TimeMap class provides methods for transport of sets (or points) by a given flow over some time interval. More...

#include <capd/poincare/TimeMap.h>

Public Types
typedef SolverT	Solver

typedef Solver::VectorFieldType	VectorFieldType

typedef Solver::MatrixType	MatrixType

typedef Solver::VectorType	VectorType

typedef Solver::ScalarType	ScalarType

typedef Solver::SolutionCurve	CurveType

typedef capd::diffAlgebra::SolutionCurve< CurveType >	SolutionCurve

typedef CurveType::HessianType	HessianType
	data structure for storing Hessians More...

typedef CurveType::JetType	JetType
	data structure for storing jets (truncated Taylor series) More...

typedef VectorType::size_type	size_type
	integral type used to index containers (vectors, matrices, etc) More...

Public Member Functions
	TimeMap (Solver &solver)

VectorType	operator() (ScalarType time, VectorType &v)
	For a vector v it computes its position after time time. More...

VectorType	operator() (ScalarType time, VectorType &v, ScalarType &in_out_time)

VectorType	operator() (ScalarType time, VectorType &v, SolutionCurve &solution)

VectorType	operator() (ScalarType time, VectorType &v, MatrixType &derivative)
	For a vector v it computes its position after time 'time' and derivative with respect to initial conditions. More...

VectorType	operator() (ScalarType time, VectorType &v, MatrixType &derivative, ScalarType &in_out_time)

VectorType	operator() (ScalarType time, VectorType &v, MatrixType &derivative, SolutionCurve &solution)

VectorType	operator() (ScalarType time, VectorType &v, const MatrixType &initMatrix, MatrixType &derivative)

VectorType	operator() (ScalarType time, VectorType &v, const MatrixType &initMatrix, MatrixType &derivative, ScalarType &in_out_time)

VectorType	operator() (ScalarType time, VectorType &v, const MatrixType &initMatrix, MatrixType &derivative, SolutionCurve &solution)

VectorType	operator() (ScalarType time, VectorType &v, MatrixType &derivative, HessianType &hessian)
	Operators for integration of second order variational equations. More...

VectorType	operator() (ScalarType time, VectorType &v, MatrixType &derivative, HessianType &hessian, ScalarType &in_out_time)

VectorType	operator() (ScalarType time, VectorType &v, MatrixType &derivative, HessianType &hessian, SolutionCurve &solution)

VectorType	operator() (ScalarType time, VectorType &v, const MatrixType &initMatrix, const HessianType &initHessian, MatrixType &derivative, HessianType &hessian)

VectorType	operator() (ScalarType time, VectorType &v, const MatrixType &initMatrix, const HessianType &initHessian, MatrixType &derivative, HessianType &hessian, ScalarType &in_out_time)

VectorType	operator() (ScalarType time, VectorType &v, const MatrixType &initMatrix, const HessianType &initHessian, MatrixType &derivative, HessianType &hessian, SolutionCurve &solution)

VectorType	operator() (ScalarType time, VectorType &v, JetType &jet)
	For a vector v it computes its position after time 'time' and higher order derivatives with respect to initial conditions. More...

VectorType	operator() (ScalarType time, VectorType &v, JetType &jet, ScalarType &in_out_time)

VectorType	operator() (ScalarType time, VectorType &v, JetType &jet, SolutionCurve &solution)

VectorType	operator() (ScalarType time, const JetType &initJet, JetType &jet)

VectorType	operator() (ScalarType time, const JetType &initJet, JetType &jet, ScalarType &in_out_time)

VectorType	operator() (ScalarType time, const JetType &initJet, JetType &jet, SolutionCurve &solution)

template<class CnCoeffType >
VectorType	operator() (ScalarType time, VectorType &v, CnCoeffType &result)

template<typename SetType >
VectorType	operator() (ScalarType time, SetType &theSet, MatrixType &derivative)
	Integrates 'theSet' until time 'time'. More...

template<typename SetType >
VectorType	operator() (ScalarType time, SetType &theSet)
	Integrates 'theSet' until time 'time'. More...

template<typename SetType >
VectorType	operator() (ScalarType time, SetType &theSet, SolutionCurve &solution)
	Integrates 'theSet' until time 'time'. More...

const Solver &	getSolver () const
	Returns read-only reference to solver used to integrate the system. More...

Solver &	getSolver ()
	Returns reference to solver used to integrate the system. More...

const Solver &	getDynamicalSystem () const
	Returns read-only reference to solver used to integrate the system. More...

Solver &	getDynamicalSystem ()
	Returns reference to solver used to integrate the system. More...

const VectorFieldType &	getVectorField () const
	Returns read-only reference to current vector field. More...

VectorFieldType &	getVectorField ()
	Returns reference to current vector field. More...

size_type	getOrder () const
	Returns order of numerical method. More...

void	setOrder (size_type newOrder)
	sets new order of numerical method More...

ScalarType	getStep () const
	Returns step of numerical method (does make sense only when step control is disabled) More...

void	setStep (const ScalarType &newStep)
	Sets step of numerical method (does make sense only when step control is disabled) More...

void	turnOnStepControl ()
	Disables automatic step control. More...

void	turnOffStepControl ()
	Enables automatic step control. Step control strategy is builded into the dynamical system. More...

void	onOffStepControl (bool sc)
	Disables or enables automatic step control. More...

void	stopAfterStep (bool b)
	For dense output. If true, integration procedure returns after each successful step. The computation can be then resumed - see examples. More...

bool	completed () const
	For dense output. Returns true if the trajectory has been integrated to the requested time. More...

const ScalarType &	getCurrentTime () const
	For dense output. Returns current time during integration. More...

template<typename SetType >
SolverT::VectorType	operator() (ScalarType Time, SetType &originalSet)

template<typename SetType >
SolverT::VectorType	operator() (ScalarType Time, SetType &originalSet, SolutionCurve &solution)

template<typename SetType >
SolverT::VectorType	operator() (ScalarType Time, SetType &originalSet, MatrixType &derivative)

Protected Member Functions
template<class SetType >
void	initComputations (SetType &originalSet, void *current)

template<class SetType >
void	moveSet (ScalarType time, SetType &originalSet, void *current)

Protected Attributes
Solver &	m_solver
	an abstract solver of dynamical system More...

void *	m_currentSet
	for dense output. Pointer to an object representing initial condition that is integrated. More...

bool	m_oneStep
	for dense output. True if the procedure should return after each successful step. More...

ScalarType	m_currentTime
	Holds current time during integration. More...

bool	m_completed
	flag: true if trajectory has been integrated until requested time. More...

SolutionCurve *	m_solution

Detailed Description

template<typename SolverT>
class capd::poincare::TimeMap< SolverT >

TimeMap class provides methods for transport of sets (or points) by a given flow over some time interval.

Template parameter is an abstract solver of dynamical system. It is assumed that it provides methods for one-step transport (both for discrete and continuous case).

Member Typedef Documentation

◆ CurveType

template<typename SolverT >

typedef Solver::SolutionCurve capd::poincare::TimeMap< SolverT >::CurveType

◆ HessianType

template<typename SolverT >

typedef CurveType::HessianType capd::poincare::TimeMap< SolverT >::HessianType

data structure for storing Hessians

◆ JetType

template<typename SolverT >

typedef CurveType::JetType capd::poincare::TimeMap< SolverT >::JetType

data structure for storing jets (truncated Taylor series)

◆ MatrixType

template<typename SolverT >

typedef Solver::MatrixType capd::poincare::TimeMap< SolverT >::MatrixType

◆ ScalarType

template<typename SolverT >

typedef Solver::ScalarType capd::poincare::TimeMap< SolverT >::ScalarType

◆ size_type

template<typename SolverT >

typedef VectorType::size_type capd::poincare::TimeMap< SolverT >::size_type

integral type used to index containers (vectors, matrices, etc)

◆ SolutionCurve

template<typename SolverT >

typedef capd::diffAlgebra::SolutionCurve<CurveType> capd::poincare::TimeMap< SolverT >::SolutionCurve

◆ Solver

template<typename SolverT >

typedef SolverT capd::poincare::TimeMap< SolverT >::Solver

◆ VectorFieldType

template<typename SolverT >

typedef Solver::VectorFieldType capd::poincare::TimeMap< SolverT >::VectorFieldType

◆ VectorType

template<typename SolverT >

typedef Solver::VectorType capd::poincare::TimeMap< SolverT >::VectorType

Member Function Documentation

◆ operator()() [1/3]

template<typename SolverT >

template<typename SetType >

VectorType capd::poincare::TimeMap< SolverT >::operator()	(	ScalarType	time,
		SetType &	theSet
	)

Integrates 'theSet' until time 'time'.

Parameters

[in,out] theSet - initial condition for integration. 'theSet.getCurrentTime()' should be an initial time for nonautonomous systems. On output 'theSet' represents solution to ODE at time 'time'

◆ operator()() [2/3]

template<typename SolverT >

template<typename SetType >

VectorType capd::poincare::TimeMap< SolverT >::operator()	(	ScalarType	time,
		SetType &	theSet,
		MatrixType &	derivative
	)

Integrates 'theSet' until time 'time'.

Parameters

[in,out]	theSet	- initial condition for integration. 'theSet.getCurrentTime()' should be an initial time for nonautonomous systems. On output 'theSet' represents solution to ODE at time 'time'
[out]	derivative	monodromy matrix wrt to initial condition at time 'time'.

◆ operator()() [3/3]

template<typename SolverT >

template<typename SetType >

VectorType capd::poincare::TimeMap< SolverT >::operator()	(	ScalarType	time,
		SetType &	theSet,
		SolutionCurve &	solution
	)

Integrates 'theSet' until time 'time'.

Parameters

[in,out]	theSet	- initial condition for integration. 'theSet.getCurrentTime()' should be an initial time for nonautonomous systems. On output 'theSet' represents solution to ODE at time 'time'
[out]	solution	- after successful integration becomes a functional object representing entire solution to ODE that can be evaluated at any intermediate time.

Member Data Documentation

◆ m_completed

template<typename SolverT >

bool capd::poincare::TimeMap< SolverT >::m_completed

protected

flag: true if trajectory has been integrated until requested time.

◆ m_currentSet

template<typename SolverT >

void* capd::poincare::TimeMap< SolverT >::m_currentSet

protected

for dense output. Pointer to an object representing initial condition that is integrated.

◆ m_currentTime

template<typename SolverT >

ScalarType capd::poincare::TimeMap< SolverT >::m_currentTime

protected

Holds current time during integration.

◆ m_oneStep

template<typename SolverT >

bool capd::poincare::TimeMap< SolverT >::m_oneStep

protected

for dense output. True if the procedure should return after each successful step.

◆ m_solution

template<typename SolverT >

SolutionCurve* capd::poincare::TimeMap< SolverT >::m_solution

protected

◆ m_solver

template<typename SolverT >

Solver& capd::poincare::TimeMap< SolverT >::m_solver

protected

an abstract solver of dynamical system

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ CurveType

◆ HessianType

◆ JetType

◆ MatrixType

◆ ScalarType

◆ size_type

◆ SolutionCurve

◆ Solver

◆ VectorFieldType

◆ VectorType

Member Function Documentation

◆ operator()() [1/3]

◆ operator()() [2/3]

◆ operator()() [3/3]

Member Data Documentation

◆ m_completed

◆ m_currentSet

◆ m_currentTime

◆ m_oneStep

◆ m_solution

◆ m_solver