[SciPy-user] interpolate

[Paul Barrett]

Nils Wagner wrote:
> Hi all,
> 
> Let us consider a curve which is given by m points (x_1,y_1) ...
> (x_m,y_m).
> How can I find the first and second derivative of this curve in
> x_1,...,x_m ?
> A small example illustrating the solution to this task would be
> appreciated.
> 
> Thanks in advance
> 
>                   Nils

I'd suggest using Neville's algorithm, which allows you to fit an exact 
polynomial of degree N-1 to a set of N points.  Finding the first and 
second derivatives should then be straight forward.  Usually it isn't 
necessary to fit all N points, but to take 2 (3) points on either side 
of the region that you want to interpolate and then fit the 4 (6) points 
using a 3rd (5th) order polynomial.  I've attached a Python version of 
the algorithm.

I learned about this algorithm a couple of years ago and have wondered 
how I did with out for so long.  This is real forgotten gem as far as 
I'm concerned.

Cheers,
Paul

-- 
Paul Barrett, PhD      Space Telescope Science Institute
Phone: 410-338-4475    ESS/Science Software Group
FAX:   410-338-4767    Baltimore, MD 21218
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