CAPD DynSys Library  5.2.0
capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT > Class Template Referenceabstract

#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< MatrixTypeC1TimeJetType
 
typedef capd::vectalg::Norm< VectorType, MatrixTypeNormType
 
typedef capd::dynsys::ILastTermsStepControl StepControlType
 
typedef capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve< typename MapT::MatrixType > > SolutionCurve
 
typedef VectorFieldType::JetType JetType
 
typedef JetType::Multipointer Multipointer
 
typedef JetType::Multiindex Multiindex
 
typedef TypeTraits< ScalarType >::Real Real
 
typedef Hessian< ScalarType, VectorType::csDim, VectorType::csDim > HessianType
 
typedef __difference_type difference_type
 
typedef VectorType::iterator iterator
 
typedef VectorType::const_iterator const_iterator
 

Public Member Functions

 OdeSolver (VectorFieldType &vField, size_type order, const StepControlPolicy &stepControl=StepControlPolicy())
 
void setOrder (size_type order)
 Sets the order of the Taylor method. More...
 
VectorType Phi (const ScalarType &t, const VectorType &iv)
 Computes value of function (usually numerical scheme for an ODE) at time t and point iv. More...
 
MatrixType JacPhi (const ScalarType &t, const VectorType &iv)
 Computes derivative of function (usually numerical scheme for an ODE) at time t and point iv. More...
 
VectorType enclosure (const ScalarType &t, const VectorType &x)
 Used for ODEs. It verifies the existence of solutions to IVP at time t and set of initial conditions x over the time step. If the function succeeds, a rigorous bound for the trajectories is returned. Otherwise, an exception is thrown. More...
 
VectorType Remainder (const ScalarType &t, const VectorType &iv, VectorType &o_enc)
 Computes and returns bound for local error of a function (for instance if Phi is finite Taylor series of a map then this method computes bound for Lagrange remainder). If DynSys is an ODE, then out_enc contains enclosure of trajectories over the time step. If the function cannot validate existence of solutions to ODE over the time step, out_enc might be in an inconsistent state. More...
 
void encloseC0Map (const ScalarType &t, const VectorType &x0, const VectorType &x, VectorType &o_phi, VectorType &o_rem, VectorType &o_enc, MatrixType &o_jacPhi)
 
void encloseC1Map (const ScalarType &t, const VectorType &x0, const VectorType &x, VectorType &o_phi, VectorType &o_rem, VectorType &o_enc, MatrixType &o_jacPhi, MatrixType &o_jacRem, MatrixType &o_jacEnc)
 
template<typename SetType >
void operator() (SetType &set)
 This operator computes image of the set (in given representation) using set.move function, see capd/dynsys/Move.h for details This template together with SetTraits prevent usage of various types of jets with incompatible solvers. The user will get an exception at runtime with clear message instead of unreadable compiler error. In this case a specialization C1SetMove is used meaning that this solver can integrate C^0 and C^1 sets only. Moreover, it cannot integrate nonrigorous jets (for user safety). More...
 
template<typename SetType >
void operator() (SetType &set, SetType &result)
 Computes image of the set (in set's representation) and stores it in the result set. More...
 
void computeRemainderCoefficients (const VectorType &x)
 
void computeRemainderCoefficients (const VectorType &x, const MatrixType &M)
 
void computeRemainderCoefficients (ScalarType t, const VectorType &x)
 
void computeRemainderCoefficients (ScalarType t, const VectorType &x, const MatrixType &M)
 
void initRemainderCoefficients (ScalarType t, const VectorType &x, unsigned degree)
 
virtual void computeRemainder (ScalarType t, const VectorType &xx, VectorType &o_enc, VectorType &o_rem)
 
virtual void computeRemainder (ScalarType t, const VectorType &xx, C1TimeJetType &o_enc, C1TimeJetType &o_rem)
 
void computeTaylorCoefficients (ScalarType t, const VectorType &x, const VectorType &xx)
 
void computeImplicitCoefficients (ScalarType t, const VectorType &x, const VectorType &xx, size_type order)
 
ScalarType getCoeffNorm (size_type, size_type degree) const
 
ScalarType getStep () const
 
const CurveT & getImplicitCurve () const
 
void computeTimeStep (const ScalarType &t, const VectorType &x)
 
virtual void encloseC1Map (const ScalarType &t, const VectorType &x, const VectorType &xx, VectorType &o_phi, VectorType &o_rem, VectorType &o_enc, MapT::MatrixType &o_jacPhi, MapT::MatrixType &o_jacRem, MapT::MatrixType &o_jacEnc)=0
 
virtual ScalarType Lipschitz (const ScalarType &t, const VectorType &iv, NormType &n)
 this function returns Lipschitz contants for maps. It should be overriden in classes implementing flows. More...
 
virtual void encloseC0Map (const ScalarType &t, const VectorType &x, const VectorType &xx, VectorType &o_phi, VectorType &o_rem, VectorType &o_enc, MatrixType &o_jacPhi)=0
 For given set xx, time t and a point x from the set xx It simultaneously computes and returns enclosures for: More...
 
virtual ScalarType getStep () const
 Returns time step of the dynamical system. By default it returns one - time step for discrete DS (maps). Shall be overridden in classes that implement numerical schemes for ODEs. More...
 
VectorType operator() (VectorType)
 Computes image of vector v after one time step. More...
 
VectorType operator() (ScalarType &t, const VectorType &u)
 Computes image of vector v after one time step. The argument t is updated in this procedure. More...
 
VectorType operator() (VectorType, MatrixType &o_resultDerivative)
 Computes image of vector v and derivatives of the flow with respect to init condition (v,identity). Version for autonomous systems. More...
 
VectorType operator() (ScalarType &t, const VectorType &, MatrixType &o_resultDerivative)
 Computes image of vector v and derivatives of the flow with respect to init condition (v,identity). Version for nonautonomous systems. The argument t is updated in this procedure. More...
 
VectorType operator() (VectorType, const MatrixType &derivative, MatrixType &o_resultDerivative)
 Computes image of vector v and derivatives of a flow with respect to init condition (v, derivative) More...
 
VectorType operator() (ScalarType &t, const VectorType &v, const MatrixType &derivative, MatrixType &o_resultDerivative)
 Computes image of vector v and derivatives of a flow with respect to init condition (v, derivative). The argument t is updated in this procedure. More...
 
void operator() (JetT &jet)
 This operator computes image of the set (in given representation) using set.move function, see capd/dynsys/Move.h for details This template together with SetTraits prevent usage of various types of jets with incompatible solvers. The user will get an exception at runtime with clear message instead of unreadable compiler error. In this case a specialization C1JetMove is used meaning that this solver can integrate C^0 and C^1 jets only. More...
 
VectorType operator() (const ScalarType &h) const
 
const VectorFieldTypegetVectorField () const
 Returns vector field. More...
 
VectorFieldTypegetVectorField ()
 
void setOrder (size_type order)
 Sets the order of the Taylor method. More...
 
ScalarType getStep () const
 Returns the time step made in the last call to this solver. More...
 
void setStep (const ScalarType &newStep)
 Sets fixed time step and turns off step control. More...
 
void computeCoefficientsAtCenter (const VectorType &x, size_type order)
 
void computeCoefficientsAtCenter (ScalarType t, const VectorType &x, size_type order)
 
void computeCoefficients (const VectorType &x, size_type order)
 
void computeCoefficients (ScalarType t, const VectorType &x, size_type order)
 
void computeCoefficients (const VectorType &x, const MatrixType &M, size_type order)
 
void computeCoefficients (ScalarType t, const VectorType &x, const MatrixType &M, size_type order)
 
const SolutionCurvegetCurve ()
 
virtual ScalarType getCoeffNorm (size_type i, size_type degree) const
 
size_type dimension () const
 
void adjustTimeStep (const ScalarType &newStep)
 sets time step but does not change step control settings (compare setStep) More...
 
void setMask (Iterator b, Iterator e)
 The iterator range [b,e) should contain a range of Multiinideces the user requires to compute. More...
 
void addMultiindexToMask (const Multiindex &mi)
 Adds new multiindex (along with dependencies) to the existing mask. More...
 
void resetMask ()
 Resets the mask of derivatives. More...
 
void turnOnStepControl ()
 
void turnOffStepControl ()
 
void onOffStepControl (bool _onOffStepControl)
 
const StepControlTypegetStepControl () const
 
void setStepControl (const StepControlType &stepControl)
 
bool isStepChangeAllowed () const
 
void setAbsoluteTolerance (TolScalarType tol)
 
void setRelativeTolerance (TolScalarType tol)
 
TolScalarType getAbsoluteTolerance () const
 
TolScalarType getRelativeTolerance () const
 
MapT::ScalarType getMaxStep () const
 
void setMaxStep (MapT::ScalarType maxStep)
 
VectorType timeDerivative (const ScalarType &h) const
 
MatrixType derivative (const ScalarType &h) const
 
MatrixType operator[] (const ScalarType &h) const
 
size_type getOrder () const
 Returns the order of Taylor interpolation. More...
 
size_type getAllocatedOrder () const
 Returns maximal allocated order - used to avoid memory reallocation. More...
 
void clearCoefficients ()
 sets all coefficients to zero More...
 
const ScalarTypecenterCoefficient (size_type i, size_type j) const
 
ScalarTypecenterCoefficient (size_type i, size_type j)
 
const ScalarTypecoefficient (size_type i, size_type j) const
 
const ScalarTypecoefficient (size_type i, size_type j, size_type k) const
 
ScalarTypecoefficient (size_type i, size_type j)
 
ScalarTypecoefficient (size_type i, size_type j, size_type k)
 
const ScalarTyperemainderCoefficient (size_type i, size_type j) const
 
const ScalarTyperemainderCoefficient (size_type i, size_type j, size_type k) const
 
ScalarTyperemainderCoefficient (size_type i, size_type j)
 
ScalarTyperemainderCoefficient (size_type i, size_type j, size_type k)
 
const VectorTypegetCoefficientsAtCenter () const
 
VectorTypegetCoefficientsAtCenter ()
 
const VectorTypegetCoefficients () const
 
VectorTypegetCoefficients ()
 
const VectorTypegetRemainderCoefficients () const
 
VectorTypegetRemainderCoefficients ()
 
const MatrixTypegetMatrixCoefficients () const
 
MatrixTypegetMatrixCoefficients ()
 
const MatrixTypegetMatrixRemainderCoefficients () const
 
MatrixTypegetMatrixRemainderCoefficients ()
 
iterator beginCenterCoefficients (size_type j)
 
const_iterator beginCenterCoefficients (size_type j) const
 
iterator beginCoefficients (size_type j)
 
const_iterator beginCoefficients (size_type j) const
 
iterator beginRemainderCoefficients (size_type j)
 
const_iterator beginRemainderCoefficients (size_type j) const
 
iterator beginMatrixCoefficients (size_type j)
 
const_iterator beginMatrixCoefficients (size_type j) const
 
iterator beginMatrixRemainderCoefficients (size_type j)
 
const_iterator beginMatrixRemainderCoefficients (size_type j) const
 
iterator endCenterCoefficients (size_type j)
 
const_iterator endCenterCoefficients (size_type j) const
 
iterator endCoefficients (size_type j)
 
const_iterator endCoefficients (size_type j) const
 
iterator endRemainderCoefficients (size_type j)
 
const_iterator endRemainderCoefficients (size_type j) const
 
iterator endMatrixCoefficients (size_type j)
 
const_iterator endMatrixCoefficients (size_type j) const
 
iterator endMatrixRemainderCoefficients (size_type j)
 
const_iterator endMatrixRemainderCoefficients (size_type j) const
 
void setInitMatrix (const MatrixType &)
 
void setInitHessian (const HessianType &)
 
void setInitJet (const JetType &)
 
std::runtime_error domainErrorMessage (std::string msg, ScalarType h, Real left, Real right) const
 
virtual HessianType hessian (const ScalarType &) const
 
virtual JetType jet (const ScalarType &) const
 
virtual void eval (ScalarType, JetType &) const
 
virtual void setDomain (Real left, Real right)
 
virtual Real getLeftDomain () const
 
virtual Real getRightDomain () const
 

Static Public Member Functions

static TolScalarType getEffectiveTolerance (Solver &solver, const SetType &s)
 

Protected Member Functions

void saveCurrentSet (const capd::diffAlgebra::TimeRange< ScalarType > &)
 
void saveCurrentSet (const capd::dynset::C1Set< MatrixType > &set)
 
void operator= (const OdeSolver &)
 
 OdeSolver (const OdeSolver &t)
 
void setCurrentTime (const ScalarType &a_time) const
 
const ScalarTypegetCurrentTime () const
 
const boolgetMask () 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...
 
VectorFieldTypem_vField
 we do not allow copying of objects More...
 
ScalarType m_fixedTimeStep
 
ScalarType m_step
 
StepControlType m_stepControl
 
bool m_onOffStepControl
 
TolScalarType m_absoluteTolerance
 
TolScalarType m_relativeTolerance
 
MapT::ScalarType m_maxStep
 
VectorTypem_coefficientsAtCenter
 
VectorTypem_coefficients
 
VectorTypem_remainderCoefficients
 
MatrixTypem_matrixCoefficients
 
MatrixTypem_matrixRemainderCoefficients
 
size_type m_order
 
size_type m_allocatedOrder
 
size_type m_dimension
 
Real m_left
 
Real m_right
 domain More...
 

Member Typedef Documentation

◆ BaseTaylor

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>
typedef BasicOdeSolver<MapT,StepControlPolicy,CurveT> capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::BaseTaylor

◆ C1TimeJetType

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>
typedef diffAlgebra::C1TimeJet<MatrixType> capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::C1TimeJetType

◆ const_iterator

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

◆ difference_type

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

◆ FunctionType

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

◆ HessianType

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

◆ iterator

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

◆ JetType

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

◆ MatrixType

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

◆ Multiindex

◆ Multipointer

◆ NormType

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

◆ Real

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

◆ ScalarType

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

◆ size_type

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

◆ SolutionCurve

◆ 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

◆ 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
mimultiindex to be added to the mask
Warning
causes undefined behavior if the mask has not been set before call to this method.

◆ adjustTimeStep()

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

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

◆ allocate()

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

◆ beginCenterCoefficients() [1/2]

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

◆ beginCenterCoefficients() [2/2]

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

◆ beginCoefficients() [1/2]

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

◆ beginCoefficients() [2/2]

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

◆ beginMatrixCoefficients() [1/2]

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

◆ beginMatrixCoefficients() [2/2]

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

◆ beginMatrixRemainderCoefficients() [1/2]

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

◆ beginMatrixRemainderCoefficients() [2/2]

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

◆ beginRemainderCoefficients() [1/2]

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

◆ beginRemainderCoefficients() [2/2]

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

◆ centerCoefficient() [1/2]

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

◆ centerCoefficient() [2/2]

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

◆ clearCoefficients()

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

sets all coefficients to zero

◆ coefficient() [1/4]

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

◆ coefficient() [2/4]

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

◆ coefficient() [3/4]

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

◆ coefficient() [4/4]

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

◆ computeCoefficients() [1/4]

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

◆ computeCoefficients() [2/4]

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

◆ computeCoefficients() [3/4]

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

◆ computeCoefficients() [4/4]

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

◆ computeCoefficientsAtCenter() [1/2]

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

◆ computeCoefficientsAtCenter() [2/2]

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

◆ computeImplicitCoefficients()

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

◆ computeRemainder() [1/2]

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

◆ computeRemainder() [2/2]

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

◆ computeRemainderCoefficients() [1/4]

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

◆ computeRemainderCoefficients() [2/4]

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

◆ computeRemainderCoefficients() [3/4]

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

◆ computeRemainderCoefficients() [4/4]

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

◆ computeTaylorCoefficients()

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

◆ computeTimeStep() [1/2]

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>
void capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::computeTimeStep ( const ScalarType t,
const VectorType x 
)
inline

◆ computeTimeStep() [2/2]

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

◆ copyData()

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

◆ deallocate()

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

◆ derivative()

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

◆ dimension()

◆ domainErrorMessage()

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

◆ encloseC0Map() [1/2]

virtual void capd::dynsys::DynSys< MapT::MatrixType >::encloseC0Map ( const ScalarType t,
const VectorType x,
const VectorType xx,
VectorType o_phi,
VectorType o_rem,
VectorType o_enc,
MatrixType o_jacPhi 
)
pure virtualinherited

For given set xx, time t and a point x from the set xx It simultaneously computes and returns enclosures for:

  • numerical scheme Phi(t,x),
  • derivative of numerical scheme D_x Phi(t,xx)
  • error of numerical scheme Remainder(t,xx)
  • an enclosure for the trajectories over the time step (ODEs only) If the function cannot compute any of the output results, an exception is thrown and the output parameters o_* might be in inconsistent state.

◆ encloseC0Map() [2/2]

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

◆ encloseC1Map() [1/2]

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

◆ encloseC1Map() [2/2]

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

◆ enclosure()

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

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

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

◆ endCenterCoefficients() [1/2]

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

◆ endCenterCoefficients() [2/2]

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

◆ endCoefficients() [1/2]

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

◆ endCoefficients() [2/2]

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

◆ endMatrixCoefficients() [1/2]

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

◆ endMatrixCoefficients() [2/2]

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

◆ endMatrixRemainderCoefficients() [1/2]

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

◆ endMatrixRemainderCoefficients() [2/2]

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

◆ endRemainderCoefficients() [1/2]

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

◆ endRemainderCoefficients() [2/2]

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

◆ eval()

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

◆ getAbsoluteTolerance()

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

◆ getAllocatedOrder()

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

Returns maximal allocated order - used to avoid memory reallocation.

◆ getCoefficients() [1/2]

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

◆ getCoefficients() [2/2]

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

◆ getCoefficientsAtCenter() [1/2]

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

◆ getCoefficientsAtCenter() [2/2]

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

◆ getCoeffNorm() [1/2]

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

◆ getCoeffNorm() [2/2]

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

◆ getCurrentTime()

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

◆ getCurve()

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

◆ getEffectiveTolerance()

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

◆ getImplicitCurve()

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>
const CurveT& capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::getImplicitCurve ( ) const
inline

◆ getLeftDomain()

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

◆ getMask() [1/2]

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

◆ getMask() [2/2]

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

◆ getMatrixCoefficients() [1/2]

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

◆ getMatrixCoefficients() [2/2]

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

◆ getMatrixRemainderCoefficients() [1/2]

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

◆ getMatrixRemainderCoefficients() [2/2]

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

◆ getMaxStep()

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

◆ getOrder()

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

Returns the order of Taylor interpolation.

◆ getRelativeTolerance()

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

◆ getRemainderCoefficients() [1/2]

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

◆ getRemainderCoefficients() [2/2]

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

◆ getRightDomain()

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

◆ getStep() [1/3]

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

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

◆ getStep() [2/3]

virtual ScalarType capd::dynsys::DynSys< MapT::MatrixType >::getStep ( ) const
inlinevirtualinherited

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

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

◆ getStep() [3/3]

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>
ScalarType capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::getStep ( ) const
inline

◆ getStepControl()

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

◆ getVectorField() [1/2]

◆ getVectorField() [2/2]

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

Returns vector field.

◆ hessian()

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

◆ initRemainderCoefficients()

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>
void capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::initRemainderCoefficients ( ScalarType  t,
const VectorType x,
unsigned  degree 
)
inline

◆ isStepChangeAllowed()

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

◆ JacPhi()

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

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

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

◆ jet()

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

◆ Lipschitz()

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

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

◆ onOffStepControl()

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

◆ operator()() [1/10]

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

◆ 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]setC^0 or C^1 set representing initial conditions
[out]resulton return contains image of the set

◆ operator()() [8/10]

Computes image of vector v after one time step.

◆ operator()() [9/10]

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

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

◆ operator()() [10/10]

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

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

◆ operator=()

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>
void capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::operator= ( const OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT > &  )
inlineprotected

◆ operator[]()

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

◆ Phi()

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

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

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

◆ Remainder()

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

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

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

◆ remainderCoefficient() [1/4]

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

◆ remainderCoefficient() [2/4]

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

◆ remainderCoefficient() [3/4]

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

◆ remainderCoefficient() [4/4]

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

◆ resetMask()

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

Resets the mask of derivatives.

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

◆ saveCurrentSet() [1/2]

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>
void capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::saveCurrentSet ( const capd::diffAlgebra::TimeRange< ScalarType > &  )
inlineprotected

◆ saveCurrentSet() [2/2]

template<typename MapT , typename StepControlPolicyT = capd::dynsys::ILastTermsStepControl, typename EnclosurePolicy = HighOrderEnclosure, typename CurveT = capd::diffAlgebra::Curve< capd::diffAlgebra::BasicCurve<typename MapT::MatrixType> >>
void capd::dynsys::OdeSolver< MapT, StepControlPolicyT, EnclosurePolicy, CurveT >::saveCurrentSet ( const capd::dynset::C1Set< MatrixType > &  set)
inlineprotected

◆ setAbsoluteTolerance()

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

◆ setCurrentTime()

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

◆ setDomain()

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

◆ setInitHessian()

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

◆ setInitJet()

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

◆ setInitMatrix()

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

◆ setMask()

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

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

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

Parameters
[b,e)iterator range which contains collection of multiindices
Warning
The method causes undefined behavior if a multiindex in the collection exceeds limits of the vector field (like dimension, maximal allowed degree).

◆ setMaxStep()

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

◆ setOrder() [1/2]

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

Sets the order of the Taylor method.

◆ setOrder() [2/2]

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

Sets the order of the Taylor method.

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

◆ setRelativeTolerance()

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

◆ setStep()

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

Sets fixed time step and turns off step control.

◆ setStepControl()

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

◆ sumTaylorSeries() [1/2]

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

◆ sumTaylorSeries() [2/2]

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

◆ timeDerivative()

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

◆ turnOffStepControl()

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

◆ turnOnStepControl()

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

Member Data Documentation

◆ implicitCurve

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

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

◆ m_absoluteTolerance

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

◆ m_allocatedOrder

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

◆ m_coefficients

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

◆ m_coefficientsAtCenter

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

◆ m_dimension

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

◆ m_fixedTimeStep

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

◆ m_left

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

◆ m_matrixCoefficients

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

◆ m_matrixRemainderCoefficients

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

◆ m_maxStep

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

◆ m_onOffStepControl

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

◆ m_order

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

◆ m_relativeTolerance

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

◆ m_remainderCoefficients

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

◆ m_right

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

domain

◆ m_step

◆ m_stepControl

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

◆ m_vField

we do not allow copying of objects