Interpolation of arrays python

Question

I have a program where I want the user to choose a temperature (T_user), whatever he wants. Knowing that I have a temperature array: T=np.array([10,20,30,50,100,150,200]). I have found a way to get the index and closest value for T_user compared to the values in T. I then have X=np.array([1,2,3,4,5,6]) and Y=np.array([3,6,9,12,15,18]) using numpy.interp(). Now lets say that T_user=12 and that X,Y are respectively linked to T[0]=10 and T[1]=20 how can I create a new array interpolated with X,T arrays and "the distance"/ratio from T_user to T[0]=10 and T[1]=20. Let me know if this is not clear at all.

Answer 1

You can use the apply_along_axis method:

Code:

import numpy as np

T = np.array([10, 20, 30, 50, 100, 150, 200])
W1 = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
W2 = np.array([3, 6, 9, 12, 15, 18, 21, 24, 27, 30])

T_user = 12

# Get the neighbor values
t1 = T[T<=T_user].max(initial=T.min())
t2 = T[T_user<=T].min(initial=T.max())

# Interpolate the values
arr_interp = np.apply_along_axis(lambda e: np.interp(T_user, [t1, t2], e), 1, np.stack([W1, W2]).T)

Tests:

f = lambda t: np.apply_along_axis(lambda e: np.interp(t, [T[T<=t].max(initial=T.min()), T[t<=T].min(initial=T.max())], e), 1, np.stack([W1, W2]).T)

T_user = 12
np.testing.assert_array_equal(f(T_user), np.array([1.4, 2.8, 4.2, 5.6, 7.0, 8.4, 9.8, 11.2, 12.6, 14.0]))

T_user = 15
np.testing.assert_array_equal(f(T_user), np.array([ 2.,  4.,  6.,  8., 10., 12., 14., 16., 18., 20.]))

T_user = 31
np.testing.assert_array_equal(f(T_user), np.array([ 1.1,  2.2,  3.3,  4.4,  5.5,  6.6,  7.7,  8.8,  9.9, 11. ]))

T_user = 0
np.testing.assert_array_equal(f(T_user), np.array([ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10.]))

T_user = 10
np.testing.assert_array_equal(f(T_user), np.array([ 3.,  6.,  9., 12., 15., 18., 21., 24., 27., 30.]))

T_user = 100
np.testing.assert_array_equal(f(T_user), np.array([ 3.,  6.,  9., 12., 15., 18., 21., 24., 27., 30.]))

T_user = 200
np.testing.assert_array_equal(f(T_user), np.array([ 3.,  6.,  9., 12., 15., 18., 21., 24., 27., 30.]))

T_user = 300
np.testing.assert_array_equal(f(T_user), np.array([ 3.,  6.,  9., 12., 15., 18., 21., 24., 27., 30.]))

Explanation:

If you have a minimal sample dataset as follows, what is the interpolation going to be like in my implementation?

T = np.array([10, 20])
W1 = np.array([1,])
W2 = np.array([3,])

# Case.1 (T_user = 12)

# Case.2 (T_user = 5)

# Case.3 (T_user = 10)

# Case.4 (T_user = 25)