Class for rigorous integration of differential inclusions. More...

#include <capd/diffIncl/DiffInclusionCW.h>

Public Types
typedef DiffInclusion< MapT, DynSysT >	BaseClass

typedef BaseClass::MultiMapType	MultiMapType

typedef BaseClass::MapType	MapType

typedef BaseClass::FunctionType	FunctionType

typedef BaseClass::MatrixType	MatrixType

typedef BaseClass::VectorType	VectorType

typedef BaseClass::ScalarType	ScalarType

typedef BaseClass::NormType	NormType

typedef MatrixType::size_type	size_type

typedef MapT::MapType	VectorFieldType

typedef capd::dynsys::OdeSolver< typename MapT::MapType >	DynSysType

typedef DynSysType::SolutionCurve	SolutionCurve

typedef capd::dynsys::OdeSolver< typename MapT::MapType > ::StepControlType	StepControlType

Public Member Functions
	DiffInclusionCW (MultiMapType &diffIncl, size_type order, NormType const &norm, ScalarType const &expErrorTolerance=capd::TypeTraits< ScalarType >::epsilon())

VectorType	perturbations (const ScalarType &time, const VectorType &x)
	Bounds for perturbation of solution of selected ODE after one time step. More...

template<typename SetType >
void	operator() (SetType &set)
	This operator computes image of the set (in given representation) using set.move function, see capd/dynsys/Move.h for details This template together with SetTraits prevent usage of various types of jets with incompatible solvers. The user will get an exception at runtime with clear message instead of unreadable compiler error. More...

template<typename SetType >
void	operator() (SetType &set, SetType &result)
	Computes image of the set (in set's representation) and stores it in the result set. More...

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

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...

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

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...

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 ()

ScalarType	computeNextTimeStep (const SetType &x, const ScalarType &maxStep)

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
static double	getEffectiveTolerance (Solver &solver, const SetType &s)

Protected Attributes
ScalarType	m_errorTolerance
	error tolerance in the exp(A) computations More...

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::DiffInclusionCW< MapT, DynSysT >

Class for rigorous integration of differential inclusions.

It uses Component Wise method to bound perturbations.

For more details on algorithm see:
T. Kapela, P. Zgliczyński, A Lohner-type algorithm for control systems and ordinary differential inclusions, Discrete and Continuous Dynamical Systems B, 11 (2009), 365-385.

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

Member Typedef Documentation

◆ BaseClass

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

typedef DiffInclusion<MapT, DynSysT> capd::diffIncl::DiffInclusionCW< MapT, DynSysT >::BaseClass

◆ DynSysType

typedef capd::dynsys::OdeSolver< typename MapT::MapType > capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::DynSysType

inherited

◆ FunctionType

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

typedef BaseClass::FunctionType capd::diffIncl::DiffInclusionCW< MapT, DynSysT >::FunctionType

◆ MapType

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

typedef BaseClass::MapType capd::diffIncl::DiffInclusionCW< MapT, DynSysT >::MapType

◆ MatrixType

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

typedef BaseClass::MatrixType capd::diffIncl::DiffInclusionCW< MapT, DynSysT >::MatrixType

◆ MultiMapType

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

typedef BaseClass::MultiMapType capd::diffIncl::DiffInclusionCW< MapT, DynSysT >::MultiMapType

◆ NormType

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

typedef BaseClass::NormType capd::diffIncl::DiffInclusionCW< MapT, DynSysT >::NormType

◆ ScalarType

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

typedef BaseClass::ScalarType capd::diffIncl::DiffInclusionCW< MapT, DynSysT >::ScalarType

◆ size_type

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

typedef MatrixType::size_type capd::diffIncl::DiffInclusionCW< MapT, DynSysT >::size_type

◆ SolutionCurve

typedef DynSysType::SolutionCurve capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::SolutionCurve

inherited

◆ StepControlType

typedef capd::dynsys::OdeSolver< typename MapT::MapType > ::StepControlType capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::StepControlType

inherited

◆ VectorFieldType

typedef MapT::MapType capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::VectorFieldType

inherited

◆ VectorType

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

typedef BaseClass::VectorType capd::diffIncl::DiffInclusionCW< MapT, DynSysT >::VectorType

Constructor & Destructor Documentation

◆ DiffInclusionCW()

template<typename MapT , typename DynSysT >

capd::diffIncl::DiffInclusionCW< MapT, DynSysT >::DiffInclusionCW	(	MultiMapType &	diffIncl,
		size_type	order,
		NormType const &	norm,
		ScalarType const &	expErrorTolerance = `capd::TypeTraits<ScalarType>::epsilon()`
	)

Member Function Documentation

◆ adjustTimeStep()

void capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::adjustTimeStep ( const ScalarType & newStep )

inlineinherited

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

◆ clearCoefficients()

void capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::clearCoefficients

inlineinherited

◆ computeNextTimeStep()

ScalarType capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::computeNextTimeStep	(	const SetType &	x,
		const ScalarType &	maxStep
	)

inlineinherited

◆ diffInclusionEnclosure() [1/2]

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

DiffInclusion< MapT, DynSysT >::VectorType capd::diffIncl::DiffInclusion< MapT, DynSysT >::diffInclusionEnclosure

inline

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.

◆ diffInclusionEnclosure() [2/2]

DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::VectorType capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::diffInclusionEnclosure	(	const ScalarType &	t,
		const VectorType &	x
	)

inlinevirtualinherited

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()

int capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::dimension

inlineinherited

◆ dynamicalSystemEnclosure() [1/2]

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

DiffInclusion< MapT, DynSysT >::VectorType capd::diffIncl::DiffInclusion< MapT, DynSysT >::dynamicalSystemEnclosure

inline

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

◆ dynamicalSystemEnclosure() [2/2]

DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::VectorType capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::dynamicalSystemEnclosure	(	const ScalarType &	t,
		const VectorType &	x
	)

inlinevirtualinherited

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

◆ enclosure() [1/2]

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

DiffInclusion< MapT, DynSysT >::VectorType capd::diffIncl::DiffInclusion< MapT, DynSysT >::enclosure

inline

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

◆ enclosure() [2/2]

DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::VectorType capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::enclosure	(	const ScalarType &	t,
		const VectorType &	x
	)

inlinevirtualinherited

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

◆ getAbsoluteTolerance()

double capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::getAbsoluteTolerance

inlineinherited

◆ getCoeffNorm()

virtual ScalarType capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::getCoeffNorm	(	unsigned	i,
		int	degree
	)		const

inlinevirtualinherited

◆ getCurve()

const SolutionCurve& capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::getCurve

inlineinherited

◆ getDynamicalSystem() [1/2]

const DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::DynSysType & capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::getDynamicalSystem

inlineinherited

returns dynamical system (numerical ODE integrator)

◆ getDynamicalSystem() [2/2]

const DynSysType& capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::getDynamicalSystem

inherited

returns dynamical system (numerical ODE integrator)

◆ getEffectiveTolerance()

static double capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::getEffectiveTolerance	(	Solver &	solver,
		const SetType &	s
	)

inlinestaticinherited

◆ getFirstTimeStep()

ScalarType capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::getFirstTimeStep	(	const SetType &	x,
		const ScalarType &	maxStep
	)

inlineinherited

◆ getMaxStep()

ScalarType capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::getMaxStep

inlineinherited

◆ getOrder()

int capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::getOrder

inlineinherited

returns order of numerical method

◆ getRelativeTolerance()

double capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::getRelativeTolerance

inlineinherited

◆ getStep()

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

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

inline

returns current time step

◆ getStepControl()

const StepControlType& capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::getStepControl

inlineinherited

◆ getVectorField() [1/2]

MapType& capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::getVectorField

inherited

returns RHS of a diff. inclusion

◆ getVectorField() [2/2]

MapT & capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::getVectorField

inlineinherited

returns RHS of a diff. inclusion

◆ isStepChangeAllowed()

bool capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::isStepChangeAllowed

inlineinherited

◆ onOffStepControl()

void capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::onOffStepControl ( bool _onOffStepControl )

inlineinherited

◆ operator()() [1/2]

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

template<typename SetType >

void capd::diffIncl::DiffInclusionCW< MapT, DynSysT >::operator() ( SetType & set )

inline

This operator computes image of the set (in given representation) using set.move function, see capd/dynsys/Move.h for details This template together with SetTraits prevent usage of various types of jets with incompatible solvers. The user will get an exception at runtime with clear message instead of unreadable compiler error.

◆ operator()() [2/2]

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

template<typename SetType >

void capd::diffIncl::DiffInclusionCW< MapT, DynSysT >::operator()	(	SetType &	set,
		SetType &	result
	)

inline

Computes image of the set (in set's representation) and stores it in the result set.

Parameters

[in]	set	C^0 or C^1 set representing initial conditions
[out]	result	on return contains image of the set

◆ perturbations()

template<typename MapT , typename DynSysT >

DiffInclusionCW< MapT, DynSysT >::VectorType capd::diffIncl::DiffInclusionCW< MapT, DynSysT >::perturbations	(	const ScalarType &	time,
		const VectorType &	x
	)

Bounds for perturbation of solution of selected ODE after one time step.

We use Component Wise algorithm

Parameters

x	set before the the step

Returns: rigorous bounds for perturbations

◆ setAbsoluteTolerance()

void capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::setAbsoluteTolerance ( double tol )

inlineinherited

◆ setMaxStep()

void capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::setMaxStep ( ScalarType maxStep )

inlineinherited

◆ setOrder()

void capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::setOrder ( int newOrder )

inlineinherited

sets order of numerical method

◆ setRelativeTolerance()

void capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::setRelativeTolerance ( double tol )

inlineinherited

◆ setStep()

void capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::setStep ( const ScalarType & newStep )

inlineinherited

sets currect time step

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

◆ setStepControl()

void capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::setStepControl ( const StepControlType & stepControl )

inlineinherited

◆ turnOffStepControl()

void capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::turnOffStepControl

inlineinherited

◆ turnOnStepControl()

void capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::turnOnStepControl

inlineinherited

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

DynSysType capd::diffIncl::DiffInclusion< MapT, capd::dynsys::OdeSolver< typename MapT::MapType > >::m_dynamicalSystem

protectedinherited

dynamical system of selected ODE (numerical integrator)

◆ m_errorTolerance

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

ScalarType capd::diffIncl::DiffInclusionCW< MapT, DynSysT >::m_errorTolerance

protected

error tolerance in the exp(A) computations

◆ 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::DiffInclusionCW< MapT, DynSysT >

Member Typedef Documentation

◆ BaseClass

◆ DynSysType

◆ FunctionType

◆ MapType

◆ MatrixType

◆ MultiMapType

◆ NormType

◆ ScalarType

◆ size_type

◆ SolutionCurve

◆ StepControlType

◆ VectorFieldType

◆ VectorType

Constructor & Destructor Documentation

◆ DiffInclusionCW()

Member Function Documentation

◆ adjustTimeStep()

◆ clearCoefficients()

◆ computeNextTimeStep()

◆ diffInclusionEnclosure() [1/2]

◆ diffInclusionEnclosure() [2/2]

◆ dimension()

◆ dynamicalSystemEnclosure() [1/2]

◆ dynamicalSystemEnclosure() [2/2]

◆ enclosure() [1/2]

◆ enclosure() [2/2]

◆ getAbsoluteTolerance()

◆ getCoeffNorm()

◆ getCurve()

◆ getDynamicalSystem() [1/2]

◆ getDynamicalSystem() [2/2]

◆ getEffectiveTolerance()

◆ getFirstTimeStep()

◆ getMaxStep()

◆ getOrder()

◆ getRelativeTolerance()

◆ getStep()

◆ getStepControl()

◆ getVectorField() [1/2]

◆ getVectorField() [2/2]

◆ isStepChangeAllowed()

◆ onOffStepControl()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ perturbations()

◆ setAbsoluteTolerance()

◆ setMaxStep()

◆ setOrder()

◆ setRelativeTolerance()

◆ setStep()

◆ setStepControl()

◆ turnOffStepControl()

◆ turnOnStepControl()

Member Data Documentation

◆ m_diffIncl

◆ m_dynamicalSystem

◆ m_errorTolerance

◆ m_norm

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