Dynsys

Files
file	dynsysLib.h
file	Linear2d.h
file	Linear3d.h
file	OdeNumTaylor.h
file	OdeNumTaylor.hpp
file	VLin3D.h
file	DynSys.h
file	MpStepControl.h
file	OdeSolver.h
file	OdeSolver.hpp
file	StepControl.h
file	DynSys.cpp

Classes
class	capd::dynsys::BasicC2OdeSolver< MapT, StepControlT, CurveT >
class	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >
class	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >
class	capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >
	MapT constraints: type definitions: More...
class	capd::dynsys::C1DynSys< MatrixType >
class	capd::dynsys::C2DynSys< MatrixT >
class	capd::dynsys::C2OdeSolver< MapT, StepControlPolicyT, EnclosurePolicyT, CurveT >
class	capd::dynsys::CnDynSys< MatrixT >
class	capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >
class	capd::dynsys::DiscreteDynSys< MapT >
	DiscreteDynSys is a proxy to convert any Map into discrete Dynamical System. More...
class	capd::dynsys::FlowballSet< MatrixType >
class	capd::dynsys::DynSys< MatrixT >
	Class dynsys is an abstract class representing a discrete dynamical system. More...
class	capd::dynsys::HOSolver< MatrixT >
class	capd::dynsys::DynSysMap< MapT >
	DynSysMap is a proxy to convert any Map into discrete Dynamical System. More...
class	capd::dynsys::FadFunction< VectorT >
class	capd::dynsys::FadMap< Scalar, D >
class	capd::dynsys::LorenzFadMap< Scalar, D >
	Sample implementation of FadMap. This class implements the vector field for the Lorenz system. Template parameters are: Scalar: double, interval, MpFloat, MpInterval, etc. D: in this case either 3 or 0. If D=3 then vectors and matrices are allocated on stack and the computations are much faster but we must know they dimension at compile time. This forces separate compilation of all the classes like vectors and matrices for this particular dimension. D=0 means that vectors and matrices are allocated on the storage and they can be of arbitrary dimension specified at runtime. More...
class	capd::dynsys::LorenzSection< Scalar, D >
class	capd::dynsys::FadOdeSolver< FadMapT, StepControlT >
class	capd::dynsys::FirstOrderEnclosure
class	capd::dynsys::HighOrderEnclosure
	This file defines class for computation of [C0-C2] rough enclosure to an ODE by high order Taylor method. More...
class	capd::dynsys::SolverException< VectorType >

Typedefs
typedef capd::dynsys::DynSys< IMatrix >	DynSys
typedef capd::dynsys::Ode< IMatrix >	Ode
typedef capd::dynsys::OdeNum< IMatrix >	OdeNum
typedef capd::dynsys::OdeNumTaylor< IMatrix >	OdeNumTaylor
typedef capd::dynsys::VLin3D< IMatrix >	VLin3D
typedef capd::dynsys::Linear2d< IMatrix >	linear2d
typedef capd::dynsys::Linear3d< IMatrix >	linear3d
typedef capd::dynsys::Solver< IMap >	Taylor
typedef capd::dynsys::C2Solver< IC2Map >	C2Taylor
typedef capd::dynsys::CnSolver< ICnMap >	CnTaylor
typedef capd::dynsys::SolverException< IVector >	TaylorException
typedef capd::dynsys::DynSys< IMatrixMD >	DynSysMD
typedef capd::dynsys::Ode< IMatrixMD >	OdeMD
typedef capd::dynsys::OdeNum< IMatrixMD >	OdeNumMD
typedef capd::dynsys::OdeNumTaylor< IMatrixMD >	OdeNumTaylorMD
typedef capd::dynsys::VLin3D< IMatrixMD >	VLin3DMD
typedef capd::dynsys::Linear2d< IMatrixMD >	linear2dMD
typedef capd::dynsys::Linear3d< IMatrixMD >	linear3dMD
typedef capd::dynsys::Solver< IMapMD >	TaylorMD
typedef capd::dynsys::C2Solver< IC2MapMD >	C2TaylorMD
typedef capd::dynsys::CnSolver< ICnMapMD >	CnTaylorMD
typedef capd::dynsys::SolverException< IVectorMD >	TaylorExceptionMD
typedef capd::dynsys::BasicSolver< DMap >	BasicTaylor
typedef capd::dynsys::BasicC2Solver< DC2Map >	BasicC2Taylor
typedef capd::dynsys::BasicCnSolver< DCnMap >	BasicCnTaylor
typedef capd::dynsys::BasicSolver< LDMap >	LDTaylor
typedef capd::dynsys::BasicC2Solver< LDC2Map >	LDC2Taylor
typedef capd::dynsys::BasicCnSolver< LDCnMap >	LDCnTaylor
typedef capd::dynsys::BasicSolver< DMapMD >	BasicTaylorMD
typedef capd::dynsys::BasicC2Solver< DC2MapMD >	BasicC2TaylorMD
typedef capd::dynsys::BasicCnSolver< DCnMapMD >	BasicCnTaylorMD
typedef capd::dynsys::BasicSolver< LDMapMD >	LDTaylorMD
typedef capd::dynsys::BasicC2Solver< LDC2MapMD >	LDC2TaylorMD
typedef capd::dynsys::BasicCnSolver< LDCnMapMD >	LDCnTaylorMD
typedef capd::dynsys::DynSys< MpIMatrix >	MpDynSys
typedef capd::dynsys::Ode< MpIMatrix >	MpOde
typedef capd::dynsys::OdeNum< MpIMatrix >	MpOdeNum
typedef capd::dynsys::OdeNumTaylor< MpIMatrix >	MpOdeNumTaylor
typedef capd::dynsys::VLin3D< MpIMatrix >	MpVLin3D
typedef capd::dynsys::Linear2d< MpIMatrix >	MpLinear2d
typedef capd::dynsys::Linear3d< MpIMatrix >	MpLinear3d
typedef capd::dynsys::Solver< MpIMap >	MpTaylor
typedef capd::dynsys::C2Solver< MpIC2Map >	MpC2Taylor
typedef capd::dynsys::CnSolver< MpICnMap >	MpCnTaylor
typedef capd::dynsys::SolverException< MpIVector >	MpTaylorException
typedef capd::dynsys::BasicSolver< MpMap >	MpBasicTaylor
typedef capd::dynsys::BasicC2Solver< MpC2Map >	MpBasicC2Taylor
typedef capd::dynsys::BasicCnSolver< MpCnMap >	MpBasicCnTaylor
typedef capd::dynsys::DynSys< MpIMatrixMD >	MpDynSysMD
typedef capd::dynsys::Ode< MpIMatrixMD >	MpOdeMD
typedef capd::dynsys::OdeNum< MpIMatrixMD >	MpOdeNumMD
typedef capd::dynsys::OdeNumTaylor< MpIMatrixMD >	MpOdeNumTaylorMD
typedef capd::dynsys::VLin3D< MpIMatrixMD >	MpVLin3DMD
typedef capd::dynsys::Linear2d< MpIMatrixMD >	MpLinear2dMD
typedef capd::dynsys::Linear3d< MpIMatrixMD >	MpLinear3dMD
typedef capd::dynsys::Solver< MpIMapMD >	MpTaylorMD
typedef capd::dynsys::C2Solver< MpIC2MapMD >	MpC2TaylorMD
typedef capd::dynsys::CnSolver< MpICnMapMD >	MpCnTaylorMD
typedef capd::dynsys::SolverException< MpIVectorMD >	MpTaylorExceptionMD
typedef capd::dynsys::BasicSolver< MpMapMD >	MpBasicTaylorMD
typedef capd::dynsys::BasicC2Solver< MpC2MapMD >	MpBasicC2TaylorMD
typedef capd::dynsys::BasicCnSolver< MpCnMapMD >	MpBasicCnTaylorMD

Functions
template<class Solver , class RemainderType >
void	capd::dynsys::computeAndApproveRemainder (Solver &solver, const typename Solver::ScalarType &t, const typename Solver::VectorType &xx, RemainderType &o_rem, RemainderType &o_enc)
template<typename MapType >
DiscreteDynSys< MapType >	capd::dynsys::makeDiscreteDynSys (const MapType &map)
	Makes DiscreteDynSys object from given map. Template parameters are recognized automatically. More...
template<typename MapType >
DynSysMap< MapType >	capd::dynsys::makeDynSysMap (const MapType &map)
	Makes DynSysMap object from given map. Template parameters are recognized automatically. More...
VectorType	capd::dynsys::BasicC2OdeSolver< MapT, StepControlT, CurveT >::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	capd::dynsys::BasicC2OdeSolver< MapT, StepControlT, CurveT >::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...
	capd::dynsys::BasicC2OdeSolver< MapT, StepControlT, CurveT >::BasicC2OdeSolver (VectorFieldType &vectorField, size_type order, const StepControlT &stepControl=StepControlT())
VectorType	capd::dynsys::BasicC2OdeSolver< MapT, StepControlT, CurveT >::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	capd::dynsys::BasicC2OdeSolver< MapT, StepControlT, CurveT >::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...
void	capd::dynsys::BasicC2OdeSolver< MapT, StepControlT, CurveT >::sumTaylorSeries (VectorType &v, MatrixType &der, HessianType &hessian, VectorType *coeff, MatrixType *matrixCoeff, HessianType *hessianCoeff, size_type order)
const VectorFieldType &	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::getVectorField () const
	Returns vector field. More...
VectorFieldType &	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::getVectorField ()
ScalarType	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::getStep () const
	Returns current time step. More...
void	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::setStep (const ScalarType &newStep)
	Sets time step and turns off step control. More...
void	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::adjustTimeStep (const ScalarType &newStep)
	sets time step but does not change step control settings (compare setStep) More...
void	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::computeTimeStep (const VectorType &v)
VectorType	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::operator() (ScalarType &t, const VectorType &)
	Computes image of vector v after one time step. The argument t is updated in this procedure. More...
VectorType	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::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	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::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	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::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...
VectorType	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::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...
size_type	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::degree () const
void	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::computeCoefficientsAtCenter (const VectorType &x, size_type order)
void	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::computeCoefficientsAtCenter (ScalarType t, const VectorType &x, size_type order)
void	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::computeCoefficients (const VectorType &x, size_type order)
void	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::computeCoefficients (ScalarType t, const VectorType &x, size_type order)
void	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::computeCoefficients (const VectorType &x, const MatrixType &M, size_type order)
void	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::computeCoefficients (ScalarType t, const VectorType &x, const MatrixType &M, size_type order)
virtual	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::~BasicCnOdeSolver ()
	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::BasicCnOdeSolver (VectorFieldType &a_vectorField, size_type a_order, const StepControlT &stepControl=StepControlT())
VectorType	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::operator() (VectorType)
	Computes image of vector v after one time step. More...
VectorType	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::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	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::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	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::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	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::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	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::operator() (ScalarType &t, JetType &)
	Initial conditions for the trajectory and for variational equations up to given degree are given in argument in_out_coeffs. The full result is stored in in_out_coeffs and also the new point on the trajectory is returned. Note: CnCoeffType is a data structure that stores current time. More...
void	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::setOrder (size_type order)
	Sets the order of the Taylor method. More...
ScalarType	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::getCoeffNorm (size_type i, size_type degree) const
void	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::evalAndSum (VectorType &v, MatrixType &der, HessianType &hessian)
void	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::evalAndSum (VectorType &v, MatrixType &der)
void	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::sum (VectorType &v)
void	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::evalAndSum (VectorType &v)
void	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::evalAndSum (JetType &v)
void	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::setInitialCondition (const JetType &coeff)
const SolutionCurve &	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::getCurve ()
void	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::setInitialCondition (const VectorType &v, const MatrixType &D)
void	capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::setInitialCondition (const VectorType &v, const MatrixType &D, const HessianType &H)
template<class AVector >
void	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::computeCoeff (AVector &in, AVector &out, size_type order)
const VectorFieldType &	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::getVectorField () const
	Returns vector field. More...
VectorFieldType &	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::getVectorField ()
ScalarType	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::getStep () const
	Returns current time step. More...
void	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::setStep (const ScalarType &newStep)
	Sets time step for the next step of integration and turns off step control. More...
void	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::adjustTimeStep (const ScalarType &newStep)
	sets time step but does not change step control settings (compare setStep) More...
void	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::computeTimeStep (VectorType &v)
VectorType	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::operator() (ScalarType &t, VectorType)
	Computes image of vector v after one time step. The argument t is updated in this procedure. More...
VectorType	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::operator() (ScalarType &t, VectorType v, const MatrixType &derivative, MatrixType &o_resultDerivative)
	Computes image of vector v and derivatives of a flow with respect to init condition (v, derivative). The argument t is updated in this procedure. More...
VectorType	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::operator() (ScalarType &t, VectorType v, MatrixType &o_resultDerivative)
	Computes image of vector v and derivatives of the flow with respect to init condition (v,identity). Version for nonautonomous systems. The argument t is updated in this procedure. More...
void	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::computeCoefficientsAtCenter (const VectorType &x, size_type order)
void	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::computeCoefficientsAtCenter (ScalarType t, const VectorType &x, size_type order)
void	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::computeCoefficients (const VectorType &x, size_type order)
void	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::computeCoefficients (ScalarType t, const VectorType &x, size_type order)
void	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::computeCoefficients (const VectorType &x, const MatrixType &M, size_type order)
void	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::computeCoefficients (ScalarType t, const VectorType &x, const MatrixType &M, size_type order)
void	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::recordDags ()
void	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::reset ()
	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::BasicFadOdeSolver (VectorFieldType &f, size_type _order, const StepControlT &stepControl=StepControlT())
void	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::setInitialCondition (const VectorType &u, TVector &in)
void	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::setInitialCondition (const VectorType &u, TFVector &in)
void	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::setInitialCondition (const VectorType &u, const MatrixType &M, TFVector &in)
void	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::sumTaylorSeries (VectorType &u, TVector &in, size_type order)
void	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::sumTaylorSeries (MatrixType &M, TFVector &in, size_type order)
void	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::sumTaylorSeries (VectorType &u, MatrixType &M, TFVector &in, size_type order)
VectorType	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::operator() (VectorType)
	Computes image of vector v after one time step. More...
VectorType	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::operator() (VectorType v, const MatrixType &derivative, MatrixType &o_resultDerivative)
	Computes image of vector v and derivatives of a flow with respect to init condition (v, derivative) More...
VectorType	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::operator() (VectorType v, MatrixType &o_resultDerivative)
	Computes image of vector v and derivatives of the flow with respect to init condition (v,identity). Version for autonomous systems. More...
virtual ScalarType	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::getCoeffNorm (size_type i, size_type degree) const
const SolutionCurve &	capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::getCurve ()
const VectorFieldType &	capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::getVectorField () const
	Returns vector field. More...
VectorFieldType &	capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::getVectorField ()
ScalarType	capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::getStep () const
	Returns the time step made in the last call to this solver. More...
void	capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::setStep (const ScalarType &newStep)
	Sets fixed time step and turns off step control. More...
void	capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::adjustTimeStep (const ScalarType &newStep)
	sets time step but does not change step control settings (compare setStep) More...
void	capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::computeTimeStep (VectorType &v)
VectorType	capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::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	capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::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	capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::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	capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::computeCoefficientsAtCenter (const VectorType &x, size_type order)
void	capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::computeCoefficientsAtCenter (ScalarType t, const VectorType &x, size_type order)
void	capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::computeCoefficients (const VectorType &x, size_type order)
void	capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::computeCoefficients (ScalarType t, const VectorType &x, size_type order)
void	capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::computeCoefficients (const VectorType &x, const MatrixType &M, size_type order)
void	capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::computeCoefficients (ScalarType t, const VectorType &x, const MatrixType &M, size_type order)
void	capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::sumTaylorSeries (VectorType &v, VectorType *coeff, size_type order)
	capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::BasicOdeSolver (VectorFieldType &field, size_type order, const StepControlT &stepControl=StepControlT())
void	capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::setOrder (size_type order)
	Sets the order of the Taylor method. More...
VectorType	capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::operator() (VectorType)
	Computes image of vector v after one time step. More...
VectorType	capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::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	capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::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...
void	capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::sumTaylorSeries (VectorType &v, MatrixType &der, VectorType *coeff, MatrixType *matrixCoeff, size_type order)
const SolutionCurve &	capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::getCurve ()
virtual ScalarType	capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::getCoeffNorm (size_type i, size_type degree) const
void	capd::dynsys::C2OdeSolver< MapT, StepControlPolicyT, EnclosurePolicyT, CurveT >::computeRemainderCoefficients (ScalarType t, const VectorType &x, const MatrixType &M, const HessianType &H)
	capd::dynsys::C2OdeSolver< MapT, StepControlPolicyT, EnclosurePolicyT, CurveT >::C2OdeSolver (VectorFieldType &vectorField, size_type order)
void	capd::dynsys::C2OdeSolver< MapT, StepControlPolicyT, EnclosurePolicyT, CurveT >::computeRemainderCoefficients (const VectorType &x, const MatrixType &M, const HessianType &H)
void	capd::dynsys::C2OdeSolver< MapT, StepControlPolicyT, EnclosurePolicyT, CurveT >::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	capd::dynsys::C2OdeSolver< MapT, StepControlPolicyT, EnclosurePolicyT, CurveT >::computeRemainder (ScalarType t, const VectorType &xx, C2TimeJetType &o_enc, C2TimeJetType &o_rem)
void	capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::computeRemainderCoefficients (const VectorType &x)
void	capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::computeRemainderCoefficients (ScalarType t, const VectorType &x)
void	capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::computeRemainderCoefficients (const VectorType &x, const MatrixType &M)
void	capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::computeRemainderCoefficients (ScalarType t, const VectorType &x, const MatrixType &M)
	capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::CnOdeSolver (VectorFieldType &vectorField, size_type order, const StepControlT &stepControl=StepControlT())
void	capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::setInitialCondition (ScalarType t, const VectorType &x, const VectorType &xx)
void	capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::encloseC2Map (const ScalarType &t, const VectorType &x, const VectorType &xx, VectorType &o_phi, VectorType &o_rem, VectorType &o_enc, MatrixType &o_jacPhi, MatrixType &o_jacRem, MatrixType &o_jacEnc, HessianType &o_hessianPhi, HessianType &o_hessianRem, HessianType &o_hessianEnc)
void	capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::encloseC1Map (const ScalarType &t, const VectorType &x0, const VectorType &x, VectorType &o_phi, VectorType &o_rem, VectorType &o_enc, MatrixType &o_jacPhi, MatrixType &o_jacRem, MatrixType &o_jacEnc)
void	capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::encloseC0Map (const ScalarType &t, const VectorType &x0, const VectorType &x, VectorType &o_phi, VectorType &o_rem, VectorType &o_enc, MatrixType &o_jacPhi)
void	capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::sumTaylorSeries (VectorType &o_phi, MatrixType &o_jacPhi)
void	capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::sumTaylorSeries (VectorType &o_phi, MatrixType &o_jacPhi, HessianType &o_hessianPhi)
ScalarType	capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::getCoeffNorm (size_type i, size_type degree) const
VectorType	capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::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	capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::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	capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::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	capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::JacRemainder (const ScalarType &t, const VectorType &vecEnclosure, const MatrixType &jacEnclosure, VectorType &Remainder, MatrixType &jacRemainder)
void	capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::c2Remainder (const VectorType &Enc, const MatrixType &jacEnc, const HessianType &hessianEnc, VectorType &o_Rem, MatrixType &o_jacRem, HessianType &o_hessianRem)
virtual void	capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::computeRemainder (ScalarType t, const VectorType &xx, VectorType &o_enc, VectorType &o_rem)
virtual void	capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::computeRemainder (ScalarType t, const VectorType &xx, C1TimeJetType &o_enc, C1TimeJetType &o_rem)
virtual void	capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::computeRemainder (ScalarType t, const VectorType &xx, C2TimeJetType &o_enc, C2TimeJetType &o_rem)
template<class JetT >
VectorType	capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::encloseCnMap (const ScalarType &t, const VectorType &x, const VectorType &xx, JetT &phi, JetT &rem, JetT &enc)
template<class JetT >
void	capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::sumTaylorSeries (JetT &o_phi)
template<class JetT >
void	capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::cnRemainder (const JetT &enc, JetT &result)
template<class JetT >
VectorType	capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::cnEnclosure (const ScalarType &t, const VectorType &x, JetT &result)
template<class JetT >
void	capd::dynsys::CnOdeSolver< MapT, StepControlT, EnclosurePolicyT, CurveT >::computeRemainder (ScalarType t, const VectorType &xx, JetT &o_enc, JetT &o_rem)
virtual ScalarType	capd::dynsys::DynSys< MatrixT >::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...
void	capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::computeRemainderCoefficients (const VectorType &x)
void	capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::computeRemainderCoefficients (ScalarType t, const VectorType &x)
void	capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::computeRemainderCoefficients (const VectorType &x, const MatrixType &M)
void	capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::computeRemainderCoefficients (ScalarType t, const VectorType &x, const MatrixType &M)
	capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::FadOdeSolver (VectorFieldType &f, size_type _order, const StepControlT &_stepControl=StepControlT())
VectorType	capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::Phi (const ScalarType &t, const VectorType &iv)
	Computes value of function (usually numerical scheme for an ODE) at time t and point iv. More...
VectorType	capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::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...
MatrixType	capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::JacPhi (const ScalarType &t, const VectorType &iv)
	Computes derivative of function (usually numerical scheme for an ODE) at time t and point iv. More...
void	capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::computeTaylorCoefficients (ScalarType t, const VectorType &x, const VectorType &xx)
void	capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::encloseC0Map (const ScalarType &t, const VectorType &x0, const VectorType &x, VectorType &o_phi, VectorType &o_rem, VectorType &o_enc, MatrixType &o_jacPhi)
	For given set xx, time t and a point x from the set xx It simultaneously computes and returns enclosures for: More...
void	capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::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)
VectorType	capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::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	capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::JacRemainder (const ScalarType &t, const VectorType &vecEnclosure, const MatrixType &jacEnclosure, VectorType &Remainder, MatrixType &jRemainder)
MatrixType	capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::jacEnclosure (const ScalarType &t, const VectorType &enc)
ScalarType	capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::getCoeffNorm (size_type i, size_type degree) const
template<typename MapType >
static MapType::VectorType	capd::dynsys::FirstOrderEnclosure::enclosure (MapType &vectorField, typename MapType::ScalarType const &currentTime, typename MapType::MatrixType::RowVectorType const &x, typename MapType::ScalarType const &step)
	Computes enclosure of solution of ODE during one time step i.e . More...
template<typename MapType , typename NormType >
static MapType::MatrixType	capd::dynsys::FirstOrderEnclosure::jacEnclosure (const MapType &vectorField, const typename MapType::ScalarType &currentTime, const typename MapType::ScalarType &step, const typename MapType::VectorType &enc, const NormType &the_norm, typename MapType::ScalarType *o_logNormOfDerivative=0)
	Finds enclosure for Jacobian matrix (variational part) for whole time step. More...
template<typename MapType >
static MapType::ScalarType	capd::dynsys::FirstOrderEnclosure::c2Enclosure (const MapType &vectorField, const typename MapType::ScalarType &step, const typename MapType::VectorType &enc, typename MapType::MatrixType &jacEnclosure, typename MapType::HessianType &hessEnclosure)
	Finds enclosure for second order variational equations for whole time step. More...

Detailed Description

Typedef Documentation

BasicC2Taylor

typedef capd::dynsys::BasicC2Solver<DC2Map> BasicC2Taylor

BasicC2TaylorMD

typedef capd::dynsys::BasicC2Solver<DC2MapMD> BasicC2TaylorMD

BasicCnTaylor

typedef capd::dynsys::BasicCnSolver<DCnMap> BasicCnTaylor

BasicCnTaylorMD

typedef capd::dynsys::BasicCnSolver<DCnMapMD> BasicCnTaylorMD

BasicTaylor

typedef capd::dynsys::BasicSolver<DMap> BasicTaylor

BasicTaylorMD

typedef capd::dynsys::BasicSolver<DMapMD> BasicTaylorMD

C2Taylor

typedef capd::dynsys::C2Solver<IC2Map> C2Taylor

C2TaylorMD

typedef capd::dynsys::C2Solver<IC2MapMD> C2TaylorMD

CnTaylor

typedef capd::dynsys::CnSolver<ICnMap> CnTaylor

CnTaylorMD

typedef capd::dynsys::CnSolver<ICnMapMD> CnTaylorMD

DynSys

typedef capd::dynsys::DynSys<IMatrix> DynSys

DynSysMD

typedef capd::dynsys::DynSys<IMatrixMD> DynSysMD

LDC2Taylor

typedef capd::dynsys::BasicC2Solver<LDC2Map> LDC2Taylor

LDC2TaylorMD

typedef capd::dynsys::BasicC2Solver<LDC2MapMD> LDC2TaylorMD

LDCnTaylor

typedef capd::dynsys::BasicCnSolver<LDCnMap> LDCnTaylor

LDCnTaylorMD

typedef capd::dynsys::BasicCnSolver<LDCnMapMD> LDCnTaylorMD

LDTaylor

typedef capd::dynsys::BasicSolver<LDMap> LDTaylor

LDTaylorMD

typedef capd::dynsys::BasicSolver<LDMapMD> LDTaylorMD

linear2d

typedef capd::dynsys::Linear2d<IMatrix> linear2d

linear2dMD

typedef capd::dynsys::Linear2d<IMatrixMD> linear2dMD

linear3d

typedef capd::dynsys::Linear3d<IMatrix> linear3d

linear3dMD

typedef capd::dynsys::Linear3d<IMatrixMD> linear3dMD

MpBasicC2Taylor

typedef capd::dynsys::BasicC2Solver<MpC2Map> MpBasicC2Taylor

MpBasicC2TaylorMD

typedef capd::dynsys::BasicC2Solver<MpC2MapMD> MpBasicC2TaylorMD

MpBasicCnTaylor

typedef capd::dynsys::BasicCnSolver<MpCnMap> MpBasicCnTaylor

MpBasicCnTaylorMD

typedef capd::dynsys::BasicCnSolver<MpCnMapMD> MpBasicCnTaylorMD

MpBasicTaylor

typedef capd::dynsys::BasicSolver<MpMap> MpBasicTaylor

MpBasicTaylorMD

typedef capd::dynsys::BasicSolver<MpMapMD> MpBasicTaylorMD

MpC2Taylor

typedef capd::dynsys::C2Solver<MpIC2Map> MpC2Taylor

MpC2TaylorMD

typedef capd::dynsys::C2Solver<MpIC2MapMD> MpC2TaylorMD

MpCnTaylor

typedef capd::dynsys::CnSolver<MpICnMap> MpCnTaylor

MpCnTaylorMD

typedef capd::dynsys::CnSolver<MpICnMapMD> MpCnTaylorMD

MpDynSys

typedef capd::dynsys::DynSys<MpIMatrix> MpDynSys

MpDynSysMD

typedef capd::dynsys::DynSys<MpIMatrixMD> MpDynSysMD

MpLinear2d

typedef capd::dynsys::Linear2d<MpIMatrix> MpLinear2d

MpLinear2dMD

typedef capd::dynsys::Linear2d<MpIMatrixMD> MpLinear2dMD

MpLinear3d

typedef capd::dynsys::Linear3d<MpIMatrix> MpLinear3d

MpLinear3dMD

typedef capd::dynsys::Linear3d<MpIMatrixMD> MpLinear3dMD

MpOde

typedef capd::dynsys::Ode<MpIMatrix> MpOde

MpOdeMD

typedef capd::dynsys::Ode<MpIMatrixMD> MpOdeMD

MpOdeNum

typedef capd::dynsys::OdeNum<MpIMatrix> MpOdeNum

MpOdeNumMD

typedef capd::dynsys::OdeNum<MpIMatrixMD> MpOdeNumMD

MpOdeNumTaylor

typedef capd::dynsys::OdeNumTaylor<MpIMatrix> MpOdeNumTaylor

MpOdeNumTaylorMD

typedef capd::dynsys::OdeNumTaylor<MpIMatrixMD> MpOdeNumTaylorMD

MpTaylor

typedef capd::dynsys::Solver<MpIMap> MpTaylor

MpTaylorException

typedef capd::dynsys::SolverException<MpIVector> MpTaylorException

MpTaylorExceptionMD

typedef capd::dynsys::SolverException<MpIVectorMD> MpTaylorExceptionMD

MpTaylorMD

typedef capd::dynsys::Solver<MpIMapMD> MpTaylorMD

MpVLin3D

typedef capd::dynsys::VLin3D<MpIMatrix> MpVLin3D

MpVLin3DMD

typedef capd::dynsys::VLin3D<MpIMatrixMD> MpVLin3DMD

Ode

typedef capd::dynsys::Ode<IMatrix> Ode

OdeMD

typedef capd::dynsys::Ode<IMatrixMD> OdeMD

OdeNum

typedef capd::dynsys::OdeNum<IMatrix> OdeNum

OdeNumMD

typedef capd::dynsys::OdeNum<IMatrixMD> OdeNumMD

OdeNumTaylor

typedef capd::dynsys::OdeNumTaylor<IMatrix> OdeNumTaylor

OdeNumTaylorMD

typedef capd::dynsys::OdeNumTaylor<IMatrixMD> OdeNumTaylorMD

Taylor

typedef capd::dynsys::Solver<IMap> Taylor

TaylorException

typedef capd::dynsys::SolverException<IVector> TaylorException

TaylorExceptionMD

typedef capd::dynsys::SolverException<IVectorMD> TaylorExceptionMD

TaylorMD

typedef capd::dynsys::Solver<IMapMD> TaylorMD

VLin3D

typedef capd::dynsys::VLin3D<IMatrix> VLin3D

VLin3DMD

typedef capd::dynsys::VLin3D<IMatrixMD> VLin3DMD

Function Documentation

adjustTimeStep() [1/3]

template<typename MapType , typename StepControlType , typename CurveT >

void capd::dynsys::BasicCnOdeSolver< MapType, StepControlType, CurveT >::adjustTimeStep ( const ScalarType &  newStep )

inline

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

adjustTimeStep() [2/3]

template<typename FadMapT , typename StepControlType >

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

inline

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

adjustTimeStep() [3/3]

template<typename MapType , typename StepControlType , typename CurveT >

void capd::dynsys::BasicOdeSolver< MapType, StepControlType, CurveT >::adjustTimeStep ( const ScalarType &  newStep )

inline

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

BasicC2OdeSolver()

template<typename MapType , typename StepControlType , typename CurveT >

capd::dynsys::BasicC2OdeSolver< MapType, StepControlType, CurveT >::BasicC2OdeSolver	(	VectorFieldType &	vectorField,
		size_type	order,
		const StepControlT &	stepControl = StepControlT()
	)

BasicCnOdeSolver()

template<typename MapT , typename StepControlT , typename CurveT >

capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::BasicCnOdeSolver	(	VectorFieldType &	a_vectorField,
		size_type	a_order,
		const StepControlT &	stepControl = StepControlT()
	)

BasicFadOdeSolver()

template<class FadMapT , typename StepControlT >

capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlT >::BasicFadOdeSolver	(	VectorFieldType &	f,
		size_type	_order,
		const StepControlT &	stepControl = StepControlT()
	)

BasicOdeSolver()

template<typename MapType , typename StepControlType , typename CurveT >

capd::dynsys::BasicOdeSolver< MapType, StepControlType, CurveT >::BasicOdeSolver	(	VectorFieldType &	field,
		size_type	order,
		const StepControlT &	stepControl = StepControlT()
	)

c2Enclosure()

template<typename MapType >

MapType::ScalarType capd::dynsys::FirstOrderEnclosure::c2Enclosure ( const MapType &  vectorField, const typename MapType::ScalarType &  step, const typename MapType::VectorType &  enc, typename MapType::MatrixType &  jacEnclosure, typename MapType::HessianType &  hessEnclosure  )

static

Finds enclosure for second order variational equations for whole time step.

Parameters

	vectorField	vector field
	timeStep	time step
	enclosure	enclosure of solution of ODE during whole time step
[out]	jacEnclosure	computed enclosure of solution to first order variational equations during whole time step
[out]	hessEnclosure	computed enclosure of solution to second order variational equations during whole time step

Returns

computed logarithmic norm of derivative

C2OdeSolver()

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

capd::dynsys::C2OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveT >::C2OdeSolver	(	VectorFieldType &	vectorField,
		size_type	order
	)

c2Remainder()

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

void capd::dynsys::CnOdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::c2Remainder	(	const VectorType &	Enc,
		const MatrixType &	jacEnc,
		const HessianType &	hessianEnc,
		VectorType &	o_Rem,
		MatrixType &	o_jacRem,
		HessianType &	o_hessianRem
	)

cnEnclosure()

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

template<class JetT >

CnOdeSolver< MapT, StepControlPolicy, EnclosurePolicy, CurveType >::VectorType capd::dynsys::CnOdeSolver< MapT, StepControlPolicy, EnclosurePolicy, CurveType >::cnEnclosure	(	const ScalarType &	t,
		const VectorType &	x,
		JetT &	result
	)

CnOdeSolver()

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

capd::dynsys::CnOdeSolver< MapT, StepControlPolicy, EnclosurePolicy, CurveT >::CnOdeSolver	(	VectorFieldType &	vectorField,
		size_type	order,
		const StepControlT &	stepControl = StepControlT()
	)

cnRemainder()

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

template<class JetT >

void capd::dynsys::CnOdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::cnRemainder	(	const JetT &	enc,
		JetT &	result
	)

computeAndApproveRemainder()

template<class Solver , class RemainderType >

void capd::dynsys::computeAndApproveRemainder	(	Solver &	solver,
		const typename Solver::ScalarType &	t,
		const typename Solver::VectorType &	xx,
		RemainderType &	o_rem,
		RemainderType &	o_enc
	)

computeCoeff()

template<class FadMapT , typename StepControlT >

template<class AVector >

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

protected

computeCoefficients() [1/12]

template<typename MapT , typename StepControlT , typename CurveT >

void capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::computeCoefficients ( const VectorType &  x, const MatrixType &  M, size_type  order  )

inline

computeCoefficients() [2/12]

template<class FadMapT , typename StepControlT >

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

inline

computeCoefficients() [3/12]

template<typename MapType , typename StepControlType , typename CurveType >

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

inline

computeCoefficients() [4/12]

template<typename MapT , typename StepControlT , typename CurveT >

void capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::computeCoefficients ( const VectorType &  x, size_type  order  )

inline

computeCoefficients() [5/12]

template<class FadMapT , typename StepControlT >

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

inline

computeCoefficients() [6/12]

template<typename MapType , typename StepControlType , typename CurveType >

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

inline

computeCoefficients() [7/12]

template<typename MapT , typename StepControlT , typename CurveT >

void capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::computeCoefficients ( ScalarType  t, const VectorType &  x, const MatrixType &  M, size_type  order  )

inline

computeCoefficients() [8/12]

template<class FadMapT , typename StepControlT >

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

inline

computeCoefficients() [9/12]

template<typename MapType , typename StepControlType , typename CurveType >

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

inline

computeCoefficients() [10/12]

template<typename MapT , typename StepControlT , typename CurveT >

void capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::computeCoefficients ( ScalarType  t, const VectorType &  x, size_type  order  )

inline

computeCoefficients() [11/12]

template<class FadMapT , typename StepControlT >

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

inline

computeCoefficients() [12/12]

template<typename MapType , typename StepControlType , typename CurveType >

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

inline

computeCoefficientsAtCenter() [1/6]

template<typename MapT , typename StepControlT , typename CurveT >

void capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::computeCoefficientsAtCenter ( const VectorType &  x, size_type  order  )

inline

computeCoefficientsAtCenter() [2/6]

template<class FadMapT , typename StepControlT >

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

inline

computeCoefficientsAtCenter() [3/6]

template<typename MapType , typename StepControlType , typename CurveType >

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

inline

computeCoefficientsAtCenter() [4/6]

template<typename MapT , typename StepControlT , typename CurveT >

void capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::computeCoefficientsAtCenter ( ScalarType  t, const VectorType &  x, size_type  order  )

inline

computeCoefficientsAtCenter() [5/6]

template<class FadMapT , typename StepControlT >

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

inline

computeCoefficientsAtCenter() [6/6]

template<typename MapType , typename StepControlType , typename CurveType >

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

inline

computeRemainder() [1/5]

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

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

virtual

computeRemainder() [2/5]

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

void capd::dynsys::C2OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveT >::computeRemainder ( ScalarType  t, const VectorType &  xx, C2TimeJetType &  o_enc, C2TimeJetType &  o_rem  )

virtual

computeRemainder() [3/5]

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

void capd::dynsys::CnOdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::computeRemainder ( ScalarType  t, const VectorType &  xx, C2TimeJetType &  o_enc, C2TimeJetType &  o_rem  )

virtual

computeRemainder() [4/5]

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

template<class JetT >

void capd::dynsys::CnOdeSolver< MapT, StepControlPolicy, EnclosurePolicy, CurveT >::computeRemainder	(	ScalarType	t,
		const VectorType &	xx,
		JetT &	o_enc,
		JetT &	o_rem
	)

computeRemainder() [5/5]

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

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

virtual

computeRemainderCoefficients() [1/10]

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

void capd::dynsys::CnOdeSolver< MapT, StepControlPolicy, EnclosurePolicy, CurveT >::computeRemainderCoefficients ( const VectorType &  x )

inline

computeRemainderCoefficients() [2/10]

template<class FadMapT , typename StepControlT >

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

inline

computeRemainderCoefficients() [3/10]

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

void capd::dynsys::CnOdeSolver< MapT, StepControlPolicy, EnclosurePolicy, CurveT >::computeRemainderCoefficients ( const VectorType &  x, const MatrixType &  M  )

inline

computeRemainderCoefficients() [4/10]

template<class FadMapT , typename StepControlT >

void capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::computeRemainderCoefficients ( const VectorType &  x, const MatrixType &  M  )

inline

computeRemainderCoefficients() [5/10]

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

void capd::dynsys::C2OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveT >::computeRemainderCoefficients	(	const VectorType &	x,
		const MatrixType &	M,
		const HessianType &	H
	)

computeRemainderCoefficients() [6/10]

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

void capd::dynsys::CnOdeSolver< MapT, StepControlPolicy, EnclosurePolicy, CurveT >::computeRemainderCoefficients ( ScalarType  t, const VectorType &  x  )

inline

computeRemainderCoefficients() [7/10]

template<class FadMapT , typename StepControlT >

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

inline

computeRemainderCoefficients() [8/10]

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

void capd::dynsys::CnOdeSolver< MapT, StepControlPolicy, EnclosurePolicy, CurveT >::computeRemainderCoefficients ( ScalarType  t, const VectorType &  x, const MatrixType &  M  )

inline

computeRemainderCoefficients() [9/10]

template<class FadMapT , typename StepControlT >

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

inline

computeRemainderCoefficients() [10/10]

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

void capd::dynsys::C2OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveT >::computeRemainderCoefficients ( ScalarType  t, const VectorType &  x, const MatrixType &  M, const HessianType &  H  )

inline

computeTaylorCoefficients()

template<class FadMapT , typename StepControlT >

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

computeTimeStep() [1/3]

template<typename MapType , typename StepControlType , typename CurveT >

void capd::dynsys::BasicCnOdeSolver< MapType, StepControlType, CurveT >::computeTimeStep ( const VectorType &  v )

inlineprotected

computeTimeStep() [2/3]

template<typename FadMapT , typename StepControlType >

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

inlineprotected

computeTimeStep() [3/3]

template<typename MapType , typename StepControlType , typename CurveT >

void capd::dynsys::BasicOdeSolver< MapType, StepControlType, CurveT >::computeTimeStep ( VectorType &  v )

inlineprotected

degree()

template<typename MapT , typename StepControlT , typename CurveT >

BasicCnOdeSolver< MapT, StepControlT, CurveT >::size_type capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::degree

inline

encloseC0Map() [1/2]

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

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

encloseC0Map() [2/2]

template<typename MapType , typename StepControlType >

void capd::dynsys::FadOdeSolver< MapType, StepControlType >::encloseC0Map ( const ScalarType &  t, const VectorType &  x, const VectorType &  xx, VectorType &  o_phi, VectorType &  o_rem, VectorType &  o_enc, MatrixType &  o_jacPhi  )

virtual

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.

Implements capd::dynsys::DynSys< MatrixT >.

encloseC1Map() [1/2]

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

void capd::dynsys::CnOdeSolver< MapT, StepControlPolicy, EnclosurePolicy, CurveT >::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
	)

encloseC1Map() [2/2]

template<typename MapType , typename StepControlType >

void capd::dynsys::FadOdeSolver< MapType, StepControlType >::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
	)

encloseC2Map() [1/2]

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

void capd::dynsys::C2OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveT >::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
	)

encloseC2Map() [2/2]

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

void capd::dynsys::CnOdeSolver< MapT, StepControlPolicy, EnclosurePolicy, CurveT >::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
	)

encloseCnMap()

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

template<class JetT >

CnOdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::VectorType capd::dynsys::CnOdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::encloseCnMap	(	const ScalarType &	t,
		const VectorType &	x,
		const VectorType &	xx,
		JetT &	phi,
		JetT &	rem,
		JetT &	enc
	)

enclosure() [1/2]

template<class FadMapT , typename StepControlT >

FadOdeSolver< FadMapT, StepControlT >::VectorType capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::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< MatrixT >.

enclosure() [2/2]

template<typename MapType >

MapType::VectorType capd::dynsys::FirstOrderEnclosure::enclosure ( MapType &  vectorField, typename MapType::ScalarType const &  currentTime, typename MapType::MatrixType::RowVectorType const &  x, typename MapType::ScalarType const &  step  )

static

Computes enclosure of solution of ODE during one time step i.e .

Parameters

vectorField	vector field
currentTime	(for nonautonomous ODEs)
x0	initial condition
timeStep	final time

Returns

enclosure of solution of ODE

evalAndSum() [1/4]

template<typename MapT , typename StepControlT , typename CurveT >

void capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::evalAndSum ( JetType &  v )

protected

evalAndSum() [2/4]

template<typename MapT , typename StepControlT , typename CurveT >

void capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::evalAndSum ( VectorType &  v )

protected

evalAndSum() [3/4]

template<typename MapT , typename StepControlT , typename CurveT >

void capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::evalAndSum ( VectorType &  v, MatrixType &  der  )

protected

evalAndSum() [4/4]

template<typename MapT , typename StepControlT , typename CurveT >

void capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::evalAndSum ( VectorType &  v, MatrixType &  der, HessianType &  hessian  )

protected

FadOdeSolver()

template<class FadMapT , typename StepControlT >

capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::FadOdeSolver	(	VectorFieldType &	f,
		size_type	_order,
		const StepControlT &	_stepControl = StepControlT()
	)

getCoeffNorm() [1/5]

template<typename MapType , typename StepControlType , typename CurveT >

BasicCnOdeSolver< MapType, StepControlType, CurveT >::ScalarType capd::dynsys::BasicCnOdeSolver< MapType, StepControlType, CurveT >::getCoeffNorm	(	size_type	i,
		size_type	degree
	)		const

getCoeffNorm() [2/5]

template<typename FadMapT , typename StepControlType >

BasicFadOdeSolver< FadMapT, StepControlType >::ScalarType capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlType >::getCoeffNorm ( size_type  i, size_type  degree  ) const

virtual

Reimplemented in capd::dynsys::FadOdeSolver< FadMapT, StepControlT >.

getCoeffNorm() [3/5]

template<typename MapType , typename StepControlType , typename CurveT >

BasicOdeSolver< MapType, StepControlType, CurveT >::ScalarType capd::dynsys::BasicOdeSolver< MapType, StepControlType, CurveT >::getCoeffNorm ( size_type  i, size_type  degree  ) const

virtual

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

getCoeffNorm() [4/5]

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

CnOdeSolver< MapT, StepControlPolicy, EnclosurePolicy, CurveT >::ScalarType capd::dynsys::CnOdeSolver< MapT, StepControlPolicy, EnclosurePolicy, CurveT >::getCoeffNorm	(	size_type	i,
		size_type	degree
	)		const

getCoeffNorm() [5/5]

template<class FadMapT , typename StepControlT >

FadOdeSolver< FadMapT, StepControlT >::ScalarType capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::getCoeffNorm ( size_type  i, size_type  degree  ) const

virtual

Reimplemented from capd::dynsys::BasicFadOdeSolver< FadMapT, capd::dynsys::IEncFoundStepControl >.

getCurve() [1/3]

template<typename MapType , typename StepControlType , typename CurveT >

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

getCurve() [2/3]

template<typename FadMapT , typename StepControlType >

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

getCurve() [3/3]

template<typename MapType , typename StepControlType , typename CurveT >

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

getStep() [1/3]

template<typename MapType , typename StepControlType , typename CurveT >

BasicCnOdeSolver< MapType, StepControlType, CurveT >::ScalarType capd::dynsys::BasicCnOdeSolver< MapType, StepControlType, CurveT >::getStep

inline

Returns current time step.

getStep() [2/3]

template<typename FadMapT , typename StepControlType >

BasicFadOdeSolver< FadMapT, StepControlType >::ScalarType capd::dynsys::BasicFadOdeSolver< FadMapT, StepControlType >::getStep

inline

Returns current time step.

getStep() [3/3]

template<typename MapType , typename StepControlType , typename CurveT >

BasicOdeSolver< MapType, StepControlType, CurveT >::ScalarType capd::dynsys::BasicOdeSolver< MapType, StepControlType, CurveT >::getStep

inline

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

getVectorField() [1/6]

template<typename MapType , typename StepControlType , typename CurveT >

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

inline

getVectorField() [2/6]

template<typename FadMapT , typename StepControlType >

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

inline

getVectorField() [3/6]

template<typename MapType , typename StepControlType , typename CurveT >

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

inline

getVectorField() [4/6]

template<typename MapType , typename StepControlType , typename CurveT >

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

inline

Returns vector field.

getVectorField() [5/6]

template<typename FadMapT , typename StepControlType >

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

inline

Returns vector field.

getVectorField() [6/6]

template<typename MapType , typename StepControlType , typename CurveT >

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

inline

Returns vector field.

jacEnclosure() [1/2]

template<typename MapType , typename NormType >

MapType::MatrixType capd::dynsys::FirstOrderEnclosure::jacEnclosure ( const MapType &  vectorField, const typename MapType::ScalarType &  currentTime, const typename MapType::ScalarType &  step, const typename MapType::VectorType &  enc, const NormType &  the_norm, typename MapType::ScalarType *  o_logNormOfDerivative = 0  )

static

Finds enclosure for Jacobian matrix (variational part) for whole time step.

Parameters

vectorField	vector field
currentTime	(for nonautonomous ODEs)
timeStep	time step
enclosure	enclosure of solution of ODE during whole time step
the_norm	logarithmic norm used to bound solution

Returns

matrix containing enclosure of Jacobian

jacEnclosure() [2/2]

template<class FadMapT , typename StepControlT >

FadOdeSolver< FadMapT, StepControlT >::MatrixType capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::jacEnclosure	(	const ScalarType &	t,
		const VectorType &	enc
	)

JacPhi() [1/2]

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

CnOdeSolver< MapT, StepControlPolicy, EnclosurePolicy, CurveT >::MatrixType capd::dynsys::CnOdeSolver< MapT, StepControlPolicy, EnclosurePolicy, CurveT >::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 >.

JacPhi() [2/2]

template<class FadMapT , typename StepControlT >

FadOdeSolver< FadMapT, StepControlT >::MatrixType capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::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< MatrixT >.

JacRemainder() [1/2]

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

void capd::dynsys::CnOdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::JacRemainder	(	const ScalarType &	t,
		const VectorType &	vecEnclosure,
		const MatrixType &	jacEnclosure,
		VectorType &	Remainder,
		MatrixType &	jacRemainder
	)

JacRemainder() [2/2]

template<class FadMapT , typename StepControlT >

void capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::JacRemainder	(	const ScalarType &	t,
		const VectorType &	vecEnclosure,
		const MatrixType &	jacEnclosure,
		VectorType &	Remainder,
		MatrixType &	jRemainder
	)

Lipschitz()

template<typename MatrixType >

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

virtual

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

makeDiscreteDynSys()

template<typename MapType >

DiscreteDynSys<MapType> capd::dynsys::makeDiscreteDynSys

(

const MapType &

map

)

Makes DiscreteDynSys object from given map. Template parameters are recognized automatically.

makeDynSysMap()

template<typename MapType >

DynSysMap<MapType> capd::dynsys::makeDynSysMap

(

const MapType &

map

)

Makes DynSysMap object from given map. Template parameters are recognized automatically.

operator()() [1/27]

template<typename MapT , typename StepControlT , typename CurveT >

BasicCnOdeSolver< MapT, StepControlT, CurveT >::VectorType capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::operator() ( ScalarType &  t, const VectorType &  v  )

inline

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

operator()() [2/27]

template<typename MapType , typename StepControlType , typename CurveT >

BasicC2OdeSolver< MapType, StepControlType, CurveT >::VectorType capd::dynsys::BasicC2OdeSolver< MapType, StepControlType, CurveT >::operator() ( ScalarType &  t, const VectorType &  v, MatrixType &  der, HessianType &  coeff  )

inline

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()() [3/27]

template<typename MapT , typename StepControlT , typename CurveT >

BasicCnOdeSolver< MapT, StepControlT, CurveT >::VectorType capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::operator() ( ScalarType &  t, const VectorType &  v, MatrixType &  der, HessianType &  coeff  )

inline

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()() [4/27]

template<typename MapT , typename StepControlT , typename CurveT >

BasicCnOdeSolver< MapT, StepControlT, CurveT >::VectorType capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::operator() ( ScalarType &  t, const VectorType &  v, MatrixType &  o_resultDerivative  )

inline

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

operator()() [5/27]

template<typename MapType , typename StepControlType , typename CurveT >

BasicOdeSolver< MapType, StepControlType, CurveT >::VectorType capd::dynsys::BasicOdeSolver< MapType, StepControlType, CurveT >::operator() ( ScalarType &  t, const VectorType &  v, MatrixType &  o_resultDerivative  )

inline

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

operator()() [6/27]

template<typename MapType , typename StepControlType , typename CurveT >

BasicOdeSolver< MapType, StepControlType, CurveT >::VectorType capd::dynsys::BasicOdeSolver< MapType, StepControlType, CurveT >::operator() ( ScalarType &  t, const VectorType &  u  )

inline

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

operator()() [7/27]

template<typename MapT , typename StepControlT , typename CurveT >

BasicCnOdeSolver< MapT, StepControlT, CurveT >::VectorType capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::operator() ( ScalarType &  t, const VectorType &  v, const MatrixType &  derivative, MatrixType &  o_resultDerivative  )

inline

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()() [8/27]

template<typename MapType , typename StepControlType , typename CurveT >

BasicOdeSolver< MapType, StepControlType, CurveT >::VectorType capd::dynsys::BasicOdeSolver< MapType, StepControlType, CurveT >::operator() ( ScalarType &  t, const VectorType &  v, const MatrixType &  derivative, MatrixType &  o_resultDerivative  )

inline

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()() [9/27]

template<typename MapType , typename StepControlType , typename CurveT >

BasicC2OdeSolver< MapType, StepControlType, CurveT >::VectorType capd::dynsys::BasicC2OdeSolver< MapType, StepControlType, CurveT >::operator() ( ScalarType &  t, const VectorType &  x, const MatrixType &  V, const HessianType &  H, MatrixType &  out_der, HessianType &  out_hessian  )

inline

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()() [10/27]

template<typename MapT , typename StepControlT , typename CurveT >

BasicCnOdeSolver< MapT, StepControlT, CurveT >::VectorType capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::operator() ( ScalarType &  t, const VectorType &  x, const MatrixType &  V, const HessianType &  H, MatrixType &  out_der, HessianType &  out_hessian  )

inline

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()() [11/27]

template<typename MapT , typename StepControlT , typename CurveT >

BasicCnOdeSolver< MapT, StepControlT, CurveT >::VectorType capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::operator()	(	ScalarType &	t,
		JetType &	coeff
	)

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

operator()() [12/27]

template<class FadMapT , typename StepControlT >

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

inline

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()() [13/27]

template<class FadMapT , typename StepControlT >

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

inline

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()() [14/27]

template<class FadMapT , typename StepControlT >

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

inline

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

operator()() [15/27]

template<class FadMapT , typename StepControlT >

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

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

operator()() [16/27]

template<class FadMapT , typename StepControlT >

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

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

operator()() [17/27]

template<typename MapType , typename StepControlType , typename CurveT >

BasicCnOdeSolver< MapType, StepControlType, CurveT >::VectorType capd::dynsys::BasicCnOdeSolver< MapType, StepControlType, CurveT >::operator()

(

VectorType

v

)

Computes image of vector v after one time step.

operator()() [18/27]

template<class FadMapT , typename StepControlT >

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

(

VectorType

u

)

Computes image of vector v after one time step.

operator()() [19/27]

template<typename MapType , typename StepControlType , typename CurveT >

BasicOdeSolver< MapType, StepControlType, CurveT >::VectorType capd::dynsys::BasicOdeSolver< MapType, StepControlType, CurveT >::operator()

(

VectorType

v

)

Computes image of vector v after one time step.

operator()() [20/27]

template<typename MapT , typename StepControlT , typename CurveT >

BasicCnOdeSolver< MapT, StepControlT, CurveT >::VectorType capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::operator()	(	VectorType	v,
		const MatrixType &	derivative,
		MatrixType &	o_resultDerivative
	)

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

operator()() [21/27]

template<typename MapType , typename StepControlType , typename CurveT >

BasicOdeSolver< MapType, StepControlType, CurveT >::VectorType capd::dynsys::BasicOdeSolver< MapType, StepControlType, CurveT >::operator()	(	VectorType	v,
		const MatrixType &	derivative,
		MatrixType &	o_resultDerivative
	)

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

operator()() [22/27]

template<typename MapType , typename StepControlType , typename CurveT >

BasicC2OdeSolver< MapType, StepControlType, CurveT >::VectorType capd::dynsys::BasicC2OdeSolver< MapType, StepControlType, CurveT >::operator()	(	VectorType	x,
		const MatrixType &	V,
		const HessianType &	H,
		MatrixType &	out_der,
		HessianType &	out_hessian
	)

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

operator()() [23/27]

template<typename MapT , typename StepControlT , typename CurveT >

BasicCnOdeSolver< MapT, StepControlT, CurveT >::VectorType capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::operator()	(	VectorType	v,
		const MatrixType &	V,
		const HessianType &	H,
		MatrixType &	out_der,
		HessianType &	out_hessian
	)

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

operator()() [24/27]

template<typename MapType , typename StepControlType , typename CurveT >

BasicC2OdeSolver< MapType, StepControlType, CurveT >::VectorType capd::dynsys::BasicC2OdeSolver< MapType, StepControlType, CurveT >::operator()	(	VectorType	v,
		MatrixType &	der,
		HessianType &	hessian
	)

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()() [25/27]

template<typename MapT , typename StepControlT , typename CurveT >

BasicCnOdeSolver< MapT, StepControlT, CurveT >::VectorType capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::operator()	(	VectorType	v,
		MatrixType &	der,
		HessianType &	hessian
	)

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()() [26/27]

template<typename MapT , typename StepControlT , typename CurveT >

BasicCnOdeSolver< MapT, StepControlT, CurveT >::VectorType capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::operator()	(	VectorType	v,
		MatrixType &	o_resultDerivative
	)

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

operator()() [27/27]

template<typename MapType , typename StepControlType , typename CurveT >

BasicOdeSolver< MapType, StepControlType, CurveT >::VectorType capd::dynsys::BasicOdeSolver< MapType, StepControlType, CurveT >::operator()	(	VectorType	v,
		MatrixType &	o_resultDerivative
	)

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

Phi() [1/2]

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

CnOdeSolver< MapT, StepControlPolicy, EnclosurePolicy, CurveT >::VectorType capd::dynsys::CnOdeSolver< MapT, StepControlPolicy, EnclosurePolicy, CurveT >::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 >.

Phi() [2/2]

template<class FadMapT , typename StepControlT >

FadOdeSolver< FadMapT, StepControlT >::VectorType capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::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< MatrixT >.

recordDags()

template<class FadMapT , typename StepControlT >

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

protected

Remainder() [1/2]

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

CnOdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::VectorType capd::dynsys::CnOdeSolver< 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 >.

Remainder() [2/2]

template<class FadMapT , typename StepControlT >

FadOdeSolver< FadMapT, StepControlT >::VectorType capd::dynsys::FadOdeSolver< FadMapT, StepControlT >::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< MatrixT >.

reset()

template<class FadMapT , typename StepControlT >

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

protected

setInitialCondition() [1/7]

template<typename MapT , typename StepControlT , typename CurveT >

void capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::setInitialCondition ( const JetType &  coeff )

protected

setInitialCondition() [2/7]

template<class FadMapT , typename StepControlT >

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

protected

setInitialCondition() [3/7]

template<class FadMapT , typename StepControlT >

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

protected

setInitialCondition() [4/7]

template<class FadMapT , typename StepControlT >

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

protected

setInitialCondition() [5/7]

template<typename MapT , typename StepControlT , typename CurveT >

void capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::setInitialCondition ( const VectorType &  v, const MatrixType &  D  )

protected

setInitialCondition() [6/7]

template<typename MapT , typename StepControlT , typename CurveT >

void capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::setInitialCondition ( const VectorType &  v, const MatrixType &  D, const HessianType &  H  )

protected

setInitialCondition() [7/7]

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

void capd::dynsys::CnOdeSolver< MapT, StepControlPolicy, EnclosurePolicy, CurveT >::setInitialCondition ( ScalarType  t, const VectorType &  x, const VectorType &  xx  )

protected

setOrder() [1/2]

template<typename MapType , typename StepControlType , typename CurveT >

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

(

size_type

order

)

Sets the order of the Taylor method.

setOrder() [2/2]

template<typename MapType , typename StepControlType , typename CurveT >

void capd::dynsys::BasicOdeSolver< MapType, StepControlType, CurveT >::setOrder ( size_type  order )

virtual

Sets the order of the Taylor method.

Reimplemented from capd::diffAlgebra::BasicCurve< MatrixT >.

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

setStep() [1/3]

template<typename MapType , typename StepControlType , typename CurveT >

void capd::dynsys::BasicCnOdeSolver< MapType, StepControlType, CurveT >::setStep ( const ScalarType &  newStep )

inline

Sets time step and turns off step control.

setStep() [2/3]

template<typename FadMapT , typename StepControlType >

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

inline

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

setStep() [3/3]

template<typename MapType , typename StepControlType , typename CurveT >

void capd::dynsys::BasicOdeSolver< MapType, StepControlType, CurveT >::setStep ( const ScalarType &  newStep )

inline

Sets fixed time step and turns off step control.

sum()

template<typename MapT , typename StepControlT , typename CurveT >

void capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::sum ( VectorType &  v )

protected

sumTaylorSeries() [1/9]

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

template<class JetT >

void capd::dynsys::CnOdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::sumTaylorSeries

(

JetT &

o_phi

)

sumTaylorSeries() [2/9]

template<class FadMapT , typename StepControlT >

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

protected

sumTaylorSeries() [3/9]

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

void capd::dynsys::CnOdeSolver< MapT, StepControlPolicy, EnclosurePolicy, CurveT >::sumTaylorSeries	(	VectorType &	o_phi,
		MatrixType &	o_jacPhi
	)

sumTaylorSeries() [4/9]

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

void capd::dynsys::CnOdeSolver< MapT, StepControlPolicy, EnclosurePolicy, CurveT >::sumTaylorSeries	(	VectorType &	o_phi,
		MatrixType &	o_jacPhi,
		HessianType &	o_hessianPhi
	)

sumTaylorSeries() [5/9]

template<class FadMapT , typename StepControlT >

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

protected

sumTaylorSeries() [6/9]

template<class FadMapT , typename StepControlT >

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

protected

sumTaylorSeries() [7/9]

template<typename MapType , typename StepControlType , typename CurveT >

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

protected

sumTaylorSeries() [8/9]

template<typename MapType , typename StepControlType , typename CurveT >

void capd::dynsys::BasicOdeSolver< MapType, StepControlType, CurveT >::sumTaylorSeries ( VectorType &  v, MatrixType &  der, VectorType *  coeff, MatrixType *  matrixCoeff, size_type  order  )

protected

sumTaylorSeries() [9/9]

template<typename MapType , typename StepControlType , typename CurveT >

void capd::dynsys::BasicOdeSolver< MapType, StepControlType, CurveT >::sumTaylorSeries ( VectorType &  v, VectorType *  coeff, size_type  order  )

inlineprotected

~BasicCnOdeSolver()

template<typename MapT , typename StepControlT , typename CurveT >

capd::dynsys::BasicCnOdeSolver< MapT, StepControlT, CurveT >::~BasicCnOdeSolver

virtual