How to set first and last slope of cubic spline interpolation in scipy.interpolate?

Question

I have a data set containing n two-dimensional points (x₀,y₀),(x₁,y₁), ... (x_n-1,y_n-1) where x₀ < x₁ < ... < x_n-1. I want to interpolate this data set using cubic splines with explicit slope values S_BEGIN and S_END set at both end points (x₀,y₀) and (x_n-1,y_n-1). I mean, let the produced n-1 cubic functions be f₀(x)=a₀x³+b₀x²+c₀x+d₀, f₁, ... , f_n-2, then df₀/dx(x₀) = S_BEGIN, df_n-2/dx(x_n-1) = S_END.

I looked in scipy.interpolate but can't find out how to set S_BEGIN and S_END to the current instance.

import numpy
import scipy

xi = numpy.array([1, 2, 3, 4, ... , 100])
yi = numpy.array([3, 5, 18, 9, ... , 42])
s_begin = 2
s_end = -1

# How can I set s_begin and s_end?
f = scipy.interpolate.interp1d(xi,yi,type='cubic')

Also, I would like to know how to get the 4(n-1) coefficients a₀,b₀,c₀,d₀,a₁,...,d_n-2 of each cubic splines which should all be built in f.

Answer 1

This is not possible with interp1d. You can get the spline coefficients from splrep though.