#include <capd/dynsys/OdeSolver.h>

Public Types
typedef MapT	VectorFieldType

typedef StepControlPolicyT	StepControlPolicy

typedef MapT::FunctionType	FunctionType

typedef VectorFieldType::MatrixType	MatrixType

typedef MatrixType::RowVectorType	VectorType

typedef MatrixType::ScalarType	ScalarType

typedef BasicOdeSolver< MapT, StepControlPolicy, CurveT >	BaseTaylor

typedef MatrixType::size_type	size_type

typedef diffAlgebra::C1TimeJet< MatrixType >	C1TimeJetType

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

typedef capd::dynsys::ILastTermsStepControl	StepControlType

typedef capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > >	SolutionCurve

typedef VectorFieldType::JetType	JetType

typedef JetType::Multipointer	Multipointer

typedef JetType::Multiindex	Multiindex

typedef TypeTraits< ScalarType >::Real	Real

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

typedef __difference_type	difference_type

typedef VectorType::iterator	iterator

typedef VectorType::const_iterator	const_iterator

Public Member Functions
	OdeSolver (VectorFieldType &vField, size_type order, const StepControlPolicy &stepControl=StepControlPolicy())

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

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	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...

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	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)

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

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

ScalarType	getCoeffNorm (size_type, size_type degree) const

ScalarType	getStep () const

const CurveT &	getImplicitCurve () const

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

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...

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...

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

VectorType	operator() (ScalarType &t, const VectorType &u)
	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 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	setOrder (size_type order)
	Sets the order of the Taylor method. More...

ScalarType	getStep () const
	Returns the time step made in the last call to this solver. More...

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

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 SolutionCurve &	getCurve ()

virtual ScalarType	getCoeffNorm (size_type i, size_type degree) const

size_type	dimension () 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 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

MapT::ScalarType	getMaxStep () const

void	setMaxStep (MapT::ScalarType maxStep)

VectorType	timeDerivative (const ScalarType &h) const

MatrixType	derivative (const ScalarType &h) const

MatrixType	operator[] (const ScalarType &h) const

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...

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)

const VectorType *	getCoefficientsAtCenter () const

VectorType *	getCoefficientsAtCenter ()

const VectorType *	getCoefficients () const

VectorType *	getCoefficients ()

const VectorType *	getRemainderCoefficients () const

VectorType *	getRemainderCoefficients ()

const MatrixType *	getMatrixCoefficients () const

MatrixType *	getMatrixCoefficients ()

const MatrixType *	getMatrixRemainderCoefficients () const

MatrixType *	getMatrixRemainderCoefficients ()

iterator	beginCenterCoefficients (size_type j)

const_iterator	beginCenterCoefficients (size_type j) const

iterator	beginCoefficients (size_type j)

const_iterator	beginCoefficients (size_type j) const

iterator	beginRemainderCoefficients (size_type j)

const_iterator	beginRemainderCoefficients (size_type j) const

iterator	beginMatrixCoefficients (size_type j)

const_iterator	beginMatrixCoefficients (size_type j) const

iterator	beginMatrixRemainderCoefficients (size_type j)

const_iterator	beginMatrixRemainderCoefficients (size_type j) const

iterator	endCenterCoefficients (size_type j)

const_iterator	endCenterCoefficients (size_type j) const

iterator	endCoefficients (size_type j)

const_iterator	endCoefficients (size_type j) const

iterator	endRemainderCoefficients (size_type j)

const_iterator	endRemainderCoefficients (size_type j) const

iterator	endMatrixCoefficients (size_type j)

const_iterator	endMatrixCoefficients (size_type j) const

iterator	endMatrixRemainderCoefficients (size_type j)

const_iterator	endMatrixRemainderCoefficients (size_type j) const

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
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	operator= (const OdeSolver &)

	OdeSolver (const OdeSolver &t)

void	setCurrentTime (const ScalarType &a_time) const

const ScalarType &	getCurrentTime () const

const bool *	getMask () const

bool	getMask (size_type j) const

void	computeTimeStep (VectorType &v)

void	sumTaylorSeries (VectorType &v, VectorType *coeff, size_type order)

void	sumTaylorSeries (VectorType &v, MatrixType &der, VectorType coeff, MatrixType matrixCoeff, size_type order)

void	allocate ()

void	deallocate ()

void	copyData (const BasicCurve &c)

Protected Attributes
CurveT	implicitCurve
	an extra storage for Taylor coefficients used in implicit HO-method More...

VectorFieldType *	m_vField
	we do not allow copying of objects More...

ScalarType	m_fixedTimeStep

ScalarType	m_step

StepControlType	m_stepControl

bool	m_onOffStepControl

TolScalarType	m_absoluteTolerance

TolScalarType	m_relativeTolerance

MapT::ScalarType	m_maxStep

VectorType *	m_coefficientsAtCenter

VectorType *	m_coefficients

VectorType *	m_remainderCoefficients

MatrixType *	m_matrixCoefficients

MatrixType *	m_matrixRemainderCoefficients

size_type	m_order

size_type	m_allocatedOrder

size_type	m_dimension

Real	m_left

Real	m_right
	domain More...

Member Typedef Documentation

◆ BaseTaylor

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

typedef BasicOdeSolver<MapT,StepControlPolicy,CurveT> capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::BaseTaylor

◆ C1TimeJetType

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

typedef diffAlgebra::C1TimeJet<MatrixType> capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::C1TimeJetType

◆ const_iterator

typedef VectorType::const_iterator capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::const_iterator

inherited

◆ difference_type

typedef __difference_type capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > , capd::TypeTraits<typename capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > ::ScalarType>::isInterval >::difference_type

inherited

◆ FunctionType

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

typedef MapT::FunctionType capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::FunctionType

◆ HessianType

typedef Hessian<ScalarType,VectorType::csDim,VectorType::csDim> capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > , capd::TypeTraits<typename capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > ::ScalarType>::isInterval >::HessianType

inherited

◆ iterator

typedef VectorType::iterator capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::iterator

inherited

◆ JetType

typedef VectorFieldType::JetType capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::JetType

inherited

◆ MatrixType

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

typedef VectorFieldType::MatrixType capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::MatrixType

◆ Multiindex

typedef JetType::Multiindex capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::Multiindex

inherited

◆ Multipointer

typedef JetType::Multipointer capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::Multipointer

inherited

◆ NormType

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

inherited

◆ Real

typedef TypeTraits<ScalarType>::Real capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > , capd::TypeTraits<typename capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > ::ScalarType>::isInterval >::Real

inherited

◆ ScalarType

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

typedef MatrixType::ScalarType capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::ScalarType

◆ size_type

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

typedef MatrixType::size_type capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::size_type

◆ SolutionCurve

typedef capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::SolutionCurve

inherited

◆ StepControlPolicy

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

typedef StepControlPolicyT capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::StepControlPolicy

◆ StepControlType

typedef capd::dynsys::ILastTermsStepControl capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::StepControlType

inherited

◆ VectorFieldType

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

typedef MapT capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::VectorFieldType

◆ VectorType

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

typedef MatrixType::RowVectorType capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::VectorType

Constructor & Destructor Documentation

◆ OdeSolver() [1/2]

template<typename MapType , typename StepControlPolicy , typename EnclosurePolicy , typename CurveType >

capd::dynsys::OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::OdeSolver	(	VectorFieldType &	vField,
		size_type	order,
		const StepControlPolicy &	stepControl = `StepControlPolicy()`
	)

◆ OdeSolver() [2/2]

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::OdeSolver ( const OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT > & t )

inlineprotected

Member Function Documentation

◆ addMultiindexToMask()

void capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::addMultiindexToMask ( const 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::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::adjustTimeStep ( const ScalarType & newStep )

inlineinherited

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

◆ allocate()

void capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::allocate

protectedinherited

◆ beginCenterCoefficients() [1/2]

iterator capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::beginCenterCoefficients ( size_type j )

inlineinherited

◆ beginCenterCoefficients() [2/2]

const_iterator capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::beginCenterCoefficients ( size_type j ) const

inlineinherited

◆ beginCoefficients() [1/2]

iterator capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::beginCoefficients ( size_type j )

inlineinherited

◆ beginCoefficients() [2/2]

const_iterator capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::beginCoefficients ( size_type j ) const

inlineinherited

◆ beginMatrixCoefficients() [1/2]

iterator capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::beginMatrixCoefficients ( size_type j )

inlineinherited

◆ beginMatrixCoefficients() [2/2]

const_iterator capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::beginMatrixCoefficients ( size_type j ) const

inlineinherited

◆ beginMatrixRemainderCoefficients() [1/2]

iterator capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::beginMatrixRemainderCoefficients ( size_type j )

inlineinherited

◆ beginMatrixRemainderCoefficients() [2/2]

const_iterator capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::beginMatrixRemainderCoefficients ( size_type j ) const

inlineinherited

◆ beginRemainderCoefficients() [1/2]

iterator capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::beginRemainderCoefficients ( size_type j )

inlineinherited

◆ beginRemainderCoefficients() [2/2]

const_iterator capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::beginRemainderCoefficients ( size_type j ) const

inlineinherited

◆ centerCoefficient() [1/2]

BasicCurve< typename MapT::MatrixType >::ScalarType & capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::centerCoefficient	(	size_type	i,
		size_type	j
	)

inlineinherited

◆ centerCoefficient() [2/2]

const BasicCurve< typename MapT::MatrixType >::ScalarType & capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::centerCoefficient	(	size_type	i,
		size_type	j
	)		const

inlineinherited

◆ clearCoefficients()

void capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::clearCoefficients

inherited

sets all coefficients to zero

◆ coefficient() [1/4]

BasicCurve< typename MapT::MatrixType >::ScalarType & capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::coefficient	(	size_type	i,
		size_type	j
	)

inlineinherited

◆ coefficient() [2/4]

const BasicCurve< typename MapT::MatrixType >::ScalarType & capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::coefficient	(	size_type	i,
		size_type	j
	)		const

inlineinherited

◆ coefficient() [3/4]

BasicCurve< typename MapT::MatrixType >::ScalarType & capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::coefficient	(	size_type	i,
		size_type	j,
		size_type	k
	)

inlineinherited

◆ coefficient() [4/4]

const BasicCurve< typename MapT::MatrixType >::ScalarType & capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::coefficient	(	size_type	i,
		size_type	j,
		size_type	k
	)		const

inlineinherited

◆ computeCoefficients() [1/4]

void capd::dynsys::BasicOdeSolver< MapType, StepControlType, CurveType >::computeCoefficients	(	const VectorType &	x,
		const MatrixType &	M,
		size_type	order
	)

inlineinherited

◆ computeCoefficients() [2/4]

void capd::dynsys::BasicOdeSolver< MapType, StepControlType, CurveType >::computeCoefficients	(	const VectorType &	x,
		size_type	order
	)

inlineinherited

◆ computeCoefficients() [3/4]

void capd::dynsys::BasicOdeSolver< MapType, StepControlType, CurveType >::computeCoefficients	(	ScalarType	t,
		const VectorType &	x,
		const MatrixType &	M,
		size_type	order
	)

inlineinherited

◆ computeCoefficients() [4/4]

void capd::dynsys::BasicOdeSolver< MapType, StepControlType, CurveType >::computeCoefficients	(	ScalarType	t,
		const VectorType &	x,
		size_type	order
	)

inlineinherited

◆ computeCoefficientsAtCenter() [1/2]

void capd::dynsys::BasicOdeSolver< MapType, StepControlType, CurveType >::computeCoefficientsAtCenter	(	const VectorType &	x,
		size_type	order
	)

inlineinherited

◆ computeCoefficientsAtCenter() [2/2]

void capd::dynsys::BasicOdeSolver< MapType, StepControlType, CurveType >::computeCoefficientsAtCenter	(	ScalarType	t,
		const VectorType &	x,
		size_type	order
	)

inlineinherited

◆ computeImplicitCoefficients()

template<typename MapType , typename StepControlPolicy , typename EnclosurePolicy , typename CurveType >

void capd::dynsys::OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::computeImplicitCoefficients	(	ScalarType	t,
		const VectorType &	x,
		const VectorType &	xx,
		size_type	order
	)

inline

◆ computeRemainder() [1/2]

template<typename MapType , typename StepControlPolicy , typename EnclosurePolicy , typename CurveType >

void capd::dynsys::OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::computeRemainder	(	ScalarType	t,
		const VectorType &	xx,
		C1TimeJetType &	o_enc,
		C1TimeJetType &	o_rem
	)

inlinevirtual

◆ computeRemainder() [2/2]

template<typename MapType , typename StepControlPolicy , typename EnclosurePolicy , typename CurveType >

void capd::dynsys::OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::computeRemainder	(	ScalarType	t,
		const VectorType &	xx,
		VectorType &	o_enc,
		VectorType &	o_rem
	)

inlinevirtual

◆ computeRemainderCoefficients() [1/4]

template<typename MapType , typename StepControlPolicy , typename EnclosurePolicy , typename CurveType >

void capd::dynsys::OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::computeRemainderCoefficients ( const VectorType & x )

inline

◆ computeRemainderCoefficients() [2/4]

template<typename MapType , typename StepControlPolicy , typename EnclosurePolicy , typename CurveType >

void capd::dynsys::OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::computeRemainderCoefficients	(	const VectorType &	x,
		const MatrixType &	M
	)

inline

◆ computeRemainderCoefficients() [3/4]

template<typename MapType , typename StepControlPolicy , typename EnclosurePolicy , typename CurveType >

void capd::dynsys::OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::computeRemainderCoefficients	(	ScalarType	t,
		const VectorType &	x
	)

inline

◆ computeRemainderCoefficients() [4/4]

template<typename MapType , typename StepControlPolicy , typename EnclosurePolicy , typename CurveType >

void capd::dynsys::OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::computeRemainderCoefficients	(	ScalarType	t,
		const VectorType &	x,
		const MatrixType &	M
	)

inline

◆ computeTaylorCoefficients()

template<typename MapType , typename StepControlPolicy , typename EnclosurePolicy , typename CurveType >

void capd::dynsys::OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::computeTaylorCoefficients	(	ScalarType	t,
		const VectorType &	x,
		const VectorType &	xx
	)

inline

◆ computeTimeStep() [1/2]

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

void capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::computeTimeStep	(	const ScalarType &	t,
		const VectorType &	x
	)

inline

◆ computeTimeStep() [2/2]

void capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::computeTimeStep ( VectorType & v )

inlineprotectedinherited

◆ copyData()

void capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::copyData ( const BasicCurve< typename MapT::MatrixType > & c )

protectedinherited

◆ deallocate()

void capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::deallocate

protectedinherited

◆ derivative()

Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > , capd::TypeTraits<typename capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > ::ScalarType>::isInterval >::MatrixType capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > , capd::TypeTraits<typename capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > ::ScalarType>::isInterval >::derivative ( const ScalarType & h ) const

virtualinherited

Implements capd::diffAlgebra::ParametricCurve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > ::MatrixType >.

◆ dimension()

size_type capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::dimension

inlineinherited

◆ domainErrorMessage()

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

inlineinherited

◆ encloseC0Map() [1/2]

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.

◆ encloseC0Map() [2/2]

template<typename MapType , typename StepControlPolicy , typename EnclosurePolicy , typename CurveType >

void capd::dynsys::OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::encloseC0Map	(	const ScalarType &	t,
		const VectorType &	x0,
		const VectorType &	x,
		VectorType &	o_phi,
		VectorType &	o_rem,
		VectorType &	o_enc,
		MatrixType &	o_jacPhi
	)

◆ encloseC1Map() [1/2]

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

◆ encloseC1Map() [2/2]

template<typename MapType , typename StepControlPolicy , typename EnclosurePolicy , typename CurveType >

void capd::dynsys::OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::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
	)

◆ enclosure()

template<typename MapType , typename StepControlPolicy , typename EnclosurePolicy , typename CurveType >

OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::VectorType capd::dynsys::OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::enclosure	(	const ScalarType &	t,
		const VectorType &	x
	)

virtual

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 >.

◆ endCenterCoefficients() [1/2]

iterator capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::endCenterCoefficients ( size_type j )

inlineinherited

◆ endCenterCoefficients() [2/2]

const_iterator capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::endCenterCoefficients ( size_type j ) const

inlineinherited

◆ endCoefficients() [1/2]

iterator capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::endCoefficients ( size_type j )

inlineinherited

◆ endCoefficients() [2/2]

const_iterator capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::endCoefficients ( size_type j ) const

inlineinherited

◆ endMatrixCoefficients() [1/2]

iterator capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::endMatrixCoefficients ( size_type j )

inlineinherited

◆ endMatrixCoefficients() [2/2]

const_iterator capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::endMatrixCoefficients ( size_type j ) const

inlineinherited

◆ endMatrixRemainderCoefficients() [1/2]

iterator capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::endMatrixRemainderCoefficients ( size_type j )

inlineinherited

◆ endMatrixRemainderCoefficients() [2/2]

const_iterator capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::endMatrixRemainderCoefficients ( size_type j ) const

inlineinherited

◆ endRemainderCoefficients() [1/2]

iterator capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::endRemainderCoefficients ( size_type j )

inlineinherited

◆ endRemainderCoefficients() [2/2]

const_iterator capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::endRemainderCoefficients ( size_type j ) const

inlineinherited

◆ eval()

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

inlinevirtualinherited

◆ getAbsoluteTolerance()

TolScalarType capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , MapT::ScalarType >::getAbsoluteTolerance ( ) const

inlineinherited

◆ getAllocatedOrder()

BasicCurve< typename MapT::MatrixType >::size_type capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::getAllocatedOrder

inlineinherited

Returns maximal allocated order - used to avoid memory reallocation.

◆ getCoefficients() [1/2]

VectorType* capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::getCoefficients ( )

inherited

◆ getCoefficients() [2/2]

BasicCurve< typename MapT::MatrixType >::VectorType * capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::getCoefficients

inlineinherited

◆ getCoefficientsAtCenter() [1/2]

VectorType* capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::getCoefficientsAtCenter ( )

inherited

◆ getCoefficientsAtCenter() [2/2]

BasicCurve< typename MapT::MatrixType >::VectorType * capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::getCoefficientsAtCenter

inlineinherited

◆ getCoeffNorm() [1/2]

BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::ScalarType capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::getCoeffNorm	(	size_type	i,
		size_type	degree
	)		const

virtualinherited

◆ getCoeffNorm() [2/2]

template<typename MapType , typename StepControlPolicy , typename EnclosurePolicy , typename CurveType >

OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::ScalarType capd::dynsys::OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::getCoeffNorm	(	size_type	r,
		size_type	degree
	)		const

◆ getCurrentTime()

const ScalarType& capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::getCurrentTime

inlineprotectedinherited

◆ getCurve()

const BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::SolutionCurve & capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::getCurve

inherited

◆ getEffectiveTolerance()

static TolScalarType capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , MapT::ScalarType >::getEffectiveTolerance	(	Solver &	solver,
		const SetType &	s
	)

inlinestaticinherited

◆ getImplicitCurve()

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

const CurveT& capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::getImplicitCurve ( ) const

inline

◆ getLeftDomain()

ParametricCurve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > ::MatrixType , typename capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > ::MatrixType ::RowVectorType >::Real capd::diffAlgebra::ParametricCurve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > ::MatrixType , typename capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > ::MatrixType ::RowVectorType >::getLeftDomain

inlinevirtualinherited

◆ getMask() [1/2]

const bool* capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::getMask

inlineprotectedinherited

◆ getMask() [2/2]

bool capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::getMask ( size_type j ) const

inlineprotectedinherited

◆ getMatrixCoefficients() [1/2]

MatrixType* capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::getMatrixCoefficients ( )

inherited

◆ getMatrixCoefficients() [2/2]

typename MapT::MatrixType * capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::getMatrixCoefficients

inlineinherited

◆ getMatrixRemainderCoefficients() [1/2]

MatrixType* capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::getMatrixRemainderCoefficients ( )

inherited

◆ getMatrixRemainderCoefficients() [2/2]

typename MapT::MatrixType * capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::getMatrixRemainderCoefficients

inlineinherited

◆ getMaxStep()

MapT::ScalarType capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , MapT::ScalarType >::getMaxStep ( ) const

inlineinherited

◆ getOrder()

BasicCurve< typename MapT::MatrixType >::size_type capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::getOrder

inlineinherited

Returns the order of Taylor interpolation.

◆ getRelativeTolerance()

TolScalarType capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , MapT::ScalarType >::getRelativeTolerance ( ) const

inlineinherited

◆ getRemainderCoefficients() [1/2]

VectorType* capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::getRemainderCoefficients ( )

inherited

◆ getRemainderCoefficients() [2/2]

BasicCurve< typename MapT::MatrixType >::VectorType * capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::getRemainderCoefficients

inlineinherited

◆ getRightDomain()

ParametricCurve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > ::MatrixType , typename capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > ::MatrixType ::RowVectorType >::Real capd::diffAlgebra::ParametricCurve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > ::MatrixType , typename capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > ::MatrixType ::RowVectorType >::getRightDomain

inlinevirtualinherited

◆ getStep() [1/3]

BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::ScalarType capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::getStep

inlineinherited

Returns the time step made in the last call to this solver.

◆ getStep() [2/3]

virtual ScalarType capd::dynsys::DynSys< MapT::MatrixType >::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< MapT, capd::dynsys::ILastTermsStepControl, HighOrderEnclosure, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >.

◆ getStep() [3/3]

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

ScalarType capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::getStep ( ) const

inline

◆ getStepControl()

const StepControlType& capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , MapT::ScalarType >::getStepControl ( ) const

inlineinherited

◆ getVectorField() [1/2]

VectorFieldType& capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::getVectorField

inherited

◆ getVectorField() [2/2]

MapType & capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::getVectorField

inlineinherited

Returns vector field.

◆ hessian()

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

inlinevirtualinherited

◆ initRemainderCoefficients()

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

void capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::initRemainderCoefficients	(	ScalarType	t,
		const VectorType &	x,
		unsigned	degree
	)

inline

◆ isStepChangeAllowed()

bool capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , MapT::ScalarType >::isStepChangeAllowed ( ) const

inlineinherited

◆ JacPhi()

template<typename MapType , typename StepControlPolicy , typename EnclosurePolicy , typename CurveType >

OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::MatrixType capd::dynsys::OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::JacPhi	(	const ScalarType &	t,
		const VectorType &	iv
	)

virtual

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

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

◆ jet()

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

inlinevirtualinherited

◆ 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()

void capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , MapT::ScalarType >::onOffStepControl ( bool _onOffStepControl )

inlineinherited

◆ operator()() [1/10]

Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > , capd::TypeTraits<typename capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > ::ScalarType>::isInterval >::VectorType capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > , capd::TypeTraits<typename capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > ::ScalarType>::isInterval >::operator() ( const ScalarType & h ) const

virtualinherited

Implements capd::diffAlgebra::ParametricCurve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > ::MatrixType >.

◆ operator()() [2/10]

void capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< 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 C1JetMove is used meaning that this solver can integrate C^0 and C^1 jets only.

◆ operator()() [3/10]

BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< 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()() [4/10]

BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::operator()	(	ScalarType &	t,
		const VectorType &	u
	)

inlineinherited

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

◆ operator()() [5/10]

BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< 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()() [6/10]

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

template<typename SetType >

void capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, 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 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<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

template<typename SetType >

void capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::operator()	(	SetType &	set,
		SetType &	result
	)

inline

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

Parameters

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

◆ operator()() [8/10]

BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::operator() ( VectorType v )

inherited

Computes image of vector v after one time step.

◆ operator()() [9/10]

BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< 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()() [10/10]

BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< 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 StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

void capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::operator= ( const OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT > & )

inlineprotected

◆ operator[]()

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

inlinevirtualinherited

Implements capd::diffAlgebra::ParametricCurve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > ::MatrixType >.

◆ Phi()

template<typename MapType , typename StepControlPolicy , typename EnclosurePolicy , typename CurveType >

OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::VectorType capd::dynsys::OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::Phi	(	const ScalarType &	t,
		const VectorType &	iv
	)

virtual

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

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

◆ Remainder()

template<typename MapType , typename StepControlPolicy , typename EnclosurePolicy , typename CurveType >

OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::VectorType capd::dynsys::OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::Remainder	(	const ScalarType &	t,
		const VectorType &	iv,
		VectorType &	out_enc
	)

virtual

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.

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

◆ remainderCoefficient() [1/4]

BasicCurve< typename MapT::MatrixType >::ScalarType & capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::remainderCoefficient	(	size_type	i,
		size_type	j
	)

inlineinherited

◆ remainderCoefficient() [2/4]

const BasicCurve< typename MapT::MatrixType >::ScalarType & capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::remainderCoefficient	(	size_type	i,
		size_type	j
	)		const

inlineinherited

◆ remainderCoefficient() [3/4]

BasicCurve< typename MapT::MatrixType >::ScalarType & capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::remainderCoefficient	(	size_type	i,
		size_type	j,
		size_type	k
	)

inlineinherited

◆ remainderCoefficient() [4/4]

const BasicCurve< typename MapT::MatrixType >::ScalarType & capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::remainderCoefficient	(	size_type	i,
		size_type	j,
		size_type	k
	)		const

inlineinherited

◆ resetMask()

void capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< 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() [1/2]

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

void capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::saveCurrentSet ( const capd::diffAlgebra::TimeRange< ScalarType > & )

inlineprotected

◆ saveCurrentSet() [2/2]

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

void capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::saveCurrentSet ( const capd::dynset::C1Set< MatrixType > & set )

inlineprotected

◆ setAbsoluteTolerance()

void capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , MapT::ScalarType >::setAbsoluteTolerance ( TolScalarType tol )

inlineinherited

◆ setCurrentTime()

void capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::setCurrentTime ( const ScalarType & a_time ) const

inlineprotectedinherited

◆ setDomain()

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

inlinevirtualinherited

◆ setInitHessian()

void capd::diffAlgebra::CurveInterface< typename MapT::MatrixType >::setInitHessian ( const HessianType & )

inlineinherited

◆ setInitJet()

void capd::diffAlgebra::CurveInterface< typename MapT::MatrixType >::setInitJet ( const JetType & )

inlineinherited

◆ setInitMatrix()

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

inlineinherited

◆ setMask()

void capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< 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()

void capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , MapT::ScalarType >::setMaxStep ( Scalar maxStep )

inlineinherited

◆ setOrder() [1/2]

template<typename MapType , typename StepControlPolicy , typename EnclosurePolicy , typename CurveT >

void capd::dynsys::OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveT >::setOrder ( size_type order )

Sets the order of the Taylor method.

◆ setOrder() [2/2]

void capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::setOrder ( size_type order )

virtualinherited

Sets the order of the Taylor method.

Reimplemented from capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >.

◆ setRelativeTolerance()

void capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , MapT::ScalarType >::setRelativeTolerance ( TolScalarType tol )

inlineinherited

◆ setStep()

void capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::setStep ( const ScalarType & newStep )

inlineinherited

Sets fixed time step and turns off step control.

◆ setStepControl()

void capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , MapT::ScalarType >::setStepControl ( const StepControlType & stepControl )

inlineinherited

◆ sumTaylorSeries() [1/2]

void capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::sumTaylorSeries	(	VectorType &	v,
		MatrixType &	der,
		VectorType *	coeff,
		MatrixType *	matrixCoeff,
		size_type	order
	)

protectedinherited

◆ sumTaylorSeries() [2/2]

void capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::sumTaylorSeries	(	VectorType &	v,
		VectorType *	coeff,
		size_type	order
	)

inlineprotectedinherited

◆ timeDerivative()

Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > , capd::TypeTraits<typename capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > ::ScalarType>::isInterval >::VectorType capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > , capd::TypeTraits<typename capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > ::ScalarType>::isInterval >::timeDerivative ( const ScalarType & h ) const

inherited

◆ turnOffStepControl()

void capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , MapT::ScalarType >::turnOffStepControl ( )

inlineinherited

◆ turnOnStepControl()

void capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , MapT::ScalarType >::turnOnStepControl ( )

inlineinherited

Member Data Documentation

◆ implicitCurve

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

CurveT capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::implicitCurve

protected

an extra storage for Taylor coefficients used in implicit HO-method

◆ m_absoluteTolerance

TolScalarType capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , MapT::ScalarType >::m_absoluteTolerance

protectedinherited

◆ m_allocatedOrder

size_type capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::m_allocatedOrder

protectedinherited

◆ m_coefficients

VectorType* capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::m_coefficients

protectedinherited

◆ m_coefficientsAtCenter

VectorType* capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::m_coefficientsAtCenter

protectedinherited

◆ m_dimension

size_type capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::m_dimension

protectedinherited

◆ m_fixedTimeStep

ScalarType capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::m_fixedTimeStep

protectedinherited

◆ m_left

Real capd::diffAlgebra::ParametricCurve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > ::MatrixType , typename capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > ::MatrixType ::RowVectorType >::m_left

protectedinherited

◆ m_matrixCoefficients

MatrixType* capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::m_matrixCoefficients

protectedinherited

◆ m_matrixRemainderCoefficients

MatrixType* capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::m_matrixRemainderCoefficients

protectedinherited

◆ m_maxStep

MapT::ScalarType capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , MapT::ScalarType >::m_maxStep

protectedinherited

◆ m_onOffStepControl

bool capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , MapT::ScalarType >::m_onOffStepControl

protectedinherited

◆ m_order

size_type capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::m_order

protectedinherited

◆ m_relativeTolerance

TolScalarType capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , MapT::ScalarType >::m_relativeTolerance

protectedinherited

◆ m_remainderCoefficients

VectorType* capd::diffAlgebra::BasicCurve< typename MapT::MatrixType >::m_remainderCoefficients

protectedinherited

◆ m_right

Real capd::diffAlgebra::ParametricCurve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > ::MatrixType , typename capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > ::MatrixType ::RowVectorType >::m_right

protectedinherited

domain

◆ m_step

ScalarType capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::m_step

protectedinherited

◆ m_stepControl

StepControlType capd::dynsys::StepControlInterface< capd::dynsys::ILastTermsStepControl , MapT::ScalarType >::m_stepControl

protectedinherited

◆ m_vField

VectorFieldType* capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::m_vField

protectedinherited

we do not allow copying of objects

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Member Typedef Documentation

◆ BaseTaylor

◆ C1TimeJetType

◆ const_iterator

◆ difference_type

◆ FunctionType

◆ HessianType

◆ iterator

◆ JetType

◆ MatrixType

◆ Multiindex

◆ Multipointer

◆ NormType

◆ Real

◆ ScalarType

◆ size_type

◆ SolutionCurve

◆ StepControlPolicy

◆ StepControlType

◆ VectorFieldType

◆ VectorType

Constructor & Destructor Documentation

◆ OdeSolver() [1/2]

◆ OdeSolver() [2/2]

Member Function Documentation

◆ addMultiindexToMask()

◆ adjustTimeStep()

◆ allocate()

◆ beginCenterCoefficients() [1/2]

◆ beginCenterCoefficients() [2/2]

◆ beginCoefficients() [1/2]

◆ beginCoefficients() [2/2]

◆ beginMatrixCoefficients() [1/2]

◆ beginMatrixCoefficients() [2/2]

◆ beginMatrixRemainderCoefficients() [1/2]

◆ beginMatrixRemainderCoefficients() [2/2]

◆ beginRemainderCoefficients() [1/2]

◆ beginRemainderCoefficients() [2/2]

◆ centerCoefficient() [1/2]

◆ centerCoefficient() [2/2]

◆ clearCoefficients()

◆ coefficient() [1/4]

◆ coefficient() [2/4]

◆ coefficient() [3/4]

◆ coefficient() [4/4]

◆ computeCoefficients() [1/4]

◆ computeCoefficients() [2/4]

◆ computeCoefficients() [3/4]

◆ computeCoefficients() [4/4]

◆ computeCoefficientsAtCenter() [1/2]

◆ computeCoefficientsAtCenter() [2/2]

◆ computeImplicitCoefficients()

◆ computeRemainder() [1/2]

◆ computeRemainder() [2/2]

◆ computeRemainderCoefficients() [1/4]

◆ computeRemainderCoefficients() [2/4]

◆ computeRemainderCoefficients() [3/4]

◆ computeRemainderCoefficients() [4/4]

◆ computeTaylorCoefficients()

◆ computeTimeStep() [1/2]

◆ computeTimeStep() [2/2]

◆ copyData()

◆ deallocate()

◆ derivative()

◆ dimension()

◆ domainErrorMessage()

◆ encloseC0Map() [1/2]

◆ encloseC0Map() [2/2]

◆ encloseC1Map() [1/2]

◆ encloseC1Map() [2/2]

◆ enclosure()

◆ endCenterCoefficients() [1/2]

◆ endCenterCoefficients() [2/2]

◆ endCoefficients() [1/2]

◆ endCoefficients() [2/2]