       Re: problem with nonlinearfit

• To: mathgroup at smc.vnet.net
• Subject: [mg25578] Re: [mg25489] problem with nonlinearfit
• From: "Dragan Grgic" <Dragan.Grgic at ensg.inpl-nancy.fr>
• Date: Mon, 9 Oct 2000 01:16:43 -0400 (EDT)
• References: <200010060350.XAA24764@smc.vnet.net> <39DDFC2D.446BC2DD@students.wisc.edu>
• Sender: owner-wri-mathgroup at wolfram.com

```Thank you for your answer Timothy,
but I have already realized that it is not possible to specify a range to
use for parameter values in NonlinearFit (or NonlinearRegress). In fact, the
problem seems to be the difference between values of the two variables (e
and t):
e is the deformation and its range is: 0 to 10^-5 (without unit)
t is the time and its range is: 0 to 10^6 seconds
a and N are exposants: 0,2 to 1 for a and ~5 for N.
For the time it is possible to use an other unit (days for example); then
the range of the unit is: 0 to 10 days.
For the deformation, the only solution is to use a reduced variable (i.e.
e'=e*100000). Then the parameter K is reduced too. But mathematica reports
always the same error messages:
"Objetive function or gradient is not real at {K,N,A}={in general starting
values}"
The final solution that I have found is to use the Log function (logarithm
to base e) for the variable e', then the function is: Log[e'] =
Log[(s/K')^(Na)*(t/a)^a]
The Logarithm makes it possible to reduce the range of the e' variable (~0
to ~5). Then, all the variables and all the parameters are of the same
order; and the program work well.
Why the y variable of a function y=f(x) must have a reduced range of values
to perform a nonlinear fit?

Thanks, Dragan.

----- Original Message -----
From: "Timothy Stiles" <tastiles at students.wisc.edu>
To: mathgroup at smc.vnet.net
<mathgroup at smc.vnet.net>
Subject: [mg25578] Re: [mg25489] problem with nonlinearfit

> I'm not sure if it's possible to specify a range to use for parameter
> values in NonlinearFit, but it is possible to specify starting values by
> giving a list of {parameter, starting value} instead of just a list of
> parameters. It may be an "undocumented" feature, but it seems to work
well.
> For instance if your data is contained in the variable data and the
> function is as you describe, you could use
>
> NonlinearFit[data, (s/K)^(N a)*(t/a)^a, t, {{K, 5}, {N, 7}, {a, 9}}]
>
> if you wanted to start the fit with K=5, N=7, a=9. You could use any other
> starting values for the parameters, but if you want to specify a starting
> value for one parameter, you have to specify a starting value for all
> parameters, you can's use the following
>
> NonlinearFit[data, (s/K)^(N a)*(t/a)^a, t, {{K, 5}, N, a}]
>
> to specify a starting value for K but not for N or a.
>
> Since Mathematica does not have a constrained minimization function, it
may
> not be possible to specify a "range" for the parameters.
>
> -- Tim Stiles
>
> Dragan Grgic wrote:
>
> > Hi everybody,
> >
> > I have to fit the function e = (s/K)^(Na)*(t/a)^a    (s = constant;
> > t = variable; K,N,a = parameters) to a given set of datas.
> > Then, I have used the NonlinearFit function (Statistics'NonlinearFit'
> > package), but I have two problems:
> >
> > 1) I can't specify any start values or range using. I tried to give them
> > as any forms, but I always got error messages concerning these
> > parameters.
> >
> > 2) mathematica shows kind of a strange behavior when repeating the fit
> > operation, sometimes it keeps old values and sometimes it reports
> > different error messages.
> >
> > Any help welcome,
> > Thanks in advance, Dragan.
>
>

```

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