Add MEDIAN group function

[jimtng]

Resolve #4341

[openhab-bot]

This pull request has been mentioned on openHAB Community. There might be relevant details there:

https://community.openhab.org/t/feature-request-median/157728/12

[J-N-K]

Otherwise LGTM. Thanks!

[mherwege]

@jimtng Great you took this one. I am wondering if it makes sense to use a more performant algorithm using heaps? See https://www.baeldung.com/java-stream-integers-median-using-heap. I expect it will for the other case with persistence when looking at a longer period with many data points. Here the impact could be important because this recalculation (and sorting) will be done for every state change of an item in the group.

[mherwege]

And here is a text on another, at first side even better, algorithm: https://rcoh.me/posts/linear-time-median-finding/

[jimtng]

@mherwege great idea! I'm going to do some tests comparing the two/three implementations.

I'm also wondering about keeping an in-memory sorted list and update it whenever the members changed. That would involve a sorting operation at the beginning, and only deletion + insertion of (changed|added|removed) item(s), which should probably be even faster than any quickselect / heap median algorithm. However, the way it's currently done, we got given a list of items with no knowledge of the groupitem (only the baseitem). So to do that, a lot of things would need to be changed.

[mherwege]

@jimtng I am not sure the extra complexity of handling item state changes + item addition + item removal in a group are worth it for this use case. Using an algorithm that scales linearly (or at least most of the time) with number of items I suspect does.
Looking at the algorithms, the advantage of the heap methods is when you want to have a stream of medians with every item you add. It avoids sorting (or quickselect) every time. That is not the case here. You only need to calculate once for a change every time, so quickselect looks like the most promising. I of course applaud you intending to test it.

[mherwege]

deletion + insertion of (changed|added|removed) item(s)

That’s what the heap approach could optimise.

[jimtng]

Note: waiting for #4345 to be merged, and refactor to use the Statistics.median method.

[mherwege]

@jimtng #4345 has been merged.

[jimtng]

Thanks, updated!

[J-N-K]

LGTM

[geert-claes]

Thanks y'all guys for implementing.