This class defines a map for the nonlinear density dependent overcompensatory Leslie population model. More...

#include <odeapprox.h>

Inheritance diagram for MapOdeApprox:

Public Member Functions
	MapOdeApprox (double step, int nSteps, int nSamples, double margin=0.01)
	The constructor in which one sets the step size and the number of steps for the non-rigorous integration, the number of sample points in each direction, and the margin to add around the box (as a fraction of its actual width). More...

	~MapOdeApprox ()
	The destructor. More...

void	setParam (const double left, const double right, int n)
	Sets the parameters to the given intervals defined by their left and right coordinates. More...

void	compute (const double xleft, const double xright, double yleft, double yright, int dim, const spcCoord *coord, int subdiv) const
	Computes the image of a box whose left and right coordinates are given. More...

Public Member Functions inherited from MapOdeTimeT
	MapOdeTimeT (const std::string &formula, int order, double step, int n)
	The constructor which takes the formula for the ODE in the format used in the CAPD library. More...

	~MapOdeTimeT ()
	The destructor. More...

void	setParam (const double left, const double right, int n)
	Sets the parameters to the given intervals defined by their left and right coordinates. More...

void	compute (const IntervalVectorType &x, RectSetType &y, int dim, const spcCoord *coord, int subdiv) const
	Computes a rectangular set that is an outer enclosure of the image of the given box. More...

void	setBoundingBox (const double left, const double right, int dim, int stepsBetweenChecks)
	Sets a bounding box for the area of interest. More...

void	setDefaultBoundingBox ()
	Sets the bounding box to the default one, as defined when setting the phase space. More...

bool	adjust (bool successful, int subdiv)
	Adjusts parameters if necessary after a successful computation or after an unsuccessful computation of the graph of the map at a specific subdivision depth. More...

std::string	getOptInfo () const
	Gets a single line of information on optimization of the computation of the map, so that it can be used by maps created for the same and nearby parameter values. More...

void	useOptInfo (const std::string &info)
	Uses a prevously saved line of information on optimization of the computation of the map for the same or nearby parameter values. More...

void	saveInternals (chomp::multiwork::mwData &data) const
	Saves the internal parameters and other data of the map to the mwData structure. More...

void	loadInternals (chomp::multiwork::mwData &data)
	Retrieves the internal paramters and other data of the map from the mwData structure. More...

double	getTimeStep (int subdiv) const
	Returns an approximation of the currently recommended integration time t for the time-t map at the given subdivision depth. More...

Public Member Functions inherited from MapTight
	MapTight ()
	The default constructor of an object which describes a map. More...

	~MapTight ()
	The destructor of an object which describe a map. More...

void	compute (const double xleft, const double xright, double yleft, double yright, int dim, const spcCoord *coord, int subdiv) const
	Computes an interval bounding box for the image of a given box. More...

virtual void	compute (const IntervalVectorType &x, RectSetType &y, int dim, const spcCoord *coord, int subdiv) const =0
	Computes a rectangular set that is an outer enclosure of the image of the given box. More...

Public Member Functions inherited from MapType
	MapType ()
	The default constructor of an object which describes a map. More...

virtual	~MapType ()
	The destructor of an object which describe a map. More...

virtual void	setParam (const double left, const double right, int n)
	Sets the parameters to the given intervals defined by their left and right coordinates. More...

const double &	getLeftParam (int n) const
	Returns the left value of the given parameter. More...

const double &	getRightParam (int n) const
	Returns the right value of the given parameter. More...

virtual void	compute (const double xleft, const double xright, double yleft, double yright, int dim, const spcCoord *coord, int subdiv) const =0
	Computes the image of a box whose left and right coordinates are given. More...

void	operator() (const IntervalType x, IntervalType y, int dim, const spcCoord *coord, int subdiv) const
	An interface to the function 'compute' based on intervals. More...

bool	adjust (bool successful, int subdiv)
	Adjusts parameters if necessary after a successful computation or after an unsuccessful computation of the graph of the map at a specific subdivision level. More...

std::string	getOptInfo () const
	Gets a single line of information on optimization of the computation of the map, so that it can be used by maps created for the same and nearby parameter values. More...

void	useOptInfo (const std::string &info)
	Uses a prevously saved line of information on optimization of the computation of the map for the same or nearby parameter values. More...

void	saveInternals (chomp::multiwork::mwData &data) const
	Saves the internal parameters and other data of the map to the mwData structure. More...

void	loadInternals (chomp::multiwork::mwData &data)
	Retrieves the internal paramters and other data of the map from the mwData structure. More...

virtual double	getTimeStep (int subdiv) const
	Returns the time step, which is 1 for a map, or the time t of integration in case of a time-t map of a flow. More...

virtual std::string	name () const
	Returns the name of the map. More...

Private Member Functions
virtual void	vectorField (double t, const double x, double y, int dim) const =0
	The vector field. More...

	MapOdeApprox (const MapOdeApprox &)
	The copy constructor should not be used. More...

MapOdeApprox &	operator= (const MapOdeApprox &)
	The assignment operator should not be used. More...

void	RungeKutta (double t, double x, double step, int dim, double buffer) const
	The Runge-Kutta method for iterating a point, using the vector field defined in this class. More...

void	fadeVectorField (const double x, double y, int dim) const
	Makes a correction to the vector field to make it fade gradually outside the bounding box if one is in defined and in use for the parent class MapOdeTimeT. More...

Static Private Member Functions
static void	computeRanges (const double samples, int nSamples, int dim, double minimal, double *maximal)
	Computes the ranges of coordinates. More...

Private Attributes
double	step_
	The size of the step for itegrating the flow. More...

int	nSteps_
	The number of steps to use. More...

int	nSamples_
	The number of samples in each direction. More...

double	margin_
	The margin to add around the box (a fraction of its width). More...

Additional Inherited Members
Static Public Member Functions inherited from MapOdeTimeT
template<class Array1 , class Array2 >
static void	setPhaseSpace (const Array1 &offset, const Array2 &width, int dim, int subdivDepth, int stepsBetweenChecks=2)
	Sets the phase space for an automatic generation of bounding boxes. More...

Protected Attributes inherited from MapOdeTimeT
double *	boundingBox
	A bounding box for the area where the trajectories are computed. More...

int	boundingBoxDim
	The dimension of the bounding box. More...

Detailed Description

This class defines a map for the nonlinear density dependent overcompensatory Leslie population model.

The interpretation of parameters depends on the dimension.

Definition at line 60 of file odeapprox.h.

Constructor & Destructor Documentation

◆ MapOdeApprox() [1/2]

MapOdeApprox::MapOdeApprox	(	double	step,
		int	nSteps,
		int	nSamples,
		double	margin = `0.01`
	)

inline

The constructor in which one sets the step size and the number of steps for the non-rigorous integration, the number of sample points in each direction, and the margin to add around the box (as a fraction of its actual width).

Definition at line 131 of file odeapprox.h.

References nSamples_, nSteps_, and step_.

◆ ~MapOdeApprox()

MapOdeApprox::~MapOdeApprox ( )

inline

The destructor.

Definition at line 162 of file odeapprox.h.

◆ MapOdeApprox() [2/2]

MapOdeApprox::MapOdeApprox ( const MapOdeApprox & )

private

The copy constructor should not be used.

Member Function Documentation

◆ compute()

void MapOdeApprox::compute	(	const double *	xleft,
		const double *	xright,
		double *	yleft,
		double *	yright,
		int	dim,
		const spcCoord *	coord,
		int	subdiv
	)		const

inlinevirtual

Computes the image of a box whose left and right coordinates are given.

Fills in the images with the left and right coordinates of the image box.

Reimplemented from MapTight.

Definition at line 279 of file odeapprox.h.

References computeRanges(), margin_, nSamples_, nSteps_, RungeKutta(), and step_.

◆ computeRanges()

void MapOdeApprox::computeRanges	(	const double *	samples,
		int	nSamples,
		int	dim,
		double *	minimal,
		double *	maximal
	)

inlinestaticprivate

Computes the ranges of coordinates.

Definition at line 261 of file odeapprox.h.

Referenced by compute().

◆ fadeVectorField()

void MapOdeApprox::fadeVectorField	(	const double *	x,
		double *	y,
		int	dim
	)		const

inlineprivate

Makes a correction to the vector field to make it fade gradually outside the bounding box if one is in defined and in use for the parent class MapOdeTimeT.

Definition at line 177 of file odeapprox.h.

References MapOdeTimeT::boundingBox, and MapOdeTimeT::boundingBoxDim.

Referenced by RungeKutta().

◆ operator=()

MapOdeApprox & MapOdeApprox::operator= ( const MapOdeApprox & )

private

The assignment operator should not be used.

◆ RungeKutta()

void MapOdeApprox::RungeKutta	(	double	t,
		double *	x,
		double	step,
		int	dim,
		double *	buffer
	)		const

inlineprivate

The Runge-Kutta method for iterating a point, using the vector field defined in this class.

The buffer should be preallocated for 5*dim entries.

Definition at line 225 of file odeapprox.h.

References fadeVectorField(), and vectorField().

Referenced by compute().

◆ setParam()

void MapOdeApprox::setParam	(	const double *	left,
		const double *	right,
		int	n
	)

inlinevirtual

Sets the parameters to the given intervals defined by their left and right coordinates.

This function calls the original function from the class MapType, and skips the function from MapOdeTimeT.

Reimplemented from MapType.

Definition at line 168 of file odeapprox.h.

References MapType::setParam().

◆ vectorField()

virtual void MapOdeApprox::vectorField	(	double	t,
		const double *	x,
		double *	y,
		int	dim
	)		const

privatepure virtual

The vector field.

Parameters (if any) should be determined using the methods of the class MapType: getLeftParam and getRightParam.

Implemented in MapDuffingApprox, MapLorenzApprox, MapRoesslerApprox, and MapVanderPolApprox.

Referenced by RungeKutta().

Member Data Documentation

◆ margin_

double MapOdeApprox::margin_

private

The margin to add around the box (a fraction of its width).

Definition at line 98 of file odeapprox.h.

Referenced by compute().

◆ nSamples_

int MapOdeApprox::nSamples_

private

The number of samples in each direction.

Definition at line 95 of file odeapprox.h.

Referenced by compute(), and MapOdeApprox().

◆ nSteps_

int MapOdeApprox::nSteps_

private

The number of steps to use.

Definition at line 92 of file odeapprox.h.

Referenced by compute(), and MapOdeApprox().

◆ step_

double MapOdeApprox::step_

private

The size of the step for itegrating the flow.

Definition at line 89 of file odeapprox.h.

Referenced by compute(), and MapOdeApprox().

The documentation for this class was generated from the following file:

odeapprox.h

Public Member Functions

Private Member Functions

Static Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ MapOdeApprox() [1/2]

◆ ~MapOdeApprox()

◆ MapOdeApprox() [2/2]

Member Function Documentation

◆ compute()

◆ computeRanges()

◆ fadeVectorField()

◆ operator=()

◆ RungeKutta()

◆ setParam()

◆ vectorField()

Member Data Documentation

◆ margin_

◆ nSamples_

◆ nSteps_

◆ step_