capd::dynsys::BasicC2OdeSolver< MapT, StepControlT, CurveT > Class Template Reference

#include <capd/dynsys/BasicC2OdeSolver.h>

Public Types
typedef MapT	VectorFieldType
typedef StepControlT	StepControlType
typedef MapT::FunctionType	FunctionType
typedef VectorFieldType::MatrixType	MatrixType
typedef MatrixType::RowVectorType	VectorType
typedef MatrixType::ScalarType	ScalarType
typedef VectorFieldType::HessianType	HessianType
typedef BasicOdeSolver< MapT, StepControlT, CurveT >	BaseTaylor
typedef CurveT	SolutionCurve
typedef MatrixType::size_type	size_type
typedef VectorFieldType::JetType	JetType
typedef JetType::Multipointer	Multipointer
typedef JetType::Multiindex	Multiindex
typedef TypeTraits< ScalarType >::Real	Real
typedef __difference_type	difference_type

Public Member Functions
	BasicC2OdeSolver (VectorFieldType &vectorField, size_type order, const StepControlT &stepControl=StepControlT())
VectorType	operator() (VectorType, MatrixType &, HessianType &)
	Computes next point on the trajectory, first and second order derivatives with respect to initial conditions. Initial conditions for variational equations are Id and zero, respectively. More...
VectorType	operator() (ScalarType &t, const VectorType &, MatrixType &, HessianType &)
	Computes next point on the trajectory of a nonautonomous system, first and second order derivatives with respect to initial conditions. Initial conditions for variational equations are Id and zero, respectively. More...
VectorType	operator() (VectorType, const MatrixType &V, const HessianType &H, MatrixType &, HessianType &)
	The routine computes next point, derivatives and second order derivatives of a flow. Initial conditions for variational equations are V and H, respectively. More...
VectorType	operator() (ScalarType &t, const VectorType &x, const MatrixType &V, const HessianType &H, MatrixType &, HessianType &)
	The routine computes next point, derivatives and second order derivatives of a nonautonomous flow. Initial conditions for variational equations are V and H, respectively. More...
template<typename JetT >
void	operator() (JetT &jet)
	This operator computes image of the set (in given representation) using set.move function, see capd/dynsys/Move.h for details This template together with SetTraits prevent usage of various types of jets with incompatible solvers. The user will get an exception at runtime with clear message instead of unreadable compiler error. In this case a specialization C2JetMove is used meaning that this solver can integrate C^0, C^1 and C^2 jets only. More...
const VectorFieldType &	getVectorField () const
	Returns vector field. More...
VectorFieldType &	getVectorField ()
size_type	dimension () const
const SolutionCurve &	getCurve ()
void	setStep (const ScalarType &newStep)
	Sets fixed time step and turns off step control. More...
ScalarType	getStep () const
	Returns the time step made in the last call to this solver. More...
void	setOrder (size_type order)
	Sets the order of the Taylor method. More...
void	setCurrentTime (const ScalarType &a_time) const
const ScalarType &	getCurrentTime () const
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...
VectorType	operator() (const ScalarType &h) const
const VectorFieldType &	getVectorField () const
	Returns vector field. More...
void	setOrder (size_type order)
	Sets the order of the Taylor method. More...
ScalarType	getStep () const
	Returns the time step made in the last call to this solver. More...
void	setStep (const ScalarType &newStep)
	Sets fixed time step and turns off step control. More...
void	computeCoefficientsAtCenter (const VectorType &x, size_type order)
void	computeCoefficientsAtCenter (ScalarType t, const VectorType &x, size_type order)
void	computeCoefficients (const VectorType &x, size_type order)
void	computeCoefficients (ScalarType t, const VectorType &x, size_type order)
void	computeCoefficients (const VectorType &x, const MatrixType &M, size_type order)
void	computeCoefficients (ScalarType t, const VectorType &x, const MatrixType &M, size_type order)
virtual ScalarType	getCoeffNorm (size_type i, size_type degree) const
size_type	dimension () const
VectorType	enclosure (const ScalarType &, const VectorType &)
void	adjustTimeStep (const ScalarType &newStep)
	sets time step but does not change step control settings (compare setStep) More...
void	setMask (Iterator b, Iterator e)
	The iterator range [b,e) should contain a range of Multiinideces the user requires to compute. More...
void	addMultiindexToMask (const Multiindex &mi)
	Adds new multiindex (along with dependencies) to the existing mask. More...
void	resetMask ()
	Resets the mask of derivatives. More...
void	turnOnStepControl ()
void	turnOffStepControl ()
void	onOffStepControl (bool _onOffStepControl)
const StepControlType &	getStepControl () const
void	setStepControl (const StepControlType &stepControl)
bool	isStepChangeAllowed () const
void	setAbsoluteTolerance (TolScalarType tol)
void	setRelativeTolerance (TolScalarType tol)
TolScalarType	getAbsoluteTolerance () const
TolScalarType	getRelativeTolerance () const
MapT::ScalarType	getMaxStep () const
void	setMaxStep (MapT::ScalarType maxStep)
HessianType	hessian (const ScalarType &h) const
VectorType	timeDerivative (const ScalarType &h) const
MatrixType	derivative (const ScalarType &h) const
MatrixType	operator[] (const ScalarType &h) const
virtual JetType	jet (const ScalarType &) const
virtual void	eval (ScalarType, JetType &) const
virtual void	setDomain (Real left, Real right)
virtual Real	getLeftDomain () const
virtual Real	getRightDomain () const

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

Protected Member Functions
bool	getMask (size_type j, size_type c) const
	BasicC2OdeSolver (const BasicC2OdeSolver &t)
void	operator= (const BasicC2OdeSolver &)
void	sumTaylorSeries (VectorType &v, MatrixType &der, HessianType &hessian, VectorType *coeff, MatrixType *matrixCoeff, HessianType *hessianCoeff, size_type order)
const bool *	getMask () const
bool	getMask (size_type j) const
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)

Protected Attributes
VectorFieldType *	m_vField
	we do not allow copying of objects More...
ScalarType	m_step
ScalarType	m_fixedTimeStep
StepControlType	m_stepControl
bool	m_onOffStepControl
TolScalarType	m_absoluteTolerance
TolScalarType	m_relativeTolerance
MapT::ScalarType	m_maxStep
Real	m_left
Real	m_right
	domain More...

Member Typedef Documentation

BaseTaylor

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

typedef BasicOdeSolver<MapT, StepControlT, CurveT> capd::dynsys::BasicC2OdeSolver< MapT, StepControlT, CurveT >::BaseTaylor

difference_type

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

typedef __difference_type capd::diffAlgebra::C2Curve< BaseCurveT, isInterval >::difference_type

inherited

FunctionType

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

typedef MapT::FunctionType capd::dynsys::BasicC2OdeSolver< MapT, StepControlT, CurveT >::FunctionType

HessianType

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

typedef VectorFieldType::HessianType capd::dynsys::BasicC2OdeSolver< MapT, StepControlT, CurveT >::HessianType

JetType

typedef VectorFieldType::JetType capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::DLastTermsStepControl , capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::JetType

inherited

MatrixType

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

typedef VectorFieldType::MatrixType capd::dynsys::BasicC2OdeSolver< MapT, StepControlT, CurveT >::MatrixType

Multiindex

typedef JetType::Multiindex capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::DLastTermsStepControl , capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::Multiindex

inherited

Multipointer

typedef JetType::Multipointer capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::DLastTermsStepControl , capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::Multipointer

inherited

Real

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

typedef TypeTraits<ScalarType>::Real capd::diffAlgebra::C2Curve< BaseCurveT, isInterval >::Real

inherited

ScalarType

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

typedef MatrixType::ScalarType capd::dynsys::BasicC2OdeSolver< MapT, StepControlT, CurveT >::ScalarType

size_type

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

typedef MatrixType::size_type capd::dynsys::BasicC2OdeSolver< MapT, StepControlT, CurveT >::size_type

SolutionCurve

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

typedef CurveT capd::dynsys::BasicC2OdeSolver< MapT, StepControlT, CurveT >::SolutionCurve

StepControlType

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

typedef StepControlT capd::dynsys::BasicC2OdeSolver< MapT, StepControlT, CurveT >::StepControlType

VectorFieldType

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

typedef MapT capd::dynsys::BasicC2OdeSolver< MapT, StepControlT, CurveT >::VectorFieldType

VectorType

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

typedef MatrixType::RowVectorType capd::dynsys::BasicC2OdeSolver< MapT, StepControlT, CurveT >::VectorType

Constructor & Destructor Documentation

BasicC2OdeSolver()

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

capd::dynsys::BasicC2OdeSolver< MapT, StepControlT, CurveT >::BasicC2OdeSolver ( const BasicC2OdeSolver< MapT, StepControlT, CurveT > &  t )

inlineprotected

Member Function Documentation

addMultiindexToMask()

void capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::DLastTermsStepControl , capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< 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::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::adjustTimeStep ( const ScalarType &  newStep )

inlineinherited

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

computeCoefficients() [1/4]

void capd::dynsys::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

computeTimeStep()

void capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::computeTimeStep ( VectorType &  v )

inlineprotectedinherited

derivative()

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

virtualinherited

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

dimension() [1/2]

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

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

inline

dimension() [2/2]

size_type capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::DLastTermsStepControl , capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::dimension ( ) const

inlineinherited

enclosure()

VectorType capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::DLastTermsStepControl , capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::enclosure ( const ScalarType &  , const VectorType &    )

inlineinherited

eval()

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

inlinevirtualinherited

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

getAbsoluteTolerance()

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

inlineinherited

getCoeffNorm()

BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::ScalarType capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::getCoeffNorm ( size_type  i, size_type  degree  ) const

virtualinherited

getCurrentTime() [1/2]

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

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

inline

getCurrentTime() [2/2]

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

inlineprotectedinherited

getCurve()

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

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

getEffectiveTolerance()

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

inlinestaticinherited

getLeftDomain()

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

inlinevirtualinherited

getMask() [1/5]

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

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

inlineprotected

getMask() [2/5]

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

inlineprotectedinherited

getMask() [3/5]

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

bool capd::dynsys::BasicOdeSolver< MapT, StepControlT, CurveT >::getMask

inlineprotected

getMask() [4/5]

bool capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::DLastTermsStepControl , capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::getMask ( size_type  j ) const

inlineprotectedinherited

getMask() [5/5]

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

bool capd::dynsys::BasicC2OdeSolver< MapT, StepControlT, CurveT >::getMask ( size_type  j, size_type  c  ) const

inlineprotected

getMaxStep()

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

inlineinherited

getRelativeTolerance()

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

inlineinherited

getRightDomain()

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

inlinevirtualinherited

getStep() [1/2]

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

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.

getStep() [2/2]

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

inlineinherited

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

getStepControl()

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

inlineinherited

getVectorField() [1/3]

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

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

inline

getVectorField() [2/3]

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

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

inline

Returns vector field.

getVectorField() [3/3]

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

inlineinherited

Returns vector field.

isStepChangeAllowed()

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

inlineinherited

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 > >.

onOffStepControl()

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

inlineinherited

operator()() [1/8]

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

virtualinherited

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

operator()() [2/8]

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

template<typename JetT >

void capd::dynsys::BasicC2OdeSolver< MapT, StepControlT, CurveT >::operator() ( JetT &  jet )

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

operator()() [3/8]

BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< 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()() [4/8]

BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< 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()() [5/8]

BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< 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()() [6/8]

BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::operator() ( VectorType  v )

inherited

Computes image of vector v after one time step.

operator()() [7/8]

BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< 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()() [8/8]

BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::VectorType capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::operator() ( VectorType  v, MatrixType &  o_resultDerivative  )

inherited

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

operator=()

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

void capd::dynsys::BasicC2OdeSolver< MapT, StepControlT, CurveT >::operator= ( const BasicC2OdeSolver< MapT, StepControlT, CurveT > &  )

inlineprotected

operator[]()

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

inlinevirtualinherited

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

resetMask()

void capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::DLastTermsStepControl , capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< 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.

setAbsoluteTolerance()

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

inlineinherited

setCurrentTime() [1/2]

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

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

inline

setCurrentTime() [2/2]

void capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::DLastTermsStepControl , capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< 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

setMask()

void capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::DLastTermsStepControl , capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::setMask ( Iterator  b, Iterator  e  )

inlineinherited

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

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

Parameters

[b,e)

iterator range which contains collection of multiindices

Warning

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

setMaxStep()

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

inlineinherited

setOrder() [1/2]

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

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

Sets the order of the Taylor method.

setOrder() [2/2]

void capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::setOrder ( size_type  order )

inherited

Sets the order of the Taylor method.

setRelativeTolerance()

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

inlineinherited

setStep() [1/2]

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

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

inline

Sets fixed time step and turns off step control.

setStep() [2/2]

void capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::setStep ( const ScalarType &  newStep )

inlineinherited

Sets fixed time step and turns off step control.

setStepControl()

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

inlineinherited

sumTaylorSeries() [1/2]

void capd::dynsys::BasicOdeSolver< MapType, StepControlType, capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< 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::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::sumTaylorSeries ( VectorType &  v, VectorType *  coeff, size_type  order  )

inlineprotectedinherited

timeDerivative()

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

inherited

turnOffStepControl()

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

inlineinherited

turnOnStepControl()

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

inlineinherited

Member Data Documentation

m_absoluteTolerance

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

protectedinherited

m_fixedTimeStep

ScalarType capd::dynsys::BasicOdeSolver< MapT, capd::dynsys::DLastTermsStepControl , capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve< typename MapT::MatrixType > > >::m_fixedTimeStep

protectedinherited

m_left

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

protectedinherited

m_maxStep

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

protectedinherited

m_onOffStepControl

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

protectedinherited

m_relativeTolerance

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

protectedinherited

m_right

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

protectedinherited

domain

m_step

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

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

protected

m_stepControl

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

protectedinherited

m_vField

template<typename MapT , typename StepControlT = capd::dynsys::DLastTermsStepControl, typename CurveT = capd::diffAlgebra::C2Curve< capd::diffAlgebra::BasicC2Curve<typename MapT::MatrixType> >>

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

protected

we do not allow copying of objects

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

• capd/dynsys/BasicC2OdeSolver.h
• capd/dynsys/BasicC2OdeSolver.hpp