Details
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Improvement
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Status: Closed
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Major
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Resolution: Fixed
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3.0
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None
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None
Description
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:
MATH-586: Allow using a custom root-finding algorithm to detect state eventsMATH-599: Re-implementation of Secant-based 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 MATH-484. 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 (non-bracketed 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 root-finding 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 root-finding algorithms?