Problems with python's interp 2D

Question

I am writing some functions to interpolate data. While using interp2D, somehow, a sample matrix works but when I change the size of the matrix, it returns an error.

#!/usr/bin/python3

# 
# Useful interpolation functions in python.
# 

import numpy as np
import scipy.interpolate

def interp_2d(x,y,fxy,x_desired,y_desired):

    interp_func = scipy.interpolate.interp2d(x, y, fxy, kind='cubic')

    return interp_func(x_desired,y_desired)

#
# Main function.
#

def main():

    x   =  np.array([0.0,1.0,2.0,3.0])
    y   =  np.array([0.0,1.0,2.0,3.0])
    fxy =  np.array([[50.0,60.0,70.0,80.0],
                     [50.0,60.0,70.0,80.0],
                     [50.0,60.0,70.0,80.0],
                     [50.0,60.0,70.0,80.0]])

    # With the current definition of x,y and fxy works.

    x_desired = 1.0
    y_desired = 1.0

    print(interp_2d(x,y,fxy,x_desired,y_desired)[0]) # returns 60.0, ok !

    # With this definition, it crashes.

    x   =  np.array([0.0,1.0])
    y   =  np.array([0.0,1.0])
    fxy =  np.array([[50.0,60.0],[50.0,60.0]])

    x_desired = 1.0
    y_desired = 1.0

    print(interp_2d(x,y,fxy,x_desired,y_desired)[0]) # Crashes, should be 60 as well.


if __name__== "__main__":
    main()

It is still a squared matrix, however, it do not handles the problem properly.

The error it returns is:
Traceback (most recent call last):
  File "./interp_ask.py", line 49, in <module>
    main()
  File "./interp_ask.py", line 45, in main
    print(interp_2d(x,y,fxy,x_desired,y_desired)[0]) # Crashes
  File "./interp_ask.py", line 12, in interp_2d
    interp_func = scipy.interpolate.interp2d(x, y, fxy, kind='cubic')
  File "/usr/lib/python3.7/site-packages/scipy/interpolate/interpolate.py", line 249, in __init__
    kx=kx, ky=ky, s=0.0)
dfitpack.error: (mx>kx) failed for hidden mx: regrid_smth:mx=2

Thank you all !

Answer 1

According to the documentation, the minimum number of data points in the matrix should be $(k+1)^2$, where $k=1$, $k=3$ and $k=5$ for linear, cubic and quintic interpolations, respectively. Indeed, changing kind='cubic' to kind='linear' in your code gets rid of the error.

You probably want to check the size of the matrix at the beginning of the interp_2d function to either change the interpolation type and/or return an error if the matrix size is too small.