#include <capd/dynsys/FadOdeSolver.h>

Public Types
typedef FadMapT	VectorFieldType

typedef BasicFadOdeSolver< FadMapT, StepControlT >	BaseTaylor

typedef StepControlT	StepControlType

typedef BaseTaylor::ScalarType	ScalarType

typedef BaseTaylor::FScalar	FScalar

typedef BaseTaylor::TFScalar	TFScalar

typedef BaseTaylor::MatrixType	MatrixType

typedef BaseTaylor::VectorType	VectorType

typedef BaseTaylor::FVector	FVector

typedef BaseTaylor::TFVector	TFVector

typedef BaseTaylor::FunctionType	FunctionType

typedef MatrixType::size_type	size_type

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

typedef fadbad::T< ScalarType >	TScalar

typedef VectorType::template rebind< TScalar >::other	TVector

typedef capd::diffAlgebra::Curve< capd::diffAlgebra::FadCurve< typename FadMapT::MatrixType > >	SolutionCurve

typedef TypeTraits< ScalarType >::Real	Real

typedef Hessian< ScalarType, VectorType::csDim, VectorType::csDim >	HessianType

typedef Jet< MatrixType, 0 >	JetType

typedef __difference_type	difference_type

Public Member Functions
	FadOdeSolver (VectorFieldType &f, size_type _order, const StepControlT &_stepControl=StepControlT())

VectorType	Phi (const ScalarType &t, const VectorType &iv)
	Computes value of function (usually numerical scheme for an ODE) at time t and point iv. More...

MatrixType	JacPhi (const ScalarType &t, const VectorType &iv)
	Computes derivative of function (usually numerical scheme for an ODE) at time t and point iv. More...

VectorType	enclosure (const ScalarType &t, const VectorType &x)
	Used for ODEs. It verifies the existence of solutions to IVP at time t and set of initial conditions x over the time step. If the function succeeds, a rigorous bound for the trajectories is returned. Otherwise, an exception is thrown. More...

VectorType	Remainder (const ScalarType &t, const VectorType &iv, VectorType &o_enc)
	Computes and returns bound for local error of a function (for instance if Phi is finite Taylor series of a map then this method computes bound for Lagrange remainder). If DynSys is an ODE, then out_enc contains enclosure of trajectories over the time step. If the function cannot validate existence of solutions to ODE over the time step, out_enc might be in an inconsistent state. More...

void	computeTaylorCoefficients (ScalarType t, const VectorType &x, const VectorType &xx)

void	encloseC0Map (const ScalarType &t, const VectorType &x0, const VectorType &x, VectorType &o_phi, VectorType &o_rem, VectorType &o_enc, MatrixType &o_jacPhi)
	For given set xx, time t and a point x from the set xx It simultaneously computes and returns enclosures for: More...

MatrixType	jacEnclosure (const ScalarType &t, const VectorType &enc)

void	JacRemainder (const ScalarType &t, const VectorType &vecEnclosure, const MatrixType &jacEnclosure, VectorType &Remainder, MatrixType &jRemainder)

void	encloseC1Map (const ScalarType &t, const VectorType &x0, const VectorType &x, VectorType &o_phi, VectorType &o_rem, VectorType &o_enc, MatrixType &o_jacPhi, MatrixType &o_jacRem, MatrixType &o_jacEnc)

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. In this case a specialization C1SetMove is used meaning that this solver can integrate C^0 and C^1 sets only. Moreover, it cannot integrate nonrigorous jets (for user safety). 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...

ScalarType	getCoeffNorm (size_type i, size_type degree) const

ScalarType	getStep () const
	Returns time step of the dynamical system. By default it returns one - time step for discrete DS (maps). Shall be overridden in classes that implement numerical schemes for ODEs. More...

void	computeRemainderCoefficients (const VectorType &x)

void	computeRemainderCoefficients (const VectorType &x, const MatrixType &M)

void	computeRemainderCoefficients (ScalarType t, const VectorType &x)

void	computeRemainderCoefficients (ScalarType t, const VectorType &x, const MatrixType &M)

void	initRemainderCoefficients (ScalarType t, const VectorType &x, unsigned degree)

virtual void	encloseC1Map (const ScalarType &t, const VectorType &x, const VectorType &xx, VectorType &o_phi, VectorType &o_rem, VectorType &o_enc, FadMapT::MatrixType &o_jacPhi, FadMapT::MatrixType &o_jacRem, FadMapT::MatrixType &o_jacEnc)=0

virtual ScalarType	Lipschitz (const ScalarType &t, const VectorType &iv, NormType &n)
	this function returns Lipschitz contants for maps. It should be overriden in classes implementing flows. More...

VectorType	operator() (VectorType)
	Computes image of vector v after one time step. More...

VectorType	operator() (ScalarType &t, VectorType)
	Computes image of vector v after one time step. The argument t is updated in this procedure. More...

VectorType	operator() (VectorType v, MatrixType &o_resultDerivative)
	Computes image of vector v and derivatives of the flow with respect to init condition (v,identity). Version for autonomous systems. More...

VectorType	operator() (ScalarType &t, VectorType v, MatrixType &o_resultDerivative)
	Computes image of vector v and derivatives of the flow with respect to init condition (v,identity). Version for nonautonomous systems. The argument t is updated in this procedure. More...

VectorType	operator() (VectorType v, const MatrixType &derivative, MatrixType &o_resultDerivative)
	Computes image of vector v and derivatives of a flow with respect to init condition (v, derivative) More...

VectorType	operator() (ScalarType &t, VectorType v, const MatrixType &derivative, MatrixType &o_resultDerivative)
	Computes image of vector v and derivatives of a flow with respect to init condition (v, derivative). The argument t is updated in this procedure. More...

void	operator() (JetT &jet)
	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. In this case a specialization C1JetMove is used meaning that this solver can integrate C^0 and C^1 jets only. More...

VectorType	operator() (const ScalarType &h) const

const VectorFieldType &	getVectorField () const
	Returns vector field. More...

VectorFieldType &	getVectorField ()

void	setStep (const ScalarType &newStep)
	Sets time step for the next step of integration and turns off step control. More...

const SolutionCurve &	getCurve ()

void	setParameter (Description name, const ScalarType &value)

void	computeCoefficientsAtCenter (const VectorType &x, size_type order)

void	computeCoefficientsAtCenter (ScalarType t, const VectorType &x, size_type order)

void	computeCoefficients (const VectorType &x, size_type order)

void	computeCoefficients (ScalarType t, const VectorType &x, size_type order)

void	computeCoefficients (const VectorType &x, const MatrixType &M, size_type order)

void	computeCoefficients (ScalarType t, const VectorType &x, const MatrixType &M, size_type order)

void	adjustTimeStep (const ScalarType &newStep)
	sets time step but does not change step control settings (compare setStep) More...

void	turnOnStepControl ()

void	turnOffStepControl ()

void	onOffStepControl (bool _onOffStepControl)

const StepControlType &	getStepControl () const

void	setStepControl (const StepControlType &stepControl)

bool	isStepChangeAllowed () const

void	setAbsoluteTolerance (TolScalarType tol)

void	setRelativeTolerance (TolScalarType tol)

TolScalarType	getAbsoluteTolerance () const

TolScalarType	getRelativeTolerance () const

Scalar	getMaxStep () const

void	setMaxStep (Scalar maxStep)

VectorType	timeDerivative (const ScalarType &h) const

MatrixType	derivative (const ScalarType &h) const

MatrixType	operator[] (const ScalarType &h) const

virtual void	setOrder (size_type order)
	Sets the order of Taylor interpolation. More...

size_type	getOrder () const
	Returns the order of Taylor interpolation. More...

size_type	getAllocatedOrder () const
	Returns maximal allocated order - used to avoid memory reallocation. More...

size_type	dimension () const
	Returns the dimension in which the parametric curve is embedded. More...

void	clearCoefficients ()
	sets all coefficients to zero More...

const ScalarType &	centerCoefficient (size_type i, size_type j) const

ScalarType &	centerCoefficient (size_type i, size_type j)

const ScalarType &	coefficient (size_type i, size_type j) const

const ScalarType &	coefficient (size_type i, size_type j, size_type k) const

ScalarType &	coefficient (size_type i, size_type j)

ScalarType &	coefficient (size_type i, size_type j, size_type k)

const ScalarType &	remainderCoefficient (size_type i, size_type j) const

const ScalarType &	remainderCoefficient (size_type i, size_type j, size_type k) const

ScalarType &	remainderCoefficient (size_type i, size_type j)

ScalarType &	remainderCoefficient (size_type i, size_type j, size_type k)

void	setInitMatrix (const MatrixType &)

void	setInitHessian (const HessianType &)

void	setInitJet (const JetType &)

std::runtime_error	domainErrorMessage (std::string msg, ScalarType h, Real left, Real right) const

virtual HessianType	hessian (const ScalarType &) const

virtual JetType	jet (const ScalarType &) const

virtual void	eval (ScalarType, JetType &) const

virtual void	setDomain (Real left, Real right)

virtual Real	getLeftDomain () const

virtual Real	getRightDomain () const

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

Protected Member Functions
void	saveCurrentSet (const capd::diffAlgebra::TimeRange< ScalarType > &)

void	saveCurrentSet (const capd::dynset::C1Set< MatrixType > &set)

void	computeTimeStep (const ScalarType &t, const VectorType &x)

void	setCurrentTime (const ScalarType &a_time) const

const ScalarType &	getCurrentTime () const

void	computeTimeStep (VectorType &v)

void	recordDags ()

void	reset ()

void	computeCoeff (AVector &in, AVector &out, size_type order)

void	setInitialCondition (const VectorType &u, TVector &in)

void	setInitialCondition (const VectorType &u, TFVector &in)

void	setInitialCondition (const VectorType &u, const MatrixType &M, TFVector &in)

void	sumTaylorSeries (VectorType &u, TVector &in, size_type order)

void	sumTaylorSeries (MatrixType &M, TFVector &in, size_type order)

void	sumTaylorSeries (VectorType &u, MatrixType &M, TFVector &in, size_type order)

Protected Attributes
VectorFieldType &	m_vectorField

TVector	m_centerOut

TFVector	m_out

TVector	m_remOut

TFVector	m_jacRemOut

TScalar	m_time

TFScalar	m_ftime

ScalarType	m_fixedTimeStep

ScalarType	m_step

StepControlType	m_stepControl

bool	m_onOffStepControl

TolScalarType	m_absoluteTolerance

TolScalarType	m_relativeTolerance

Scalar	m_maxStep

size_type	m_order

size_type	m_dimension

TVector	m_center

TFVector	m_in

TVector	m_rem

TFVector	m_jacRem

Real	m_left

Real	m_right
	domain More...

Member Typedef Documentation

◆ BaseTaylor

template<class FadMapT , typename StepControlT = capd::dynsys::IEncFoundStepControl>

typedef BasicFadOdeSolver<FadMapT,StepControlT> capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::BaseTaylor

◆ difference_type

typedef __difference_type capd::diffAlgebra::Curve< capd::diffAlgebra::FadCurve< FadMapT::MatrixType > , capd::TypeTraits<typename BaseCurveT::ScalarType>::isInterval >::difference_type

inherited

◆ FScalar

template<class FadMapT , typename StepControlT = capd::dynsys::IEncFoundStepControl>

typedef BaseTaylor::FScalar capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::FScalar

◆ FunctionType

template<class FadMapT , typename StepControlT = capd::dynsys::IEncFoundStepControl>

typedef BaseTaylor::FunctionType capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::FunctionType

◆ FVector

template<class FadMapT , typename StepControlT = capd::dynsys::IEncFoundStepControl>

typedef BaseTaylor::FVector capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::FVector

◆ HessianType

typedef Hessian<ScalarType,VectorType::csDim,VectorType::csDim> capd::diffAlgebra::Curve< capd::diffAlgebra::FadCurve< FadMapT::MatrixType > , capd::TypeTraits<typename BaseCurveT::ScalarType>::isInterval >::HessianType

inherited

◆ JetType

typedef Jet<MatrixType,0> capd::diffAlgebra::Curve< capd::diffAlgebra::FadCurve< FadMapT::MatrixType > , capd::TypeTraits<typename BaseCurveT::ScalarType>::isInterval >::JetType

inherited

◆ MatrixType

template<class FadMapT , typename StepControlT = capd::dynsys::IEncFoundStepControl>

typedef BaseTaylor::MatrixType capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::MatrixType

◆ NormType

template<class FadMapT , typename StepControlT = capd::dynsys::IEncFoundStepControl>

typedef capd::vectalg::Norm<VectorType,MatrixType> capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::NormType

◆ Real

typedef TypeTraits<ScalarType>::Real capd::diffAlgebra::Curve< capd::diffAlgebra::FadCurve< FadMapT::MatrixType > , capd::TypeTraits<typename BaseCurveT::ScalarType>::isInterval >::Real

inherited

◆ ScalarType

template<class FadMapT , typename StepControlT = capd::dynsys::IEncFoundStepControl>

typedef BaseTaylor::ScalarType capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::ScalarType

◆ size_type

template<class FadMapT , typename StepControlT = capd::dynsys::IEncFoundStepControl>

typedef MatrixType::size_type capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::size_type

◆ SolutionCurve

typedef capd::diffAlgebra::Curve< capd::diffAlgebra::FadCurve<typename FadMapT::MatrixType> > capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::SolutionCurve

inherited

◆ StepControlType

template<class FadMapT , typename StepControlT = capd::dynsys::IEncFoundStepControl>

typedef StepControlT capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::StepControlType

◆ TFScalar

template<class FadMapT , typename StepControlT = capd::dynsys::IEncFoundStepControl>

typedef BaseTaylor::TFScalar capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::TFScalar

◆ TFVector

template<class FadMapT , typename StepControlT = capd::dynsys::IEncFoundStepControl>

typedef BaseTaylor::TFVector capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::TFVector

◆ TScalar

typedef fadbad::T<ScalarType> capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::TScalar

inherited

◆ TVector

typedef VectorType::template rebind<TScalar>::other capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::TVector

inherited

◆ VectorFieldType

template<class FadMapT , typename StepControlT = capd::dynsys::IEncFoundStepControl>

typedef FadMapT capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::VectorFieldType

◆ VectorType

template<class FadMapT , typename StepControlT = capd::dynsys::IEncFoundStepControl>

typedef BaseTaylor::VectorType capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::VectorType

Member Function Documentation

◆ adjustTimeStep()

void capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlType >::adjustTimeStep ( const ScalarType & newStep )

inlineinherited

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

◆ computeCoeff()

void capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::computeCoeff	(	AVector &	in,
		AVector &	out,
		size_type	order
	)

protectedinherited

◆ computeCoefficients() [1/4]

void capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::computeCoefficients	(	const VectorType &	x,
		const MatrixType &	M,
		size_type	order
	)

inlineinherited

◆ computeCoefficients() [2/4]

void capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::computeCoefficients	(	const VectorType &	x,
		size_type	order
	)

inlineinherited

◆ computeCoefficients() [3/4]

void capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::computeCoefficients	(	ScalarType	t,
		const VectorType &	x,
		const MatrixType &	M,
		size_type	order
	)

inlineinherited

◆ computeCoefficients() [4/4]

void capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::computeCoefficients	(	ScalarType	t,
		const VectorType &	x,
		size_type	order
	)

inlineinherited

◆ computeCoefficientsAtCenter() [1/2]

void capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::computeCoefficientsAtCenter	(	const VectorType &	x,
		size_type	order
	)

inlineinherited

◆ computeCoefficientsAtCenter() [2/2]

void capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::computeCoefficientsAtCenter	(	ScalarType	t,
		const VectorType &	x,
		size_type	order
	)

inlineinherited

◆ computeTimeStep() [1/2]

template<class FadMapT , typename StepControlT = capd::dynsys::IEncFoundStepControl>

void capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::computeTimeStep	(	const ScalarType &	t,
		const VectorType &	x
	)

inlineprotected

◆ computeTimeStep() [2/2]

void capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlType >::computeTimeStep ( VectorType & v )

inlineprotectedinherited

◆ derivative()

Curve< capd::diffAlgebra::FadCurve< FadMapT::MatrixType > , capd::TypeTraits<typename BaseCurveT::ScalarType>::isInterval >::MatrixType capd::diffAlgebra::Curve< capd::diffAlgebra::FadCurve< FadMapT::MatrixType > , capd::TypeTraits<typename BaseCurveT::ScalarType>::isInterval >::derivative ( const ScalarType & h ) const

virtualinherited

Implements capd::diffAlgebra::ParametricCurve< BaseCurveT::MatrixType >.

◆ domainErrorMessage()

template<class MatrixT >

std::runtime_error capd::diffAlgebra::CurveInterface< MatrixT >::domainErrorMessage	(	std::string	msg,
		ScalarType	h,
		Real	left,
		Real	right
	)		const

inlineinherited

◆ encloseC1Map()

virtual void capd::dynsys::C1DynSys< FadMapT::MatrixType >::encloseC1Map	(	const ScalarType &	t,
		const VectorType &	x,
		const VectorType &	xx,
		VectorType &	o_phi,
		VectorType &	o_rem,
		VectorType &	o_enc,
		FadMapT::MatrixType &	o_jacPhi,
		FadMapT::MatrixType &	o_jacRem,
		FadMapT::MatrixType &	o_jacEnc
	)

pure virtualinherited

◆ eval()

virtual void capd::diffAlgebra::ParametricCurve< BaseCurveT::MatrixType , typename MatrixT::RowVectorType >::eval	(	ScalarType	,
		JetType &
	)		const

inlinevirtualinherited

Reimplemented in capd::diffAlgebra::CnCurve< BaseCurveT, true >, capd::diffAlgebra::CnCurve< BaseCurveT, isInterval >, and capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >.

◆ getAbsoluteTolerance()

template<class StepControlT , class Scalar >

TolScalarType capd::dynsys::StepControlInterface< StepControlT, Scalar >::getAbsoluteTolerance ( ) const

inlineinherited

◆ getCurrentTime()

const ScalarType& capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::getCurrentTime ( ) const

inlineprotectedinherited

◆ getCurve()

const BasicFadOdeSolver< FadMapT, StepControlType >::SolutionCurve & capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlType >::getCurve

inherited

◆ getEffectiveTolerance()

template<class StepControlT , class Scalar >

template<class Solver , class SetType >

static TolScalarType capd::dynsys::StepControlInterface< StepControlT, Scalar >::getEffectiveTolerance	(	Solver &	solver,
		const SetType &	s
	)

inlinestaticinherited

◆ getLeftDomain()

ParametricCurve< BaseCurveT::MatrixType , typename MatrixT::RowVectorType >::Real capd::diffAlgebra::ParametricCurve< BaseCurveT::MatrixType , typename MatrixT::RowVectorType >::getLeftDomain

inlinevirtualinherited

◆ getMaxStep()

template<class StepControlT , class Scalar >

Scalar capd::dynsys::StepControlInterface< StepControlT, Scalar >::getMaxStep ( ) const

inlineinherited

◆ getRelativeTolerance()

template<class StepControlT , class Scalar >

TolScalarType capd::dynsys::StepControlInterface< StepControlT, Scalar >::getRelativeTolerance ( ) const

inlineinherited

◆ getRightDomain()

ParametricCurve< BaseCurveT::MatrixType , typename MatrixT::RowVectorType >::Real capd::diffAlgebra::ParametricCurve< BaseCurveT::MatrixType , typename MatrixT::RowVectorType >::getRightDomain

inlinevirtualinherited

◆ getStep()

template<class FadMapT , typename StepControlT = capd::dynsys::IEncFoundStepControl>

ScalarType capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::getStep ( ) const

inlinevirtual

Returns time step of the dynamical system. By default it returns one - time step for discrete DS (maps). Shall be overridden in classes that implement numerical schemes for ODEs.

Reimplemented from capd::dynsys::DynSys< MatrixT >.

◆ getStepControl()

template<class StepControlT , class Scalar >

const StepControlType& capd::dynsys::StepControlInterface< StepControlT, Scalar >::getStepControl ( ) const

inlineinherited

◆ getVectorField() [1/2]

FadMapT & capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlType >::getVectorField

inlineinherited

◆ getVectorField() [2/2]

const FadMapT & capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlType >::getVectorField

inlineinherited

Returns vector field.

◆ hessian()

virtual HessianType capd::diffAlgebra::ParametricCurve< BaseCurveT::MatrixType , typename MatrixT::RowVectorType >::hessian ( const ScalarType & ) const

inlinevirtualinherited

Reimplemented in capd::diffAlgebra::CnCurve< BaseCurveT, true >, capd::diffAlgebra::CnCurve< BaseCurveT, isInterval >, capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >, capd::diffAlgebra::C2Curve< BaseCurveT, true >, and capd::diffAlgebra::C2Curve< BaseCurveT, isInterval >.

◆ initRemainderCoefficients()

template<class FadMapT , typename StepControlT = capd::dynsys::IEncFoundStepControl>

void capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::initRemainderCoefficients	(	ScalarType	t,
		const VectorType &	x,
		unsigned	degree
	)

inline

◆ isStepChangeAllowed()

template<class StepControlT , class Scalar >

bool capd::dynsys::StepControlInterface< StepControlT, Scalar >::isStepChangeAllowed ( ) const

inlineinherited

◆ jet()

virtual JetType capd::diffAlgebra::ParametricCurve< BaseCurveT::MatrixType , typename MatrixT::RowVectorType >::jet ( const ScalarType & ) const

inlinevirtualinherited

Reimplemented in capd::diffAlgebra::CnCurve< BaseCurveT, true >, capd::diffAlgebra::CnCurve< BaseCurveT, isInterval >, and capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >.

◆ onOffStepControl()

template<class StepControlT , class Scalar >

void capd::dynsys::StepControlInterface< StepControlT, Scalar >::onOffStepControl ( bool _onOffStepControl )

inlineinherited

◆ operator()() [1/10]

Curve< capd::diffAlgebra::FadCurve< FadMapT::MatrixType > , capd::TypeTraits<typename BaseCurveT::ScalarType>::isInterval >::VectorType capd::diffAlgebra::Curve< capd::diffAlgebra::FadCurve< FadMapT::MatrixType > , capd::TypeTraits<typename BaseCurveT::ScalarType>::isInterval >::operator() ( const ScalarType & h ) const

virtualinherited

Implements capd::diffAlgebra::ParametricCurve< BaseCurveT::MatrixType >.

◆ operator()() [2/10]

void capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::operator() ( JetT & jet )

inlineinherited

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. In this case a specialization C1JetMove is used meaning that this solver can integrate C^0 and C^1 jets only.

◆ operator()() [3/10]

BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::VectorType capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::operator()	(	ScalarType &	t,
		VectorType	v,
		const MatrixType &	derivative,
		MatrixType &	o_resultDerivative
	)

inlineinherited

Computes image of vector v and derivatives of a flow with respect to init condition (v, derivative). The argument t is updated in this procedure.

◆ operator()() [4/10]

BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::VectorType capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::operator()	(	ScalarType &	t,
		VectorType	v,
		MatrixType &	o_resultDerivative
	)

inlineinherited

Computes image of vector v and derivatives of the flow with respect to init condition (v,identity). Version for nonautonomous systems. The argument t is updated in this procedure.

◆ operator()() [5/10]

BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::VectorType capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::operator()	(	ScalarType &	t,
		VectorType	u
	)

inlineinherited

Computes image of vector v after one time step. The argument t is updated in this procedure.

◆ operator()() [6/10]

template<class FadMapT , typename StepControlT = capd::dynsys::IEncFoundStepControl>

template<typename SetType >

void capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::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. In this case a specialization C1SetMove is used meaning that this solver can integrate C^0 and C^1 sets only. Moreover, it cannot integrate nonrigorous jets (for user safety).

◆ operator()() [7/10]

template<class FadMapT , typename StepControlT = capd::dynsys::IEncFoundStepControl>

template<typename SetType >

void capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::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, C^1 set representing initial conditions
[out]	result	on return contains image of the set

◆ operator()() [8/10]

BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::VectorType capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::operator()	(	VectorType	v,
		const MatrixType &	derivative,
		MatrixType &	o_resultDerivative
	)

inherited

Computes image of vector v and derivatives of a flow with respect to init condition (v, derivative)

◆ operator()() [9/10]

BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::VectorType capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::operator()	(	VectorType	v,
		MatrixType &	o_resultDerivative
	)

inherited

Computes image of vector v and derivatives of the flow with respect to init condition (v,identity). Version for autonomous systems.

◆ operator()() [10/10]

BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::VectorType capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::operator() ( VectorType u )

inherited

Computes image of vector v after one time step.

◆ operator[]()

MatrixType capd::diffAlgebra::Curve< capd::diffAlgebra::FadCurve< FadMapT::MatrixType > , capd::TypeTraits<typename BaseCurveT::ScalarType>::isInterval >::operator[] ( const ScalarType & h ) const

inlinevirtualinherited

Implements capd::diffAlgebra::ParametricCurve< BaseCurveT::MatrixType >.

◆ recordDags()

void capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::recordDags

protectedinherited

◆ reset()

void capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::reset

protectedinherited

◆ saveCurrentSet() [1/2]

template<class FadMapT , typename StepControlT = capd::dynsys::IEncFoundStepControl>

void capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::saveCurrentSet ( const capd::diffAlgebra::TimeRange< ScalarType > & )

inlineprotected

◆ saveCurrentSet() [2/2]

template<class FadMapT , typename StepControlT = capd::dynsys::IEncFoundStepControl>

void capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::saveCurrentSet ( const capd::dynset::C1Set< MatrixType > & set )

inlineprotected

◆ setAbsoluteTolerance()

template<class StepControlT , class Scalar >

void capd::dynsys::StepControlInterface< StepControlT, Scalar >::setAbsoluteTolerance ( TolScalarType tol )

inlineinherited

◆ setCurrentTime()

void capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::setCurrentTime ( const ScalarType & a_time ) const

inlineprotectedinherited

◆ setDomain()

void capd::diffAlgebra::ParametricCurve< BaseCurveT::MatrixType , typename MatrixT::RowVectorType >::setDomain	(	Real	left,
		Real	right
	)

inlinevirtualinherited

◆ setInitHessian()

template<class MatrixT >

void capd::diffAlgebra::CurveInterface< MatrixT >::setInitHessian ( const HessianType & )

inlineinherited

◆ setInitialCondition() [1/3]

void capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::setInitialCondition	(	const VectorType &	u,
		const MatrixType &	M,
		TFVector &	in
	)

protectedinherited

◆ setInitialCondition() [2/3]

void capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::setInitialCondition	(	const VectorType &	u,
		TFVector &	in
	)

protectedinherited

◆ setInitialCondition() [3/3]

void capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::setInitialCondition	(	const VectorType &	u,
		TVector &	in
	)

protectedinherited

◆ setInitJet()

template<class MatrixT >

void capd::diffAlgebra::CurveInterface< MatrixT >::setInitJet ( const JetType & )

inlineinherited

◆ setInitMatrix()

template<class MatrixT >

void capd::diffAlgebra::CurveInterface< MatrixT >::setInitMatrix ( const MatrixType & )

inlineinherited

◆ setMaxStep()

template<class StepControlT , class Scalar >

void capd::dynsys::StepControlInterface< StepControlT, Scalar >::setMaxStep ( Scalar maxStep )

inlineinherited

◆ setParameter()

void capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::setParameter	(	Description	name,
		const ScalarType &	value
	)

inlineinherited

◆ setRelativeTolerance()

template<class StepControlT , class Scalar >

void capd::dynsys::StepControlInterface< StepControlT, Scalar >::setRelativeTolerance ( TolScalarType tol )

inlineinherited

◆ setStep()

void capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlType >::setStep ( const ScalarType & newStep )

inlineinherited

Sets time step for the next step of integration and turns off step control.

◆ setStepControl()

template<class StepControlT , class Scalar >

void capd::dynsys::StepControlInterface< StepControlT, Scalar >::setStepControl ( const StepControlType & stepControl )

inlineinherited

◆ sumTaylorSeries() [1/3]

void capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::sumTaylorSeries	(	MatrixType &	M,
		TFVector &	in,
		size_type	order
	)

protectedinherited

◆ sumTaylorSeries() [2/3]

void capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::sumTaylorSeries	(	VectorType &	u,
		MatrixType &	M,
		TFVector &	in,
		size_type	order
	)

protectedinherited

◆ sumTaylorSeries() [3/3]

void capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::sumTaylorSeries	(	VectorType &	u,
		TVector &	in,
		size_type	order
	)

protectedinherited

◆ timeDerivative()

Curve< capd::diffAlgebra::FadCurve< FadMapT::MatrixType > , capd::TypeTraits<typename BaseCurveT::ScalarType>::isInterval >::VectorType capd::diffAlgebra::Curve< capd::diffAlgebra::FadCurve< FadMapT::MatrixType > , capd::TypeTraits<typename BaseCurveT::ScalarType>::isInterval >::timeDerivative ( const ScalarType & h ) const

inherited

◆ turnOffStepControl()

template<class StepControlT , class Scalar >

void capd::dynsys::StepControlInterface< StepControlT, Scalar >::turnOffStepControl ( )

inlineinherited

◆ turnOnStepControl()

template<class StepControlT , class Scalar >

void capd::dynsys::StepControlInterface< StepControlT, Scalar >::turnOnStepControl ( )

inlineinherited

Member Data Documentation

◆ m_absoluteTolerance

template<class StepControlT , class Scalar >

TolScalarType capd::dynsys::StepControlInterface< StepControlT, Scalar >::m_absoluteTolerance

protectedinherited

◆ m_center

template<class MatrixT >

TVector capd::diffAlgebra::FadCurve< MatrixT >::m_center

mutableprotectedinherited

◆ m_centerOut

TVector capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::m_centerOut

mutableprotectedinherited

◆ m_dimension

template<class MatrixT >

size_type capd::diffAlgebra::FadCurve< MatrixT >::m_dimension

protectedinherited

◆ m_fixedTimeStep

ScalarType capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::m_fixedTimeStep

protectedinherited

◆ m_ftime

TFScalar capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::m_ftime

mutableprotectedinherited

◆ m_in

template<class MatrixT >

TFVector capd::diffAlgebra::FadCurve< MatrixT >::m_in

mutableprotectedinherited

◆ m_jacRem

template<class MatrixT >

TFVector capd::diffAlgebra::FadCurve< MatrixT >::m_jacRem

mutableprotectedinherited

◆ m_jacRemOut

TFVector capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::m_jacRemOut

mutableprotectedinherited

◆ m_left

Real capd::diffAlgebra::ParametricCurve< BaseCurveT::MatrixType , typename MatrixT::RowVectorType >::m_left

protectedinherited

◆ m_maxStep

template<class StepControlT , class Scalar >

Scalar capd::dynsys::StepControlInterface< StepControlT, Scalar >::m_maxStep

protectedinherited

◆ m_onOffStepControl

template<class StepControlT , class Scalar >

bool capd::dynsys::StepControlInterface< StepControlT, Scalar >::m_onOffStepControl

protectedinherited

◆ m_order

template<class MatrixT >

size_type capd::diffAlgebra::FadCurve< MatrixT >::m_order

protectedinherited

◆ m_out

TFVector capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::m_out

mutableprotectedinherited

◆ m_relativeTolerance

template<class StepControlT , class Scalar >

TolScalarType capd::dynsys::StepControlInterface< StepControlT, Scalar >::m_relativeTolerance

protectedinherited

◆ m_rem

template<class MatrixT >

TVector capd::diffAlgebra::FadCurve< MatrixT >::m_rem

mutableprotectedinherited

◆ m_remOut

TVector capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::m_remOut

mutableprotectedinherited

◆ m_right

Real capd::diffAlgebra::ParametricCurve< BaseCurveT::MatrixType , typename MatrixT::RowVectorType >::m_right

protectedinherited

domain

◆ m_step

ScalarType capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::m_step

protectedinherited

◆ m_stepControl

template<class StepControlT , class Scalar >

StepControlType capd::dynsys::StepControlInterface< StepControlT, Scalar >::m_stepControl

protectedinherited

◆ m_time

TScalar capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::m_time

mutableprotectedinherited

◆ m_vectorField

VectorFieldType& capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >::m_vectorField

protectedinherited

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

capd/dynsys/FadOdeSolver.h
capd/dynsys/FadOdeSolver.hpp

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Member Typedef Documentation

◆ BaseTaylor

◆ difference_type

◆ FScalar

◆ FunctionType

◆ FVector

◆ HessianType

◆ JetType

◆ MatrixType

◆ NormType

◆ Real

◆ ScalarType

◆ size_type

◆ SolutionCurve

◆ StepControlType

◆ TFScalar

◆ TFVector

◆ TScalar

◆ TVector

◆ VectorFieldType

◆ VectorType

Member Function Documentation

◆ adjustTimeStep()

◆ computeCoeff()

◆ computeCoefficients() [1/4]

◆ computeCoefficients() [2/4]

◆ computeCoefficients() [3/4]

◆ computeCoefficients() [4/4]

◆ computeCoefficientsAtCenter() [1/2]

◆ computeCoefficientsAtCenter() [2/2]

◆ computeTimeStep() [1/2]

◆ computeTimeStep() [2/2]

◆ derivative()

◆ domainErrorMessage()

◆ encloseC1Map()

◆ eval()

◆ getAbsoluteTolerance()

◆ getCurrentTime()

◆ getCurve()

◆ getEffectiveTolerance()

◆ getLeftDomain()

◆ getMaxStep()

◆ getRelativeTolerance()

◆ getRightDomain()

◆ getStep()

◆ getStepControl()

◆ getVectorField() [1/2]

◆ getVectorField() [2/2]

◆ hessian()

◆ initRemainderCoefficients()

◆ isStepChangeAllowed()

◆ jet()

◆ onOffStepControl()

◆ operator()() [1/10]

◆ operator()() [2/10]

◆ operator()() [3/10]

◆ operator()() [4/10]

◆ operator()() [5/10]

◆ operator()() [6/10]

◆ operator()() [7/10]

◆ operator()() [8/10]

◆ operator()() [9/10]

◆ operator()() [10/10]

◆ operator[]()

◆ recordDags()

◆ reset()

◆ saveCurrentSet() [1/2]

◆ saveCurrentSet() [2/2]

◆ setAbsoluteTolerance()

◆ setCurrentTime()

◆ setDomain()

◆ setInitHessian()

◆ setInitialCondition() [1/3]

◆ setInitialCondition() [2/3]

◆ setInitialCondition() [3/3]