restarting an ODE solver that has been stopped by an event doesn't work

Key: MATH421
URL: https://issues.apache.org/jira/browse/MATH421
Project: Commons Math
Issue Type: Bug
Affects Versions: 2.1
Environment: Linux
Reporter: Luc Maisonobe
Assignee: Luc Maisonobe
Priority: Minor
Fix For: 2.2
If an ODE solver is setup with an EventHandler that return STOP when the even is triggered,
the integrators stops (which is exactly the expected behavior).
If however the user want to restart the solver from the final state reached at the event with
the same configuration (expecting the event to be triggered again at a later time), then the
integrator may fail to start. It can get stuck at the previous event.
The occurrence of the bug depends on the residual sign of the g function which is not exactly
0, it depends on the convergence of the first event.
As this use case is fairly general, event occurring less than epsilon after the solver start
in the first step should be ignored, where epsilon is the convergence threshold of the event.
The sign of the g function should be evaluated after this initial ignore zone, not exactly
at beginning (if there are no event at the very beginning g(t0) and g(t0+epsilon) have the
same sign, so this does not hurt ; if there is an event at the very beginning, g(t0) and g(t0+epsilon)
have opposite signs and we want to start with the second one. Of course, the sign of epsilon
depend on the integration direction (forward or backward).

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