The results obtained by a kind='cubic' interpolation using interp1d seem to change between scipy 0.18.1 and 1.2.1. I use python 2.7.12/numpy 1.12.0 with the former and python 3.6.8/numpy 1.16.2 with the latter. Which change in the source code is responsible for the different results?
Example code:
import numpy as np
from scipy.interpolate import interp1d
import matplotlib.pyplot as plt
np.random.seed(1000)
n_p = 6
n_p_interpolated = 11
a = np.linspace(0,5,n_p)
a_interpolated = np.linspace(0,5,n_p_interpolated)
b = np.random.rand(n_p)
b_interpolated = interp1d(a,b,kind='cubic')(a_interpolated)
print('b:', b)
print('b_interpolated:', b_interpolated)
plt.ion()
plt.figure()
plt.plot(a,b,label='original data')
plt.plot(a_interpolated,b_interpolated,label='interpolated data')
plt.legend()
plt.xlim(-1,6)
plt.ylim(-0.2,1)
With scipy 0.18.1:
('b:', array([ 0.65358959, 0.11500694, 0.95028286, 0.4821914 , 0.87247454,
0.21233268]))
('b_interpolated:', array([ 0.65358959, -0.1292027 , 0.11500694, 0.64514961, 0.95028286,
0.75328508, 0.4821914 , 0.58350879, 0.87247454, 0.95267129,
0.21233268]))
With scipy 1.2.1:
b: [0.65358959 0.11500694 0.95028286 0.4821914 0.87247454 0.21233268]
b_interpolated: [ 0.65358959 -0.05237073 0.11500694 0.62584926 0.95028286 0.75365451
0.4821914 0.60133139 0.87247454 0.88101143 0.21233268]
All interpolated values (that are not in the original grid) are different, some quite drastically (such as the second one).
Yes, the algorithm for constructing the spline was changed. In scipy 0.18 and below, it used the find_smoothest algorithm (see scipy/interpolate/interpolate.py in the scipy source repository, pre scipy 0.19.0). From version 0.19.0 onwards, the default algorithm for cubics is not-a-knot.