capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT > Class Template Reference

#include <capd/dynsys/OdeSolver.h>

Public Types
typedef MapT	VectorFieldType
typedef StepControlPolicyT	StepControlPolicy
typedef MapT::FunctionType	FunctionType
typedef VectorFieldType::MatrixType	MatrixType
typedef MatrixType::RowVectorType	VectorType
typedef MatrixType::ScalarType	ScalarType
typedef BasicOdeSolver< MapT, StepControlPolicy, CurveT >	BaseTaylor
typedef MatrixType::size_type	size_type
typedef diffAlgebra::C1TimeJet< MatrixType >	C1TimeJetType
typedef capd::vectalg::Norm< VectorType, MatrixType >	NormType
typedef capd::dynsys::ILastTermsStepControl	StepControlType
typedef capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > >	SolutionCurve
typedef VectorFieldType::JetType	JetType
typedef JetType::Multipointer	Multipointer
typedef JetType::Multiindex	Multiindex
typedef TypeTraits< ScalarType >::Real	Real
typedef Hessian< ScalarType, VectorType::csDim, VectorType::csDim >	HessianType
typedef __difference_type	difference_type
typedef VectorType::iterator	iterator
typedef VectorType::const_iterator	const_iterator

Public Member Functions
	OdeSolver (VectorFieldType &vField, size_type order, const StepControlPolicy &stepControl=StepControlPolicy())
void	setOrder (size_type order)
	Sets the order of the Taylor method. More...
VectorType	Phi (const ScalarType &t, const VectorType &iv)
	Computes value of function (usually numerical scheme for an ODE) at time t and point iv. More...
MatrixType	JacPhi (const ScalarType &t, const VectorType &iv)
	Computes derivative of function (usually numerical scheme for an ODE) at time t and point iv. More...
VectorType	enclosure (const ScalarType &t, const VectorType &x)
	Used for ODEs. It verifies the existence of solutions to IVP at time t and set of initial conditions x over the time step. If the function succeeds, a rigorous bound for the trajectories is returned. Otherwise, an exception is thrown. More...
VectorType	Remainder (const ScalarType &t, const VectorType &iv, VectorType &o_enc)
	Computes and returns bound for local error of a function (for instance if Phi is finite Taylor series of a map then this method computes bound for Lagrange remainder). If DynSys is an ODE, then out_enc contains enclosure of trajectories over the time step. If the function cannot validate existence of solutions to ODE over the time step, out_enc might be in an inconsistent state. More...
void	encloseC0Map (const ScalarType &t, const VectorType &x0, const VectorType &x, VectorType &o_phi, VectorType &o_rem, VectorType &o_enc, MatrixType &o_jacPhi)
void	encloseC1Map (const ScalarType &t, const VectorType &x0, const VectorType &x, VectorType &o_phi, VectorType &o_rem, VectorType &o_enc, MatrixType &o_jacPhi, MatrixType &o_jacRem, MatrixType &o_jacEnc)
template<typename SetType >
void	operator() (SetType &set)
	This operator computes image of the set (in given representation) using set.move function, see capd/dynsys/Move.h for details This template together with SetTraits prevent usage of various types of jets with incompatible solvers. The user will get an exception at runtime with clear message instead of unreadable compiler error. In this case a specialization C1SetMove is used meaning that this solver can integrate C^0 and C^1 sets only. Moreover, it cannot integrate nonrigorous jets (for user safety). More...
template<typename SetType >
void	operator() (SetType &set, SetType &result)
	Computes image of the set (in set's representation) and stores it in the result set. More...
void	computeRemainderCoefficients (const VectorType &x)
void	computeRemainderCoefficients (const VectorType &x, const MatrixType &M)
void	computeRemainderCoefficients (ScalarType t, const VectorType &x)
void	computeRemainderCoefficients (ScalarType t, const VectorType &x, const MatrixType &M)
void	initRemainderCoefficients (ScalarType t, const VectorType &x, unsigned degree)
virtual void	computeRemainder (ScalarType t, const VectorType &xx, VectorType &o_enc, VectorType &o_rem)
virtual void	computeRemainder (ScalarType t, const VectorType &xx, C1TimeJetType &o_enc, C1TimeJetType &o_rem)
void	computeTaylorCoefficients (ScalarType t, const VectorType &x, const VectorType &xx)
void	computeImplicitCoefficients (ScalarType t, const VectorType &x, const VectorType &xx, size_type order)
ScalarType	getCoeffNorm (size_type, size_type degree) const
ScalarType	getStep () const
	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...
const CurveT &	getImplicitCurve () const
void	computeTimeStep (const ScalarType &t, const VectorType &x)
virtual void	encloseC1Map (const ScalarType &t, const VectorType &x, const VectorType &xx, VectorType &o_phi, VectorType &o_rem, VectorType &o_enc, MapT::MatrixType &o_jacPhi, MapT::MatrixType &o_jacRem, MapT::MatrixType &o_jacEnc)=0
virtual ScalarType	Lipschitz (const ScalarType &t, const VectorType &iv, NormType &n)
	this function returns Lipschitz contants for maps. It should be overriden in classes implementing flows. More...
virtual void	encloseC0Map (const ScalarType &t, const VectorType &x, const VectorType &xx, VectorType &o_phi, VectorType &o_rem, VectorType &o_enc, MatrixType &o_jacPhi)=0
	For given set xx, time t and a point x from the set xx It simultaneously computes and returns enclosures for: More...
VectorType	operator() (VectorType)
	Computes image of vector v after one time step. More...
VectorType	operator() (ScalarType &t, const VectorType &u)
	Computes image of vector v after one time step. The argument t is updated in this procedure. More...
VectorType	operator() (VectorType, MatrixType &o_resultDerivative)
	Computes image of vector v and derivatives of the flow with respect to init condition (v,identity). Version for autonomous systems. More...
VectorType	operator() (ScalarType &t, const VectorType &, MatrixType &o_resultDerivative)
	Computes image of vector v and derivatives of the flow with respect to init condition (v,identity). Version for nonautonomous systems. The argument t is updated in this procedure. More...
VectorType	operator() (VectorType, const MatrixType &derivative, MatrixType &o_resultDerivative)
	Computes image of vector v and derivatives of a flow with respect to init condition (v, derivative) More...
VectorType	operator() (ScalarType &t, const VectorType &v, const MatrixType &derivative, MatrixType &o_resultDerivative)
	Computes image of vector v and derivatives of a flow with respect to init condition (v, derivative). The argument t is updated in this procedure. More...
void	operator() (JetT &jet)
	This operator computes image of the set (in given representation) using set.move function, see capd/dynsys/Move.h for details This template together with SetTraits prevent usage of various types of jets with incompatible solvers. The user will get an exception at runtime with clear message instead of unreadable compiler error. In this case a specialization C1JetMove is used meaning that this solver can integrate C^0 and C^1 jets only. More...
VectorType	operator() (const ScalarType &h) const
const VectorFieldType &	getVectorField () const
	Returns vector field. More...
VectorFieldType &	getVectorField ()
void	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...
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
Scalar	getMaxStep () const
void	setMaxStep (Scalar maxStep)
VectorType	timeDerivative (const ScalarType &h) const
MatrixType	derivative (const ScalarType &h) const
MatrixType	operator[] (const ScalarType &h) const
size_type	getOrder () const
	Returns the order of Taylor interpolation. More...
size_type	getAllocatedOrder () const
	Returns maximal allocated order - used to avoid memory reallocation. More...
void	clearCoefficients ()
	sets all coefficients to zero More...
const ScalarType &	centerCoefficient (size_type i, size_type j) const
ScalarType &	centerCoefficient (size_type i, size_type j)
const ScalarType &	coefficient (size_type i, size_type j) const
const ScalarType &	coefficient (size_type i, size_type j, size_type k) const
ScalarType &	coefficient (size_type i, size_type j)
ScalarType &	coefficient (size_type i, size_type j, size_type k)
const ScalarType &	remainderCoefficient (size_type i, size_type j) const
const ScalarType &	remainderCoefficient (size_type i, size_type j, size_type k) const
ScalarType &	remainderCoefficient (size_type i, size_type j)
ScalarType &	remainderCoefficient (size_type i, size_type j, size_type k)
const VectorType *	getCoefficientsAtCenter () const
VectorType *	getCoefficientsAtCenter ()
const VectorType *	getCoefficients () const
VectorType *	getCoefficients ()
const VectorType *	getRemainderCoefficients () const
VectorType *	getRemainderCoefficients ()
const MatrixType *	getMatrixCoefficients () const
MatrixType *	getMatrixCoefficients ()
const MatrixType *	getMatrixRemainderCoefficients () const
MatrixType *	getMatrixRemainderCoefficients ()
iterator	beginCenterCoefficients (size_type j)
const_iterator	beginCenterCoefficients (size_type j) const
iterator	beginCoefficients (size_type j)
const_iterator	beginCoefficients (size_type j) const
iterator	beginRemainderCoefficients (size_type j)
const_iterator	beginRemainderCoefficients (size_type j) const
iterator	beginMatrixCoefficients (size_type j)
const_iterator	beginMatrixCoefficients (size_type j) const
iterator	beginMatrixRemainderCoefficients (size_type j)
const_iterator	beginMatrixRemainderCoefficients (size_type j) const
iterator	endCenterCoefficients (size_type j)
const_iterator	endCenterCoefficients (size_type j) const
iterator	endCoefficients (size_type j)
const_iterator	endCoefficients (size_type j) const
iterator	endRemainderCoefficients (size_type j)
const_iterator	endRemainderCoefficients (size_type j) const
iterator	endMatrixCoefficients (size_type j)
const_iterator	endMatrixCoefficients (size_type j) const
iterator	endMatrixRemainderCoefficients (size_type j)
const_iterator	endMatrixRemainderCoefficients (size_type j) const
void	setInitMatrix (const MatrixType &)
void	setInitHessian (const HessianType &)
void	setInitJet (const JetType &)
std::runtime_error	domainErrorMessage (std::string msg, ScalarType h, Real left, Real right) const
virtual HessianType	hessian (const ScalarType &) const
virtual JetType	jet (const ScalarType &) const
virtual void	eval (ScalarType, JetType &) const
virtual void	setDomain (Real left, Real right)
virtual Real	getLeftDomain () const
virtual Real	getRightDomain () const

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

Protected Member Functions
void	saveCurrentSet (const capd::diffAlgebra::TimeRange< ScalarType > &)
void	saveCurrentSet (const capd::dynset::C1Set< MatrixType > &set)
void	operator= (const OdeSolver &)
	OdeSolver (const OdeSolver &t)
void	setCurrentTime (const ScalarType &a_time) const
const ScalarType &	getCurrentTime () const
const bool *	getMask () const
bool	getMask (size_type j) const
void	computeTimeStep (VectorType &v)
void	sumTaylorSeries (VectorType &v, VectorType *coeff, size_type order)
void	sumTaylorSeries (VectorType &v, MatrixType &der, VectorType *coeff, MatrixType *matrixCoeff, size_type order)
void	allocate ()
void	deallocate ()
void	copyData (const BasicCurve &c)

Protected Attributes
CurveT	implicitCurve
	an extra storage for Taylor coefficients used in implicit HO-method More...
VectorFieldType *	m_vField
	we do not allow copying of objects More...
ScalarType	m_fixedTimeStep
ScalarType	m_step
StepControlType	m_stepControl
bool	m_onOffStepControl
TolScalarType	m_absoluteTolerance
TolScalarType	m_relativeTolerance
Scalar	m_maxStep
VectorType *	m_coefficientsAtCenter
VectorType *	m_coefficients
VectorType *	m_remainderCoefficients
MatrixType *	m_matrixCoefficients
MatrixType *	m_matrixRemainderCoefficients
size_type	m_order
size_type	m_allocatedOrder
size_type	m_dimension
Real	m_left
Real	m_right
	domain More...

Member Typedef Documentation

BaseTaylor

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

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

C1TimeJetType

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

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

const_iterator

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

FunctionType

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

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

HessianType

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

inherited

iterator

template<class MatrixT >

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

inherited

JetType

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

inherited

MatrixType

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

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

Multiindex

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

inherited

Multipointer

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

inherited

NormType

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

inherited

Real

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

inherited

ScalarType

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

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

size_type

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

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

SolutionCurve

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

inherited

StepControlPolicy

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

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

StepControlType

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

inherited

VectorFieldType

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

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

VectorType

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

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

Constructor & Destructor Documentation

OdeSolver() [1/2]

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

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

OdeSolver() [2/2]

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

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

inlineprotected

Member Function Documentation

addMultiindexToMask()

void capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::addMultiindexToMask ( const Multiindex &  mi )

inlineinherited

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

Parameters

mi	multiindex to be added to the mask

Warning

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

adjustTimeStep()

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

inlineinherited

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

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

computeCoefficients() [1/4]

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

inlineinherited

computeCoefficients() [2/4]

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

inlineinherited

computeCoefficients() [3/4]

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

inlineinherited

computeCoefficients() [4/4]

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

inlineinherited

computeCoefficientsAtCenter() [1/2]

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

inlineinherited

computeCoefficientsAtCenter() [2/2]

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

inlineinherited

computeImplicitCoefficients()

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

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

inline

computeRemainder() [1/2]

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

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

inlinevirtual

computeRemainder() [2/2]

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

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

inlinevirtual

computeRemainderCoefficients() [1/4]

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

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

inline

computeRemainderCoefficients() [2/4]

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

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

inline

computeRemainderCoefficients() [3/4]

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

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

inline

computeRemainderCoefficients() [4/4]

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

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

inline

computeTaylorCoefficients()

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

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

inline

computeTimeStep() [1/2]

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

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

inline

computeTimeStep() [2/2]

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

inlineprotectedinherited

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()

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

inlineinherited

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]

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

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

encloseC1Map() [1/2]

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

pure virtualinherited

encloseC1Map() [2/2]

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

void capd::dynsys::OdeSolver< MapType, StepControlPolicy, EnclosurePolicy, CurveType >::encloseC1Map	(	const ScalarType &	t,
		const VectorType &	x0,
		const VectorType &	x,
		VectorType &	o_phi,
		VectorType &	o_rem,
		VectorType &	o_enc,
		MatrixType &	o_jacPhi,
		MatrixType &	o_jacRem,
		MatrixType &	o_jacEnc
	)

enclosure()

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

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

virtual

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

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

endCenterCoefficients() [1/2]

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()

template<class StepControlT , class Scalar >

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

inlineinherited

getCoeffNorm()

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

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

virtual

Reimplemented from capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl, capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >.

getCurrentTime()

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

inlineprotectedinherited

getCurve()

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

inherited

getEffectiveTolerance()

template<class StepControlT , class Scalar >

template<class Solver , class SetType >

static TolScalarType capd::dynsys::StepControlInterface< StepControlT, Scalar >::getEffectiveTolerance ( Solver &  solver, const SetType &  s  )

inlinestaticinherited

getImplicitCurve()

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

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

inline

getLeftDomain()

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

inlinevirtualinherited

getMask() [1/2]

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

inlineprotectedinherited

getMask() [2/2]

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

inlineprotectedinherited

getMaxStep()

template<class StepControlT , class Scalar >

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

inlineinherited

getRelativeTolerance()

template<class StepControlT , class Scalar >

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

inlineinherited

getRightDomain()

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

inlinevirtualinherited

getStep()

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

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

inlinevirtual

Returns time step of the dynamical system. By default it returns one - time step for discrete DS (maps). Shall be overridden in classes that implement numerical schemes for ODEs.

Reimplemented from capd::dynsys::DynSys< MapT::MatrixType >.

getStepControl()

template<class StepControlT , class Scalar >

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

inlineinherited

getVectorField() [1/2]

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

inlineinherited

getVectorField() [2/2]

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

inlineinherited

Returns vector field.

hessian()

virtual HessianType capd::diffAlgebra::ParametricCurve< 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 EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>

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

inline

isStepChangeAllowed()

template<class StepControlT , class Scalar >

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

inlineinherited

JacPhi()

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

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

virtual

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

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

jet()

virtual JetType capd::diffAlgebra::ParametricCurve< 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()

template<class StepControlT , class Scalar >

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

inlineinherited

operator()() [1/10]

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()() [2/10]

void capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::operator() ( JetT &  jet )

inlineinherited

This operator computes image of the set (in given representation) using set.move function, see capd/dynsys/Move.h for details This template together with SetTraits prevent usage of various types of jets with incompatible solvers. The user will get an exception at runtime with clear message instead of unreadable compiler error. In this case a specialization C1JetMove is used meaning that this solver can integrate C^0 and C^1 jets only.

operator()() [3/10]

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

inlineinherited

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

operator()() [4/10]

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

inlineinherited

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

operator()() [5/10]

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

inlineinherited

Computes image of vector v and derivatives of a flow with respect to init condition (v, derivative). The argument t is updated in this procedure.

operator()() [6/10]

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

template<typename SetType >

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

inline

This operator computes image of the set (in given representation) using set.move function, see capd/dynsys/Move.h for details This template together with SetTraits prevent usage of various types of jets with incompatible solvers. The user will get an exception at runtime with clear message instead of unreadable compiler error. In this case a specialization C1SetMove is used meaning that this solver can integrate C^0 and C^1 sets only. Moreover, it cannot integrate nonrigorous jets (for user safety).

operator()() [7/10]

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

template<typename SetType >

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

inline

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

Parameters

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

operator()() [8/10]

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

inherited

Computes image of vector v after one time step.

operator()() [9/10]

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

inherited

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

operator()() [10/10]

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

inherited

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

operator=()

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

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

inlineprotected

operator[]()

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

inlinevirtualinherited

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

Phi()

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

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

virtual

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

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

Remainder()

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

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

virtual

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

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

resetMask()

void capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::resetMask ( )

inlineinherited

Resets the mask of derivatives.

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

saveCurrentSet() [1/2]

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

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

inlineprotected

saveCurrentSet() [2/2]

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

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

inlineprotected

setAbsoluteTolerance()

template<class StepControlT , class Scalar >

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

inlineinherited

setCurrentTime()

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

inlineprotectedinherited

setDomain()

void capd::diffAlgebra::ParametricCurve< 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()

void capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::ILastTermsStepControl , capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > >::setMask ( Iterator  b, Iterator  e  )

inlineinherited

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

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

Parameters

[b,e)

iterator range which contains collection of multiindices

Warning

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

setMaxStep()

template<class StepControlT , class Scalar >

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

inlineinherited

setOrder()

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

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

virtual

Sets the order of the Taylor method.

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

setRelativeTolerance()

template<class StepControlT , class Scalar >

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

inlineinherited

setStep()

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

inlineinherited

Sets fixed time step and turns off step control.

setStepControl()

template<class StepControlT , class Scalar >

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

inlineinherited

sumTaylorSeries() [1/2]

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

protectedinherited

sumTaylorSeries() [2/2]

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

inlineprotectedinherited

timeDerivative()

Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > , capd::TypeTraits<typename 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()

template<class StepControlT , class Scalar >

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

inlineinherited

turnOnStepControl()

template<class StepControlT , class Scalar >

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

inlineinherited

Member Data Documentation

implicitCurve

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

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

protected

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

m_absoluteTolerance

template<class StepControlT , class Scalar >

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

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

protectedinherited

m_left

Real capd::diffAlgebra::ParametricCurve< 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

template<class StepControlT , class Scalar >

Scalar capd::dynsys::StepControlInterface< StepControlT, Scalar >::m_maxStep

protectedinherited

m_onOffStepControl

template<class StepControlT , class Scalar >

bool capd::dynsys::StepControlInterface< StepControlT, Scalar >::m_onOffStepControl

protectedinherited

m_order

template<class MatrixT >

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

protectedinherited

m_relativeTolerance

template<class StepControlT , class Scalar >

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

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

protectedinherited

m_stepControl

template<class StepControlT , class Scalar >

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

protectedinherited

m_vField

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

protectedinherited

we do not allow copying of objects

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

• capd/dynsys/OdeSolver.h
• capd/dynsys/OdeSolver.hpp