Re: Interpolation undocumented error

• To: mathgroup at smc.vnet.net
• Subject: [mg113664] Re: Interpolation undocumented error
• From: "Ingolf Dahl" <ingolf.dahl at telia.com>
• Date: Sat, 6 Nov 2010 05:01:59 -0500 (EST)

```Maybe you have some points with identical or very close coordinates? Then
you might get this kind of error for the RBF interpolation. It would be easy
to put a filter in the interpolation routine before the interpolation, but I
did not find it attractive to tamper with the input data behind the back of
the user. It is thus the responsibility of the user to remove such doublets,
and I think it should be that way.
Another warning: RBF interpolation can be very good for "mathematical data",
e.g. solutions of differential equations, but can give big oscillations for
noisy experimental data.

Best regards

Ingolf Dahl

> -----Original Message-----
> From: Hyatt, John S [mailto:jshyatt at gatech.edu]
> Sent: den 5 november 2010 11:13
> To: mathgroup at smc.vnet.net
> Subject: [mg113630] Re: Interpolation undocumented error
>
> Hi all,
>
> I have tried both the Obtuse and Imtek packages suggested.  They are
installed and working
> correctly.  However, I cannot get a meaningful interpolation function to
my data.  Using
> Imtek's imsUnstructuredInterpolation, I get the following error message:
>
> LinearSolve::luc: Result for LinearSolve of badly conditioned matrix
{{-3.1356*10^21,-
> 2.01921*10^21,-1.27651*10^21,-7.89872*10^20,-4.77313*10^20,-
> 2.81064*10^20,<<40>>,-5.56912*10^18,-5.56912*10^18,-2.43624*10^18,-
> 2.43624*10^18,<<315>>},<<49>>,<<315>>} may contain significant numerical
errors. >>
>
> And for Obtuse, using the RBF method for Interpolation, I get:
>
> LinearSolve::luc: Result for LinearSolve of badly conditioned matrix
{<<1>>} may contain
> significant numerical errors. >>
>
> Both of these messages are similar.  However, I don't know how to make
sense of this error
> either:  first, what is <<...>>, and second, what is the message trying to
say?  The data is
> single-valued and obviously lies on a smooth surface - I can eyeball what
a given value
> should be, but I want a specific interpolation function so I can make it
part of my analysis
> routine.  Does anyone recognize this message, and for those of you
familiar with Obtuse and
> Imtek, has this problem cropped up before?  As far as I can tell I'm
setting up my data and
> interpolation in the same format as in the examples in both packages'
documentation.  I am
> making sure that the third element of each data point is the "z" value,
and that the "x" and
> "y" designations are consistent within all the different data sets I'm
trying to interpolate.
> I've tried different orders of fitting and different fit types, and each
time, while I do get an
> interpolation surface, it's complete nonsense (i.e. nowhere near t!
> he data).
>
> John H
>
> ----- Original Message -----
> From: "Ingolf Dahl" <Ingolf.Dahl at physics.gu.se>
> To: mathgroup at smc.vnet.net
> Sent: Thursday, October 21, 2010 7:03:01 AM
> Subject: [mg113630] [mg113269] Re: Interpolation undocumented error
>
http://www.familydahl.
> se/mathematica/ .
> This package was inspired by exactly this error message, and it contains
five different
> interpolation methods, defined as "methods" to the Interpolation function.
Which method to
> choose depends strongly on the character of the data, so you probably need
to experiment a
> little to see what suits your case.
>
> Best regards
>
> Ingolf Dahl
> Ingolf.dahl at telia.com
>
> -----Ursprungligt meddelande-----
> Fr==E5n: Hyatt, John S [mailto:jshyatt at gatech.edu]
> Skickat: den 20 oktober 2010 10:06
> Till: mathgroup at smc.vnet.net
> ==C4mne: [mg113232] Interpolation undocumented error
>
> I am trying to use Interpolation to get an interpolation function of
multidimensional data
> from light scattering.  I specifically want to be able to calculate the
value of the function at
> any point within certain parameters. I have entered the data points as
usual into
> Interpolation, but receive an error message:
>
> "Interpolation::indim: The coordinates do not lie on a structured tensor
product grid."
>
> This error is undocumented in the Mathematica Help as far as I can tell,
an
> d I don't know what the error means (i.e. what is a structured tensor
produ=
> ==
> ct grid).  After searching the web for other people with the same issue, I
=
> ==
> found only one thread on Wolfram's archives where the Imtek Mathematica
Sup=
> ==
> plement was suggested as a fix and seemed to help the person.  However,
the=
> ==
>  IMS seems to be intended for use with an earlier version of Mathematica
(I=
> ==
>  have v7.0) and the installation instructions in any case aren't
applicable=
> ==
>  to this version.  Is there a fix for this in Mathematica, or does anyone
k=
> ==
> now of any way to get the interpolation function I am looking for?  Would
u=
> ==
> ninstalling Mathematica and installing version 6 followed by the IMS be
the=
> ==
>  only way to fix this?
>
> Thanks in advance for any help,
> John H

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