[PICMI] Implement a BASE_DENSITY heuristic #5598
Description
There's a plan to implement a heuristic to set BASE_DENSITY appropriately in our PICMI implementation if not given by the user. Currently, it uses a hardcoded value.
Naively, one would expect that base_density = max(density(grid_points)) is the straightforward answer but grid_points might be quite a few, so this will quickly become computationally infeasible in production scenarios and was thus never implemented as such.
The necessary information might be obtainable by different means:
- For many of our densities (including free-formula densities due to sympy's analytical capabilities), this maximum could probably be derived analytically.
- For (potential future-) point-wise-given densities (like read from a file), we'd have to process the content O(N) anyways, so doing a reduction during that reading wouldn't be a lot of overhead.
One would have to come up with a prototype to find out how brittle/restrictive/(much maintenance overhead)/... this would be.
Originally posted by @PrometheusPi in #5578 (comment)