Let be given a set of measurements $\left\{(x_1,y_1), (x_2,y_2),\ldots, (x_n,y_n)\right\}$. For these points, we further are given the slopes $y'_i$ measured at the support points $x_i$ for $i \in \{1,\ldots,n\}$.
I am looking for a common interpolation method that can incorporate this information efficiently. What I need is an interpolation function $y=f(x)$ with values $y_i$ and first derivatives $y'_i$ at the support points $x_i$.
I first checked for cubic splines, but these just assure that the splines have the same first and second order derivative at the support points (knots). Prescribing the actual slope (for all knots) is not foreseen.
Hints on existing implementations in Python, Matlab, C++, … would be highly appreciated too.
Best Answer
Cubic Hermite spline will interpolate given set of points and first derivatives. This should be what you need. See here for details.