Class C0HOTripletonSet represents a subset of $ R^n $ in the following form. More...

#include <capd/dynset/C0HOTripletonSet.h>

Public Types
typedef C0TripletonSet< 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 C0Set< MatrixT >	SetType

typedef TripletonData< MatrixT >	Data

typedef Policies	Policy

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...

virtual ScalarType	evalAffineFunctional (const VectorType &gradient, const VectorType &u) const

template<class Solver >
void	move (Solver &solver)

std::string	name () const

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 ()

std::string	show () const


	C0HOTripletonSet (BaseSet &set)

	C0HOTripletonSet (const VectorType &x, ScalarType t=TypeTraits< ScalarType >::zero())

	C0HOTripletonSet (const VectorType &x, const VectorType &r0, ScalarType t=TypeTraits< ScalarType >::zero())

	C0HOTripletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0, ScalarType t=TypeTraits< ScalarType >::zero())

	C0HOTripletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0, const VectorType &r, ScalarType t=TypeTraits< ScalarType >::zero())

	C0HOTripletonSet (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, C0HOTripletonSet &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...

Public Attributes
BaseSet	predictor

Detailed Description

template<class MatrixT, class Policies>
class capd::dynset::C0HOTripletonSet< MatrixT, Policies >

Class C0HOTripletonSet 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

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 C0TripletonSet<MatrixT,Policies> capd::dynset::C0HOTripletonSet< MatrixT, Policies >::BaseSet

◆ Data

template<typename MatrixT , typename Policies >

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

inherited

◆ DynSysType

template<class MatrixT , class Policies >

typedef BaseSet::DynSysType capd::dynset::C0HOTripletonSet< MatrixT, Policies >::DynSysType

◆ MatrixType

template<class MatrixT , class Policies >

typedef BaseSet::MatrixType capd::dynset::C0HOTripletonSet< MatrixT, Policies >::MatrixType

◆ Policy

template<typename MatrixT , typename Policies >

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

inherited

◆ ScalarType

template<class MatrixT , class Policies >

typedef MatrixType::ScalarType capd::dynset::C0HOTripletonSet< MatrixT, Policies >::ScalarType

◆ SetType

template<typename MatrixT , typename Policies >

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

inherited

◆ size_type

template<class MatrixT , class Policies >

typedef MatrixType::size_type capd::dynset::C0HOTripletonSet< MatrixT, Policies >::size_type

◆ VectorType

template<class MatrixT , class Policies >

typedef BaseSet::VectorType capd::dynset::C0HOTripletonSet< MatrixT, Policies >::VectorType

Constructor & Destructor Documentation

◆ C0HOTripletonSet() [1/6]

template<class MatrixT , class Policies >

capd::dynset::C0HOTripletonSet< MatrixT, Policies >::C0HOTripletonSet ( BaseSet & set )

◆ C0HOTripletonSet() [2/6]

template<class MatrixT , class Policies >

capd::dynset::C0HOTripletonSet< MatrixT, Policies >::C0HOTripletonSet	(	const VectorType &	x,
		ScalarType	t = `TypeTraits<ScalarType>::zero()`
	)

explicit

◆ C0HOTripletonSet() [3/6]

template<class MatrixT , class Policies >

capd::dynset::C0HOTripletonSet< MatrixT, Policies >::C0HOTripletonSet	(	const VectorType &	x,
		const VectorType &	r0,
		ScalarType	t = `TypeTraits<ScalarType>::zero()`
	)

◆ C0HOTripletonSet() [4/6]

template<class MatrixT , class Policies >

capd::dynset::C0HOTripletonSet< MatrixT, Policies >::C0HOTripletonSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0,
		ScalarType	t = `TypeTraits<ScalarType>::zero()`
	)

◆ C0HOTripletonSet() [5/6]

template<class MatrixT , class Policies >

capd::dynset::C0HOTripletonSet< MatrixT, Policies >::C0HOTripletonSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0,
		const VectorType &	r,
		ScalarType	t = `TypeTraits<ScalarType>::zero()`
	)

◆ C0HOTripletonSet() [6/6]

template<class MatrixT , class Policies >

capd::dynset::C0HOTripletonSet< MatrixT, Policies >::C0HOTripletonSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0,
		const MatrixType &	B,
		const VectorType &	r,
		ScalarType	t = `TypeTraits<ScalarType>::zero()`
	)

Member Function Documentation

◆ evalAffineFunctional()

template<class MatrixT , class Policies >

virtual ScalarType capd::dynset::C0HOTripletonSet< MatrixT, Policies >::evalAffineFunctional	(	const VectorType &	gradient,
		const VectorType &	u
	)		const

inlinevirtual

◆ evalAt()

template<class MatrixT , class Policies >

template<class Functional >

ScalarType capd::dynset::C0HOTripletonSet< 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.

◆ move() [1/5]

template<typename MatrixType , typename Policies >

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

inherited

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

◆ move() [3/5]

template<typename MatrixType , typename Policies >

void capd::dynset::C0TripletonSet< MatrixType, Policies >::move	(	DynSysType &	dynsys,
		C0TripletonSet< 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::C0HOTripletonSet< MatrixT, Policies >::move ( Solver & solver )

inline

◆ move() [5/5]

template<class MatrixT , class Policies >

template<class Solver >

void capd::dynset::C0HOTripletonSet< MatrixT, Policies >::move	(	Solver &	solver,
		C0HOTripletonSet< MatrixT, Policies > &	result
	)

◆ name()

template<class MatrixT , class Policies >

std::string capd::dynset::C0HOTripletonSet< MatrixT, Policies >::name ( ) const

inline

◆ setToIdentity()

template<typename MatrixT , typename Policies >

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

inlineinherited

◆ show()

template<typename MatrixType , typename Policies >

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

inherited

Member Data Documentation

◆ predictor

template<class MatrixT , class Policies >

BaseSet capd::dynset::C0HOTripletonSet< MatrixT, Policies >::predictor

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description

template<class MatrixT, class Policies> class capd::dynset::C0HOTripletonSet< MatrixT, Policies >

Member Typedef Documentation

◆ BaseSet

◆ Data

◆ DynSysType

◆ MatrixType

◆ Policy

◆ ScalarType

◆ SetType

◆ size_type

◆ VectorType

Constructor & Destructor Documentation

◆ C0HOTripletonSet() [1/6]

◆ C0HOTripletonSet() [2/6]

◆ C0HOTripletonSet() [3/6]

◆ C0HOTripletonSet() [4/6]

◆ C0HOTripletonSet() [5/6]

◆ C0HOTripletonSet() [6/6]

Member Function Documentation

◆ evalAffineFunctional()

◆ evalAt()

◆ move() [1/5]

◆ move() [2/5]

◆ move() [3/5]

◆ move() [4/5]

◆ move() [5/5]

◆ name()

◆ setToIdentity()

◆ show()

Member Data Documentation

◆ predictor

template<class MatrixT, class Policies>
class capd::dynset::C0HOTripletonSet< MatrixT, Policies >