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Gilles commented on MATH605:

It would be easier if you could provide separate patches for distinct issues ("solvers" vs
"ode").
> Missing state events due to events between t0 and t0+e being ignored
> 
>
> Key: MATH605
> URL: https://issues.apache.org/jira/browse/MATH605
> Project: Commons Math
> Issue Type: Improvement
> Affects Versions: 3.0
> Reporter: Dennis Hendriks
> Attachments: OverlappingEventsTest.java, overlappingeventstestsv3.patch, overlappingeventstests.patch,
overlappingeventstests.patch
>
>
> The Commons Math page on ODEs (http://commons.apache.org/math/userguide/ode.html) states
in section 13.3 (Discrete Events Handling), that: "Note that g function signs changes at the
very beginning of the integration (from t0 to t0 + ε where ε is the events detection convergence
threshold) are explicitely ignored. This prevents having the integration stuck at its initial
point when a new integration is restarted just at the same point a previous one had been stopped
by an event."
> However, due the following issues:
>  MATH586: Allow using a custom rootfinding algorithm to detect state events
>  MATH599: Reimplementation of Secantbased root finding algorithms
> we can now use for instance the PegasusSolver to detect state events. Using the AllowedSolutions.RIGHT_SIDE
we can guarantee that we have passed the event. As such, skipping (future) events between
t0 and t0+e is not desired.
> I attached a Java class to show this issue. It has 2 continuous variables, each starts
at 0.0. The first has derivative 1.0, the second 2.0. Whenever they become larger than 1.0,
they are reset. We thus expect resets for event 1 at 1.0, 2.0, 3.0, etc. We expect resets
for event 2 at 0.5, 1.0, 1.5, etc. The events overlap (at 1.0, 2.0, etc). Due to numerical
differences, the events however are not detected at the exact same times. After we processed
the first, the 'skip everything between t0 and t0+e' may result in skipping events, as can
be observed from the failing unit test. The second test has a hack to get around this problem:
it is manually checked whether the guard changes, by evaluating t0 and t0+e. If an event is
detected, a step of e is done, and integration is restarted from t0+e. This solves the issue,
and the unit tests succeeds (we get the events at the expected times, and we don't miss any
events).
> From what I understand, event detection is complicated, as discussed in MATH484. I propose
to make the skipping of events betweeen t0 and t0+e optional, as that is no longer needed
in the cases I described above, and in fact causes severe problems that can only be solved
by hacks. For other (nonbracketed solution) algorithms, it may still be necessary to skip
such roots. Maybe an option could be introduced to control this behavior?
> So, if an event is detected at time t, integration may continue from t0=t, and if there
is a sign change for t0 and t0+e, then the step handler should be called for t0+e, and the
step handler should be called for t0+e as well, with isLast=true. I'm not sure what the value
of e should be. It could be the absolute accuracy of the rootfinding algorithm. if there
are multiple ones, maybe the maximum of all of them. Maybe even the minimal integration step
should be taken into account, taking the maximum of that an dall the absolute accuracies of
the rootfinding algorithms?

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