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From: =?ISO-8859-1?Q?Hans-Bernhard_Br=F6ker?= <HBBroeker@t-online.de>
Newsgroups: comp.graphics.apps.gnuplot
Subject: Re: Wrong fit direction / zrange / unreadable graph file
Date: Thu, 19 May 2011 14:02:33 +0200
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On 19.05.2011 11:07, Ingo Thies wrote:

> Hmm, I do not see why
>
> d/da (a+b*x)
>
> should cause troubles at a=0, unless there is some kind of scaling the
> differences (rather than differentials in numerics) da by a, so that da
> may become zero if a is.

... which is exactly what we do.  The derivative in question is usually 
computed as (f(a*1.001,b)-f(a,b))/(a*0.001).  As that would yield 
nonsense for a==zero, we replace all values in the region of 
-1e30<a<+1e-30 by +1e-30.

>> The second part of the problem is that we don't normalize parameters to
>> a common scale, so parameters of wildly different magnitude cause the
>> fit to grind to a halt.

> In the given example the number of iterations is pretty small, so that I
> won't assume any kind of numerical stall here.

Actually, in the problematic cases reported here, the reason the number 
of iterations was so small was that the fit progress was so slow that 
the algorithm mistook it for convergence (relative change of chisquare 
below the limit).  Note how 'n' got stuck at basically the first 
non-zero value it acquired (1e-30), and never changed again.  That's a 
typical symptom of parameter scale mismatch.