On 9/25/06, Robert Kern <robert.kern@gmail.com > wrote:

Bill Dandreta wrote:
> What I want is a smooth curve that serves as an upper limit for a data
> plot. I would like it to be close to the data at the local maxima.
>
> Does such a function exist?

No, not really. It would be quite tricky to construct such a beast. At the one
end would be a complete interpolating curve that goes through every point;
however, this will almost certainly not be as "smooth" as you want it. You would
need to choose the length scale at which variations in the data are ignored.
E.g. you need to find some means of determining why the curve should skip over A
but try to get close to B.

   ________
  /*      *\
/    A     \
      *      \_______
                    *B

Possibly limiting the order of an interpolating polynomial or spline will be
sufficient.

You might be able to formulate this as a constrained minimization problem using
scipy.optimize.fmin_cobyla(). Take some curve f(x), minimize (f(x) - y) under
the constraint (f(x) - y >= 0).

--
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless enigma
  that is made terrible by our own mad attempt to interpret it as though it had
  an underlying truth."
   -- Umberto Eco
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