ODEBND
Continuous-time set-valued integration of parametric ODEs

Classes

struct  mc::ODEBND_GSL< T, PMT, PVT >::Results
 Integration results at a given time instant. More...
struct  mc::ODEBND_GSL< T, PMT, PVT >::Options
 Integrator options. More...
class  mc::ODEBND_GSL< T, PMT, PVT >::Exceptions
 Structure for setting up storing the solver exceptions. More...

Functions

 mc::ODEBND_GSL< T, PMT, PVT >::ODEBND_GSL ()
 Default constructor.
virtual mc::ODEBND_GSL< T, PMT, PVT >::~ODEBND_GSL ()
 Virtual destructor.
STATUS mc::ODEBND_GSL< T, PMT, PVT >::bounds (const unsigned int ns, const double *tk, const T *Ip, T **Ixk, std::ostream &os=std::cout)
 Computes interval enclosure of reachable set of parametric ODEs.
STATUS mc::ODEBND_GSL< T, PMT, PVT >::bounds (const unsigned int ns, const double *tk, const PVT *PMp, PVT **PMxk, E *Exk=0, std::ostream &os=std::cout)
 Computes polynomial model enclosure of reachable set of parametric ODEs.
STATUS mc::ODEBND_GSL< T, PMT, PVT >::hausdorff (const unsigned int ns, const double *tk, const T *Ip, double **Hxk, const unsigned int nsamp, std::ostream &os=std::cout)
 Computes Hausdorff distance between interval enclosure and actual reachable set of parametric ODEs, using parameter sampling.
STATUS mc::ODEBND_GSL< T, PMT, PVT >::hausdorff (const unsigned int ns, const double *tk, const PVT *PMp, double **Hxk, const unsigned int nsamp, std::ostream &os=std::cout)
 Computes Hausdorff distance between polynomial model remainder enclosure and actual remainder function range, using parameter sampling.
void mc::ODEBND_GSL< T, PMT, PVT >::record (std::ofstream &bndrec, const unsigned int iprec=5) const
 Record results in file bndrec, with accuracy of iprec digits.
double mc::ODEBND_GSL< T, PMT, PVT >::final_time () const
 Return value of final time reached.

Variables

Stats mc::ODEBND_GSL< T, PMT, PVT >::stats_traj
 Statistics for state bounds integration.
 mc::BASE_GSL::BASE_GSL ()
 Default class constructor.
virtual mc::BASE_GSL::~BASE_GSL ()
 Class destructor.

Function Documentation

template<typename T , typename PMT , typename PVT >
ODEBND_GSL< T, PMT, PVT >::STATUS mc::ODEBND_GSL< T, PMT, PVT >::bounds ( const unsigned int  ns,
const double *  tk,
const T *  Ip,
T **  Ixk,
std::ostream &  os = std::cout 
) [inline]

This function computes an interval enclosure of the reachable set of the parametric ODEs defined in IVP using equally spaced samples:

  • ns [input] number of time stages
  • tk [input] stage times, including the initial time
  • Ip [input] interval parameter set
  • Ixk [output] interval state enclosures at stage times
  • os [input] output stream

The return value is the status.

template<typename T , typename PMT , typename PVT >
ODEBND_GSL< T, PMT, PVT >::STATUS mc::ODEBND_GSL< T, PMT, PVT >::bounds ( const unsigned int  ns,
const double *  tk,
const PVT *  PMp,
PVT **  PMxk,
E *  Exk = 0,
std::ostream &  os = std::cout 
) [inline]

This function computes an enclosure of the reachable set of the parametric ODEs using propagation of polynomial models with convex remainders (intervals, ellipsoids):

  • ns [input] number of time stages
  • tk [input] stage times, including the initial time
  • PMp [input] polynomial model of parameter set
  • PMxk [output] polynomial model of state enclosures at stage times
  • Exk [output] ellipsoidal remainders of polynomial models at stage times (default: NULL)
  • os [input] output stream (default: std::cout)

The return value is the status.

template<typename T , typename PMT , typename PVT >
ODEBND_GSL< T, PMT, PVT >::STATUS mc::ODEBND_GSL< T, PMT, PVT >::hausdorff ( const unsigned int  ns,
const double *  tk,
const T *  Ip,
double **  Hxk,
const unsigned int  nsamp,
std::ostream &  os = std::cout 
) [inline]

This function computes the Hausdorff distance between the interval enclosure and the exact reachable set projected onto each variable:

  • ns [input] number of time stages
  • tk [input] stage times, including the initial time
  • Ip [input] interval parameter set
  • Hxk [output] Hausdorff distance between the interval enclosure and the exact reachable set projected onto each variable, at stage times
  • nsamp [input] number of samples for each parameter
  • os [input] output stream

The return value is the status.

template<typename T , typename PMT , typename PVT >
ODEBND_GSL< T, PMT, PVT >::STATUS mc::ODEBND_GSL< T, PMT, PVT >::hausdorff ( const unsigned int  ns,
const double *  tk,
const PVT *  PMp,
double **  Hxk,
const unsigned int  nsamp,
std::ostream &  os = std::cout 
) [inline]

This function computes the Hausdorff distance between the polynomial model remainder and the actual (sampled) range of the remainder function in projection onto each variable and for each stage time remainder and the actual range of the remainder function:

  • ns [input] number of time stages
  • tk [input] stage times, including the initial time
  • PMp [input] polynomial model of parameter set
  • Hxk [output] Hausdorff distance between the polynomial model remainder and the actual (sampled) range of the remainder function, at stage times
  • nsamp [input] number of samples for each parameter
  • os [input] output stream (default: std::cout)