Interpolation of gridded data

Question

I was hoping someone could help me with a problem that Ive been having (I'm still very new to python). I have been trying to interpolate data from a 50x4 array that is read from an excel sheet seen below.

 [ 60.      0.     23.88   22.38 ]  
 [ 60.      5.     19.508  28.2  ]  
 [ 60.     10.     16.9    32.23 ]  
 [ 60.     15.     15.4    34.03 ]  
 [ 60.     20.     14.4    35.12 ]  
 [ 60.     25.     13.66   36.02 ]  
 [ 60.     30.     13.14   36.61 ]  
 [ 60.     35.     12.69   37.14 ]  
 [ 60.     40.     12.53   37.56 ]  
 [ 60.     50.     12.33   38.32 ]  
 [ 70.      0.     19.3    21.34 ]  
 [ 70.      5.     16.06   25.37 ]  
 [ 70.     10.     13.74   28.08 ]  
 [ 70.     15.     12.33   40.07 ]  
 [ 70.     20.     11.45   41.78 ]  
 [ 70.     25.     10.77   42.8  ]

etc...

What I'm trying to achieve is to enter 2 values (say 65 and 12) which correspond to interpolated values in the 1st and 2nd column, and it would return the interpolated values for columns 3 and 4. I managed to get it working using the griddata function in matlab. However no luck in python yet.

Thanks in advance

Answer 1

I think that scipy.interpolate might do the same (or at least similar) as MATLAB's Griddata . Below code uses the Radial Basis Function for interpolation. I've only made the example for your column 3 as z-axis.

import numpy as np
from scipy import interpolate
import matplotlib.pyplot as plt
x = np.array([60] * 10 + [70] * 6)
y = np.array([0,5,10,15,20,25,30,35,40,50,0,5,10,15,20,25])
z = np.array([23.88, 19.508, 16.9, 15.4, 14.4, 13.66, 13.14, 12.69, 12.53, 12.33, 19.3, 16.06, 13.74, 12.33, 11.45, 10.77])
x_ticks = np.linspace(60, 70, 11)
y_ticks = np.linspace(0, 50, 51)    
XI, YI = np.meshgrid(x_ticks, y_ticks)

rbf = interpolate.Rbf(x, y, z, epsilon=2)
ZI = rbf(XI, YI)
print(ZI[np.argwhere(y_ticks==12)[0][0], np.argwhere(x_ticks==65)[0][0]])

>>> 14.222288614849171

Be aware that the result is ZI[y,x] , not ZI[x,y] . Also be aware that your ticks must contain the x and y values you query, otherwise you'll get an IndexError.

Maybe you can build up on that solution depending on your needs.