# [SciPy-User] scipy.interpolate.rbf sensitive to input noise ?

denis denis-bz-gg@t-online...
Mon Feb 22 06:35:35 CST 2010

```On Feb 19, 5:41 pm, josef.p...@gmail.com wrote:
> On Fri, Feb 19, 2010 at 11:26 AM, denis <denis-bz...@t-online.de> wrote:

> > Use "smooth" ? rbf.py just does
> >    self.A = self._function(r) - eye(self.N)*self.smooth
> > and you don't know A .

That's a line from scipy/interpolate/rbf.py: it solves
(A - smooth*I)x = b  instead of
Ax = b
Looks to me like a hack for A singular, plus the caller doesn't know A
anyway.

I had looked at the eigenvalues too (100 points, 2d, like
test_rbf.py):
gauss     : 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1.2e-10 ... 44
linear    : -1.8e+02 ... -0.027 5.6e+02
thinplate : -4.7e+03 ... -5.4e+02 0.0032

So gauss is singular => don't do that then.
(Odd that linalg.solve didn't LinAlgError though.)

> rbf is a global interpolator, and as Robert said for some cases you
> get very unstable results.
>
> with a large number of points self._function(r)  is not very well
> behaved and you need the penalization to make it smoother. In a
> variation of your example, I printed out the eigenvalues for self.A
> and they don't look nice without penalization.
> There are still some strange things that I don't understand with the
> behavior rbf, but when I looked at it in the past, I got better
> results by using only local information, i.e. fit rbf only to a
> neighborhood of the points, although I think thinplate did pretty well
> also with a larger number of points.

Yes -- but you don't know which points are local
without some k-nearest-neighbor algorithm ? in 2d, might as well
triangulate.
Gaussian weights nearer points automatically BUT rbf gauss looks to me
singular / unusable.

cheers
-- denis
```