verry.integrate.Tracker#
- class verry.integrate.Tracker#
Bases:
ABC,GenericAbstract base class for trackers.
Each instance of this class corresponds to a pair of a closed star set and its center.
This class is usually not instantiated directly, but is created by
TrackerFactory.- abstractmethod hull()#
Return an interval hull of the current set.
- Return type:
IntervalMatrix, shape (n,)
- abstractmethod sample()#
Return an interval vector containing the center.
- Return type:
IntervalMatrix, shape (n,)
- abstractmethod update(a, b)#
Update the current pair.
- Parameters:
a (IntervalMatrix, shape (n, n)) – The image of
hull()mapped by \(DF(x)\).b (IntervalMatrix, shape (n,)) – The value obtained by mapping
sample()with \(F(x)\).
Notes
This method updates a pair \((S,c)\to(S',c')\) with the following rule:
\[S' \supseteq \{A(x-c)+b\mid\text{$A\in[A]$, $b\in[b]$, and $x\in S$}\}.\]Note that \(S'\supseteq F(S)\) holds by the mean value theorem.