How spline extrapolate?

Hi all, I appreciate it if anyone inform me of this question:

I want to use spline command as p=spline(x,y) and then use the coefficients that are stored in the p, which is a structure object, to evaluate a function at nodes that are not in x, say xx=[0.5*x(1):0.1:2*x(end)].

I know that for the points below x(1), the evaluation takes the first break point in the p, like

               a_0+a_1*(x-x(1))+a_2*(x-x(1))^2 + a_3*(x-x(1))^3

However, I am not sure how it is done for points beyond the last break point that is stored in p. I appreciate any help

Answer 1

[Torsten]

It does not make any sense at all to evaluate splines below x(1) or above x(end).

Best wishes

Torsten.

[omid mousavi]

Well it does, you can do that your self and verify that. The question is that how it is done?

[John D'Errico]

Torsten is entirely correct. You will get a prediction of no value beyond those points. For example, in my own spline tools, I tend to use only constant extrapolation, unless the user explicitly forces the tool to do more. I do this because of the danger of extrapolation.

Can you extrapolate a spline created by spline? Yes. It will do so. In fact, a tool like ppval simply evaluates that same cubic polynomial. But doing so outside of the support of the simple will yield a result of little value. This is simply a bad idea in general.