Behavior of the LeftRootFind/RightRootFind options for backward integration

[dcourteville]

Hi, I've been wondering about the intended behavior of the LeftRootFind/RightRootFind options for callback root finding. There is two possibilities:

1. "right" is toward increasing t
2. "right" is toward integration direction

With backward integration both definitions are opposite, and the current root finding algorithm implements the first definition. Is this the intended behavior ?
Then, it would be convenient to have additional options that implements the second behavior. A typical use case would be taking the root toward integration direction to avoid an infinite loop with simultaneous event occurrences (like suggested in #889 (comment)). The new options could be named for example PrevRootFind/NextRootFind.

[ChrisRackauckas]

Yeah renaming it would probably be a good idea.

[dcourteville]

I just checked the documentation for ODE solution interpolation https://docs.sciml.ai/DiffEqDocs/stable/basics/solution/#Interpolations-and-Calculating-Derivatives :

continuity describes whether to satisfy left or right continuity when a discontinuity is saved. The default is :left, i.e. grab the value before the callback's change, but can be changed to :right.

According to this definition of left and right, the current behavior of LeftRootFind/RightRootFind with backward integration is most likely an error. If you agree with this, I can make the fix so that RightRootFind is always toward integration direction (and vice-versa for LeftRootFind). Renaming would be a breaking change, I can simply clarify the documentation instead.

[ChrisRackauckas]

Yes, what you propose is what is intended, and we can deprecate the old names to the new one. The deprecation path is straightforward.

[dcourteville]

I just pushed the fix for now. I'll do the renaming later.