Spline with constraints at border

Question

I have measured data on a three dimensional grid, e.g. f(x, y, t). I want to interpolate and smooth this data in the direction of t with splines. C

Answer 1

Your example does not work ( on python 2.7.9), so I only sketch my idea:

1. calculate sp
2. take the derivative via sp.derivative and evaluate it at the relevant times (probably the same times at which you measured your data)
3. Set the relevant points to zero (e.g. the value at t=0)
4. Calculate another spline from the derivative values.
5. Integrate your spline function. I guess you will have to do this numerically, but that should not be a problem. Do not forget to add a constant, to get your original function.