Base class for rigorous integration of differential inclusions. More...

#include <capd/diffIncl/DiffInclusion.h>

Public Types
typedef MapT	MultiMapType

typedef MultiMapType	MapType

typedef MapT::MapType	VectorFieldType

typedef MapT::FunctionType	FunctionType

typedef MapType::MatrixType	MatrixType

typedef MatrixType::RowVectorType	VectorType

typedef MatrixType::ScalarType	ScalarType

typedef capd::vectalg::Norm< VectorType, MatrixType >	NormType

typedef DynSysT	DynSysType

typedef DynSysType::SolutionCurve	SolutionCurve

typedef DynSysT::StepControlType	StepControlType

Public Member Functions
	DiffInclusion (MultiMapType &diffInclusion, int order, NormType const &norm)

virtual	~DiffInclusion ()

virtual VectorType	diffInclusionEnclosure (const ScalarType &t, const VectorType &x)
	eclosure of solution of diff. inclusion during one time step starting at x More...

virtual VectorType	dynamicalSystemEnclosure (const ScalarType &t, const VectorType &x)
	eclosure of solution of selected ODE during one time step starting at x More...

virtual VectorType	enclosure (const ScalarType &t, const VectorType &x)
	eclosure of solution of diff. inclusion during one time step starting at x More...

const MapType &	getVectorField () const
	returns RHS of a diff. inclusion More...

MapType &	getVectorField ()
	returns RHS of a diff. inclusion More...

int	getOrder () const
	returns order of numerical method More...

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

ScalarType	getStep () const
	returns current time step More...

void	setStep (const ScalarType &newStep)
	sets currect time step More...

void	adjustTimeStep (const ScalarType &newStep)

DynSysType &	getDynamicalSystem ()
	returns dynamical system (numerical ODE integrator) More...

const DynSysType &	getDynamicalSystem () const
	returns dynamical system (numerical ODE integrator) More...

int	dimension () const

const SolutionCurve &	getCurve ()

virtual ScalarType	getCoeffNorm (unsigned i, int degree) const

void	clearCoefficients ()

template<class SetType >
ScalarType	computeNextTimeStep (const SetType &x, const ScalarType &maxStep)

template<class SetType >
ScalarType	getFirstTimeStep (const SetType &x, const ScalarType &maxStep)

void	turnOnStepControl ()

void	turnOffStepControl ()

void	onOffStepControl (bool _onOffStepControl)

const StepControlType &	getStepControl () const

void	setStepControl (const StepControlType &stepControl)

bool	isStepChangeAllowed () const

void	setAbsoluteTolerance (double tol)

void	setRelativeTolerance (double tol)

double	getAbsoluteTolerance () const

double	getRelativeTolerance () const

ScalarType	getMaxStep () const

void	setMaxStep (ScalarType maxStep)

Static Public Member Functions
template<class Solver , class SetType >
static double	getEffectiveTolerance (Solver &solver, const SetType &s)

Protected Attributes
NormType *	m_norm
	norm used in perturbation estimations More...

MultiMapType &	m_diffIncl
	RHS of differential inclusion. More...

DynSysType	m_dynamicalSystem
	dynamical system of selected ODE (numerical integrator) More...

Detailed Description

template<typename MapT, typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>
class capd::diffIncl::DiffInclusion< MapT, DynSysT >

Base class for rigorous integration of differential inclusions.

Template arguments:

MapT - MultiMap that stores RHS of the differential inclusion in the form : selection + 'error bounds' (we assume that it implements all methods that class capd::diffIncl::MultiMap has).
DynSysT - numerical method for ODE integration

See also: capd::diffIncl::DiffInclusionLN,; capd::diffIncl::DiffInclusionCW

Member Typedef Documentation

◆ DynSysType

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

typedef DynSysT capd::diffIncl::DiffInclusion< MapT, DynSysT >::DynSysType

◆ FunctionType

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

typedef MapT::FunctionType capd::diffIncl::DiffInclusion< MapT, DynSysT >::FunctionType

◆ MapType

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

typedef MultiMapType capd::diffIncl::DiffInclusion< MapT, DynSysT >::MapType

◆ MatrixType

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

typedef MapType::MatrixType capd::diffIncl::DiffInclusion< MapT, DynSysT >::MatrixType

◆ MultiMapType

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

typedef MapT capd::diffIncl::DiffInclusion< MapT, DynSysT >::MultiMapType

◆ NormType

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

typedef capd::vectalg::Norm<VectorType, MatrixType> capd::diffIncl::DiffInclusion< MapT, DynSysT >::NormType

◆ ScalarType

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

typedef MatrixType::ScalarType capd::diffIncl::DiffInclusion< MapT, DynSysT >::ScalarType

◆ SolutionCurve

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

typedef DynSysType::SolutionCurve capd::diffIncl::DiffInclusion< MapT, DynSysT >::SolutionCurve

◆ StepControlType

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

typedef DynSysT::StepControlType capd::diffIncl::DiffInclusion< MapT, DynSysT >::StepControlType

◆ VectorFieldType

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

typedef MapT::MapType capd::diffIncl::DiffInclusion< MapT, DynSysT >::VectorFieldType

◆ VectorType

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

typedef MatrixType::RowVectorType capd::diffIncl::DiffInclusion< MapT, DynSysT >::VectorType

Constructor & Destructor Documentation

◆ DiffInclusion()

template<typename MapT , typename DynSysT >

capd::diffIncl::DiffInclusion< MapT, DynSysT >::DiffInclusion	(	MultiMapType &	diffInclusion,
		int	order,
		NormType const &	norm
	)

◆ ~DiffInclusion()

template<typename MapT , typename DynSysT >

capd::diffIncl::DiffInclusion< MapT, DynSysT >::~DiffInclusion

virtual

Member Function Documentation

◆ adjustTimeStep()

template<typename MapT , typename DynSysT >

void capd::diffIncl::DiffInclusion< MapT, DynSysT >::adjustTimeStep ( const ScalarType & newStep )

inline

< sets time step but does not change step control settings (compare setStep)

◆ clearCoefficients()

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

void capd::diffIncl::DiffInclusion< MapT, DynSysT >::clearCoefficients ( )

inline

◆ computeNextTimeStep()

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

template<class SetType >

ScalarType capd::diffIncl::DiffInclusion< MapT, DynSysT >::computeNextTimeStep	(	const SetType &	x,
		const ScalarType &	maxStep
	)

inline

◆ diffInclusionEnclosure()

template<typename MapT , typename DynSysT >

DiffInclusion< MapT, DynSysT >::VectorType capd::diffIncl::DiffInclusion< MapT, DynSysT >::diffInclusionEnclosure	(	const ScalarType &	t,
		const VectorType &	x
	)

inlinevirtual

eclosure of solution of diff. inclusion during one time step starting at x

Computes enclosure of image of given set for differential inclusion during whole time step.

◆ dimension()

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

int capd::diffIncl::DiffInclusion< MapT, DynSysT >::dimension ( ) const

inline

◆ dynamicalSystemEnclosure()

template<typename MapT , typename DynSysT >

DiffInclusion< MapT, DynSysT >::VectorType capd::diffIncl::DiffInclusion< MapT, DynSysT >::dynamicalSystemEnclosure	(	const ScalarType &	t,
		const VectorType &	x
	)

inlinevirtual

eclosure of solution of selected ODE during one time step starting at x

◆ enclosure()

template<typename MapT , typename DynSysT >

DiffInclusion< MapT, DynSysT >::VectorType capd::diffIncl::DiffInclusion< MapT, DynSysT >::enclosure	(	const ScalarType &	t,
		const VectorType &	x
	)

inlinevirtual

eclosure of solution of diff. inclusion during one time step starting at x

◆ getAbsoluteTolerance()

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

double capd::diffIncl::DiffInclusion< MapT, DynSysT >::getAbsoluteTolerance ( ) const

inline

◆ getCoeffNorm()

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

virtual ScalarType capd::diffIncl::DiffInclusion< MapT, DynSysT >::getCoeffNorm	(	unsigned	i,
		int	degree
	)		const

inlinevirtual

◆ getCurve()

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

const SolutionCurve& capd::diffIncl::DiffInclusion< MapT, DynSysT >::getCurve ( )

inline

◆ getDynamicalSystem() [1/2]

template<typename MapT , typename DynSysT >

const DiffInclusion< MapT, DynSysT >::DynSysType & capd::diffIncl::DiffInclusion< MapT, DynSysT >::getDynamicalSystem

inline

returns dynamical system (numerical ODE integrator)

◆ getDynamicalSystem() [2/2]

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

const DynSysType& capd::diffIncl::DiffInclusion< MapT, DynSysT >::getDynamicalSystem ( ) const

returns dynamical system (numerical ODE integrator)

◆ getEffectiveTolerance()

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

template<class Solver , class SetType >

static double capd::diffIncl::DiffInclusion< MapT, DynSysT >::getEffectiveTolerance	(	Solver &	solver,
		const SetType &	s
	)

inlinestatic

◆ getFirstTimeStep()

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

template<class SetType >

ScalarType capd::diffIncl::DiffInclusion< MapT, DynSysT >::getFirstTimeStep	(	const SetType &	x,
		const ScalarType &	maxStep
	)

inline

◆ getMaxStep()

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

ScalarType capd::diffIncl::DiffInclusion< MapT, DynSysT >::getMaxStep ( ) const

inline

◆ getOrder()

template<typename MapT , typename DynSysT >

int capd::diffIncl::DiffInclusion< MapT, DynSysT >::getOrder

inline

returns order of numerical method

◆ getRelativeTolerance()

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

double capd::diffIncl::DiffInclusion< MapT, DynSysT >::getRelativeTolerance ( ) const

inline

◆ getStep()

template<typename MapT , typename DynSysT >

DiffInclusion< MapT, DynSysT >::ScalarType capd::diffIncl::DiffInclusion< MapT, DynSysT >::getStep

inline

returns current time step

◆ getStepControl()

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

const StepControlType& capd::diffIncl::DiffInclusion< MapT, DynSysT >::getStepControl ( ) const

inline

◆ getVectorField() [1/2]

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

MapType& capd::diffIncl::DiffInclusion< MapT, DynSysT >::getVectorField ( )

returns RHS of a diff. inclusion

◆ getVectorField() [2/2]

template<typename MapT , typename DynSysT >

MapT & capd::diffIncl::DiffInclusion< MapT, DynSysT >::getVectorField

inline

returns RHS of a diff. inclusion

◆ isStepChangeAllowed()

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

bool capd::diffIncl::DiffInclusion< MapT, DynSysT >::isStepChangeAllowed ( ) const

inline

◆ onOffStepControl()

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

void capd::diffIncl::DiffInclusion< MapT, DynSysT >::onOffStepControl ( bool _onOffStepControl )

inline

◆ setAbsoluteTolerance()

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

void capd::diffIncl::DiffInclusion< MapT, DynSysT >::setAbsoluteTolerance ( double tol )

inline

◆ setMaxStep()

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

void capd::diffIncl::DiffInclusion< MapT, DynSysT >::setMaxStep ( ScalarType maxStep )

inline

◆ setOrder()

template<typename MapT , typename DynSysT >

void capd::diffIncl::DiffInclusion< MapT, DynSysT >::setOrder ( int newOrder )

inline

sets order of numerical method

◆ setRelativeTolerance()

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

void capd::diffIncl::DiffInclusion< MapT, DynSysT >::setRelativeTolerance ( double tol )

inline

◆ setStep()

template<typename MapT , typename DynSysT >

void capd::diffIncl::DiffInclusion< MapT, DynSysT >::setStep ( const ScalarType & newStep )

inline

sets currect time step

sets time step but does not change step control settings (compare setStep)

◆ setStepControl()

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

void capd::diffIncl::DiffInclusion< MapT, DynSysT >::setStepControl ( const StepControlType & stepControl )

inline

◆ turnOffStepControl()

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

void capd::diffIncl::DiffInclusion< MapT, DynSysT >::turnOffStepControl ( )

inline

◆ turnOnStepControl()

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

void capd::diffIncl::DiffInclusion< MapT, DynSysT >::turnOnStepControl ( )

inline

Member Data Documentation

◆ m_diffIncl

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

MultiMapType& capd::diffIncl::DiffInclusion< MapT, DynSysT >::m_diffIncl

protected

RHS of differential inclusion.

◆ m_dynamicalSystem

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

DynSysType capd::diffIncl::DiffInclusion< MapT, DynSysT >::m_dynamicalSystem

protected

dynamical system of selected ODE (numerical integrator)

◆ m_norm

template<typename MapT , typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>

NormType* capd::diffIncl::DiffInclusion< MapT, DynSysT >::m_norm

protected

norm used in perturbation estimations

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Detailed Description

template<typename MapT, typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >> class capd::diffIncl::DiffInclusion< MapT, DynSysT >

Member Typedef Documentation

◆ DynSysType

◆ FunctionType

◆ MapType

◆ MatrixType

◆ MultiMapType

◆ NormType

◆ ScalarType

◆ SolutionCurve

◆ StepControlType

◆ VectorFieldType

◆ VectorType

Constructor & Destructor Documentation

◆ DiffInclusion()

◆ ~DiffInclusion()

Member Function Documentation

◆ adjustTimeStep()

◆ clearCoefficients()

◆ computeNextTimeStep()

◆ diffInclusionEnclosure()

◆ dimension()

◆ dynamicalSystemEnclosure()

◆ enclosure()

◆ getAbsoluteTolerance()

◆ getCoeffNorm()

◆ getCurve()

◆ getDynamicalSystem() [1/2]

◆ getDynamicalSystem() [2/2]

◆ getEffectiveTolerance()

◆ getFirstTimeStep()

◆ getMaxStep()

◆ getOrder()

◆ getRelativeTolerance()

◆ getStep()

◆ getStepControl()

◆ getVectorField() [1/2]

◆ getVectorField() [2/2]

◆ isStepChangeAllowed()

◆ onOffStepControl()

◆ setAbsoluteTolerance()

◆ setMaxStep()

◆ setOrder()

◆ setRelativeTolerance()

◆ setStep()

◆ setStepControl()

◆ turnOffStepControl()

◆ turnOnStepControl()

Member Data Documentation

◆ m_diffIncl

◆ m_dynamicalSystem

◆ m_norm

template<typename MapT, typename DynSysT = capd::dynsys::OdeSolver< typename MapT::MapType >>
class capd::diffIncl::DiffInclusion< MapT, DynSysT >