This class provides a h-set in R^2 with one unstable and one stable direction. More...

#include <capd/covrel/HSet2D.h>

Public Types
typedef MatrixT::RowVectorType	VectorType

typedef IMatrixT::RowVectorType	IVectorType

typedef IVectorType::ScalarType	ScalarType

typedef VectorType::ScalarType	BoundType

typedef MatrixT	MatrixType

typedef IMatrixT	IMatrixType

typedef HSetMD< MatrixType, IMatrixType >	BaseHSet

typedef VectorType::size_type	size_type

Public Member Functions
	HSet2D ()

	HSet2D (const VectorType &center, const MatrixType &C, const VectorType &r)
	we assume that the set is represented as center + C * B(0, r) first column of C represent unstable direction second column of C represent stable direction More...

	HSet2D (const IVectorType &center, const IMatrixType &C, const VectorType &r)
	we assume that the set is represented as center + C * B(0, r) first column of C represent unstable direction second column of C represent stable direction More...

	HSet2D (const VectorType &center, const VectorType &unstableDirection, const VectorType &stableDirection, const VectorType &scales)
	Creates HSet from given center, unstable and stable directions and their scales. More...

	HSet2D (const IVectorType &center, const IVectorType &unstableDirection, const IVectorType &stableDirection, const VectorType &radius)
	Creates HSet from given center, unstable and stable directions and their scales. More...

	~HSet2D ()

IMatrixType::RefColumnVectorType	unstableDirection () const

IMatrixType::RefColumnVectorType	stableDirection () const

bool	onLeft (const VectorType &point) const

bool	onRight (const VectorType &point) const

bool	onLeft (const IVectorType &set) const

bool	onRight (const IVectorType &set) const

template<typename SetT >
bool	onLeft (const SetT &A_set) const

template<typename SetT >
bool	onRight (const SetT &A_set) const

template<typename IMatrix >
GridSet< IMatrix > &	gridFace (GridSet< IMatrix > &grid, size_type gridSize, size_type coordinateToFix, Side sideOfBox, size_type totalDimension=2, size_type d1=0, size_type d2=1) const
	in the `grid` it returns uniform grid of the given face More...

template<typename IMatrix >
GridSet< IMatrix > &	gridLeftEdge (GridSet< IMatrix > &G, size_type gridSize, size_type totalDimension=2, size_type d1=0, size_type d2=1) const

template<typename IMatrix >
GridSet< IMatrix > &	gridRightEdge (GridSet< IMatrix > &G, size_type gridSize, size_type totalDimension=2, size_type d1=0, size_type d2=1) const

template<typename IMatrix >
GridSet< IMatrix > &	gridBottomEdge (GridSet< IMatrix > &G, size_type gridSize, size_type totalDimension=2, size_type d1=0, size_type d2=1) const

template<typename IMatrix >
GridSet< IMatrix > &	gridTopEdge (GridSet< IMatrix > &G, size_type gridSize, size_type totalDimension=2, size_type d1=0, size_type d2=1) const

template<typename IMatrix >
GridSet< IMatrix > &	gridSet (GridSet< IMatrix > &G, size_type grid1, size_type grid2, size_type totalDimension=2, size_type d1=0, size_type d2=1) const

virtual std::string	show (void) const

virtual bool	outside (const VectorType &point) const

virtual bool	outside (const IVectorType &point) const

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

bool	inside (const VectorType &point) const

bool	inside (const IVectorType &point) const

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

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...

bool	across (const VectorType &point) const

bool	across (const IVectorType &point) const

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

virtual bool	across (const VectorType &) const=0

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

bool	mapaway (const VectorType &point) const

bool	mapaway (const IVectorType &point) const

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

virtual bool	mapaway (const VectorType &) const=0

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

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 IMatrixType &	invCoordinateSystem () const

IVectorType	box () const

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

std::string	showInfo () const


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


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...

Detailed Description

template<typename MatrixT, typename IMatrixT>
class capd::covrel::HSet2D< MatrixT, IMatrixT >

This class provides a h-set in R^2 with one unstable and one stable direction.

Member Typedef Documentation

◆ BaseHSet

template<typename MatrixT , typename IMatrixT >

typedef HSetMD<MatrixType, IMatrixType> capd::covrel::HSet2D< MatrixT, IMatrixT >::BaseHSet

◆ BoundType

template<typename MatrixT , typename IMatrixT >

typedef VectorType::ScalarType capd::covrel::HSet2D< MatrixT, IMatrixT >::BoundType

◆ IMatrixType

template<typename MatrixT , typename IMatrixT >

typedef IMatrixT capd::covrel::HSet2D< MatrixT, IMatrixT >::IMatrixType

◆ IVectorType

template<typename MatrixT , typename IMatrixT >

typedef IMatrixT::RowVectorType capd::covrel::HSet2D< MatrixT, IMatrixT >::IVectorType

◆ MatrixType

template<typename MatrixT , typename IMatrixT >

typedef MatrixT capd::covrel::HSet2D< MatrixT, IMatrixT >::MatrixType

◆ ScalarType

template<typename MatrixT , typename IMatrixT >

typedef IVectorType::ScalarType capd::covrel::HSet2D< MatrixT, IMatrixT >::ScalarType

◆ size_type

template<typename MatrixT , typename IMatrixT >

typedef VectorType::size_type capd::covrel::HSet2D< MatrixT, IMatrixT >::size_type

◆ VectorType

template<typename MatrixT , typename IMatrixT >

typedef MatrixT::RowVectorType capd::covrel::HSet2D< MatrixT, IMatrixT >::VectorType

Constructor & Destructor Documentation

◆ HSet2D() [1/5]

template<typename MatrixT , typename IMatrixT >

capd::covrel::HSet2D< MatrixT, IMatrixT >::HSet2D ( )

inline

◆ HSet2D() [2/5]

template<typename MatrixT , typename IMatrixT >

capd::covrel::HSet2D< MatrixT, IMatrixT >::HSet2D	(	const VectorType &	center,
		const MatrixType &	C,
		const VectorType &	r
	)

inline

we assume that the set is represented as center + C * B(0, r) first column of C represent unstable direction second column of C represent stable direction

◆ HSet2D() [3/5]

template<typename MatrixT , typename IMatrixT >

capd::covrel::HSet2D< MatrixT, IMatrixT >::HSet2D	(	const IVectorType &	center,
		const IMatrixType &	C,
		const VectorType &	r
	)

inline

we assume that the set is represented as center + C * B(0, r) first column of C represent unstable direction second column of C represent stable direction

◆ HSet2D() [4/5]

template<typename MatrixT , typename IMatrixT >

capd::covrel::HSet2D< MatrixT, IMatrixT >::HSet2D	(	const VectorType &	center,
		const VectorType &	unstableDirection,
		const VectorType &	stableDirection,
		const VectorType &	scales
	)

inline

Creates HSet from given center, unstable and stable directions and their scales.

◆ HSet2D() [5/5]

template<typename MatrixT , typename IMatrixT >

capd::covrel::HSet2D< MatrixT, IMatrixT >::HSet2D	(	const IVectorType &	center,
		const IVectorType &	unstableDirection,
		const IVectorType &	stableDirection,
		const VectorType &	radius
	)

inline

Creates HSet from given center, unstable and stable directions and their scales.

◆ ~HSet2D()

template<typename MatrixT , typename IMatrixT >

capd::covrel::HSet2D< MatrixT, IMatrixT >::~HSet2D ( )

inline

Member Function Documentation

◆ across() [1/5]

template<typename MatrixType , typename IMatrixType >

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

inherited

◆ 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

inherited

◆ 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

inherited

◆ box()

template<typename MatrixT , typename IMatrixT >

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

inlineinherited

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

◆ checkAcross()

template<typename MatrixType , typename IMatrixType >

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

inherited

◆ checkInside()

template<typename MatrixType , typename IMatrixType >

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

inherited

◆ checkMapaway()

template<typename MatrixType , typename IMatrixType >

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

inherited

◆ checkOutside()

template<typename MatrixType , typename IMatrixType >

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

inherited

◆ get_B()

template<typename MatrixT , typename IMatrixT >

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

inlineinherited

◆ get_I_B()

template<typename MatrixT , typename IMatrixT >

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

inlineinherited

◆ get_I_invB()

template<typename MatrixT , typename IMatrixT >

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

inlineinherited

◆ get_I_x()

template<typename MatrixT , typename IMatrixT >

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

inlineinherited

◆ get_r()

template<typename MatrixT , typename IMatrixT >

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

inlineinherited

◆ get_x()

template<typename MatrixT , typename IMatrixT >

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

inlineinherited

◆ gridFace()

template<typename MatrixT , typename IMatrixT >

template<typename IMatrix >

GridSet<IMatrix>& capd::covrel::HSet2D< MatrixT, IMatrixT >::gridFace	(	GridSet< IMatrix > &	grid,
		size_type	gridSize,
		size_type	coordinateToFix,
		Side	sideOfBox,
		size_type	totalDimension = `2`,
		size_type	d1 = `0`,
		size_type	d2 = `1`
	)		const

inline

in the grid it returns uniform grid of the given face

Parameters

gridSize	number of pieces in the grid
coordinateToFix	which wall should be subdivided
sideOfBox	which side of given coordinate should be subdivided : 0 - both, -1 - left, 1 - right
totalDimension	dimension of the space (can be bigger than 2 if we embed the set)
d1,d2	if hset is embedded in higher dimension then we put first coordinate in d1 coordinate, second in d2 and the rest set to 0.

◆ inside() [1/5]

template<typename MatrixType , typename IMatrixType >

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

inherited

◆ 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

inherited

◆ 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

inherited

◆ invCoordinateSystem()

template<typename MatrixT , typename IMatrixT >

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

inlineinherited

◆ mapaway() [1/5]

template<typename MatrixType , typename IMatrixType >

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

inherited

◆ 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

inherited

◆ 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

inherited

◆ onLeft() [1/3]

template<typename MatrixT , typename IMatrixT >

bool capd::covrel::HSet2D< MatrixT, IMatrixT >::onLeft ( const IVectorType & set ) const

inline

◆ onLeft() [2/3]

template<typename MatrixT , typename IMatrixT >

template<typename SetT >

bool capd::covrel::HSet2D< MatrixT, IMatrixT >::onLeft ( const SetT & A_set ) const

inline

◆ onLeft() [3/3]

template<typename MatrixT , typename IMatrixT >

bool capd::covrel::HSet2D< MatrixT, IMatrixT >::onLeft ( const VectorType & point ) const

inline

◆ onRight() [1/3]

template<typename MatrixT , typename IMatrixT >

bool capd::covrel::HSet2D< MatrixT, IMatrixT >::onRight ( const IVectorType & set ) const

inline

◆ onRight() [2/3]

template<typename MatrixT , typename IMatrixT >

template<typename SetT >

bool capd::covrel::HSet2D< MatrixT, IMatrixT >::onRight ( const SetT & A_set ) const

inline

◆ onRight() [3/3]

template<typename MatrixT , typename IMatrixT >

bool capd::covrel::HSet2D< MatrixT, IMatrixT >::onRight ( const VectorType & point ) const

inline

◆ outside() [1/5]

template<typename MatrixType , typename IMatrixType >

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

virtualinherited

◆ 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

inherited

◆ 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

virtualinherited

◆ show()

template<typename MatrixT , typename IMatrixT >

virtual std::string capd::covrel::HSet2D< MatrixT, IMatrixT >::show ( void ) const

inlinevirtual

Reimplemented from capd::covrel::HSetMD< MatrixT, IMatrixT >.

◆ showInfo()

template<typename MatrixType , typename IMatrixType >

std::string capd::covrel::HSetMD< MatrixType, IMatrixType >::showInfo

inherited

◆ stableDirection()

template<typename MatrixT , typename IMatrixT >

IMatrixType::RefColumnVectorType capd::covrel::HSet2D< MatrixT, IMatrixT >::stableDirection ( ) const

inline

◆ transformToHSetCoordinates() [1/2]

template<typename MatrixType , typename IMatrixType >

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

inherited

◆ transformToHSetCoordinates() [2/2]

template<typename MatrixType , typename IMatrixType >

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

inherited

◆ unstableDirection()

template<typename MatrixT , typename IMatrixT >

IMatrixType::RefColumnVectorType capd::covrel::HSet2D< MatrixT, IMatrixT >::unstableDirection ( ) const

inline

Member Data Documentation

◆ m_B

template<typename MatrixT , typename IMatrixT >

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

protectedinherited

coordinate system

◆ m_IB

template<typename MatrixT , typename IMatrixT >

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

protectedinherited

◆ m_invIB

template<typename MatrixT , typename IMatrixT >

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

protectedinherited

rigorous coordinate system and its inverse

◆ m_Ix

template<typename MatrixT , typename IMatrixT >

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

protectedinherited

rigorous center point

◆ m_r

template<typename MatrixT , typename IMatrixT >

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

protectedinherited

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

protectedinherited

number of stable dimensions

◆ m_uDim

template<typename MatrixT , typename IMatrixT >

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

protectedinherited

number of unstable dimensions

◆ m_x

template<typename MatrixT , typename IMatrixT >

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

protectedinherited

center point

Public Types

Public Member Functions

Protected Attributes

Detailed Description

template<typename MatrixT, typename IMatrixT> class capd::covrel::HSet2D< MatrixT, IMatrixT >

Member Typedef Documentation

◆ BaseHSet

◆ BoundType

◆ IMatrixType

◆ IVectorType

◆ MatrixType

◆ ScalarType

◆ size_type

◆ VectorType

Constructor & Destructor Documentation

◆ HSet2D() [1/5]

◆ HSet2D() [2/5]

◆ HSet2D() [3/5]

◆ HSet2D() [4/5]

◆ HSet2D() [5/5]

◆ ~HSet2D()

Member Function Documentation

◆ across() [1/5]

◆ across() [2/5]

◆ across() [3/5]

◆ across() [4/5]

◆ across() [5/5]

◆ box()

◆ checkAcross()

◆ checkInside()

◆ checkMapaway()

◆ checkOutside()

◆ get_B()

◆ get_I_B()

◆ get_I_invB()

◆ get_I_x()

◆ get_r()

◆ get_x()

◆ gridFace()

◆ 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]

◆ onLeft() [1/3]

◆ onLeft() [2/3]

◆ onLeft() [3/3]

◆ onRight() [1/3]

◆ onRight() [2/3]

◆ onRight() [3/3]

◆ outside() [1/5]

◆ outside() [2/5]

◆ outside() [3/5]

◆ outside() [4/5]

◆ outside() [5/5]

◆ show()

◆ showInfo()

◆ stableDirection()

◆ transformToHSetCoordinates() [1/2]

◆ transformToHSetCoordinates() [2/2]

◆ unstableDirection()

Member Data Documentation

◆ m_B

◆ m_IB

◆ m_invIB

◆ m_Ix

◆ m_r

◆ m_sDim

◆ m_uDim

◆ m_x

template<typename MatrixT, typename IMatrixT>
class capd::covrel::HSet2D< MatrixT, IMatrixT >