[SciPy-User] weighted griddata

Charles R Harris charlesr.harris@gmail....
Thu Sep 16 20:27:45 CDT 2010


On Thu, Sep 16, 2010 at 2:42 PM, Pauli Virtanen <pav@iki.fi> wrote:

> Thu, 16 Sep 2010 20:27:46 +0000, Pauli Virtanen wrote:
> [clip]
> > Data smoothing is a different problem than interpolation, and the
> > algorithms in griddata cannot do it, and they are not easily modified to
> > do it either.
>
> No, I tell a lie, the Clough-Tocher 2D spline could easily be used for
> weighed data smoothing. The only change needed would be to adjust the
> gradient estimation routine so that instead of minimizing
>
>        ||surface curvature||
>
> it would allow for changes also in the data points, and would minimize
>
>        ||weighed deviation from data points|| + ||surface curvature||
>
>
If you use the sqrt of the squares it is a Sobolev space due to the fact
that the first derivative can be omitted. but there are lots of variations
on this theme. Another is least squares with, say, lambda times the square
of the second difference added to the normal squared deviation. That tends
to keep the wiggles down but is very sensitive to lambda. There might even
be an official name for that method, it goes back a long ways.

Chuck
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