capd::invset Namespace Reference

Classes
class	CubicalMap
class	ForbiddenSet
	class that defines forbidden set More...
struct	GetKey
class	Graph
	It defines a graph that in each node can store additional data. More...
struct	GraphNode
struct	less
struct	less< capd::vectalg::Vector< short int, 2 > >
class	MapGraph
struct	MapGraphNodeData
class	Scope
	class that defines set of regions it can be used do define domain, range, allowed sets for graphs More...

Functions
template<class MapT , class V , class M >
V	computeDerivative (MapT &f, V u, M &A, int period)
	Given a map 'f' it computes the derivative of 'period' iteration of 'f' at 'u'. More...
template<class M >
std::pair< typename M::RowVectorType, typename M::RowVectorType >	computeCoordSystem (const M &A, M &rVec)
template<class MapT , class V , class M >
std::pair< V, V >	computeCoordSystem (MapT &f, V u, int period, M &rVec)
template<class Map , class V , class Jet >
void	oneDimInvariantManifold (Map &f, typename Map::VectorType &x, Jet &jet, int period)
	This is a generic algorithm for computing (nonrigorous) parameterization of one-dimensional invariant manifold at a fixed point x. More...
template<typename GraphT >
void	noVisualization (const GraphT &g)
template<class GraphT >
void	computePositiveInvariantSet (GraphT &graph, std::list< typename GraphT::VectorType > &domain, int subdiv, void(*showGraph)(const GraphT &g)=noVisualization< GraphT >)
	computes enclosure of the positive invariant set More...
template<class GraphT >
void	computeInvariantSet (GraphT &graph, std::list< typename GraphT::VectorType > &domain, int subdiv, void(*showGraph)(const GraphT &g)=noVisualization< GraphT >)
	computes enclosure of the positive invariant set More...
template<class GraphT >
void	computeInvariantSet (GraphT &graph, typename GraphT::VectorType &domain, int subdiv, void(*showGraph)(const GraphT &g)=noVisualization< GraphT >)
	computes enclosure of the positive invariant set More...
template<typename MapType , typename SetType >
void	insertMapKeysIntoSet (const MapType &map, SetType &set)
	inserts all map keys into set More...
template<typename GraphT , typename ConstraintsT >
void	propagateGraph (GraphT &graph, ConstraintsT &constraints, void(*showGraph)(const GraphT &g)=noVisualization< GraphT >)
	it iteratively compute image of all cubes in the graph and adds them if they satisfy constraints until no more new cubes can be added More...
template<typename GraphT , typename ConstraintsT >
void	propagateVertexSet (GraphT &graph, ConstraintsT &constraints, typename GraphT::VertexSet &result)
	it iteratively compute image of all cubes in the graph and adds them if they satisfy constraints until no more new cubes can be added More...

Function Documentation

computeCoordSystem() [1/2]

template<class M >

std::pair<typename M::RowVectorType,typename M::RowVectorType> capd::invset::computeCoordSystem	(	const M &	A,
		M &	rVec
	)

computeCoordSystem() [2/2]

template<class MapT , class V , class M >

std::pair<V,V> capd::invset::computeCoordSystem	(	MapT &	f,
		V	u,
		int	period,
		M &	rVec
	)

computeDerivative()

template<class MapT , class V , class M >

V capd::invset::computeDerivative	(	MapT &	f,
		V	u,
		M &	A,
		int	period
	)

Given a map 'f' it computes the derivative of 'period' iteration of 'f' at 'u'.

computeInvariantSet() [1/2]

template<class GraphT >

void capd::invset::computeInvariantSet	(	GraphT &	graph,
		std::list< typename GraphT::VectorType > &	domain,
		int	subdiv,
		void(*)(const GraphT &g)	showGraph = noVisualization<GraphT>
	)

computes enclosure of the positive invariant set

Parameters

[in,out]	graph	graph should contain map, resolution and optionally initial set of vertices (if not the parameter domain will be used)
[in]	domain	list of boxes that covers domain (even if domain is already set in graph, this information is needed to restrict range of a cubical map)
[in]	subdiv	number of the graph subdivision (in one iteration we subdivide only in one dimension)

computeInvariantSet() [2/2]

template<class GraphT >

void capd::invset::computeInvariantSet ( GraphT &  graph, typename GraphT::VectorType &  domain, int  subdiv, void(*)(const GraphT &g)  showGraph = noVisualization<GraphT>  )

inline

computes enclosure of the positive invariant set

Parameters

[in,out]	graph	graph should contain map, resolution and optionally initial set of vertices (if not the parameter domain will be used)
[in]	domain	"reclangular" domain
[in]	subdiv	number of the graph subdivision (in one iteration we subdivide only in one dimension)

computePositiveInvariantSet()

template<class GraphT >

void capd::invset::computePositiveInvariantSet	(	GraphT &	graph,
		std::list< typename GraphT::VectorType > &	domain,
		int	subdiv,
		void(*)(const GraphT &g)	showGraph = noVisualization<GraphT>
	)

computes enclosure of the positive invariant set

Parameters

[in,out]	graph	graph should contain map, resolution and optionally initial set of vertices (if not the parameter domain will be used)
[in]	domain	list of boxes that covers domain (even if domain is already set in graph, this information is needed to restrict range of a cubical map)
[in]	subdiv	number of the graph subdivision (in one iteration we subdivide only in one dimension)

insertMapKeysIntoSet()

template<typename MapType , typename SetType >

void capd::invset::insertMapKeysIntoSet	(	const MapType &	map,
		SetType &	set
	)

inserts all map keys into set

noVisualization()

template<typename GraphT >

void capd::invset::noVisualization ( const GraphT &  g )

inline

oneDimInvariantManifold()

template<class Map , class V , class Jet >

void capd::invset::oneDimInvariantManifold	(	Map &	f,
		typename Map::VectorType &	x,
		Jet &	jet,
		int	period
	)

This is a generic algorithm for computing (nonrigorous) parameterization of one-dimensional invariant manifold at a fixed point x.

propagateGraph()

template<typename GraphT , typename ConstraintsT >

void capd::invset::propagateGraph	(	GraphT &	graph,
		ConstraintsT &	constraints,
		void(*)(const GraphT &g)	showGraph = noVisualization<GraphT>
	)

it iteratively compute image of all cubes in the graph and adds them if they satisfy constraints until no more new cubes can be added

propagateVertexSet()

template<typename GraphT , typename ConstraintsT >

void capd::invset::propagateVertexSet	(	GraphT &	graph,
		ConstraintsT &	constraints,
		typename GraphT::VertexSet &	result
	)

it iteratively compute image of all cubes in the graph and adds them if they satisfy constraints until no more new cubes can be added