#include <capd/dynsys/CnDynSys.h>

Public Types
typedef MatrixT	MatrixType

typedef MatrixType::RowVectorType	VectorType

typedef MatrixType::ScalarType	ScalarType

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

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

Public Member Functions
template<class JetT >
VectorType	encloseCnMap (const ScalarType &, const VectorType &, const VectorType &, JetT &, JetT &, JetT &)

virtual void	encloseC2Map (const ScalarType &t, const VectorType &x, const VectorType &xx, VectorType &o_phi, VectorType &o_rem, VectorType &o_enc, MatrixType &o_jacPhi, MatrixType &o_jacRem, MatrixType &o_jacEnc, HessianType &o_hessianPhi, HessianType &o_hessianRem, HessianType &o_hessianEnc)=0

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

virtual VectorType	Phi (const ScalarType &t, const VectorType &iv)=0
	Computes value of function (usually numerical scheme for an ODE) at time t and point iv. More...

virtual MatrixType	JacPhi (const ScalarType &t, const VectorType &iv)=0
	Computes derivative of function (usually numerical scheme for an ODE) at time t and point iv. More...

virtual VectorType	Remainder (const ScalarType &t, const VectorType &iv, VectorType &out_enc)=0
	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...

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...

virtual VectorType	enclosure (const ScalarType &t, const VectorType &x)=0
	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...

virtual void	encloseC0Map (const ScalarType &t, const VectorType &x, const VectorType &xx, VectorType &o_phi, VectorType &o_rem, VectorType &o_enc, MatrixType &o_jacPhi)=0
	For given set xx, time t and a point x from the set xx It simultaneously computes and returns enclosures for: More...

virtual 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...

Member Typedef Documentation

◆ HessianType

template<typename MatrixT >

typedef capd::diffAlgebra::Hessian<ScalarType,VectorType::csDim,VectorType::csDim> capd::dynsys::C2DynSys< MatrixT >::HessianType

inherited

◆ MatrixType

template<typename MatrixT >

typedef MatrixT capd::dynsys::CnDynSys< MatrixT >::MatrixType

◆ NormType

template<typename MatrixT >

typedef capd::vectalg::Norm<VectorType,MatrixType> capd::dynsys::C2DynSys< MatrixT >::NormType

inherited

◆ ScalarType

template<typename MatrixT >

typedef MatrixType::ScalarType capd::dynsys::CnDynSys< MatrixT >::ScalarType

◆ VectorType

template<typename MatrixT >

typedef MatrixType::RowVectorType capd::dynsys::CnDynSys< MatrixT >::VectorType

Member Function Documentation

◆ encloseC0Map()

template<typename MatrixT >

virtual void capd::dynsys::DynSys< MatrixT >::encloseC0Map	(	const ScalarType &	t,
		const VectorType &	x,
		const VectorType &	xx,
		VectorType &	o_phi,
		VectorType &	o_rem,
		VectorType &	o_enc,
		MatrixType &	o_jacPhi
	)

pure virtualinherited

For given set xx, time t and a point x from the set xx It simultaneously computes and returns enclosures for:

numerical scheme Phi(t,x),
derivative of numerical scheme D_x Phi(t,xx)
error of numerical scheme Remainder(t,xx)
an enclosure for the trajectories over the time step (ODEs only) If the function cannot compute any of the output results, an exception is thrown and the output parameters o_* might be in inconsistent state.

◆ encloseC1Map()

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

pure virtualinherited

◆ encloseC2Map()

template<typename MatrixT >

virtual void capd::dynsys::C2DynSys< MatrixT >::encloseC2Map	(	const ScalarType &	t,
		const VectorType &	x,
		const VectorType &	xx,
		VectorType &	o_phi,
		VectorType &	o_rem,
		VectorType &	o_enc,
		MatrixType &	o_jacPhi,
		MatrixType &	o_jacRem,
		MatrixType &	o_jacEnc,
		HessianType &	o_hessianPhi,
		HessianType &	o_hessianRem,
		HessianType &	o_hessianEnc
	)

pure virtualinherited

◆ encloseCnMap()

template<typename MatrixT >

template<class JetT >

VectorType capd::dynsys::CnDynSys< MatrixT >::encloseCnMap	(	const ScalarType &	,
		const VectorType &	,
		const VectorType &	,
		JetT &	,
		JetT &	,
		JetT &
	)

inline

Parameters

	t	- time in ODE
	x	- a centre of current set
	xx	- the set
[out]	out_phi	- should contain coefficients of solution jet at (t,xx)
[out]	out_rem	- should contain remainder coefficients computed at enclosure
[out]	out_enc	- should contain enclosure for the main part and variational equations

Returns: approximate solution (without remainder) at (t,x)

◆ enclosure()

template<typename MatrixT >

virtual VectorType capd::dynsys::DynSys< MatrixT >::enclosure	(	const ScalarType &	t,
		const VectorType &	x
	)

pure virtualinherited

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.

Implemented in capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >, capd::dynsys::OdeSolver< typename MapT::MapType >, and capd::dynsys::OdeSolver< MapT, capd::dynsys::ILastTermsStepControl, HighOrderEnclosure, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >.

◆ getStep()

template<typename MatrixT >

virtual ScalarType capd::dynsys::DynSys< MatrixT >::getStep ( ) const

inlinevirtualinherited

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 in capd::dynsys::OdeSolver< typename MapT::MapType >, and capd::dynsys::OdeSolver< MapT, capd::dynsys::ILastTermsStepControl, HighOrderEnclosure, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >.

◆ JacPhi()

template<typename MatrixT >

virtual MatrixType capd::dynsys::DynSys< MatrixT >::JacPhi	(	const ScalarType &	t,
		const VectorType &	iv
	)

pure virtualinherited

Computes derivative of function (usually numerical scheme for an ODE) at time t and point iv.

Implemented in capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >, capd::dynsys::OdeSolver< typename MapT::MapType >, and capd::dynsys::OdeSolver< MapT, capd::dynsys::ILastTermsStepControl, HighOrderEnclosure, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >.

◆ Phi()

template<typename MatrixT >

virtual VectorType capd::dynsys::DynSys< MatrixT >::Phi	(	const ScalarType &	t,
		const VectorType &	iv
	)

pure virtualinherited

Computes value of function (usually numerical scheme for an ODE) at time t and point iv.

Implemented in capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >, capd::dynsys::OdeSolver< typename MapT::MapType >, and capd::dynsys::OdeSolver< MapT, capd::dynsys::ILastTermsStepControl, HighOrderEnclosure, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >.

◆ Remainder()

template<typename MatrixT >

virtual VectorType capd::dynsys::DynSys< MatrixT >::Remainder	(	const ScalarType &	t,
		const VectorType &	iv,
		VectorType &	out_enc
	)

pure virtualinherited

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.

Implemented in capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >, capd::dynsys::OdeSolver< typename MapT::MapType >, and capd::dynsys::OdeSolver< MapT, capd::dynsys::ILastTermsStepControl, HighOrderEnclosure, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >.

Public Types

Public Member Functions

Member Typedef Documentation

◆ HessianType

◆ MatrixType

◆ NormType

◆ ScalarType

◆ VectorType

Member Function Documentation

◆ encloseC0Map()

◆ encloseC1Map()

◆ encloseC2Map()

◆ encloseCnMap()

◆ enclosure()

◆ getStep()

◆ JacPhi()

◆ Phi()

◆ Remainder()