       Re: Re: problem with nonlinearfit

• To: mathgroup at smc.vnet.net
• Subject: [mg25589] Re: [mg25578] Re: [mg25489] problem with nonlinearfit
• From: "Dragan Grgic" <Dragan.Grgic at ensg.inpl-nancy.fr>
• Date: Mon, 9 Oct 2000 21:43:29 -0400 (EDT)
• References: <001901c031c0\$5a879250\$f8dcc180@als2127a.als.orst.edu>
• Sender: owner-wri-mathgroup at wolfram.com

```Mark, Thanks for your help,

but I have not converted some of my parameters to logs (e). In fact, I have
first use reduced y variable in order to reduce the scale of its values:
y=e'=e*100000; then K'=(100000^(1/N*a))/K. But the scale of the y variable
is  too large again (0 to ~ 200)
And I have convert the y' variable into Log(e); then the scale of the values
is lineary and compressed.

Dragan GRGIC.

> Dragan,
>
> >Why the y variable of a function y=f(x) must have a reduced range of
values
> to perform a nonlinear fit?
>
>     Because the part of NonlinearRegress that calculates step sizes needs
to
> invert the curvature matrix of the problem, and that matrix depends on the
> scales of the different parameters in the parameter vector.  The routine
> doesn't "know" anything about the units in which those parameters are
> expressed, it only "sees" a matirx of elements that are, maybe, different
in
> magnitude by 10^10, or something, so the problem of inverting the matrix
is
> unstable, and it either catches this problem and generates an error msg.,
or
> it goes ahead and calculates an unreasonable step size, sending your
search
> into the nether reaches of parameter space, where, maybe, your model
> function could take on even imaginary values, or whatever.
>      This is commonly a problem when fitting chemical models with chemical
> data, where one is trying to determine equilibrium constants that could be
> very small, or very much larger than one.  In this case, it is better to
> express the model in terms of standard free energies, which are
proportional
> to Ln[equilibrium constant], which compresses those parameters.
>     I suspect that since converting some of your parameters to logs has
> helped you, you might be having the same problem.  Either use logs, or
scale
> linearly (see a reference on nonlinear regression, or optimization, for a
> discussion).
> -mark harder
>
>
>
> -----Original Message-----
> From: Dragan Grgic <Dragan.Grgic at ensg.inpl-nancy.fr>
To: mathgroup at smc.vnet.net
> To: mathgroup at smc.vnet.net <mathgroup at smc.vnet.net>
> Date: Sunday, October 08, 2000 10:30 PM
> Subject: [mg25589] [mg25578] Re: [mg25489] problem with nonlinearfit
>
>
> >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
> >To: mathgroup at smc.vnet.net
> ><mathgroup at smc.vnet.net>
> >Subject: [mg25589] [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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