CAPD::DynSys Library  6.0.0
Public Types | Public Member Functions | List of all members
capd::dynsys::C1DynSys< MatrixType > Class Template Referenceabstract
Dynsys

#include <capd/dynsys/C1DynSys.h>

Public Types

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

Public Member Functions

virtual void 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)=0
 
virtual VectorType Phi (const ScalarType &t, const VectorType &iv)=0
 Computes value of function (usually numerical scheme for an ODE) at time t and point iv. More...
 
virtual MatrixType JacPhi (const ScalarType &t, const VectorType &iv)=0
 Computes derivative of function (usually numerical scheme for an ODE) at time t and point iv. More...
 
virtual VectorType Remainder (const ScalarType &t, const VectorType &iv, VectorType &out_enc)=0
 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...
 
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 VectorType enclosure (const ScalarType &t, const VectorType &x)=0
 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...
 
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...
 

Member Typedef Documentation

◆ MatrixType

typedef MatrixType capd::dynsys::DynSys< MatrixType >::MatrixType
inherited

◆ NormType

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

◆ ScalarType

template<typename MatrixType >
typedef MatrixType::ScalarType capd::dynsys::C1DynSys< MatrixType >::ScalarType

◆ VectorType

template<typename MatrixType >
typedef MatrixType::RowVectorType capd::dynsys::C1DynSys< MatrixType >::VectorType

Member Function Documentation

◆ encloseC0Map()

virtual void capd::dynsys::DynSys< 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.

◆ encloseC1Map()

template<typename MatrixType >
virtual void capd::dynsys::C1DynSys< 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 virtual

◆ enclosure()

virtual VectorType capd::dynsys::DynSys< MatrixType >::enclosure ( const ScalarType &  t,
const VectorType &  x 
)
pure virtualinherited

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

◆ getStep()

virtual ScalarType capd::dynsys::DynSys< 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.

◆ JacPhi()

virtual MatrixType capd::dynsys::DynSys< MatrixType >::JacPhi ( const ScalarType &  t,
const VectorType &  iv 
)
pure virtualinherited

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

◆ 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.

◆ Phi()

virtual VectorType capd::dynsys::DynSys< MatrixType >::Phi ( const ScalarType &  t,
const VectorType &  iv 
)
pure virtualinherited

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

◆ Remainder()

virtual VectorType capd::dynsys::DynSys< MatrixType >::Remainder ( const ScalarType &  t,
const VectorType &  iv,
VectorType &  out_enc 
)
pure virtualinherited

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

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