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Groups > comp.graphics.apps.gnuplot > #327

Re: Wrong fit direction / zrange / unreadable graph file

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On 19.05.2011 01:49, Hans-Bernhard Bröker wrote:

> The problem is not actually in the computations with matrices.  It's in
> how gnuplot computes the derivatives of the model WRT the parameters at
> each data point (a.k.a. the "Jacobian" matrix).  That derivative
> computation simply doesn't work at zero.

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.

The MINPACK and SLATEC routines I have tested are also calculating the
Jacobian numerically (unless the user wants to provide it directly,
which is also possible), in particular by forward differences, which
works fine with a=0. I could have a deeper look into the method, as far
as time permits, to understand what it does differently from gnuplot.

Indeed, there were very few cases where that algorithm failed, and, as
far as I remember, they were all caused by wrong input parameters (like
zero errors, zero powers, powers of negative x or something like that).

> 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.

-- 
Gruß,
      Ingo

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Thread

Wrong fit direction / zrange / unreadable graph file Katharina Miwege <k.miwege@googlemail.com> - 2011-05-15 23:59 -0700
  Re: Wrong fit direction / zrange / unreadable graph file Christoph Bersch <usenet@bersch.net> - 2011-05-16 11:04 +0200
    Re: Wrong fit direction / zrange / unreadable graph file Ingo Thies <ingo.thies@gmx.de> - 2011-05-16 11:34 +0200
      Re: Wrong fit direction / zrange / unreadable graph file Christoph Bersch <usenet@bersch.net> - 2011-05-16 11:52 +0200
        Re: Wrong fit direction / zrange / unreadable graph file Richard Owlett <rowlett@pcnetinc.com> - 2011-05-16 06:25 -0500
          Re: Wrong fit direction / zrange / unreadable graph file Christoph Bersch <usenet@bersch.net> - 2011-05-16 14:44 +0200
        Re: Wrong fit direction / zrange / unreadable graph file Ingo Thies <ingo.thies@gmx.de> - 2011-05-16 16:31 +0200
          Re: Wrong fit direction / zrange / unreadable graph file Katharina Miwege <k.miwege@googlemail.com> - 2011-05-16 09:01 -0700
            Re: Wrong fit direction / zrange / unreadable graph file Christoph Bersch <usenet@bersch.net> - 2011-05-17 08:46 +0200
              Re: Wrong fit direction / zrange / unreadable graph file Hans-Bernhard Bröker <HBBroeker@t-online.de> - 2011-05-19 01:34 +0200
          Re: Wrong fit direction / zrange / unreadable graph file Hans-Bernhard Bröker <HBBroeker@t-online.de> - 2011-05-19 01:49 +0200
            Re: Wrong fit direction / zrange / unreadable graph file Ingo Thies <ingo.thies@gmx.de> - 2011-05-19 11:07 +0200
              Re: Wrong fit direction / zrange / unreadable graph file Hans-Bernhard Bröker <HBBroeker@t-online.de> - 2011-05-19 14:02 +0200
      Re: Wrong fit direction / zrange / unreadable graph file Hans-Bernhard Bröker <HBBroeker@t-online.de> - 2011-05-19 01:39 +0200
        Re: Wrong fit direction / zrange / unreadable graph file Ingo Thies <ingo.thies@gmx.de> - 2011-05-19 10:58 +0200

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