Excel-like Interpolation in Python

Question

Plotting my data in excel as a scatter plot with smooth line and markers produces the type of figure I'm expecting. Image of Excel plots:

However when trying to plot the data in matplotlib I'm running into some issues with interpolation. I'm using the interpolation package from SciPy, I've tried a range of different interpolation methods including spline interpolation and BarycentricInterpolator as suggested previously. These plots are obviously very different to the excel produced plots however:

I've tried different smoothing and k values for spline interpolation, while the curve changes the root problem still exists.

How would I be able to produce a fitted curve similar to the excel-produced plots?

Thanks

Answer 1

The problem is that you interpolate the data on a linear scale but expect the outcome to look smooth on a logarithmic scale.

The idea would therefore be perform the interpolation on a log scale already by transforming the data to its logarithm first and then perform the interpolation. You can then transform it back to linear scale such that you can plot it on a log scale again.

from scipy.interpolate import interp1d, Akima1DInterpolator
import numpy as np
import matplotlib.pyplot as plt

x = np.array([0.02,0.2,2,20,200])
y = np.array([700,850,680,410, 700])
plt.plot(x,y, marker="o", ls="")

sx=np.log10(x)
xi_ = np.linspace(sx.min(),sx.max(), num=201)
xi = 10**(xi_)

f = interp1d(sx,y, kind="cubic")
yi = f(xi_)
plt.plot(xi,yi, label="cubic spline")

f2 = Akima1DInterpolator(sx, y)
yi2 = f2(xi_)
plt.plot(xi,yi2, label="Akima")


plt.gca().set_xscale("log")
plt.legend()
plt.show()