Congratulations! Pardon my ignorance, as my understanding of mathematics at this level is beyond rusty, but what are the applications of this kind of functionality?
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A common way to do that is to use a Savitzky-Golay filter [0], which does a similar thing - it can smooth out data and also provide smooth derivatives of the input data. It looks like this post's technique can also do that, so maybe it'd be useful for my ice strain-rate field project.
[0] - https://en.wikipedia.org/wiki/Savitzky%E2%80%93Golay_filter
The usual implementation is as a convolution filter based on the premise that the underlying data is regularly sampled.
The pain in the arse occassional reality is missing data and|or present but glitched|spiked data .. both of which require a "sensible infill" to continue with a convolution.
This is a nice implementation and a potentially useful bit of kit- the elephant in the room (from my PoV) is "how come the application domain is irregularly sampled data"?
Generally (engineering, geophysics, etc) great lengths are taken to clock data samples like a metronome (in time and|or space (as required most)).
I'm assuming that your gridded GeoTIFF data field is regularly sampled in both the X and Y axis?
We had, in our geophysics application, a "pre computed" coefficient cache - the primary filters (central symmetric smoothing at various lengths) were common choices and almost always there to grab - missing values were either cheaply "faked" for Quick'NDirty displays or infilled by prediction filters that were S-G's computed to use existing points within the range to replace the missing value, that was either a look up from indexed filter cache or a fresh filter generation to use and stash in cache.
It's a complication (in the mechanical watch sense) to add, but with code to generate coefficients already existing it's really just looking at the generation times versus the hassle of indexing and storing them as created and the frequency of reuse of "uncommon" patterns.