capd::dynset::C0TripletonSet< MatrixT, Policies > Class Template Reference

Class C0TripletonSet represents a subset of R^n in the following form. More...

#include <capd/dynset/C0TripletonSet.h>

Public Types
typedef MatrixT	MatrixType
typedef MatrixT::RowVectorType	VectorType
typedef MatrixType::ScalarType	ScalarType
typedef MatrixType::size_type	size_type
typedef C0Set< MatrixT >	SetType
typedef C0Set< MatrixT >::DynSysType	DynSysType
typedef capd::geomset::CenteredTripletonSet< MatrixT >	BaseSet
typedef TripletonData< MatrixT >	Data
typedef Policies	Policy

Public Member Functions
	C0TripletonSet (const VectorType &x, ScalarType t=TypeTraits< ScalarType >::zero())
	C0TripletonSet (const VectorType &x, const VectorType &r0, ScalarType t=TypeTraits< ScalarType >::zero())
	C0TripletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0, ScalarType t=TypeTraits< ScalarType >::zero())
	C0TripletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0, const VectorType &r, ScalarType t=TypeTraits< ScalarType >::zero())
	C0TripletonSet (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, C0TripletonSet &result) const
	computes image of the set after one step/iterate of the dynamical system and stores it in result More...
void	setToIdentity ()
template<class Functional >
ScalarType	evalAt (const Functional &f) const
	This method computes value of functor 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) can be computed as f(x) + (Df(X)*C)*r0 + intersection( (Df(X)*B)*r, (Df(X)*Q)*q ) More...
std::string	show () const
std::string	name () const

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...

Protected Member Functions
	C0TripletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0, const MatrixType &B, const VectorType &r, const MatrixType &Q, const VectorType &q, ScalarType t=TypeTraits< ScalarType >::zero())

Friends
C0TripletonSet	operator* (const MatrixT &, const C0TripletonSet &)

Detailed Description

template<typename MatrixT, typename Policies>
class capd::dynset::C0TripletonSet< MatrixT, Policies >

Class C0TripletonSet represents a subset of R^n in the following form.

x + C*r0 + intersection(B*r , Q*q )

where x is a point vector C,B,Q are point matrices, where B and Q are invertible and Q is close to orthogonal r0,r are interval vectors

Moreover it stores rigorous inverse matrices of B and Q

Member Typedef Documentation

BaseSet

template<typename MatrixT , typename Policies >

typedef capd::geomset::CenteredTripletonSet<MatrixT> capd::dynset::C0TripletonSet< MatrixT, Policies >::BaseSet

Data

template<typename MatrixT , typename Policies >

typedef TripletonData<MatrixT> capd::dynset::C0TripletonSet< MatrixT, Policies >::Data

DynSysType

template<typename MatrixT , typename Policies >

typedef C0Set<MatrixT>::DynSysType capd::dynset::C0TripletonSet< MatrixT, Policies >::DynSysType

MatrixType

template<typename MatrixT , typename Policies >

typedef MatrixT capd::dynset::C0TripletonSet< MatrixT, Policies >::MatrixType

Policy

template<typename MatrixT , typename Policies >

typedef Policies capd::dynset::C0TripletonSet< MatrixT, Policies >::Policy

ScalarType

template<typename MatrixT , typename Policies >

typedef MatrixType::ScalarType capd::dynset::C0TripletonSet< MatrixT, Policies >::ScalarType

SetType

template<typename MatrixT , typename Policies >

typedef C0Set<MatrixT> capd::dynset::C0TripletonSet< MatrixT, Policies >::SetType

size_type

template<typename MatrixT , typename Policies >

typedef MatrixType::size_type capd::dynset::C0TripletonSet< MatrixT, Policies >::size_type

VectorType

template<typename MatrixT , typename Policies >

typedef MatrixT::RowVectorType capd::dynset::C0TripletonSet< MatrixT, Policies >::VectorType

Constructor & Destructor Documentation

C0TripletonSet() [1/6]

template<typename MatrixType , typename Policies >

capd::dynset::C0TripletonSet< MatrixType, Policies >::C0TripletonSet	(	const VectorType &	x,
		ScalarType	t = TypeTraits<ScalarType>::zero()
	)

C0TripletonSet() [2/6]

template<typename MatrixType , typename Policies >

capd::dynset::C0TripletonSet< MatrixType, Policies >::C0TripletonSet	(	const VectorType &	x,
		const VectorType &	r0,
		ScalarType	t = TypeTraits<ScalarType>::zero()
	)

C0TripletonSet() [3/6]

template<typename MatrixType , typename Policies >

capd::dynset::C0TripletonSet< MatrixType, Policies >::C0TripletonSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0,
		ScalarType	t = TypeTraits<ScalarType>::zero()
	)

C0TripletonSet() [4/6]

template<typename MatrixType , typename Policies >

capd::dynset::C0TripletonSet< MatrixType, Policies >::C0TripletonSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0,
		const VectorType &	r,
		ScalarType	t = TypeTraits<ScalarType>::zero()
	)

C0TripletonSet() [5/6]

template<typename MatrixType , typename Policies >

capd::dynset::C0TripletonSet< MatrixType, Policies >::C0TripletonSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0,
		const MatrixType &	B,
		const VectorType &	r,
		ScalarType	t = TypeTraits<ScalarType>::zero()
	)

C0TripletonSet() [6/6]

template<typename MatrixType , typename Policies >

capd::dynset::C0TripletonSet< MatrixType, Policies >::C0TripletonSet ( const VectorType &  x, const MatrixType &  C, const VectorType &  r0, const MatrixType &  B, const VectorType &  r, const MatrixType &  Q, const VectorType &  q, ScalarType  t = TypeTraits<ScalarType>::zero()  )

protected

Member Function Documentation

evalAt()

template<typename MatrixT , typename Policies >

template<class Functional >

ScalarType capd::dynset::C0TripletonSet< MatrixT, Policies >::evalAt ( const Functional &  f ) const

inline

This method computes value of functor 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) can be computed as f(x) + (Df(X)*C)*r0 + intersection( (Df(X)*B)*r, (Df(X)*Q)*q )

move() [1/3]

template<typename MatrixType , typename Policies >

void capd::dynset::C0TripletonSet< 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::C0TripletonSet< MatrixType, Policies >::move

(

DynSysType &

dynsys

)

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

move() [3/3]

template<typename MatrixType , typename Policies >

void capd::dynset::C0TripletonSet< MatrixType, Policies >::move	(	DynSysType &	dynsys,
		C0TripletonSet< 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::C0TripletonSet< MatrixT, Policies >::name ( ) const

inline

setToIdentity()

template<typename MatrixT , typename Policies >

void capd::dynset::C0TripletonSet< MatrixT, Policies >::setToIdentity ( )

inline

show()

template<typename MatrixType , typename Policies >

std::string capd::dynset::C0TripletonSet< MatrixType, Policies >::show

Friends And Related Function Documentation

operator*

template<typename MatrixT , typename Policies >

C0TripletonSet operator* ( const MatrixT &  A, const C0TripletonSet< MatrixT, Policies > &  s  )

friend