capd::dynset::C0HODoubletonSet< MatrixT, Policies > Class Template Reference

Class C0HODoubletonSet represents a subset of R^n as doubleton, i.e. More...

#include <capd/dynset/C0HODoubletonSet.h>

Public Types
typedef C0DoubletonSet< MatrixT, Policies >	BaseSet
typedef BaseSet::MatrixType	MatrixType
typedef BaseSet::VectorType	VectorType
typedef MatrixType::ScalarType	ScalarType
typedef MatrixType::size_type	size_type
typedef BaseSet::DynSysType	DynSysType
typedef capd::vectalg::Norm< VectorType, MatrixType >	NormType
typedef C0Set< MatrixT >::SetType	SetType
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
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 &c) 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+C*r0+intersection(B*r,Q*q). Then f(X) = M*(X-x0) can be computed as M*(x-x0) + (M*C)*r0 + intersection( M*B)*r, (M*Q)*q ) More...
virtual ScalarType	evalAffineFunctional (const VectorType &gradient, const VectorType &u) 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+C*r0+B*r. Then f(X) = grad*(X-x0) can be computed as grad*(x-x0) + (grad*C)*r0 + (grad*B)*r. More...
template<class Solver >
void	move (Solver &solver)
std::string	name () const
	returns set's name More...
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...
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 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
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)
	C0HODoubletonSet (BaseSet &set)
	C0HODoubletonSet (const VectorType &x, ScalarType t=TypeTraits< ScalarType >::zero())
	C0HODoubletonSet (const VectorType &x, const VectorType &r0, ScalarType t=TypeTraits< ScalarType >::zero())
	C0HODoubletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0, ScalarType t=TypeTraits< ScalarType >::zero())
	C0HODoubletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0, const VectorType &r, ScalarType t=TypeTraits< ScalarType >::zero())
	C0HODoubletonSet (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, C0HODoubletonSet &result)

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
BaseSet	predictor
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<class MatrixT, class Policies>
class capd::dynset::C0HODoubletonSet< MatrixT, Policies >

Class C0HODoubletonSet represents a subset of R^n as doubleton, i.e.

x + C*r0 + B*r

where x is a (point) interval vector C,B are (point) interval matrices r0,r are interval vectors centered at zero.

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 only for orders of the Taylor method less or equal 32. This is due to capacity of integer type used to store binomial coefficients.

Member Typedef Documentation

BaseSet

template<class MatrixT , class Policies >

typedef C0DoubletonSet<MatrixT,Policies> capd::dynset::C0HODoubletonSet< 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

inherited

DynSysType

template<class MatrixT , class Policies >

typedef BaseSet::DynSysType capd::dynset::C0HODoubletonSet< MatrixT, Policies >::DynSysType

MatrixType

template<class MatrixT , class Policies >

typedef BaseSet::MatrixType capd::dynset::C0HODoubletonSet< MatrixT, Policies >::MatrixType

NormType

template<typename MatrixT , typename Policies >

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

inherited

Policy

template<typename MatrixT , typename Policies >

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

inherited

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<class MatrixT , class Policies >

typedef MatrixType::ScalarType capd::dynset::C0HODoubletonSet< MatrixT, Policies >::ScalarType

SetType

template<typename MatrixT , typename Policies >

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

inherited

size_type

template<class MatrixT , class Policies >

typedef MatrixType::size_type capd::dynset::C0HODoubletonSet< MatrixT, Policies >::size_type

VectorType

template<class MatrixT , class Policies >

typedef BaseSet::VectorType capd::dynset::C0HODoubletonSet< MatrixT, Policies >::VectorType

Constructor & Destructor Documentation

C0HODoubletonSet() [1/6]

template<class MatrixT , class Policies >

capd::dynset::C0HODoubletonSet< MatrixT, Policies >::C0HODoubletonSet

(

BaseSet &

set

)

C0HODoubletonSet() [2/6]

template<class MatrixT , class Policies >

capd::dynset::C0HODoubletonSet< MatrixT, Policies >::C0HODoubletonSet ( const VectorType &  x, ScalarType  t = TypeTraits<ScalarType>::zero()  )

explicit

C0HODoubletonSet() [3/6]

template<class MatrixT , class Policies >

capd::dynset::C0HODoubletonSet< MatrixT, Policies >::C0HODoubletonSet	(	const VectorType &	x,
		const VectorType &	r0,
		ScalarType	t = TypeTraits<ScalarType>::zero()
	)

C0HODoubletonSet() [4/6]

template<class MatrixT , class Policies >

capd::dynset::C0HODoubletonSet< MatrixT, Policies >::C0HODoubletonSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0,
		ScalarType	t = TypeTraits<ScalarType>::zero()
	)

C0HODoubletonSet() [5/6]

template<class MatrixT , class Policies >

capd::dynset::C0HODoubletonSet< MatrixT, Policies >::C0HODoubletonSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0,
		const VectorType &	r,
		ScalarType	t = TypeTraits<ScalarType>::zero()
	)

C0HODoubletonSet() [6/6]

template<class MatrixT , class Policies >

capd::dynset::C0HODoubletonSet< MatrixT, Policies >::C0HODoubletonSet	(	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 MatrixT , class Policies >

VectorType capd::dynset::C0HODoubletonSet< MatrixT, Policies >::affineTransformation ( const MatrixType &  M, const VectorType &  x0  ) const

inlinevirtual

This method computes value of an affine map f at interval vector represented by this set. This set is represented as tripleton X=x+C*r0+intersection(B*r,Q*q). Then f(X) = M*(X-x0) can be computed as M*(x-x0) + (M*C)*r0 + intersection( M*B)*r, (M*Q)*q )

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

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

evalAffineFunctional()

template<class MatrixT , class Policies >

virtual ScalarType capd::dynset::C0HODoubletonSet< MatrixT, Policies >::evalAffineFunctional ( const VectorType &  gradient, const VectorType &  x0  ) const

inlinevirtual

This method computes value of an affine functional f at the vector represented by this set. This set is represented as doubleton X=x+C*r0+B*r. Then f(X) = grad*(X-x0) can be computed as grad*(x-x0) + (grad*C)*r0 + (grad*B)*r.

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

evalAt()

template<class MatrixT , class Policies >

template<class Functional >

ScalarType capd::dynset::C0HODoubletonSet< MatrixT, Policies >::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.

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() [1/5]

template<typename MatrixType , typename Policies >

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

staticinherited

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

move() [2/5]

template<typename MatrixType , typename Policies >

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

virtualinherited

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

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

move() [3/5]

template<typename MatrixType , typename Policies >

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

inherited

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

move() [4/5]

template<class MatrixT , class Policies >

template<class Solver >

void capd::dynset::C0HODoubletonSet< MatrixT, Policies >::move ( Solver &  solver )

inline

move() [5/5]

template<class MatrixT , class Policies >

template<class Solver >

void capd::dynset::C0HODoubletonSet< MatrixT, Policies >::move	(	Solver &	solver,
		C0HODoubletonSet< MatrixT, Policies > &	result
	)

name()

template<class MatrixT , class Policies >

std::string capd::dynset::C0HODoubletonSet< MatrixT, Policies >::name ( ) const

inlinevirtual

returns set's name

Reimplemented from capd::dynset::C0DoubletonSet< 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

inherited

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

predictor

template<class MatrixT , class Policies >

BaseSet capd::dynset::C0HODoubletonSet< MatrixT, Policies >::predictor