What is the Python interpolate function which is the same as spapi in Matlab

Question

In Matlab, I can use the spline interpolation function spapi to generate a spline curve, so that prescribed values of the curves and its first two derivatives can be matched. For example:

spapi([0 0 0 0 1 2 2 2 2],[0 1 1 1 2],[2 0 1 2 -1])

this produces the unique cubic spline f on the interval [0..2] with exactly one interior knot, at 1, that satisfies the five conditions

f(0)=2, f(1)=0, f'(1)=1, f''(1)=2, f(2)=–1

These include 3-fold matching at 1, i.e., matching there to prescribed values of the function and its first two derivatives.

In Python, however, the spline interpolate function scipy.interpolate.splrep(x,y) can not work as x should be monotone increasing.

So, how can I get a curve with prescribed values and derivative values? Is there any Python moldue or function?

Many thanks!

Answer 1

scipy.interpolate.BPoly.from_derivatives constructs a Hermite spline where you can select the values of the derivatives:

https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.BPoly.from_derivatives.html

In your example you'd have two intervals, 0..1 and 1..2.