This class provides a h-set in an arbitrary dimension. More...

#include <capd/covrel/HSetMD.h>

Public Types
typedef MatrixT	MatrixType

typedef IMatrixT	IMatrixType

typedef MatrixType::RowVectorType	VectorType

typedef IMatrixType::RowVectorType	IVectorType

typedef IVectorType::ScalarType	ScalarType

typedef VectorType::ScalarType	BoundType

typedef VectorType::size_type	size_type

Public Member Functions
	HSetMD ()

	HSetMD (const VectorType &center, const MatrixType &Base, size_type uDim, size_type sDim, const VectorType &r)
	Constructor of HSet from approximation. More...

	HSetMD (const IVectorType &center, const IMatrixType &Base, size_type uDim, size_type sDim, const VectorType &r)
	Constructor of HSet from rigorous data. More...

	~HSetMD ()

virtual bool	outside (const VectorType &point) const

bool	inside (const VectorType &point) const

bool	across (const VectorType &point) const

bool	mapaway (const VectorType &point) const

virtual bool	outside (const IVectorType &point) const

bool	inside (const IVectorType &point) const

bool	across (const IVectorType &point) const

bool	mapaway (const IVectorType &point) const

template<typename SetType >
bool	outside (const SetType &A_set) const

template<typename SetType >
bool	inside (const SetType &A_set) const

template<typename SetType >
bool	across (const SetType &A_set) const

template<typename SetType >
bool	mapaway (const SetType &A_set) const

VectorType	transformToHSetCoordinates (const VectorType &point) const

IVectorType	transformToHSetCoordinates (const IVectorType &point) const

template<typename IMatrix >
GridSet< IMatrix > &	gridFace (GridSet< IMatrix > &grid, const std::vector< size_type > &gridSizes, const std::vector< size_type > &dimensions, size_type totalDimension, size_type coordinateToFix, Side side=bothSides) const
	in the `grid` it returns uniform grid of the given face More...

template<typename IMatrix >
GridSet< IMatrix > &	gridSet (GridSet< IMatrix > &G, const std::vector< size_type > &grid, const std::vector< size_type > &d, size_type totalDimension) const
	this procedure creates a grid of the whole h-set in the following form: G.center[i] + G.C * G.r d is a vector of indices of coordinates if the set is embeded in higher dimension More...

const IVectorType &	center () const
	center of h-set More...

const IMatrixType &	coordinateSystem () const
	matrix of base vectors More...

const IMatrixType &	invCoordinateSystem () const

IVectorType	box () const

const VectorType &	radius ()
	returns vector of radiuses (in each direction) More...

size_type	unstableDimension () const
	number of unstable dimensions More...

size_type	stableDimension () const
	number of stable dimensions More...

const VectorType &	get_x () const

const MatrixType &	get_B () const

const VectorType &	get_r () const

const IVectorType &	get_I_x () const

const IMatrixType &	get_I_B () const

const IMatrixType &	get_I_invB () const

virtual std::string	show () const

std::string	showInfo () const

virtual bool	outside (const VectorType &) const=0

virtual bool	outside (const IVectorType &set) const=0
	verifies if `set` does not intersect the support of h-set More...

virtual bool	inside (const VectorType &) const=0

virtual bool	inside (const IVectorType &set) const=0
	verifies if `set` is inside the support of h-set, More...

virtual bool	across (const VectorType &) const=0

virtual bool	across (const IVectorType &set) const=0
	verifies if `set` does not intersect N^+ More...

virtual bool	mapaway (const VectorType &) const=0

virtual bool	mapaway (const IVectorType &set) const=0
	??? More...


these functions works for interval sets expressed in HSet coordinate system
bool	checkOutside (const IVectorType &) const

bool	checkInside (const IVectorType &) const

bool	checkAcross (const IVectorType &) const

bool	checkMapaway (const IVectorType &) const

Protected Attributes
VectorType	m_x
	center point More...

MatrixType	m_B
	coordinate system More...

IVectorType	m_Ix
	rigorous center point More...

IMatrixType	m_IB

IMatrixType	m_invIB
	rigorous coordinate system and its inverse More...

size_type	m_uDim
	number of unstable dimensions More...

size_type	m_sDim
	number of stable dimensions More...

VectorType	m_r
	radiuses of balls (used both for non-rigorous and rigorous version) More...

Friends
std::ostream &	operator<< (std::ostream &stream, const HSetMD &set)

Detailed Description

template<typename MatrixT, typename IMatrixT>
class capd::covrel::HSetMD< MatrixT, IMatrixT >

This class provides a h-set in an arbitrary dimension.

We assume that the set is represented as center + Base * B(0,r) where center is vector, Base is matrix of coordinate change and B(0,r) is a ball of radius r and dimension uDim + sDim where uDim denotes a number of unstable directions sDim denotes a number of stable directions

Member Typedef Documentation

◆ BoundType

template<typename MatrixT , typename IMatrixT >

typedef VectorType::ScalarType capd::covrel::HSetMD< MatrixT, IMatrixT >::BoundType

◆ IMatrixType

template<typename MatrixT , typename IMatrixT >

typedef IMatrixT capd::covrel::HSetMD< MatrixT, IMatrixT >::IMatrixType

◆ IVectorType

template<typename MatrixT , typename IMatrixT >

typedef IMatrixType::RowVectorType capd::covrel::HSetMD< MatrixT, IMatrixT >::IVectorType

◆ MatrixType

template<typename MatrixT , typename IMatrixT >

typedef MatrixT capd::covrel::HSetMD< MatrixT, IMatrixT >::MatrixType

◆ ScalarType

template<typename MatrixT , typename IMatrixT >

typedef IVectorType::ScalarType capd::covrel::HSetMD< MatrixT, IMatrixT >::ScalarType

◆ size_type

template<typename MatrixT , typename IMatrixT >

typedef VectorType::size_type capd::covrel::HSetMD< MatrixT, IMatrixT >::size_type

◆ VectorType

template<typename MatrixT , typename IMatrixT >

typedef MatrixType::RowVectorType capd::covrel::HSetMD< MatrixT, IMatrixT >::VectorType

Constructor & Destructor Documentation

◆ HSetMD() [1/3]

template<typename MatrixT , typename IMatrixT >

capd::covrel::HSetMD< MatrixT, IMatrixT >::HSetMD ( )

inline

◆ HSetMD() [2/3]

template<typename MatrixType , typename IMatrixType >

capd::covrel::HSetMD< MatrixType, IMatrixType >::HSetMD	(	const VectorType &	center,
		const MatrixType &	Base,
		size_type	uDim,
		size_type	sDim,
		const VectorType &	r
	)

Constructor of HSet from approximation.

HSet is represented as center + Base * B(0,r) uDim denotes a number of unstable directions sDim denotes a number of stable directions It sets both nonrigorous and rigorous fields

◆ HSetMD() [3/3]

template<typename MatrixType , typename IMatrixType >

capd::covrel::HSetMD< MatrixType, IMatrixType >::HSetMD	(	const IVectorType &	center,
		const IMatrixType &	Base,
		size_type	uDim,
		size_type	sDim,
		const VectorType &	r
	)

Constructor of HSet from rigorous data.

HSet is represented as center + Base * B(0,r) uDim denotes a number of unstable directions sDim denotes a number of stable directions It sets both nonrigorous and rigorous fields

◆ ~HSetMD()

template<typename MatrixT , typename IMatrixT >

capd::covrel::HSetMD< MatrixT, IMatrixT >::~HSetMD ( )

inline

Member Function Documentation

◆ across() [1/5]

template<typename MatrixType , typename IMatrixType >

bool capd::covrel::HSetMD< MatrixType, IMatrixType >::across ( const IVectorType & point ) const

◆ across() [2/5]

virtual bool capd::covrel::HSet< MatrixT::RowVectorType , IMatrixT::RowVectorType >::across ( const IVectorType & set ) const

pure virtualinherited

verifies if set does not intersect N^+

◆ across() [3/5]

template<typename MatrixType , typename IMatrixType >

template<typename SetType >

bool capd::covrel::HSetMD< MatrixType, IMatrixType >::across ( const SetType & A_set ) const

◆ across() [4/5]

virtual bool capd::covrel::HSet< MatrixT::RowVectorType , IMatrixT::RowVectorType >::across ( const VectorType & ) const

pure virtualinherited

◆ across() [5/5]

template<typename MatrixType , typename IMatrixType >

bool capd::covrel::HSetMD< MatrixType, IMatrixType >::across ( const VectorType & point ) const

◆ box()

template<typename MatrixT , typename IMatrixT >

IVectorType capd::covrel::HSetMD< MatrixT, IMatrixT >::box ( ) const

inline

< h-set in 'proper' coordinate system (it is a product of intervals)

◆ center()

template<typename MatrixT , typename IMatrixT >

const IVectorType & capd::covrel::HSetMD< MatrixT, IMatrixT >::center ( ) const

inline

center of h-set

◆ checkAcross()

template<typename MatrixType , typename IMatrixType >

bool capd::covrel::HSetMD< MatrixType, IMatrixType >::checkAcross ( const IVectorType & x ) const

◆ checkInside()

template<typename MatrixType , typename IMatrixType >

bool capd::covrel::HSetMD< MatrixType, IMatrixType >::checkInside ( const IVectorType & x ) const

◆ checkMapaway()

template<typename MatrixType , typename IMatrixType >

bool capd::covrel::HSetMD< MatrixType, IMatrixType >::checkMapaway ( const IVectorType & x ) const

◆ checkOutside()

template<typename MatrixType , typename IMatrixType >

bool capd::covrel::HSetMD< MatrixType, IMatrixType >::checkOutside ( const IVectorType & x ) const

◆ coordinateSystem()

template<typename MatrixT , typename IMatrixT >

const IMatrixType & capd::covrel::HSetMD< MatrixT, IMatrixT >::coordinateSystem ( ) const

inline

matrix of base vectors

◆ get_B()

template<typename MatrixT , typename IMatrixT >

const MatrixType & capd::covrel::HSetMD< MatrixT, IMatrixT >::get_B ( ) const

inline

◆ get_I_B()

template<typename MatrixT , typename IMatrixT >

const IMatrixType & capd::covrel::HSetMD< MatrixT, IMatrixT >::get_I_B ( ) const

inline

◆ get_I_invB()

template<typename MatrixT , typename IMatrixT >

const IMatrixType & capd::covrel::HSetMD< MatrixT, IMatrixT >::get_I_invB ( ) const

inline

◆ get_I_x()

template<typename MatrixT , typename IMatrixT >

const IVectorType & capd::covrel::HSetMD< MatrixT, IMatrixT >::get_I_x ( ) const

inline

◆ get_r()

template<typename MatrixT , typename IMatrixT >

const VectorType & capd::covrel::HSetMD< MatrixT, IMatrixT >::get_r ( ) const

inline

◆ get_x()

template<typename MatrixT , typename IMatrixT >

const VectorType & capd::covrel::HSetMD< MatrixT, IMatrixT >::get_x ( ) const

inline

◆ inside() [1/5]

template<typename MatrixType , typename IMatrixType >

bool capd::covrel::HSetMD< MatrixType, IMatrixType >::inside ( const IVectorType & point ) const

◆ inside() [2/5]

virtual bool capd::covrel::HSet< MatrixT::RowVectorType , IMatrixT::RowVectorType >::inside ( const IVectorType & set ) const

pure virtualinherited

verifies if set is inside the support of h-set,

◆ inside() [3/5]

template<typename MatrixType , typename IMatrixType >

template<typename SetType >

bool capd::covrel::HSetMD< MatrixType, IMatrixType >::inside ( const SetType & A_set ) const

◆ inside() [4/5]

virtual bool capd::covrel::HSet< MatrixT::RowVectorType , IMatrixT::RowVectorType >::inside ( const VectorType & ) const

pure virtualinherited

◆ inside() [5/5]

template<typename MatrixType , typename IMatrixType >

bool capd::covrel::HSetMD< MatrixType, IMatrixType >::inside ( const VectorType & point ) const

◆ invCoordinateSystem()

template<typename MatrixT , typename IMatrixT >

const IMatrixType & capd::covrel::HSetMD< MatrixT, IMatrixT >::invCoordinateSystem ( ) const

inline

◆ mapaway() [1/5]

template<typename MatrixType , typename IMatrixType >

bool capd::covrel::HSetMD< MatrixType, IMatrixType >::mapaway ( const IVectorType & point ) const

◆ mapaway() [2/5]

virtual bool capd::covrel::HSet< MatrixT::RowVectorType , IMatrixT::RowVectorType >::mapaway ( const IVectorType & set ) const

pure virtualinherited

???

◆ mapaway() [3/5]

template<typename MatrixType , typename IMatrixType >

template<typename SetType >

bool capd::covrel::HSetMD< MatrixType, IMatrixType >::mapaway ( const SetType & A_set ) const

◆ mapaway() [4/5]

virtual bool capd::covrel::HSet< MatrixT::RowVectorType , IMatrixT::RowVectorType >::mapaway ( const VectorType & ) const

pure virtualinherited

◆ mapaway() [5/5]

template<typename MatrixType , typename IMatrixType >

bool capd::covrel::HSetMD< MatrixType, IMatrixType >::mapaway ( const VectorType & point ) const

◆ outside() [1/5]

template<typename MatrixType , typename IMatrixType >

bool capd::covrel::HSetMD< MatrixType, IMatrixType >::outside ( const IVectorType & point ) const

virtual

◆ outside() [2/5]

virtual bool capd::covrel::HSet< MatrixT::RowVectorType , IMatrixT::RowVectorType >::outside ( const IVectorType & set ) const

pure virtualinherited

verifies if set does not intersect the support of h-set

◆ outside() [3/5]

template<typename MatrixType , typename IMatrixType >

template<typename SetType >

bool capd::covrel::HSetMD< MatrixType, IMatrixType >::outside ( const SetType & A_set ) const

◆ outside() [4/5]

virtual bool capd::covrel::HSet< MatrixT::RowVectorType , IMatrixT::RowVectorType >::outside ( const VectorType & ) const

pure virtualinherited

◆ outside() [5/5]

template<typename MatrixType , typename IMatrixType >

bool capd::covrel::HSetMD< MatrixType, IMatrixType >::outside ( const VectorType & point ) const

virtual

◆ radius()

template<typename MatrixT , typename IMatrixT >

const VectorType & capd::covrel::HSetMD< MatrixT, IMatrixT >::radius ( )

inline

returns vector of radiuses (in each direction)

◆ show()

template<typename MatrixType , typename IMatrixType >

std::string capd::covrel::HSetMD< MatrixType, IMatrixType >::show ( void ) const

virtual

Reimplemented in capd::covrel::HSet2D< MatrixT, IMatrixT >.

◆ showInfo()

template<typename MatrixType , typename IMatrixType >

std::string capd::covrel::HSetMD< MatrixType, IMatrixType >::showInfo ( void ) const

◆ stableDimension()

template<typename MatrixT , typename IMatrixT >

size_type capd::covrel::HSetMD< MatrixT, IMatrixT >::stableDimension ( ) const

inline

number of stable dimensions

◆ transformToHSetCoordinates() [1/2]

template<typename MatrixType , typename IMatrixType >

HSetMD< MatrixType, IMatrixType >::IVectorType capd::covrel::HSetMD< MatrixType, IMatrixType >::transformToHSetCoordinates ( const IVectorType & point ) const

◆ transformToHSetCoordinates() [2/2]

template<typename MatrixType , typename IMatrixType >

HSetMD< MatrixType, IMatrixType >::VectorType capd::covrel::HSetMD< MatrixType, IMatrixType >::transformToHSetCoordinates ( const VectorType & point ) const

◆ unstableDimension()

template<typename MatrixT , typename IMatrixT >

size_type capd::covrel::HSetMD< MatrixT, IMatrixT >::unstableDimension ( ) const

inline

number of unstable dimensions

Friends And Related Function Documentation

◆ operator<<

template<typename MatrixT , typename IMatrixT >

std::ostream & operator<<	(	std::ostream &	stream,
		const HSetMD< MatrixT, IMatrixT > &	set
	)

friend

Member Data Documentation

◆ m_B

template<typename MatrixT , typename IMatrixT >

MatrixType capd::covrel::HSetMD< MatrixT, IMatrixT >::m_B

protected

coordinate system

◆ m_IB

template<typename MatrixT , typename IMatrixT >

IMatrixType capd::covrel::HSetMD< MatrixT, IMatrixT >::m_IB

protected

◆ m_invIB

template<typename MatrixT , typename IMatrixT >

IMatrixType capd::covrel::HSetMD< MatrixT, IMatrixT >::m_invIB

protected

rigorous coordinate system and its inverse

◆ m_Ix

template<typename MatrixT , typename IMatrixT >

IVectorType capd::covrel::HSetMD< MatrixT, IMatrixT >::m_Ix

protected

rigorous center point

◆ m_r

template<typename MatrixT , typename IMatrixT >

VectorType capd::covrel::HSetMD< MatrixT, IMatrixT >::m_r

protected

radiuses of balls (used both for non-rigorous and rigorous version)

◆ m_sDim

template<typename MatrixT , typename IMatrixT >

size_type capd::covrel::HSetMD< MatrixT, IMatrixT >::m_sDim

protected

number of stable dimensions

◆ m_uDim

template<typename MatrixT , typename IMatrixT >

size_type capd::covrel::HSetMD< MatrixT, IMatrixT >::m_uDim

protected

number of unstable dimensions

◆ m_x

template<typename MatrixT , typename IMatrixT >

VectorType capd::covrel::HSetMD< MatrixT, IMatrixT >::m_x

protected

center point

Public Types

Public Member Functions

Protected Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ BoundType

◆ IMatrixType

◆ IVectorType

◆ MatrixType

◆ ScalarType

◆ size_type

◆ VectorType

Constructor & Destructor Documentation

◆ HSetMD() [1/3]

◆ HSetMD() [2/3]

◆ HSetMD() [3/3]

◆ ~HSetMD()

Member Function Documentation

◆ across() [1/5]

◆ across() [2/5]

◆ across() [3/5]

◆ across() [4/5]

◆ across() [5/5]

◆ box()

◆ center()

◆ checkAcross()

◆ checkInside()

◆ checkMapaway()

◆ checkOutside()

◆ coordinateSystem()

◆ get_B()

◆ get_I_B()

◆ get_I_invB()

◆ get_I_x()

◆ get_r()

◆ get_x()

◆ inside() [1/5]

◆ inside() [2/5]

◆ inside() [3/5]

◆ inside() [4/5]

◆ inside() [5/5]

◆ invCoordinateSystem()

◆ mapaway() [1/5]

◆ mapaway() [2/5]

◆ mapaway() [3/5]

◆ mapaway() [4/5]

◆ mapaway() [5/5]

◆ outside() [1/5]

◆ outside() [2/5]

◆ outside() [3/5]

◆ outside() [4/5]

◆ outside() [5/5]

◆ radius()

◆ show()

◆ showInfo()

◆ stableDimension()

◆ transformToHSetCoordinates() [1/2]

◆ transformToHSetCoordinates() [2/2]

◆ unstableDimension()

Friends And Related Function Documentation

◆ operator<<

Member Data Documentation

◆ m_B

◆ m_IB

◆ m_invIB

◆ m_Ix

◆ m_r

◆ m_sDim

◆ m_uDim

◆ m_x