Python interpolare a function or array in a 2D (or nD) grid of parameters

Question

I have a 2D regular grid of parameters that at each point have a model for a 1D model and I would like to interpolate that 1D model array to any point of parameters space (not just the grid nodes).

For 1D grid of 1 parameter (say A) with grid values a I can do the trick using interpolate.RectBivariateSpline, which generates a function that I can call at any given value of A. ex:

from scipy import interpolate
ip = interpolate.RectBivariateSpline(a, x, model, s = 0)
new_model = ip([aa], [x])

where a is the 1D "grid" or array of values for the parameter A, x is the 1D array of discrete pixels at which the model is expressed f(x) = model(x), and aa is the new value of A at which I want to interpolate.

For the 2D case one solution would be to compute at each pixel of x (each x_i) the interpolation of the 2 parameters using RectBivariateSpline or another method, (like slicing a 3D volume in 2D planes) but that seems cumbersome and does not account for correlation between pixels on the model.

The solution here Multivariate spline interpolation in python/scipy? does not quite apply to my case as I need a complete array to be returned and I need to evaluate at different points on different moments.

From the solutions on scipy interpolation: Both LinearNDinterp and NearestNDInterp might work, but I don't know how to do a similar thing as with RectBivariateSpline, i.e. feed it the 2D (or nD) parameters grid, the pixels array for the model and the model values, and then get back a interpolated model for the same pixels but different parameter values grid(a1, a2, ... an; x) -> model(A1', A2', ... An'; x)

The solution might be here: Interpolation in vector-valued multi-variate function but I don't know how to reinterpret it to my case...

Ultimately what I would like to do is have the function f(A1, A2, ... An; x) (or something equivalent) and with some Montecarlo explore in a finer grid the parameters space when comparing the model with data.

Thanks in advance!

Answer 1

Well since nobody has come with any help I'll post my own solution. As hinted starting from the solution on Interpolation in vector-valued multi-variate function and with little more research on LinearNDinterpolation from Extrapolate with LinearNDInterpolator and basically here Python 4D linear interpolation on a rectangular grid (I missed this in my first search) I adapted it to my case in a quite straightforward way.

points = np.array((a1, a2)).T
values = np.array((models))

ip = interpolate.LinearNDInterpolator(points, values)
p = [A1_new, A2_new]
new_model = ip([point])[0]

Where a1, a2 are the arrays with the grid points of each of the parameters, for example in a 2x3 grid:

a1= [1.1, 1.1, 1.1, 2.2, 2.2, 2.2]
a2= [3.3, 4.4, 5.5, 3.3, 4.4, 5.5]

and a plot as example (of my models):

With that I can call the "function" ip at any point of the grid that I need, this is also easily extended for higher dimensions new_model = ip(A1', A2', ...). Although I have not check the scalability of it with time (if it's linear with N or most probably goes with the power of N.)

I hope this can be of some help to others.