#include <capd/dynsys/CnOdeSolver.h>

Public Types
typedef MapT	VectorFieldType

typedef StepControlT	StepControlPolicy

typedef EnclosurePolicyT	EnclosurePolicy

typedef BasicCnOdeSolver< MapT, StepControlPolicy, CurveT >	BaseTaylor

typedef VectorFieldType::ScalarType	ScalarType

typedef VectorFieldType::VectorType	VectorType

typedef VectorFieldType::MatrixType	MatrixType

typedef VectorFieldType::HessianType	HessianType

typedef VectorFieldType::FunctionType	FunctionType

typedef BaseTaylor::JetType	JetType

typedef MatrixType::size_type	size_type

typedef diffAlgebra::C1TimeJet< MatrixType >	C1TimeJetType

typedef diffAlgebra::C2TimeJet< MatrixType >	C2TimeJetType

typedef diffAlgebra::CnTimeJet< MatrixType, 0 >	CnTimeJetType

typedef CurveT	SolutionCurve

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

typedef capd::dynsys::IEncFoundStepControl	StepControlType

typedef JetType::Multipointer	Multipointer

typedef JetType::Multiindex	Multiindex

typedef TypeTraits< ScalarType >::Real	Real

typedef __difference_type	difference_type

Public Member Functions
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 CnSetMove is used meaning that this solver can integrate C^0, C^1 and C^2 sets only. Moreover, it cannot integrate nonrigorous jets (for user safety). More...

template<typename SetType >
void	operator() (SetType &set, SetType &result)

	CnOdeSolver (VectorFieldType &vectorField, 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	encloseC0Map (const ScalarType &t, const VectorType &x0, const VectorType &x, VectorType &o_phi, VectorType &o_rem, VectorType &o_enc, MatrixType &o_jacPhi)

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

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)

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)

void	c2Remainder (const VectorType &Enc, const MatrixType &jacEnc, const HessianType &hessianEnc, VectorType &o_Rem, MatrixType &o_jacRem, HessianType &o_hessianRem)

template<class JetT >
VectorType	encloseCnMap (const ScalarType &t, const VectorType &x, const VectorType &xx, JetT &phi, JetT &rem, JetT &enc)

template<class JetT >
VectorType	cnEnclosure (const ScalarType &t, const VectorType &x, JetT &result)

template<class JetT >
void	cnRemainder (const JetT &enc, JetT &result)

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...

ScalarType	getCoeffNorm (size_type i, size_type degree) const

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)

virtual void	computeRemainder (ScalarType t, const VectorType &xx, VectorType &o_enc, VectorType &o_rem)

virtual void	computeRemainder (ScalarType t, const VectorType &xx, C1TimeJetType &o_enc, C1TimeJetType &o_rem)

virtual void	computeRemainder (ScalarType t, const VectorType &xx, C2TimeJetType &o_enc, C2TimeJetType &o_rem)

template<class JetT >
void	computeRemainder (ScalarType t, const VectorType &xx, JetT &o_enc, JetT &o_rem)

void	sumTaylorSeries (VectorType &o_phi, MatrixType &o_jacPhi)

void	sumTaylorSeries (VectorType &o_phi, MatrixType &o_jacPhi, HessianType &o_hessianPhi)

template<class JetT >
void	sumTaylorSeries (JetT &o_phi)

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

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

VectorFieldType &	getVectorField ()

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

void	setStep (const ScalarType &newStep)
	Sets time step and turns off step control. More...

void	setCurrentTime (const ScalarType &a_time) const

const ScalarType &	getCurrentTime () const

const SolutionCurve &	getCurve ()

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, MapT::MatrixType &o_jacPhi, MapT::MatrixType &o_jacRem, MapT::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...

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...

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

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

VectorType	operator() (VectorType, 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, const VectorType &, 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, 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, const 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 CnJetMove is used meaning that this solver can integrate any type of jets. More...

VectorType	operator() (VectorType, MatrixType &, HessianType &)
	Computes next point on the trajectory, first and second order derivatives with respect to initial conditions. Initial conditions for variational equations are Id and zero, respectively. More...

VectorType	operator() (ScalarType &t, const VectorType &, MatrixType &, HessianType &)
	Computes next point on the trajectory of a nonautonomous system, first and second order derivatives with respect to initial conditions. Initial conditions for variational equations are Id and zero, respectively. More...

VectorType	operator() (VectorType, const MatrixType &V, const HessianType &H, MatrixType &, HessianType &)
	The routine computes next point, derivatives and second order derivatives of a flow. Initial conditions for variational equations are V and H, respectively. More...

VectorType	operator() (ScalarType &t, const VectorType &x, const MatrixType &V, const HessianType &H, MatrixType &, HessianType &)
	The routine computes next point, derivatives and second order derivatives of a nonautonomous flow. Initial conditions for variational equations are V and H, respectively. More...

VectorType	operator() (ScalarType &t, JetType &)
	Initial conditions for the trajectory and for variational equations up to given degree are given in argument in_out_coeffs. The full result is stored in in_out_coeffs and also the new point on the trajectory is returned. Note: CnCoeffType is a data structure that stores current time. More...

VectorType	operator() (const ScalarType &h) const

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)

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

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

void	setStep (const ScalarType &newStep)
	Sets time step and turns off step control. More...

size_type	degree () const

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

void	setMask (Iterator b, Iterator e)
	The iterator range [b,e) should contain a range of Multiinideces the user requires to compute. More...

void	addMultiindexToMask (const capd::vectalg::Multiindex &mi)
	Adds new multiindex (along with dependencies) to the existing mask. More...

void	resetMask ()
	Resets the mask of derivatives. 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)

HessianType	hessian (const ScalarType &h) const

JetType	jet (const ScalarType &h) const

void	eval (ScalarType h, JetType &v) const

VectorType	timeDerivative (const ScalarType &h) const

MatrixType	derivative (const ScalarType &h) const

MatrixType	operator[] (const ScalarType &h) 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	setInitialCondition (ScalarType t, const VectorType &x, const VectorType &xx)

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

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

void	saveCurrentSet (capd::dynset::C2Set< MatrixType > &set)

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

void	operator= (const CnOdeSolver &)

	CnOdeSolver (const CnOdeSolver &t)

void	setCurrentTime (const ScalarType &a_time) const

const ScalarType &	getCurrentTime () const

const bool *	getMask () const

bool	getMask (size_type j) const

bool	getMask (size_type j, size_type c) const

void	setInitialCondition (const JetType &coeff)

void	setInitialCondition (const VectorType &v, const MatrixType &D)

void	setInitialCondition (const VectorType &v, const MatrixType &D, const HessianType &H)

void	computeTimeStep (const VectorType &v)

void	evalAndSum (VectorType &v)

void	evalAndSum (VectorType &v, MatrixType &der)

void	evalAndSum (VectorType &v, MatrixType &der, HessianType &hessian)

void	evalAndSum (JetType &v)

void	sum (VectorType &v)

Protected Attributes
ScalarType	m_step

VectorFieldType *	m_vField

MatrixType	m_defaultC1InitialCondition

HessianType	m_defaultC2InitialCondition

ScalarType	m_fixedTimeStep

Multiindex::IndicesSet	m_listIndices

StepControlType	m_stepControl

bool	m_onOffStepControl

TolScalarType	m_absoluteTolerance

TolScalarType	m_relativeTolerance

Scalar	m_maxStep

Real	m_left

Real	m_right
	domain More...

Member Typedef Documentation

◆ BaseTaylor

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

typedef BasicCnOdeSolver<MapT,StepControlPolicy,CurveT> capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::BaseTaylor

◆ C1TimeJetType

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

typedef diffAlgebra::C1TimeJet<MatrixType> capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::C1TimeJetType

◆ C2TimeJetType

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

typedef diffAlgebra::C2TimeJet<MatrixType> capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::C2TimeJetType

◆ CnTimeJetType

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

typedef diffAlgebra::CnTimeJet<MatrixType,0> capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::CnTimeJetType

◆ difference_type

typedef __difference_type capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > , capd::TypeTraits<typename BaseCurveT::ScalarType>::isInterval >::difference_type

inherited

◆ EnclosurePolicy

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

typedef EnclosurePolicyT capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::EnclosurePolicy

◆ FunctionType

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

typedef VectorFieldType::FunctionType capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::FunctionType

◆ HessianType

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

typedef VectorFieldType::HessianType capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::HessianType

◆ JetType

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

typedef BaseTaylor::JetType capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::JetType

◆ MatrixType

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

typedef VectorFieldType::MatrixType capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::MatrixType

◆ Multiindex

typedef JetType::Multiindex capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::Multiindex

inherited

◆ Multipointer

typedef JetType::Multipointer capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::Multipointer

inherited

◆ NormType

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

inherited

◆ Real

typedef TypeTraits<ScalarType>::Real capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > , capd::TypeTraits<typename BaseCurveT::ScalarType>::isInterval >::Real

inherited

◆ ScalarType

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

typedef VectorFieldType::ScalarType capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::ScalarType

◆ size_type

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

typedef MatrixType::size_type capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::size_type

◆ SolutionCurve

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

typedef CurveT capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::SolutionCurve

◆ StepControlPolicy

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

typedef StepControlT capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::StepControlPolicy

◆ StepControlType

typedef capd::dynsys::IEncFoundStepControl capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::StepControlType

inherited

◆ VectorFieldType

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

typedef MapT capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::VectorFieldType

◆ VectorType

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

typedef VectorFieldType::VectorType capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::VectorType

Constructor & Destructor Documentation

◆ CnOdeSolver()

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::CnOdeSolver ( const CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT > & t )

inlineprotected

Member Function Documentation

◆ addMultiindexToMask()

void capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::addMultiindexToMask ( const capd::vectalg::Multiindex & mi )

inlineinherited

Adds new multiindex (along with dependencies) to the existing mask.

Parameters

mi	multiindex to be added to the mask

Warning: causes undefined behavior if the mask has not been set before call to this method.

◆ adjustTimeStep()

void capd::dynsys::BasicCnOdeSolver< MapType, StepControlType, capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::adjustTimeStep ( const ScalarType & newStep )

inlineinherited

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

◆ computeCoefficients() [1/4]

void capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::computeCoefficients	(	const VectorType &	x,
		const MatrixType &	M,
		size_type	order
	)

inlineinherited

◆ computeCoefficients() [2/4]

void capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::computeCoefficients	(	const VectorType &	x,
		size_type	order
	)

inlineinherited

◆ computeCoefficients() [3/4]

void capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::computeCoefficients	(	ScalarType	t,
		const VectorType &	x,
		const MatrixType &	M,
		size_type	order
	)

inlineinherited

◆ computeCoefficients() [4/4]

void capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::computeCoefficients	(	ScalarType	t,
		const VectorType &	x,
		size_type	order
	)

inlineinherited

◆ computeCoefficientsAtCenter() [1/2]

void capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::computeCoefficientsAtCenter	(	const VectorType &	x,
		size_type	order
	)

inlineinherited

◆ computeCoefficientsAtCenter() [2/2]

void capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::computeCoefficientsAtCenter	(	ScalarType	t,
		const VectorType &	x,
		size_type	order
	)

inlineinherited

◆ computeTimeStep() [1/2]

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

void capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::computeTimeStep	(	const ScalarType &	t,
		const VectorType &	x
	)

inline

◆ computeTimeStep() [2/2]

void capd::dynsys::BasicCnOdeSolver< MapType, StepControlType, capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::computeTimeStep ( const VectorType & v )

inlineprotectedinherited

◆ degree()

BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::size_type capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::degree

inlineinherited

◆ derivative()

template<class BaseCurveT , bool isInterval>

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

virtualinherited

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

◆ encloseC0Map()

virtual void capd::dynsys::DynSys< MapT::MatrixType >::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< MapT::MatrixType >::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()

virtual void capd::dynsys::C2DynSys< MapT::MatrixType >::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

◆ enclosure()

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

VectorType capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::enclosure	(	const ScalarType &	t,
		const VectorType &	x
	)

inlinevirtual

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.

Implements capd::dynsys::DynSys< MapT::MatrixType >.

◆ eval()

void capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > , capd::TypeTraits<typename BaseCurveT::ScalarType>::isInterval >::eval	(	ScalarType	h,
		JetType &	v
	)		const

virtualinherited

Reimplemented from capd::diffAlgebra::ParametricCurve< BaseCurveT::MatrixType >.

◆ evalAndSum() [1/4]

void capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::evalAndSum ( JetType & v )

protectedinherited

◆ evalAndSum() [2/4]

void capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::evalAndSum ( VectorType & v )

protectedinherited

◆ evalAndSum() [3/4]

void capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::evalAndSum	(	VectorType &	v,
		MatrixType &	der
	)

protectedinherited

◆ evalAndSum() [4/4]

void capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::evalAndSum	(	VectorType &	v,
		MatrixType &	der,
		HessianType &	hessian
	)

protectedinherited

◆ getAbsoluteTolerance()

template<class StepControlT , class Scalar >

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

inlineinherited

◆ getCurrentTime() [1/2]

const ScalarType& capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::getCurrentTime ( ) const

inlineprotectedinherited

◆ getCurrentTime() [2/2]

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

const ScalarType& capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::getCurrentTime

inline

◆ getCurve()

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

const BasicCnOdeSolver< MapType, StepControlType, CurveT >::SolutionCurve & capd::dynsys::BasicCnOdeSolver< MapType, StepControlType, CurveT >::getCurve

◆ 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

◆ getMask() [1/3]

const bool* capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::getMask ( ) const

inlineprotectedinherited

◆ getMask() [2/3]

bool capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::getMask ( size_type j ) const

inlineprotectedinherited

◆ getMask() [3/3]

bool capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::getMask	(	size_type	j,
		size_type	c
	)		const

inlineprotectedinherited

◆ 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<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

ScalarType capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::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< MapT::MatrixType >.

◆ getStepControl()

template<class StepControlT , class Scalar >

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

inlineinherited

◆ getVectorField() [1/3]

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

MapType & capd::dynsys::BasicCnOdeSolver< MapType, StepControlType, CurveT >::getVectorField

inline

◆ getVectorField() [2/3]

const MapType & capd::dynsys::BasicCnOdeSolver< MapType, StepControlType, capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::getVectorField

inlineinherited

Returns vector field.

◆ getVectorField() [3/3]

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

const MapType & capd::dynsys::BasicCnOdeSolver< MapType, StepControlType, CurveT >::getVectorField

inline

Returns vector field.

◆ hessian()

CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > , capd::TypeTraits<typename BaseCurveT::ScalarType>::isInterval >::HessianType capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > , capd::TypeTraits<typename BaseCurveT::ScalarType>::isInterval >::hessian ( const ScalarType & h ) const

virtualinherited

Reimplemented from capd::diffAlgebra::ParametricCurve< BaseCurveT::MatrixType >.

◆ isStepChangeAllowed()

template<class StepControlT , class Scalar >

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

inlineinherited

◆ jet()

CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > , capd::TypeTraits<typename BaseCurveT::ScalarType>::isInterval >::JetType capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > , capd::TypeTraits<typename BaseCurveT::ScalarType>::isInterval >::jet ( const ScalarType & h ) const

virtualinherited

Reimplemented from capd::diffAlgebra::ParametricCurve< BaseCurveT::MatrixType >.

◆ Lipschitz()

DynSys< MatrixType >::ScalarType capd::dynsys::DynSys< MatrixType >::Lipschitz	(	const ScalarType &	t,
		const VectorType &	iv,
		NormType &	n
	)

virtualinherited

this function returns Lipschitz contants for maps. It should be overriden in classes implementing flows.

◆ onOffStepControl()

template<class StepControlT , class Scalar >

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

inlineinherited

◆ operator()() [1/15]

template<class BaseCurveT , bool isInterval>

Curve< BaseCurveT, isInterval >::VectorType capd::diffAlgebra::Curve< BaseCurveT, isInterval >::operator() ( const ScalarType & h ) const

virtualinherited

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

◆ operator()() [2/15]

void capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::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 CnJetMove is used meaning that this solver can integrate any type of jets.

◆ operator()() [3/15]

BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::operator()	(	ScalarType &	t,
		const VectorType &	v
	)

inlineinherited

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

◆ operator()() [4/15]

BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::operator()	(	ScalarType &	t,
		const VectorType &	v,
		MatrixType &	der,
		HessianType &	coeff
	)

inlineinherited

Computes next point on the trajectory of a nonautonomous system, first and second order derivatives with respect to initial conditions. Initial conditions for variational equations are Id and zero, respectively.

◆ operator()() [5/15]

BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::operator()	(	ScalarType &	t,
		const 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()() [6/15]

BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::operator()	(	ScalarType &	t,
		const 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()() [7/15]

BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::operator()	(	ScalarType &	t,
		const VectorType &	x,
		const MatrixType &	V,
		const HessianType &	H,
		MatrixType &	out_der,
		HessianType &	out_hessian
	)

inlineinherited

The routine computes next point, derivatives and second order derivatives of a nonautonomous flow. Initial conditions for variational equations are V and H, respectively.

◆ operator()() [8/15]

BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::operator()	(	ScalarType &	t,
		JetType &	coeff
	)

inherited

Initial conditions for the trajectory and for variational equations up to given degree are given in argument in_out_coeffs. The full result is stored in in_out_coeffs and also the new point on the trajectory is returned. Note: CnCoeffType is a data structure that stores current time.

◆ operator()() [9/15]

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

template<typename SetType >

void capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::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 CnSetMove is used meaning that this solver can integrate C^0, C^1 and C^2 sets only. Moreover, it cannot integrate nonrigorous jets (for user safety).

◆ operator()() [10/15]

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

template<typename SetType >

void capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::operator()	(	SetType &	set,
		SetType &	result
	)

inline

◆ operator()() [11/15]

BasicCnOdeSolver< MapType, StepControlType, capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicCnOdeSolver< MapType, StepControlType, capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::operator() ( VectorType v )

inherited

Computes image of vector v after one time step.

◆ operator()() [12/15]

BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::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()() [13/15]

BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::operator()	(	VectorType	v,
		const MatrixType &	V,
		const HessianType &	H,
		MatrixType &	out_der,
		HessianType &	out_hessian
	)

inherited

The routine computes next point, derivatives and second order derivatives of a flow. Initial conditions for variational equations are V and H, respectively.

◆ operator()() [14/15]

BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::operator()	(	VectorType	v,
		MatrixType &	der,
		HessianType &	hessian
	)

inherited

Computes next point on the trajectory, first and second order derivatives with respect to initial conditions. Initial conditions for variational equations are Id and zero, respectively.

◆ operator()() [15/15]

BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::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=()

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

void capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::operator= ( const CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT > & )

inlineprotected

◆ operator[]()

template<class BaseCurveT , bool isInterval = capd::TypeTraits<typename BaseCurveT::ScalarType>::isInterval>

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

inlinevirtualinherited

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

◆ resetMask()

void capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::resetMask ( )

inlineinherited

Resets the mask of derivatives.

In consequence, full jet of derivatives will be computed after call to any method that computes derivative, hessian or jet.

◆ saveCurrentSet() [1/4]

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

void capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::saveCurrentSet ( capd::dynset::C1Set< MatrixType > & set )

inlineprotected

◆ saveCurrentSet() [2/4]

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

void capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::saveCurrentSet ( capd::dynset::C2Set< MatrixType > & set )

inlineprotected

◆ saveCurrentSet() [3/4]

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

void capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::saveCurrentSet ( capd::dynset::CnSet< MatrixType > & set )

inlineprotected

◆ saveCurrentSet() [4/4]

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

void capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::saveCurrentSet ( const capd::diffAlgebra::TimeRange< ScalarType > & )

inlineprotected

◆ setAbsoluteTolerance()

template<class StepControlT , class Scalar >

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

inlineinherited

◆ setCurrentTime() [1/2]

void capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::setCurrentTime ( const ScalarType & a_time ) const

inlineprotectedinherited

◆ setCurrentTime() [2/2]

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

void capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::setCurrentTime

inline

◆ setDomain()

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

inlinevirtualinherited

◆ setInitialCondition() [1/3]

void capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::setInitialCondition ( const JetType & coeff )

protectedinherited

◆ setInitialCondition() [2/3]

void capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::setInitialCondition	(	const VectorType &	v,
		const MatrixType &	D
	)

protectedinherited

◆ setInitialCondition() [3/3]

void capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::setInitialCondition	(	const VectorType &	v,
		const MatrixType &	D,
		const HessianType &	H
	)

protectedinherited

◆ setMask()

void capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::setMask	(	Iterator	b,
		Iterator	e
	)

inlineinherited

The iterator range [b,e) should contain a range of Multiinideces the user requires to compute.

The method automatically adds all the depending partial derivatives to this collection and defines a mask for computation of partial derivtives.

Parameters

[b,e) iterator range which contains collection of multiindices

Warning: The method causes undefined behavior if a multiindex in the collection exceeds limits of the vector field (like dimension, maximal allowed degree).

◆ setMaxStep()

template<class StepControlT , class Scalar >

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

inlineinherited

◆ setOrder() [1/2]

void capd::dynsys::BasicCnOdeSolver< MapType, StepControlType, capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::setOrder ( size_type order )

inherited

Sets the order of the Taylor method.

◆ setOrder() [2/2]

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

void capd::dynsys::BasicCnOdeSolver< MapType, StepControlType, CurveT >::setOrder

Sets the order of the Taylor method.

◆ setRelativeTolerance()

template<class StepControlT , class Scalar >

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

inlineinherited

◆ setStep() [1/2]

void capd::dynsys::BasicCnOdeSolver< MapType, StepControlType, capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::setStep ( const ScalarType & newStep )

inlineinherited

Sets time step and turns off step control.

◆ setStep() [2/2]

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

void capd::dynsys::BasicCnOdeSolver< MapType, StepControlType, CurveT >::setStep

inline

Sets time step and turns off step control.

◆ setStepControl()

template<class StepControlT , class Scalar >

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

inlineinherited

◆ sum()

void capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::sum ( VectorType & v )

protectedinherited

◆ timeDerivative()

template<class BaseCurveT , bool isInterval>

Curve< BaseCurveT, isInterval >::VectorType capd::diffAlgebra::Curve< BaseCurveT, 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_defaultC1InitialCondition

MatrixType capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::m_defaultC1InitialCondition

protectedinherited

◆ m_defaultC2InitialCondition

HessianType capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::m_defaultC2InitialCondition

protectedinherited

◆ m_fixedTimeStep

ScalarType capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::m_fixedTimeStep

protectedinherited

◆ m_left

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

protectedinherited

◆ m_listIndices

Multiindex::IndicesSet capd::dynsys::BasicCnOdeSolver< MapT, capd::dynsys::IEncFoundStepControl , capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > > >::m_listIndices

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_relativeTolerance

template<class StepControlT , class Scalar >

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

protectedinherited

◆ m_right

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

protectedinherited

domain

◆ m_step

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

ScalarType capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::m_step

protected

◆ m_stepControl

template<class StepControlT , class Scalar >

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

protectedinherited

◆ m_vField

template<typename MapT , typename StepControlT = capd::dynsys::IEncFoundStepControl, typename EnclosurePolicyT = FirstOrderEnclosure, typename CurveT = capd::diffAlgebra::CnCurve< capd::diffAlgebra::BasicCnCurve< typename MapT::MatrixType > >>

VectorFieldType* capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::m_vField

protected

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

capd/dynsys/CnOdeSolver.h
capd/dynsys/CnOdeSolver.hpp
capd/dynsys/CnOdeSolver_phi.hpp
capd/dynsys/CnOdeSolver_remainder.hpp
capd/dynsys/CnOdeSolver_templateMembers.h

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Member Typedef Documentation

◆ BaseTaylor

◆ C1TimeJetType

◆ C2TimeJetType

◆ CnTimeJetType

◆ difference_type

◆ EnclosurePolicy

◆ FunctionType

◆ HessianType

◆ JetType

◆ MatrixType

◆ Multiindex

◆ Multipointer

◆ NormType

◆ Real

◆ ScalarType

◆ size_type

◆ SolutionCurve

◆ StepControlPolicy

◆ StepControlType

◆ VectorFieldType

◆ VectorType

Constructor & Destructor Documentation

◆ CnOdeSolver()

Member Function Documentation

◆ addMultiindexToMask()

◆ adjustTimeStep()

◆ computeCoefficients() [1/4]

◆ computeCoefficients() [2/4]

◆ computeCoefficients() [3/4]

◆ computeCoefficients() [4/4]

◆ computeCoefficientsAtCenter() [1/2]

◆ computeCoefficientsAtCenter() [2/2]

◆ computeTimeStep() [1/2]

◆ computeTimeStep() [2/2]

◆ degree()

◆ derivative()

◆ encloseC0Map()

◆ encloseC1Map()

◆ encloseC2Map()

◆ enclosure()

◆ eval()

◆ evalAndSum() [1/4]

◆ evalAndSum() [2/4]

◆ evalAndSum() [3/4]

◆ evalAndSum() [4/4]

◆ getAbsoluteTolerance()

◆ getCurrentTime() [1/2]

◆ getCurrentTime() [2/2]

◆ getCurve()

◆ getEffectiveTolerance()

◆ getLeftDomain()

◆ getMask() [1/3]

◆ getMask() [2/3]

◆ getMask() [3/3]

◆ getMaxStep()

◆ getRelativeTolerance()

◆ getRightDomain()

◆ getStep()

◆ getStepControl()

◆ getVectorField() [1/3]

◆ getVectorField() [2/3]

◆ getVectorField() [3/3]

◆ hessian()

◆ isStepChangeAllowed()

◆ jet()

◆ Lipschitz()

◆ onOffStepControl()

◆ operator()() [1/15]

◆ operator()() [2/15]

◆ operator()() [3/15]

◆ operator()() [4/15]

◆ operator()() [5/15]

◆ operator()() [6/15]

◆ operator()() [7/15]