how to get derivatives from 1D interpolation

You can combine scipy.interpolate.interp1d and scipy.misc.derivative, but there is something that must be taken into account:

When calling derivative method with some dx chosen as spacing, the derivative at x0 will be computed as the first order difference between x0-dx and x0+dx:

derivative(f, x0, dx) = (f(x0+dx) - f(x0-dx)) / (2 * dx)

As a result, you can't use derivative closer than dx to your interpolated function range limits, because f will raise a ValueError telling you that your interpolated function is not defined there.

So, what can you do closer than dx to those range limits?

If f is defined inside [xmin, xmax] (range):

1. At the range limits you can move x0 a bit in:
   • x0 = xmin + dx or x0 = xmax - dx
2. For other points you can refine dx (make it smaller).

Uniform function outside interpolation range:

If your interpolated function happens to be uniform outside the interpolation range:

f(x0 < xmin) = f(x0 > xmax) = f_out

You may define your interpolated function like this:

f = interp1d(x, y, bound_errors=False, fill_value=f_out)

Linear interpolation case:

For the linear case it might be cheaper to calculate just once the differences between points:

import numpy as np
df = np.diff(y) / np.diff(x)

This way you can access them as the components of an array.

As far as I know, internally interp1d uses a BSpline. The BSpline has a derivative which gives the nuth derivative.

So for an interploation f = interp1d(x, y) you can use

fd1 = f._spline.derivative(nu=1)

However, be carful as always when using functions with leading underscore. I don't think bounds are checked if you choose values outside the interpolation region. It also seems, that BSpline appends a tailing dimension, so you have to write

val = fd1(0).item()
val_arr = fd1(np.array([0, 1]))[..., 0]

Use UnivariateSpline instead of interp1d, and use the derivative method to generate the first derivative. The example at the manual page here is pretty self-explanatory.