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From: sfeam <sfeam@users.sourceforge.net>
Newsgroups: comp.graphics.apps.gnuplot
Subject: Re: trying to get a fit to work.
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Date: Wed, 08 Jun 2011 21:48:19 -0700
Organization: gnuplot development team
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aviphysics wrote:

> So I got this HPLC peak that I am trying to fit a exponentialized
> Gaussian to. It fits decently in Mathematica but trying to fit it in
> gnuplot yields "Undefined value during funtion evaluation"
> 
> The equation is
> modeltwo(x) = 1/(2*tau)*exp(sigma**2/(2*tau**2)-(x-em)/
> tau)*erfc(sigma/
> (sqrt(2)*tau)-(x-em)/(sqrt(2)*sigma))
> 
> Here is a plot using the starting constants
> http://i283.photobucket.com/albums/kk302/keyserthomas/plot.jpg
> 
> em=10
> sigma=2.3
> tau=4.98
> 
> Any ideas what the problem might be?

I forwarded this to a colleague, who replied:

%%%%%%%%%%%%%%%%

I tried a few more experiments and found that:

                 Windows           Linux (or at least Porlock)
                ---------         -------
erfc(x)      fails for |x|>~20    works (goes from -2 to 0)
erf(x)       works                works (both go from -1 to 1)
exp(x)       overflows            overflows - both at exp(~700) = 1.2x10^307

Neither OS underflows with exp(-x) - both go to zero.
I think this means there's something wrong with the way erfc works in 
windows, other than basic underflow handling. So an even simpler fix uses 
the definition of erfc:

myerfc(x) = 1 - erf(x)

- Frank

%%%%%%%%%%%%%%%%%%

So I looked at the code and found that if the configuration tool detects
erfc() in the standard libraries, the program uses it.  If not, there is
an internal implementation.  I am guessing that you are using a machine
that has configured in the internal version, and there is an overflow bug
in it somewhere.  That should be fixable, but for now you use the
workaround above.