#include <capd/dynsys/C2OdeSolver.h>

Public Types
typedef EnclosurePolicyT	EnclosurePolicy

typedef MapT	VectorFieldType

typedef StepControlPolicyT	StepControlPolicy

typedef MapT::FunctionType	FunctionType

typedef VectorFieldType::MatrixType	MatrixType

typedef MatrixType::RowVectorType	VectorType

typedef MatrixType::ScalarType	ScalarType

typedef VectorFieldType::HessianType	HessianType

typedef BasicC2OdeSolver< MapT, StepControlPolicy, CurveT >	BaseC2Taylor

typedef OdeSolver< MapT, StepControlPolicy, EnclosurePolicy, CurveT >	BaseTaylor

typedef CurveT	SolutionCurve

typedef MatrixType::size_type	size_type

typedef diffAlgebra::C2TimeJet< MatrixType >	C2TimeJetType

typedef diffAlgebra::C1TimeJet< MatrixType >	C1TimeJetType

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

typedef StepControlT	StepControlType

typedef VectorFieldType::JetType	JetType

typedef JetType::Multipointer	Multipointer

typedef JetType::Multiindex	Multiindex

typedef TypeTraits< ScalarType >::Real	Real

typedef __difference_type	difference_type

typedef VectorType::iterator	iterator

typedef VectorType::const_iterator	const_iterator

typedef capd::dynsys::ILastTermsStepControl	StepControlType

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

Public Member Functions
	C2OdeSolver (VectorFieldType &vectorField, size_type order)

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)

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

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

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

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

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...

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 C2SetMove 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)
	Computes image of the set (in set's representation) and stores it in the result set. More...

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	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)

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 fixed time step and turns off step control. More...

size_type	dimension () const

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)

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...

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)

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

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...

template<typename JetT >
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

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)

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

const capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > &	getImplicitCurve () const

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

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...

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

size_type	dimension () const

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

template<class Iterator >
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

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...

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 C2JetMove is used meaning that this solver can integrate C^0, C^1 and C^2 jets only. More...

const SolutionCurve &	getCurve ()

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

void	setCurrentTime (const ScalarType &a_time) const

const ScalarType &	getCurrentTime () const

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

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

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

void	operator= (const C2OdeSolver &)

	C2OdeSolver (const C2OdeSolver &t)

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

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

void	computeTimeStep (VectorType &v)

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

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

void	setCurrentTime (const ScalarType &a_time) const

const ScalarType &	getCurrentTime () const

const bool *	getMask () const

bool	getMask (size_type j) const

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)

bool	getMask (size_type j, size_type c) const

const bool *	getMask () const

void	sumTaylorSeries (VectorType &v, MatrixType &der, HessianType &hessian, VectorType coeff, MatrixType matrixCoeff, HessianType *hessianCoeff, size_type order)

Protected Attributes
capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > >	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...

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

ScalarType	m_step

Member Typedef Documentation

◆ BaseC2Taylor

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

typedef BasicC2OdeSolver<MapT,StepControlPolicy,CurveT> capd::dynsys::C2OdeSolver< MapT, StepControlPolicyT, EnclosurePolicyT, CurveT >::BaseC2Taylor

◆ BaseTaylor

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

typedef OdeSolver<MapT,StepControlPolicy,EnclosurePolicy,CurveT> capd::dynsys::C2OdeSolver< MapT, StepControlPolicyT, EnclosurePolicyT, CurveT >::BaseTaylor

◆ C1TimeJetType

typedef diffAlgebra::C1TimeJet<MatrixType> capd::dynsys::OdeSolver< MapT, capd::dynsys::ILastTermsStepControl , HighOrderEnclosure , capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::C1TimeJetType

inherited

◆ C2TimeJetType

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

typedef diffAlgebra::C2TimeJet<MatrixType> capd::dynsys::C2OdeSolver< MapT, StepControlPolicyT, EnclosurePolicyT, CurveT >::C2TimeJetType

◆ const_iterator

template<class MatrixT >

typedef VectorType::const_iterator capd::diffAlgebra::BasicCurve< MatrixT >::const_iterator

inherited

◆ difference_type

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

inherited

◆ EnclosurePolicy

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

typedef EnclosurePolicyT capd::dynsys::C2OdeSolver< MapT, StepControlPolicyT, EnclosurePolicyT, CurveT >::EnclosurePolicy

◆ FunctionType

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

typedef MapT::FunctionType capd::dynsys::C2OdeSolver< MapT, StepControlPolicyT, EnclosurePolicyT, CurveT >::FunctionType

◆ HessianType

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

typedef VectorFieldType::HessianType capd::dynsys::C2OdeSolver< MapT, StepControlPolicyT, EnclosurePolicyT, CurveT >::HessianType

◆ iterator

template<class MatrixT >

typedef VectorType::iterator capd::diffAlgebra::BasicCurve< MatrixT >::iterator

inherited

◆ JetType

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

typedef VectorFieldType::JetType capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::JetType

inherited

◆ MatrixType

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

typedef VectorFieldType::MatrixType capd::dynsys::C2OdeSolver< MapT, StepControlPolicyT, EnclosurePolicyT, CurveT >::MatrixType

◆ Multiindex

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

typedef JetType::Multiindex capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::Multiindex

inherited

◆ Multipointer

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

typedef JetType::Multipointer capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::Multipointer

inherited

◆ NormType [1/2]

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

inherited

◆ NormType [2/2]

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 BaseCurveT::ScalarType>::isInterval >::Real

inherited

◆ ScalarType

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

typedef MatrixType::ScalarType capd::dynsys::C2OdeSolver< MapT, StepControlPolicyT, EnclosurePolicyT, CurveT >::ScalarType

◆ size_type

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

typedef MatrixType::size_type capd::dynsys::C2OdeSolver< MapT, StepControlPolicyT, EnclosurePolicyT, CurveT >::size_type

◆ SolutionCurve

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

typedef CurveT capd::dynsys::C2OdeSolver< MapT, StepControlPolicyT, EnclosurePolicyT, CurveT >::SolutionCurve

◆ StepControlPolicy

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

typedef StepControlPolicyT capd::dynsys::C2OdeSolver< MapT, StepControlPolicyT, EnclosurePolicyT, CurveT >::StepControlPolicy

◆ StepControlType [1/2]

typedef capd::dynsys::ILastTermsStepControl capd::dynsys::BasicC2OdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::StepControlType

inherited

◆ StepControlType [2/2]

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

typedef StepControlT capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::StepControlType

inherited

◆ VectorFieldType

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

typedef MapT capd::dynsys::C2OdeSolver< MapT, StepControlPolicyT, EnclosurePolicyT, CurveT >::VectorFieldType

◆ VectorType

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

typedef MatrixType::RowVectorType capd::dynsys::C2OdeSolver< MapT, StepControlPolicyT, EnclosurePolicyT, CurveT >::VectorType

Constructor & Destructor Documentation

◆ C2OdeSolver()

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

capd::dynsys::C2OdeSolver< MapT, StepControlPolicyT, EnclosurePolicyT, CurveT >::C2OdeSolver ( const C2OdeSolver< MapT, StepControlPolicyT, EnclosurePolicyT, CurveT > & t )

inlineprotected

Member Function Documentation

◆ addMultiindexToMask()

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

void capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::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.

◆ beginCenterCoefficients() [1/2]

template<class MatrixT >

iterator capd::diffAlgebra::BasicCurve< MatrixT >::beginCenterCoefficients ( size_type j )

inlineinherited

◆ beginCenterCoefficients() [2/2]

template<class MatrixT >

const_iterator capd::diffAlgebra::BasicCurve< MatrixT >::beginCenterCoefficients ( size_type j ) const

inlineinherited

◆ beginCoefficients() [1/2]

template<class MatrixT >

iterator capd::diffAlgebra::BasicCurve< MatrixT >::beginCoefficients ( size_type j )

inlineinherited

◆ beginCoefficients() [2/2]

template<class MatrixT >

const_iterator capd::diffAlgebra::BasicCurve< MatrixT >::beginCoefficients ( size_type j ) const

inlineinherited

◆ beginMatrixCoefficients() [1/2]

template<class MatrixT >

iterator capd::diffAlgebra::BasicCurve< MatrixT >::beginMatrixCoefficients ( size_type j )

inlineinherited

◆ beginMatrixCoefficients() [2/2]

template<class MatrixT >

const_iterator capd::diffAlgebra::BasicCurve< MatrixT >::beginMatrixCoefficients ( size_type j ) const

inlineinherited

◆ beginMatrixRemainderCoefficients() [1/2]

template<class MatrixT >

iterator capd::diffAlgebra::BasicCurve< MatrixT >::beginMatrixRemainderCoefficients ( size_type j )

inlineinherited

◆ beginMatrixRemainderCoefficients() [2/2]

template<class MatrixT >

const_iterator capd::diffAlgebra::BasicCurve< MatrixT >::beginMatrixRemainderCoefficients ( size_type j ) const

inlineinherited

◆ beginRemainderCoefficients() [1/2]

template<class MatrixT >

iterator capd::diffAlgebra::BasicCurve< MatrixT >::beginRemainderCoefficients ( size_type j )

inlineinherited

◆ beginRemainderCoefficients() [2/2]

template<class MatrixT >

const_iterator capd::diffAlgebra::BasicCurve< MatrixT >::beginRemainderCoefficients ( size_type j ) const

inlineinherited

◆ computeImplicitCoefficients()

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

inlineinherited

◆ computeRemainder() [1/4]

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

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

inline

◆ computeRemainder() [2/4]

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

inlinevirtualinherited

◆ computeRemainder() [3/4]

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

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

inline

◆ computeRemainder() [4/4]

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

inlinevirtualinherited

◆ computeRemainderCoefficients() [1/8]

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

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

inline

◆ computeRemainderCoefficients() [2/8]

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

inlineinherited

◆ computeRemainderCoefficients() [3/8]

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

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

inline

◆ computeRemainderCoefficients() [4/8]

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

inlineinherited

◆ computeRemainderCoefficients() [5/8]

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

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

inline

◆ computeRemainderCoefficients() [6/8]

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

inlineinherited

◆ computeRemainderCoefficients() [7/8]

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

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

inline

◆ computeRemainderCoefficients() [8/8]

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

inlineinherited

◆ computeTaylorCoefficients()

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

inlineinherited

◆ computeTimeStep()

void capd::dynsys::OdeSolver< MapT, capd::dynsys::ILastTermsStepControl , HighOrderEnclosure , capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::computeTimeStep	(	const ScalarType &	t,
		const VectorType &	x
	)

inlineinherited

◆ derivative()

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

virtualinherited

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

◆ dimension() [1/2]

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

size_type capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::dimension ( ) const

inlineinherited

◆ dimension() [2/2]

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

size_type capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::dimension

inline

◆ domainErrorMessage()

template<class MatrixT >

std::runtime_error capd::diffAlgebra::CurveInterface< MatrixT >::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]

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

inherited

◆ 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,
		MapT::MatrixType &	o_jacPhi,
		MapT::MatrixType &	o_jacRem,
		MapT::MatrixType &	o_jacEnc
	)

pure virtualinherited

◆ encloseC1Map() [2/2]

void capd::dynsys::OdeSolver< MapType, StepControlPolicy, HighOrderEnclosure , 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
	)

inherited

◆ 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()

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

virtualinherited

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

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

◆ endCenterCoefficients() [1/2]

template<class MatrixT >

iterator capd::diffAlgebra::BasicCurve< MatrixT >::endCenterCoefficients ( size_type j )

inlineinherited

◆ endCenterCoefficients() [2/2]

template<class MatrixT >

const_iterator capd::diffAlgebra::BasicCurve< MatrixT >::endCenterCoefficients ( size_type j ) const

inlineinherited

◆ endCoefficients() [1/2]

template<class MatrixT >

iterator capd::diffAlgebra::BasicCurve< MatrixT >::endCoefficients ( size_type j )

inlineinherited

◆ endCoefficients() [2/2]

template<class MatrixT >

const_iterator capd::diffAlgebra::BasicCurve< MatrixT >::endCoefficients ( size_type j ) const

inlineinherited

◆ endMatrixCoefficients() [1/2]

template<class MatrixT >

iterator capd::diffAlgebra::BasicCurve< MatrixT >::endMatrixCoefficients ( size_type j )

inlineinherited

◆ endMatrixCoefficients() [2/2]

template<class MatrixT >

const_iterator capd::diffAlgebra::BasicCurve< MatrixT >::endMatrixCoefficients ( size_type j ) const

inlineinherited

◆ endMatrixRemainderCoefficients() [1/2]

template<class MatrixT >

iterator capd::diffAlgebra::BasicCurve< MatrixT >::endMatrixRemainderCoefficients ( size_type j )

inlineinherited

◆ endMatrixRemainderCoefficients() [2/2]

template<class MatrixT >

const_iterator capd::diffAlgebra::BasicCurve< MatrixT >::endMatrixRemainderCoefficients ( size_type j ) const

inlineinherited

◆ endRemainderCoefficients() [1/2]

template<class MatrixT >

iterator capd::diffAlgebra::BasicCurve< MatrixT >::endRemainderCoefficients ( size_type j )

inlineinherited

◆ endRemainderCoefficients() [2/2]

template<class MatrixT >

const_iterator capd::diffAlgebra::BasicCurve< MatrixT >::endRemainderCoefficients ( size_type j ) const

inlineinherited

◆ eval()

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

inlinevirtualinherited

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

◆ getAbsoluteTolerance()

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

inlineinherited

◆ getCoeffNorm()

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

virtualinherited

Reimplemented from capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >.

◆ getCurrentTime() [1/2]

const ScalarType& capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::getCurrentTime

inlineinherited

◆ getCurrentTime() [2/2]

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

const ScalarType& capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::getCurrentTime ( ) const

inlineprotectedinherited

◆ getCurve()

const BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::SolutionCurve & capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::getCurve

inherited

◆ getEffectiveTolerance()

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

inlinestaticinherited

◆ getImplicitCurve()

const capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > & capd::dynsys::OdeSolver< MapT, capd::dynsys::ILastTermsStepControl , HighOrderEnclosure , capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::getImplicitCurve ( ) const

inlineinherited

◆ getLeftDomain()

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

inlinevirtualinherited

◆ getMask() [1/4]

const bool* capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::getMask

inlineprotectedinherited

◆ getMask() [2/4]

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

const bool* capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::getMask ( ) const

inlineprotectedinherited

◆ getMask() [3/4]

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

bool capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::getMask ( size_type j ) const

inlineprotectedinherited

◆ getMask() [4/4]

bool capd::dynsys::BasicC2OdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::getMask	(	size_type	j,
		size_type	c
	)		const

inlineprotectedinherited

◆ getMaxStep()

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

inlineinherited

◆ getRelativeTolerance()

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

inlineinherited

◆ getRightDomain()

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

inlinevirtualinherited

◆ getStep() [1/2]

BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::ScalarType capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::getStep

inlineinherited

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

◆ getStep() [2/2]

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

ScalarType capd::dynsys::C2OdeSolver< MapT, StepControlPolicyT, 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()

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

inlineinherited

◆ getVectorField() [1/2]

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

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

inline

◆ getVectorField() [2/2]

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

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

inline

Returns vector field.

◆ hessian()

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

inlinevirtualinherited

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

◆ initRemainderCoefficients()

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

void capd::dynsys::C2OdeSolver< MapT, StepControlPolicyT, EnclosurePolicyT, CurveT >::initRemainderCoefficients	(	ScalarType	t,
		const VectorType &	x,
		unsigned	degree
	)

inline

◆ isStepChangeAllowed()

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

inlineinherited

◆ JacPhi()

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

virtualinherited

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< BaseCurveT::MatrixType , typename MatrixT::RowVectorType >::jet ( const ScalarType & ) const

inlinevirtualinherited

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

◆ 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::DLastTermsStepControl , MapT::ScalarType >::onOffStepControl ( bool _onOffStepControl )

inlineinherited

◆ operator()() [1/9]

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

virtualinherited

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

◆ operator()() [2/9]

void capd::dynsys::BasicC2OdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< 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 C2JetMove is used meaning that this solver can integrate C^0, C^1 and C^2 jets only.

◆ operator()() [3/9]

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

template<typename JetT >

void capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::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()() [4/9]

BasicC2OdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicC2OdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< 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()() [5/9]

BasicC2OdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicC2OdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< 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()() [6/9]

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

template<typename SetType >

void capd::dynsys::C2OdeSolver< MapT, StepControlPolicyT, 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 C2SetMove 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()() [7/9]

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

template<typename SetType >

void capd::dynsys::C2OdeSolver< MapT, StepControlPolicyT, EnclosurePolicyT, 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, C^1 or C^2 set representing initial conditions
[out]	result	on return contains image of the set

◆ operator()() [8/9]

BasicC2OdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicC2OdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::operator()	(	VectorType	x,
		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()() [9/9]

BasicC2OdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicC2OdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< 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=()

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

void capd::dynsys::C2OdeSolver< MapT, StepControlPolicyT, EnclosurePolicyT, CurveT >::operator= ( const C2OdeSolver< MapT, StepControlPolicyT, EnclosurePolicyT, CurveT > & )

inlineprotected

◆ operator[]()

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

inlinevirtualinherited

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

◆ Phi()

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

virtualinherited

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

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

◆ Remainder()

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

virtualinherited

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

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

◆ resetMask()

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

void capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::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() [1/5]

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

void capd::dynsys::C2OdeSolver< MapT, StepControlPolicyT, EnclosurePolicyT, CurveT >::saveCurrentSet ( capd::dynset::C2Set< MatrixType > & set )

inlineprotected

◆ saveCurrentSet() [2/5]

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

void capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::saveCurrentSet

inlineprotected

◆ saveCurrentSet() [3/5]

void capd::dynsys::OdeSolver< MapT, capd::dynsys::ILastTermsStepControl , HighOrderEnclosure , capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::saveCurrentSet ( const capd::diffAlgebra::TimeRange< ScalarType > & )

inlineprotectedinherited

◆ saveCurrentSet() [4/5]

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

void capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::saveCurrentSet

inlineprotected

◆ saveCurrentSet() [5/5]

void capd::dynsys::OdeSolver< MapT, capd::dynsys::ILastTermsStepControl , HighOrderEnclosure , capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::saveCurrentSet ( const capd::dynset::C1Set< MatrixType > & set )

inlineprotectedinherited

◆ setAbsoluteTolerance()

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

inlineinherited

◆ setCurrentTime() [1/2]

void capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::setCurrentTime

inlineinherited

◆ setCurrentTime() [2/2]

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

void capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::setCurrentTime ( const ScalarType & a_time ) const

inlineprotectedinherited

◆ setDomain()

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

inlinevirtualinherited

◆ setInitHessian()

template<class MatrixT >

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

inlineinherited

◆ setInitJet()

template<class MatrixT >

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

inlineinherited

◆ setInitMatrix()

template<class MatrixT >

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

inlineinherited

◆ setMask()

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

template<class Iterator >

void capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::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::DLastTermsStepControl , MapT::ScalarType >::setMaxStep ( Scalar maxStep )

inlineinherited

◆ setOrder() [1/2]

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

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

Sets the order of the Taylor method.

◆ setOrder() [2/2]

void capd::dynsys::OdeSolver< MapType, StepControlPolicy, HighOrderEnclosure , capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::setOrder ( size_type order )

virtualinherited

Sets the order of the Taylor method.

Reimplemented from capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >.

◆ setRelativeTolerance()

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

inlineinherited

◆ setStep()

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicyT = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

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

inline

Sets fixed time step and turns off step control.

◆ setStepControl()

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

inlineinherited

◆ sumTaylorSeries()

void capd::dynsys::BasicC2OdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::sumTaylorSeries	(	VectorType &	v,
		MatrixType &	der,
		HessianType &	hessian,
		VectorType *	coeff,
		MatrixType *	matrixCoeff,
		HessianType *	hessianCoeff,
		size_type	order
	)

protectedinherited

◆ timeDerivative()

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

inherited

◆ turnOffStepControl()

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

inlineinherited

◆ turnOnStepControl()

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

inlineinherited

Member Data Documentation

◆ implicitCurve

capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > capd::dynsys::OdeSolver< MapT, capd::dynsys::ILastTermsStepControl , HighOrderEnclosure , capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::implicitCurve

protectedinherited

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

◆ m_absoluteTolerance

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

protectedinherited

◆ m_allocatedOrder

template<class MatrixT >

size_type capd::diffAlgebra::BasicCurve< MatrixT >::m_allocatedOrder

protectedinherited

◆ m_coefficients

template<class MatrixT >

VectorType* capd::diffAlgebra::BasicCurve< MatrixT >::m_coefficients

protectedinherited

◆ m_coefficientsAtCenter

template<class MatrixT >

VectorType* capd::diffAlgebra::BasicCurve< MatrixT >::m_coefficientsAtCenter

protectedinherited

◆ m_dimension

template<class MatrixT >

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

protectedinherited

◆ m_fixedTimeStep

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

ScalarType capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::m_fixedTimeStep

protectedinherited

◆ m_left

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

protectedinherited

◆ m_matrixCoefficients

template<class MatrixT >

MatrixType* capd::diffAlgebra::BasicCurve< MatrixT >::m_matrixCoefficients

protectedinherited

◆ m_matrixRemainderCoefficients

template<class MatrixT >

MatrixType* capd::diffAlgebra::BasicCurve< MatrixT >::m_matrixRemainderCoefficients

protectedinherited

◆ m_maxStep

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

protectedinherited

◆ m_onOffStepControl

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

protectedinherited

◆ m_order

template<class MatrixT >

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

protectedinherited

◆ m_relativeTolerance

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

protectedinherited

◆ m_remainderCoefficients

template<class MatrixT >

VectorType* capd::diffAlgebra::BasicCurve< MatrixT >::m_remainderCoefficients

protectedinherited

◆ m_right

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

protectedinherited

domain

◆ m_step [1/2]

ScalarType capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::m_step

protectedinherited

◆ m_step [2/2]

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

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

protectedinherited

◆ m_stepControl

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

protectedinherited

◆ m_vField [1/2]

VectorFieldType* capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::m_vField

protectedinherited

we do not allow copying of objects

◆ m_vField [2/2]

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

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

protectedinherited

we do not allow copying of objects

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

capd/dynsys/C2OdeSolver.h
capd/dynsys/C2OdeSolver.hpp

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Member Typedef Documentation

◆ BaseC2Taylor

◆ BaseTaylor

◆ C1TimeJetType

◆ C2TimeJetType

◆ const_iterator

◆ difference_type

◆ EnclosurePolicy

◆ FunctionType

◆ HessianType

◆ iterator

◆ JetType

◆ MatrixType

◆ Multiindex

◆ Multipointer

◆ NormType [1/2]

◆ NormType [2/2]

◆ Real

◆ ScalarType

◆ size_type

◆ SolutionCurve

◆ StepControlPolicy

◆ StepControlType [1/2]

◆ StepControlType [2/2]

◆ VectorFieldType

◆ VectorType

Constructor & Destructor Documentation

◆ C2OdeSolver()

Member Function Documentation

◆ addMultiindexToMask()

◆ 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]

◆ computeImplicitCoefficients()

◆ computeRemainder() [1/4]

◆ computeRemainder() [2/4]

◆ computeRemainder() [3/4]

◆ computeRemainder() [4/4]

◆ computeRemainderCoefficients() [1/8]

◆ computeRemainderCoefficients() [2/8]

◆ computeRemainderCoefficients() [3/8]

◆ computeRemainderCoefficients() [4/8]

◆ computeRemainderCoefficients() [5/8]

◆ computeRemainderCoefficients() [6/8]

◆ computeRemainderCoefficients() [7/8]

◆ computeRemainderCoefficients() [8/8]

◆ computeTaylorCoefficients()

◆ computeTimeStep()

◆ derivative()

◆ dimension() [1/2]

◆ dimension() [2/2]

◆ domainErrorMessage()

◆ encloseC0Map() [1/2]

◆ encloseC0Map() [2/2]

◆ encloseC1Map() [1/2]

◆ encloseC1Map() [2/2]

◆ encloseC2Map()

◆ enclosure()

◆ endCenterCoefficients() [1/2]

◆ endCenterCoefficients() [2/2]

◆ endCoefficients() [1/2]

◆ endCoefficients() [2/2]

◆ endMatrixCoefficients() [1/2]

◆ endMatrixCoefficients() [2/2]

◆ endMatrixRemainderCoefficients() [1/2]

◆ endMatrixRemainderCoefficients() [2/2]

◆ endRemainderCoefficients() [1/2]

◆ endRemainderCoefficients() [2/2]