spline interpolation between two arrays in python

Question

I am trying to do spline interpolation between two arrays in Python. My data set looks like this:

           |      5        15
    -------+--------------------
        1    32.68      29.16
        2    32.73      27.20
        3    32.78      28.24
        4    32.83      27.27
        5    32.88      25.27
        6    32.93      31.35
        7    32.98      27.39
        8    33.03      26.42
        9    33.08      27.46
       10    33.13      30.50
       11    33.18      27.53
       12    33.23      29.57
       13    33.23      27.99
       14    33.23      28.64
       15    33.23      26.68
       16    33.23      29.72

And I am trying to do a spline interpolation between the two points and produce the values for 10, something that will eventually look like this (but spline interpolated):

           |   10
      -----+--------
        1       30.92
        2       29.965
        3       30.51
        4       30.05
        5       29.075
        6       32.14
        7       30.185
        8       29.725
        9       30.27
        10      31.815
        11      30.355
        12      31.4
        13      30.61
        14      30.935
        15      29.955
        16      31.475

I have been looking at examples of using scipy.interpolate.InterpolatedUnivariateSpline, but it seems to take only one array for x and one for y, and I can't figure out how to make it interpolate these two arrays.

Can someone please help point me in the right direction?

Answer 1

With the amount of data you have, only two points for each x value, piecewise linear interpolation is the most practical tool. Taking your two arrays to be v5 and v15 (values along y=5 line and y=15 line), and the x-values to be 1,2, ..., 16, we can create a piecewise linear interpolant like this:

from scipy.interpolate import interp2d    
f = interp2d(np.arange(1, 17), [5, 15], np.stack((v5, v15)), kind='linear')

This can be evaluated in the usual way: for example, f(np.arange(1, 17), 10) returns precisely the numbers you expected.

[ 30.92 ,  29.965,  30.51 ,  30.05 ,  29.075,  32.14 ,  30.185,
    29.725,  30.27 ,  31.815,  30.355,  31.4  ,  30.61 ,  30.935,
    29.955,  31.475]

interp2d can also create a cubic bivariate spline, but not from this data: your grid is too small in the y-direction.