typename MatrixT, typename Policies>
class capd::dynset::C1DoubletonSet< MatrixT, Policies >

The C1 set is represented as doubleton: x + C*r0 + B*r;.

Internal representation : C*r0 - basic 'Lipschitz part' B*r - remaining errors

The class represents derivatives in a doubleton form as described in the paper C^1-Lohner algorithm by Piotr Zgliczynski (FoCM 2001).

Member Typedef Documentation

◆ BaseSet [1/2]

template<typename MatrixT >

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

inherited

◆ BaseSet [2/2]

template<typename MatrixT >

typedef MatrixAffineSet<MatrixT> capd::geomset::MatrixDoubletonSet< MatrixT >::BaseSet

inherited

◆ C0BaseSet

template<typename MatrixT , typename Policies >

typedef capd::geomset::CenteredDoubletonSet<MatrixT> capd::dynset::C1DoubletonSet< MatrixT, Policies >::C0BaseSet

◆ C1BaseSet

template<typename MatrixT , typename Policies >

typedef capd::geomset::MatrixDoubletonSet<MatrixT> capd::dynset::C1DoubletonSet< MatrixT, Policies >::C1BaseSet

◆ ColumnVectorType [1/2]

template<typename MatrixT >

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

inherited

◆ ColumnVectorType [2/2]

template<typename MatrixT >

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

inherited

◆ Data

template<typename MatrixT , typename Policies >

typedef C1DoubletonData<MatrixT> capd::dynset::C1DoubletonSet< MatrixT, Policies >::Data

◆ DynSysType

template<typename MatrixT , typename Policies >

typedef C1Set<MatrixT>::DynSysType capd::dynset::C1DoubletonSet< MatrixT, Policies >::DynSysType

◆ MatrixType

template<typename MatrixT , typename Policies >

typedef MatrixT capd::dynset::C1DoubletonSet< MatrixT, Policies >::MatrixType

◆ NormType

template<typename MatrixT >

typedef BaseSet::NormType capd::geomset::MatrixDoubletonSet< MatrixT >::NormType

inherited

◆ Policy

template<typename MatrixT , typename Policies >

typedef Policies capd::dynset::C1DoubletonSet< 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::C1DoubletonSet< MatrixT, Policies >::ScalarType

◆ SetType

template<typename MatrixT , typename Policies >

typedef C1Set<MatrixT> capd::dynset::C1DoubletonSet< MatrixT, Policies >::SetType

◆ size_type

template<typename MatrixT , typename Policies >

typedef MatrixType::size_type capd::dynset::C1DoubletonSet< MatrixT, Policies >::size_type

◆ VectorType

template<typename MatrixT , typename Policies >

typedef MatrixType::RowVectorType capd::dynset::C1DoubletonSet< MatrixT, Policies >::VectorType

Constructor & Destructor Documentation

◆ C1DoubletonSet() [1/6]

template<typename MatrixType , typename Policies >

capd::dynset::C1DoubletonSet< MatrixType, Policies >::C1DoubletonSet	(	const VectorType &	x,
		ScalarType	t = `TypeTraits<ScalarType>::zero()`
	)

◆ C1DoubletonSet() [2/6]

template<typename MatrixType , typename Policies >

capd::dynset::C1DoubletonSet< MatrixType, Policies >::C1DoubletonSet	(	const VectorType &	x,
		const VectorType &	r0,
		ScalarType	t = `TypeTraits<ScalarType>::zero()`
	)

◆ C1DoubletonSet() [3/6]

template<typename MatrixType , typename Policies >

capd::dynset::C1DoubletonSet< MatrixType, Policies >::C1DoubletonSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0,
		ScalarType	t = `TypeTraits<ScalarType>::zero()`
	)

◆ C1DoubletonSet() [4/6]

template<typename MatrixType , typename Policies >

capd::dynset::C1DoubletonSet< MatrixType, Policies >::C1DoubletonSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0,
		const VectorType &	r,
		ScalarType	t = `TypeTraits<ScalarType>::zero()`
	)

◆ C1DoubletonSet() [5/6]

template<typename MatrixType , typename Policies >

capd::dynset::C1DoubletonSet< MatrixType, Policies >::C1DoubletonSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0,
		const MatrixType &	B,
		const VectorType &	r,
		ScalarType	t = `TypeTraits<ScalarType>::zero()`
	)

◆ C1DoubletonSet() [6/6]

template<typename MatrixType , typename Policies >

capd::dynset::C1DoubletonSet< MatrixType, Policies >::C1DoubletonSet	(	const C0BaseSet &	c0part,
		const C1BaseSet &	c1part,
		ScalarType	t = `TypeTraits<ScalarType>::zero()`
	)

Member Function Documentation

◆ degree()

template<typename MatrixT >

static const size_type capd::dynset::C1Set< 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::C1DoubletonSet< 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_Bjac()

template<typename MatrixT >

const MatrixType& capd::geomset::MatrixAffineSet< MatrixT >::get_Bjac ( ) const

inlineinherited

◆ get_C()

template<typename MatrixT >

const MatrixType& capd::geomset::DoubletonSet< MatrixT >::get_C ( ) const

inlineinherited

returns matrix C

◆ get_Cjac() [1/2]

template<typename MatrixT , typename Policies >

const MatrixType& capd::geomset::MatrixDoubletonSet< MatrixT >::get_Cjac

inline

◆ get_Cjac() [2/2]

template<typename MatrixT >

const MatrixType& capd::geomset::MatrixDoubletonSet< MatrixT >::get_Cjac ( ) const

inlineinherited

◆ get_D()

template<typename MatrixT >

const MatrixType& capd::geomset::MatrixAffineSet< MatrixT >::get_D ( ) const

inlineinherited

◆ get_invB()

template<typename MatrixT >

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

inlineinherited

◆ get_invBjac()

template<typename MatrixT >

const MatrixType& capd::geomset::MatrixAffineSet< MatrixT >::get_invBjac ( ) const

inlineinherited

◆ get_r()

template<typename MatrixT >

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

inlineinherited

◆ get_R()

template<typename MatrixT >

const MatrixType& capd::geomset::MatrixAffineSet< MatrixT >::get_R ( ) const

inlineinherited

◆ get_R0() [1/2]

template<typename MatrixT , typename Policies >

const MatrixType& capd::geomset::MatrixDoubletonSet< MatrixT >::get_R0

inline

◆ get_r0()

template<typename MatrixT >

const VectorType& capd::geomset::DoubletonSet< MatrixT >::get_r0 ( ) const

inlineinherited

returns r0

◆ get_R0() [2/2]

template<typename MatrixT >

const MatrixType& capd::geomset::MatrixDoubletonSet< MatrixT >::get_R0 ( ) 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

◆ getColumn_Bjac()

template<typename MatrixT >

ColumnVectorType capd::geomset::MatrixAffineSet< MatrixT >::getColumn_Bjac ( size_type j ) const

inlineinherited

◆ getColumn_C()

template<typename MatrixT >

ColumnVectorType capd::geomset::DoubletonSet< MatrixT >::getColumn_C ( size_type j ) const

inlineinherited

returns j-th column of C

◆ getColumn_Cjac() [1/2]

template<typename MatrixT , typename Policies >

ColumnVectorType capd::geomset::MatrixDoubletonSet< MatrixT >::getColumn_Cjac

inline

◆ getColumn_Cjac() [2/2]

template<typename MatrixT >

ColumnVectorType capd::geomset::MatrixDoubletonSet< MatrixT >::getColumn_Cjac ( size_type j ) const

inlineinherited

◆ getColumn_D()

template<typename MatrixT >

ColumnVectorType capd::geomset::MatrixAffineSet< MatrixT >::getColumn_D ( size_type j ) const

inlineinherited

◆ getColumn_R()

template<typename MatrixT >

ColumnVectorType capd::geomset::MatrixAffineSet< MatrixT >::getColumn_R ( size_type j ) const

inlineinherited

◆ getColumn_R0() [1/2]

template<typename MatrixT , typename Policies >

ColumnVectorType capd::geomset::MatrixDoubletonSet< MatrixT >::getColumn_R0

inline

◆ getColumn_R0() [2/2]

template<typename MatrixT >

ColumnVectorType capd::geomset::MatrixDoubletonSet< MatrixT >::getColumn_R0 ( 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_Bjac()

template<typename MatrixT >

const ScalarType& capd::geomset::MatrixAffineSet< MatrixT >::getElement_Bjac	(	size_type	i,
		size_type	j
	)		const

inlineinherited

◆ getElement_C()

template<typename MatrixT >

const ScalarType& capd::geomset::DoubletonSet< MatrixT >::getElement_C	(	size_type	i,
		size_type	j
	)		const

inlineinherited

returns element C[i][j]

◆ getElement_Cjac() [1/2]

template<typename MatrixT , typename Policies >

const ScalarType& capd::geomset::MatrixDoubletonSet< MatrixT >::getElement_Cjac

inline

◆ getElement_Cjac() [2/2]

template<typename MatrixT >

const ScalarType& capd::geomset::MatrixDoubletonSet< MatrixT >::getElement_Cjac	(	size_type	i,
		size_type	j
	)		const

inlineinherited

◆ getElement_D()

template<typename MatrixT >

const ScalarType& capd::geomset::MatrixAffineSet< MatrixT >::getElement_D	(	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_R()

template<typename MatrixT >

const ScalarType& capd::geomset::MatrixAffineSet< MatrixT >::getElement_R	(	size_type	i,
		size_type	j
	)		const

inlineinherited

◆ getElement_r0()

template<typename MatrixT >

const ScalarType& capd::geomset::DoubletonSet< MatrixT >::getElement_r0 ( size_type i ) const

inlineinherited

returns i-th coordinate of r0

◆ getElement_R0() [1/2]

template<typename MatrixT , typename Policies >

const ScalarType& capd::geomset::MatrixDoubletonSet< MatrixT >::getElement_R0

inline

◆ getElement_R0() [2/2]

template<typename MatrixT >

const ScalarType& capd::geomset::MatrixDoubletonSet< MatrixT >::getElement_R0	(	size_type	i,
		size_type	j
	)		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

◆ getLastMatrixEnclosure()

template<class MatrixT >

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

inlineinherited

◆ getRow_B()

template<typename MatrixT >

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

inlineinherited

◆ getRow_Bjac()

template<typename MatrixT >

VectorType capd::geomset::MatrixAffineSet< MatrixT >::getRow_Bjac ( size_type i ) const

inlineinherited

◆ getRow_C()

template<typename MatrixT >

VectorType capd::geomset::DoubletonSet< MatrixT >::getRow_C ( size_type i ) const

inlineinherited

returns i-th row of C

◆ getRow_Cjac() [1/2]

template<typename MatrixT , typename Policies >

VectorType capd::geomset::MatrixDoubletonSet< MatrixT >::getRow_Cjac

inline

◆ getRow_Cjac() [2/2]

template<typename MatrixT >

VectorType capd::geomset::MatrixDoubletonSet< MatrixT >::getRow_Cjac ( size_type i ) const

inlineinherited

◆ getRow_D()

template<typename MatrixT >

VectorType capd::geomset::MatrixAffineSet< MatrixT >::getRow_D ( size_type i ) const

inlineinherited

◆ getRow_R()

template<typename MatrixT >

VectorType capd::geomset::MatrixAffineSet< MatrixT >::getRow_R ( size_type i ) const

inlineinherited

◆ getRow_R0() [1/2]

template<typename MatrixT , typename Policies >

VectorType capd::geomset::MatrixDoubletonSet< MatrixT >::getRow_R0

inline

◆ getRow_R0() [2/2]

template<typename MatrixT >

VectorType capd::geomset::MatrixDoubletonSet< MatrixT >::getRow_R0 ( size_type i ) const

inlineinherited

◆ move() [1/3]

template<typename MatrixType , typename Policies >

void capd::dynset::C1DoubletonSet< MatrixType, Policies >::move	(	const C1BaseSet &	set,
		C1BaseSet &	result,
		MatrixType &	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::C1DoubletonSet< MatrixType, Policies >::move ( DynSysType & dynsys )

virtual

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

Implements capd::dynset::C1Set< MatrixT >.

Reimplemented in capd::pdes::C1DoubletonSetGeometricTail< Policies >, and capd::pdes::C0DoubletonSetGeometricTail< capd::dynset::C1DoubletonSet< GeometricBound< capd::interval >::MatrixType, Policies > >.

◆ move() [3/3]

template<typename MatrixType , typename Policies >

void capd::dynset::C1DoubletonSet< MatrixType, Policies >::move	(	DynSysType &	dynsys,
		C1DoubletonSet< 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 >

virtual std::string capd::dynset::C1DoubletonSet< MatrixT, Policies >::name ( ) const

inlinevirtual

returns set's name

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

Reimplemented in capd::pdes::C1DoubletonSetGeometricTail< Policies >, capd::pdes::C0DoubletonSetGeometricTail< capd::dynset::C1DoubletonSet< GeometricBound< capd::interval >::MatrixType, Policies > >, and capd::dynset::C11Rect2Set< MatrixT >.

◆ 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 >

capd::geomset::MatrixDoubletonSet< MatrixT >::operator MatrixType ( ) const

inherited

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

◆ 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_Bjac()

template<typename MatrixT >

void capd::geomset::MatrixAffineSet< MatrixT >::set_Bjac ( const MatrixType & Bjac )

inlineinherited

◆ set_C()

template<typename MatrixT >

void capd::geomset::DoubletonSet< MatrixT >::set_C ( const MatrixType & B )

inlineinherited

sets matrix C:= B

◆ set_Cjac()

template<typename MatrixT >

void capd::geomset::MatrixDoubletonSet< MatrixT >::set_Cjac ( const MatrixType & C )

inlineinherited

◆ set_D()

template<typename MatrixT >

void capd::geomset::MatrixAffineSet< MatrixT >::set_D ( const MatrixType & Bjac )

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::MatrixAffineSet< MatrixT >::set_R ( const MatrixType & Bjac )

inlineinherited

◆ set_r()

template<typename MatrixT >

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

inlineinherited

◆ set_R0()

template<typename MatrixT >

void capd::geomset::MatrixDoubletonSet< MatrixT >::set_R0 ( const MatrixType & R0 )

inlineinherited

◆ set_r0()

template<typename MatrixT >

void capd::geomset::DoubletonSet< MatrixT >::set_r0 ( const VectorType & r )

inlineinherited

sets r0

◆ 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

◆ setColumn_Bjac()

template<typename MatrixT >

template<typename VectorT >

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

inlineinherited

◆ setColumn_C()

template<typename MatrixT >

template<typename VectorT >

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

inlineinherited

sets j-th columne of C to v

◆ setColumn_Cjac()

template<typename MatrixT >

template<typename VectorT >

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

inlineinherited

◆ setColumn_D()

template<typename MatrixT >

template<typename VectorT >

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

inlineinherited

◆ setColumn_R()

template<typename MatrixT >

template<typename VectorT >

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

inlineinherited

◆ setColumn_R0()

template<typename MatrixT >

template<typename VectorT >

void capd::geomset::MatrixDoubletonSet< MatrixT >::setColumn_R0	(	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_Bjac()

template<typename MatrixT >

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

inlineinherited

◆ setElement_C()

template<typename MatrixT >

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

inlineinherited

sets C[i][j] := s

◆ setElement_Cjac()

template<typename MatrixT >

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

inlineinherited

◆ setElement_D()

template<typename MatrixT >

void capd::geomset::MatrixAffineSet< MatrixT >::setElement_D	(	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_R()

template<typename MatrixT >

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

inlineinherited

◆ setElement_r0()

template<typename MatrixT >

void capd::geomset::DoubletonSet< MatrixT >::setElement_r0	(	size_type	i,
		const ScalarType &	s
	)

inlineinherited

sets i-th coordinate of r0

◆ setElement_R0()

template<typename MatrixT >

void capd::geomset::MatrixDoubletonSet< MatrixT >::setElement_R0	(	size_type	i,
		size_type	j,
		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

◆ setLastMatrixEnclosure()

template<class MatrixT >

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

inlineprotectedinherited

◆ setRow_B()

template<typename MatrixT >

template<typename VectorT >

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

inlineinherited

◆ setRow_Bjac()

template<typename MatrixT >

template<typename VectorT >

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

inlineinherited

◆ setRow_C()

template<typename MatrixT >

template<typename VectorT >

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

inlineinherited

sets i-th row of C to v

◆ setRow_Cjac()

template<typename MatrixT >

template<typename VectorT >

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

inlineinherited

◆ setRow_D()

template<typename MatrixT >

template<typename VectorT >

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

inlineinherited

◆ setRow_R()

template<typename MatrixT >

template<typename VectorT >

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

inlineinherited

◆ setRow_R0()

template<typename MatrixT >

template<typename VectorT >

void capd::geomset::MatrixDoubletonSet< MatrixT >::setRow_R0	(	size_type	i,
		const VectorT &	v
	)

inlineinherited

◆ setToIdentity()

template<typename MatrixT >

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

inlineinherited

◆ show()

template<typename MatrixType , typename Policies >

std::string capd::dynset::C1DoubletonSet< MatrixType, Policies >::show ( void ) const

virtual

returns a set detailed information

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

Member Data Documentation

◆ m_B

template<typename MatrixT >

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

inherited

B is a coordinate system.

◆ m_Bjac

template<typename MatrixT >

MatrixType capd::geomset::MatrixAffineSet< MatrixT >::m_Bjac

inherited

Bjac 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_Cjac

template<typename MatrixT , typename Policies >

MatrixType capd::geomset::MatrixDoubletonSet< MatrixT >::m_Cjac

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

◆ 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 >

MatrixType capd::geomset::MatrixAffineSet< MatrixT >::m_D

inherited

D is a center of the set.

◆ m_invB

template<typename MatrixT >

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

inherited

◆ m_invBjac

template<typename MatrixT >

MatrixType capd::geomset::MatrixAffineSet< MatrixT >::m_invBjac

inherited

◆ 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 >

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

inherited

r is a interval set in given coordinate system

◆ m_R

template<typename MatrixT >

MatrixType capd::geomset::MatrixAffineSet< MatrixT >::m_R

inherited

R is a interval set in given coordinate system.

◆ m_R0

template<typename MatrixT , typename Policies >

MatrixType capd::geomset::MatrixDoubletonSet< MatrixT >::m_R0

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

◆ 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

The documentation for this class was generated from the following files:

capd/dynset/C1DoubletonSet.h
capd/dynset/C1DoubletonSet.hpp

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::C1DoubletonSet< MatrixT, Policies >

Member Typedef Documentation

◆ BaseSet [1/2]

◆ BaseSet [2/2]

◆ C0BaseSet

◆ C1BaseSet

◆ ColumnVectorType [1/2]

◆ ColumnVectorType [2/2]

◆ Data

◆ DynSysType

◆ MatrixType

◆ NormType

◆ Policy

◆ RealMatrix

◆ RealVector

◆ ScalarType

◆ SetType

◆ size_type

◆ VectorType

Constructor & Destructor Documentation

◆ C1DoubletonSet() [1/6]

◆ C1DoubletonSet() [2/6]

◆ C1DoubletonSet() [3/6]

◆ C1DoubletonSet() [4/6]

◆ C1DoubletonSet() [5/6]

◆ C1DoubletonSet() [6/6]

Member Function Documentation

◆ degree()

◆ dimension()

◆ evalAt()

◆ get_B()

◆ get_Bjac()

◆ get_C()

◆ get_Cjac() [1/2]

◆ get_Cjac() [2/2]

◆ get_D()

◆ get_invB()

◆ get_invBjac()

◆ get_r()

◆ get_R()

◆ get_R0() [1/2]

◆ get_r0()

◆ get_R0() [2/2]

◆ get_x()

◆ getColumn_B()

◆ getColumn_Bjac()

◆ getColumn_C()

◆ getColumn_Cjac() [1/2]

◆ getColumn_Cjac() [2/2]

◆ getColumn_D()

◆ getColumn_R()

◆ getColumn_R0() [1/2]

◆ getColumn_R0() [2/2]

◆ getCurrentTime()

◆ getElement_B()

◆ getElement_Bjac()

◆ getElement_C()

◆ getElement_Cjac() [1/2]

◆ getElement_Cjac() [2/2]

◆ getElement_D()

◆ getElement_r()

◆ getElement_R()

◆ getElement_r0()

◆ getElement_R0() [1/2]

◆ getElement_R0() [2/2]

◆ getElement_x()

◆ getLastEnclosure()

◆ getLastMatrixEnclosure()

◆ getRow_B()

◆ getRow_Bjac()

◆ getRow_C()

◆ getRow_Cjac() [1/2]

◆ getRow_Cjac() [2/2]

template<typename MatrixT, typename Policies>
class capd::dynset::C1DoubletonSet< MatrixT, Policies >