Covering relations, H-sets, cones conditions. More...

Classes
struct	CheckCoveringRelation2DParameters

class	GraphicsHSet3D

class	GraphicsTripleSet

class	GridSet
	This class is used to store a grid of a sets in the form center[i] + M * r. More...

class	GridSets
	This class is used to store a grid of a sets in the form center[i] + M * r. More...

class	HSet
	this is an abstract class for h-sets - from paper by Gidea-Zgliczynski 'Covering relations ...' http://www.im.uj.edu.pl/~zgliczyn More...

class	HSet2D
	This class provides a h-set in R^2 with one unstable and one stable direction. More...

class	HSet3D
	The class HSet3D provides a h-set in R^3 with one unstable direction and two stable directions. More...

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

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

class	HSetWithCones

class	QuadraticForm

class	TripleSet
	TripleSet - a planar h-set with one unstable direction Authors: Implementation of derived classes and functions: Jaroslaw Dulak and Daniel Wilczak. More...

Typedefs
typedef HSet3D::FloatVector	FloatVector

typedef HSet3D::IntervalVector	IntervalVector

typedef HSet3D::FloatMatrix	FloatMatrix

typedef HSet3D::IntervalMatrix	IntervalMatrix

Enumerations
enum	Side { leftSide = -1, bothSides = 0, rightSide = 1 }

Functions
krak::Coord3D &	operator<< (krak::Coord3D &F, const GraphicsHSet3D &S)

krak::IFrame &	operator<< (krak::IFrame &f, GraphicsTripleSet &Set)

bool	InSide (const HSet3D &S, const IntervalVector &IV)

bool	OutSide (const HSet3D &S, const IntervalVector &IV)

bool	Across (const HSet3D &S, const IntervalVector &IV)

bool	MapAway (const HSet3D &S, const IntervalVector &IV)

bool	LeftSide (const HSet3D &S, const IntervalVector &IV)

bool	RightSide (const HSet3D &S, const IntervalVector &IV)

bool	InSide (const HSet3D &S, const FloatVector &IV)

bool	OutSide (const HSet3D &S, const FloatVector &IV)

bool	Across (const HSet3D &S, const FloatVector &IV)

bool	MapAway (const HSet3D &S, const FloatVector &IV)

bool	LeftSide (const HSet3D &S, const FloatVector &IV)

bool	RightSide (const HSet3D &S, const FloatVector &IV)

template<typename MatrixType >
bool	isPositiveDefined (const MatrixType &A)

template<typename Map , typename HSet2D , typename QuadraticForm >
bool	checkConesCondition (Map &f, const HSet2D &N1, const HSet2D &N2, const QuadraticForm &Q1, const QuadraticForm &Q2)
	Function checks cones condition. More...

template<typename Map , typename HSetWithCones >
bool	checkConesCondition (Map &f, const HSetWithCones &N1, const HSetWithCones &N2, const capd::covrel::CheckCoveringRelation2DParameters &param=capd::covrel::CheckCoveringRelation2DParameters(1, 1, 1, 1))
	Function checks cones condition. More...

template<typename C0SetType , typename Map , typename DynSys , typename HSetWithCones >
bool	checkCoveringRelationAndConesCondition (Map &f, DynSys &ds, const HSetWithCones &N1, const HSetWithCones &N2, const capd::covrel::CheckCoveringRelation2DParameters &param=capd::covrel::CheckCoveringRelation2DParameters(1, 1, 1, 1))
	Checks covering relation $N_1 \Rightarrow N_2$ and corresponding cones condition. More...

template<typename C0SetType , typename Map , typename DynSys , typename HSetWithCones >
bool	checkCoveringRelationAndConesCondition (Map &f, const HSetWithCones &N1, const HSetWithCones &N2, const capd::covrel::CheckCoveringRelation2DParameters &param=capd::covrel::CheckCoveringRelation2DParameters(1, 1, 1, 1))
	Checks covering relation $N_1 \Rightarrow N_2$ and corresponding cones condition. More...

template<typename C0SetType , typename DynSysType , typename GridSet , typename ConditionT , typename HSet >
bool	moveGridAndCheckCondition (DynSysType &dynsys, const GridSet &grid, const ConditionT &condition, const HSet &hset)
	moves each part of `grid` using dynamical system `dynsys` and checks relation between its image and `hset` given by `condition` More...

template<typename HSetType , typename SetType >
bool	outside (const HSetType &hset, const SetType &set)
	verifies if `set` does not intersect the support of h-set More...

template<typename HSetType , typename SetType >
bool	inside (const HSetType &hset, const SetType &set)
	verifies if `set` is inside the support of h-set More...

template<typename HSetType , typename SetType >
bool	across (const HSetType &hset, const SetType &set)
	verifies if `set` does not intersect N^+ More...

template<typename HSetType , typename SetType >
bool	mapaway (const HSetType &hset, const SetType &set)

template<typename HSetType , typename SetType >
bool	onLeft (const HSetType &hset, const SetType &set)
	Checks if `set` in on the left side of the `hset` (works only in 2D) More...

template<typename HSetType , typename SetType >
bool	onRight (const HSetType &hset, const SetType &set)
	Checks if `set` in on the right side of the `hset` (works only in 2D) More...

template<typename MatrixType , typename VectorType >
MatrixType	convertColumnsTo (const VectorType &column1, const VectorType &column2)
	Converts two column vectors to given MatrixType. More...

template<typename C0SetType , typename DynSysT , typename MatrixT , typename IMatrixT >
bool	checkCoveringRelation2D (DynSysT &dynsys, const capd::covrel::HSet2D< MatrixT, IMatrixT > &N1, const capd::covrel::HSet2D< MatrixT, IMatrixT > &N2, const CheckCoveringRelation2DParameters &param=CheckCoveringRelation2DParameters(1, 1, 1, 1))

template<typename Vector1 , typename Vector2 >
void	embedVector (const Vector1 &v1, Vector2 &v2, const std::vector< typename Vector1::size_type > &d)

template<typename Vector1 , typename Vector2 >
void	embedVector (const Vector1 &vector, Vector2 &result, size_t fullDimension, const std::vector< typename Vector1::size_type > &d)
	it embeds `vector` into a space of fullDimension in d[i] we pass coordiante where to put i-th coordinate of given vector other coordinates are set to 0. More...

template<typename Matrix1 , typename Matrix2 >
void	embedMatrix (const Matrix1 &m1, Matrix2 &m2, const std::vector< typename Matrix1::size_type > &d)

template<typename IVector >
bool	InSide (const TripleSet &S, const IVector &IV, typename IVector::size_type d1, typename IVector::size_type d2)

bool	InSide (const TripleSet &S, const TripleSet::IntervalVector &v)

template<typename IVector >
bool	OutSide (const TripleSet &S, const IVector &IV, typename IVector::size_type d1, typename IVector::size_type d2)

bool	OutSide (const TripleSet &S, const TripleSet::IntervalVector &v)

template<typename IVector >
bool	Across (const TripleSet &S, const IVector &IV, typename IVector::size_type d1, typename IVector::size_type d2)

bool	Across (const TripleSet &S, const TripleSet::IntervalVector &v)

template<typename IVector >
bool	MapAway (const TripleSet &S, const IVector &IV, typename IVector::size_type d1, typename IVector::size_type d2)

bool	MapAway (const TripleSet &S, const TripleSet::IntervalVector &v)

template<typename IVector >
bool	LeftSide (const TripleSet &S, const IVector &IV, typename IVector::size_type d1, typename IVector::size_type d2)

bool	LeftSide (const TripleSet &S, const TripleSet::IntervalVector &v)

template<typename IVector >
bool	RightSide (const TripleSet &S, const IVector &IV, typename IVector::size_type d1, typename IVector::size_type d2)

bool	RightSide (const TripleSet &S, const TripleSet::IntervalVector &v)

Detailed Description

Covering relations, H-sets, cones conditions.

Typedef Documentation

◆ FloatMatrix

typedef HSet3D::FloatMatrix capd::covrel::FloatMatrix

◆ FloatVector

typedef TripleSet::FloatVector capd::covrel::FloatVector

◆ IntervalMatrix

typedef HSet3D::IntervalMatrix capd::covrel::IntervalMatrix

◆ IntervalVector

typedef TripleSet::IntervalVector capd::covrel::IntervalVector

Function Documentation

◆ Across() [1/2]

bool capd::covrel::Across	(	const HSet3D &	S,
		const FloatVector &	IV
	)

◆ Across() [2/2]

bool capd::covrel::Across	(	const HSet3D &	S,
		const IntervalVector &	IV
	)

◆ InSide() [1/2]

bool capd::covrel::InSide	(	const HSet3D &	S,
		const FloatVector &	IV
	)

◆ InSide() [2/2]

bool capd::covrel::InSide	(	const HSet3D &	S,
		const IntervalVector &	IV
	)

◆ LeftSide() [1/2]

bool capd::covrel::LeftSide	(	const HSet3D &	S,
		const FloatVector &	IV
	)

◆ LeftSide() [2/2]

bool capd::covrel::LeftSide	(	const HSet3D &	S,
		const IntervalVector &	IV
	)

◆ MapAway() [1/2]

bool capd::covrel::MapAway	(	const HSet3D &	S,
		const FloatVector &	IV
	)

◆ MapAway() [2/2]

bool capd::covrel::MapAway	(	const HSet3D &	S,
		const IntervalVector &	IV
	)

◆ moveGridAndCheckCondition()

template<typename C0SetType , typename DynSysType , typename GridSet , typename ConditionT , typename HSet >

bool capd::covrel::moveGridAndCheckCondition	(	DynSysType &	dynsys,
		const GridSet &	grid,
		const ConditionT &	condition,
		const HSet &	hset
	)

moves each part of grid using dynamical system dynsys and checks relation between its image and hset given by condition

Parameters

[in]	dynsys	dynamical system : can be either continuous or discrete
[in]	grid	grid of the first h-set (whole set or one of its walls)
[in]	condition	function with two parameters: first = hset, second = C0Set
[in]	hset	second h-set (set we want to cover)

◆ operator<<() [1/2]

krak::Coord3D& capd::covrel::operator<<	(	krak::Coord3D &	F,
		const GraphicsHSet3D &	S
	)

◆ operator<<() [2/2]

krak::IFrame& capd::covrel::operator<<	(	krak::IFrame &	f,
		GraphicsTripleSet &	Set
	)

◆ OutSide() [1/2]

bool capd::covrel::OutSide	(	const HSet3D &	S,
		const FloatVector &	IV
	)

◆ OutSide() [2/2]

bool capd::covrel::OutSide	(	const HSet3D &	S,
		const IntervalVector &	IV
	)

◆ RightSide() [1/2]

bool capd::covrel::RightSide	(	const HSet3D &	S,
		const FloatVector &	IV
	)

◆ RightSide() [2/2]

bool capd::covrel::RightSide	(	const HSet3D &	S,
		const IntervalVector &	IV
	)

Classes

Typedefs

Enumerations

Functions