Fix Extrapolation

[SimonDanisch]

Combine the approaches from #15 #12 and adds comparison tests with PyMNE.
Still needs some clean up of the API and documentation + comments.

[SimonDanisch]

Ugh, I knew that a python test dependency would be trouble^^

The Python package matplotlib could not be imported by pyimport. Usually this means
that you did not install matplotlib in the Python version being used by PyCall.

PyCall is currently configured to use the Python version at:

/usr/bin/python3

and you should use whatever mechanism you usually use (apt-get, pip, conda,
etcetera) to install the Python package containing the matplotlib module.

[SimonDanisch]

Now, this adds a new geometry extrapolation, which adds points from a geometry (right now Rect + Circle), and then uses ScatteredInterpolation with Shepard distance (basically just a mean weighted by the distances to the existing points) to give those extra points values.
The code is here

TopoPlots.jl/src/extrapolation.jl

Line 41 in e51420a

# We use the original new points from boundingobx and not the extended one, so that the distances aren't becoming way too big.

(linked the likely most problematic line).

I also added some tests for creating those points:
Red: Bounding geometry
Blue: Extended geometry to minimize interference (took the 3x blow up from mne):

I also added new tests to directly compare the output to MNE.
Format is [TopoPlots.jl vs PyMNE] and if the scatter marker are very visible, it means a peak shift... I think we now do pretty well!
Circular extrapolation:

Rectangular extrapolation (like mne):

Problematic peaks:

Standard data:

[behinger]

wow! looks really good. Very impressed about the integration of matplotlib plots...

I have a quick question: for me ScatteredInterpolation.jl was super slow (#5). Did you observe the same, or is it negligible because you only interpolate few points?

[SimonDanisch]

Ah come on...why is there always a different error with the python deps every time there's a new CI run?

[SimonDanisch]

@behinger good question...
I haven't benchmarked it, but I was pretty sure that it should easily be fast enough for the few points, since it just calculates a couple of distances.
I imagine that it would be quite different for a 512x512 matrix of points to interpolate, which should be fairly slow!

[SimonDanisch]

Added a graphic to the docs to explain the extrapolation:

[palday]

how does this relate to #18?

[SimonDanisch]

Good question... I don't think it does, but I don't know MNE well enough, to know what's going wrong on there side.
I'll take a look at #18 after this PR!