Reduce code duplication

[FractalArt]

There is a lot of duplicated code in the functions integrators::plain::integrate() and integrators::plain::resume_integration_from_checkpoints() that could potentially be reduced by factoring out the main skeleton in a helper function.

[FractalArt]

I was wondering whether it would make sense to convert the integration functions to trait methods on a PlainIntegrator struct (implementing a new trait Integrator) that would hold a random number generator self.rng and a vector of checkpoints self.checkpoints.

This way, it could have additional trait methods from_rng and from_checkpoints, where the first method would construct a new integrator by providing a random number generator and initializing the checkpoints vector to an empty vector. The second method would construct a new integrator from a set of checkpoints, storing them in self.checkpoints and using the rng_after of the last checkpoint as self.rng. The struct could then have a private method that takes care of the integration which in turn is called by the methods of the Integrator trait integrate and resume_from_checkpoints (to reduce code duplication).

Another good point about this would be that there could be another Integrator-trait method store_checkpoints_to_file() which, when called would set a struct member checkpoint_file: Option<File> that would then trigger to store the checkpoints in the file when the integrator goes out of scope. I think this is more secure and robust than doing this manually in the code. If the method is not called, we have self.checkpoint_file == None and no checkpoints are stored upon dropping.

On the other hand, since checkpoint files are somewhat related to presenting examples, I was wondering whether maybe they should be part of a dedicated callback function.