Interpolate whole arrays of complex numbers

Question

I have a number of 2-dimensional np.arrays (all of equal size) containing complex numbers. Each of them belongs to one position in a 4-dimensional space. Those positions are

Answer 1

I ended up working around the problem, but after learning a good deal more about response surfaces and the like, I now understand that this is a far-from-trivial problem. I could not have expected a simple solution in numpy, and the question would have probably been better placed in a forum on mathematics than on programming.

If I had to tackle such a task again, I'd probably use scikit-learn to try and establish either a co-Kriging interpolation for both components, or two separate Kriging (or more general, Gaussian Process) models which share a common set of model constants, optimized to minimize the combined error amplitude, (i.e.: Full model error square is the sum of both partial model errors)

-- but first I'd go and have a look if there aren't any useful papers on the topic already.