Linear interpolation in Python using interpolate.interp2d

Question

I have recently started using Python and I have a problem that I would like to propose. I have three arrays (X1, X2, and X3). I need to apply linear interpolation. The goal is given new points with coordinates X1 and X2 apply interpolation in order to find the new value of X3.

Below is the code developed:

X1 = [ 0.  , 0.05, 0.1 , 0.15, 0.2 , 0.25, 0.3 , 0.35, 0.4 , 0.45, 0.51,
       0.56, 0.61, 0.66, 0.71, 0.76, 0.81, 0.86, 0.91, 0.96, 1.01, 1.06,
       1.11, 1.16, 1.21, 1.26, 1.31, 1.36, 1.41, 1.46, 1.52, 1.57, 1.62,
       1.67, 1.72, 1.77, 1.82, 1.87, 1.92, 1.97, 2.02, 2.07, 2.12, 2.17,
       2.22, 2.27, 2.32, 2.37, 2.42, 2.47, 2.53, 2.58, 2.63, 2.68, 2.73,
       2.78, 2.83, 2.88, 2.93, 2.98, 3.03, 3.08, 3.13, 3.18, 3.23, 3.28,
       3.33, 3.38, 3.43, 3.48, 3.54, 3.59, 3.64, 3.69, 3.74, 3.79, 3.84,
       3.89, 3.94, 3.99, 4.04, 4.09, 4.14, 4.19, 4.24, 4.29, 4.34, 4.39,
       4.44, 4.49, 4.55, 4.6 , 4.65, 4.7 , 4.75, 4.8 , 4.85, 4.9 , 4.95,
       5.  ]

X2 = [0.01, 0.02, 0.02, 0.02, 0.03, 0.04, 0.04, 0.04, 0.05, 0.06, 0.06,
        0.06, 0.07, 0.08, 0.08, 0.08, 0.09, 0.1 , 0.1 , 0.1 , 0.11, 0.12,
        0.12, 0.12, 0.13, 0.14, 0.14, 0.14, 0.15, 0.16, 0.16, 0.16, 0.17,
        0.18, 0.18, 0.18, 0.19, 0.2 , 0.2 , 0.2 , 0.21, 0.22, 0.22, 0.22,
        0.23, 0.24, 0.24, 0.24, 0.25, 0.26, 0.26, 0.26, 0.27, 0.28, 0.28,
        0.28, 0.29, 0.3 , 0.3 , 0.3 , 0.31, 0.32, 0.32, 0.32, 0.33, 0.34,
        0.34, 0.34, 0.35, 0.36, 0.36, 0.36, 0.37, 0.38, 0.38, 0.38, 0.39,
        0.4 , 0.4 , 0.4 , 0.41, 0.42, 0.42, 0.42, 0.43, 0.44, 0.44, 0.44,
        0.45, 0.46, 0.46, 0.46, 0.47, 0.48, 0.48, 0.48, 0.49, 0.5 , 0.5 ,
        0.5 ]

X3= [1.46, 1.47, 1.47, 1.47, 1.47, 1.48, 1.48, 1.49, 1.49, 1.49, 1.5 ,
        1.5 , 1.51, 1.51, 1.52, 1.52, 1.53, 1.54, 1.54, 1.55, 1.55, 1.56,
        1.56, 1.57, 1.57, 1.58, 1.58, 1.59, 1.6 , 1.6 , 1.61, 1.61, 1.62,
        1.62, 1.63, 1.63, 1.64, 1.64, 1.65, 1.65, 1.65, 1.66, 1.66, 1.67,
        1.67, 1.68, 1.68, 1.68, 1.69, 1.69, 1.7 , 1.7 , 1.7 , 1.71, 1.71,
        1.71, 1.72, 1.72, 1.72, 1.72, 1.73, 1.73, 1.73, 1.73, 1.73, 1.74,
        1.74, 1.74, 1.74, 1.74, 1.74, 1.74, 1.74, 1.75, 1.75, 1.75, 1.75,
        1.75, 1.75, 1.75, 1.74, 1.74, 1.74, 1.74, 1.74, 1.74, 1.74, 1.73,
        1.73, 1.73, 1.73, 1.72, 1.72, 1.72, 1.71, 1.71, 1.7 , 1.7 , 1.69,
        1.69]

import numpy as np
from scipy import interpolate

f = interpolate.interp2d(X1, X2, X3, kind='linear')

# We consider a new point
X1new = 2.5
X2new = 2.5
X3new = f(X1new, X2new)
X3new

The new value of X3 is 0, but it should actually be about 1.7. Do you think there is an error or is there something to add in the code?

Thank you in advance for your cooperation.

Mahdi F. · Accepted Answer · 2023-01-06 18:48:37Z

1

Your values for X2 between [0.01, 0.5]. For interpolation, you need to use values in your range. Try this:

import numpy as np
from scipy import interpolate

f = interpolate.interp2d(X1, X2, X3, kind='linear')

# We consider a new point
X1new = 2.5
X2new = 0.3
X3new = f([X1new], [X2new])
print(X3new)
# array([1.71597061])

answered Jan 6, 2023 at 18:48

Mahdi F.

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