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Re: Fitting a Function with no closed form
*To*: mathgroup at smc.vnet.net
*Subject*: [mg98671] Re: Fitting a Function with no closed form
*From*: dh <dh at metrohm.com>
*Date*: Thu, 16 Apr 2009 04:12:17 -0400 (EDT)
*References*: <gs47hd$7kn$1@smc.vnet.net>
Hi Adam,
you can calculate data pairs: d={{x1,y1},{x2,y2}..}
You also have the specified function F[x,p1,p2], where p1 and p2 are the
parameter to fit. Then you can calculate the parameters by e.g.:
FindFit[d,F[x,p1,p2],{p1,p2},x]
Here is an example:
=========================
d = Table[{x, RandomReal[{-1, 1}] + 2 Exp[0.1 x]}, {x, 0, 10}];
F[x_, p1_, p2_] := p1 Exp[p2 x];
FindFit[d, F[x, p1, p2], {p1, p2}, x]
=========================
Daniel
Adam Dally wrote:
> I have a histogram which I am trying to fit with a convoluted function.
>
> I get out the list of bin counts easy enough, but I can't figure out a way
> to fit the function to the data.
>
> This is the function:
> F(x)=Re[NIntegrate [normalizer*(E0 - u)^2 Sqrt[1 - m^2/(E0 - u)^2]*Exp[(-((x
> - u)^2/(2 \[Sigma]^2)))/(Sqrt[2 \[Pi]] \[Sigma])], {u, 0, E0}]]
> "E0" and "sigma" are known constants. "Normalize" and "m" are the fitting
> parameters.
>
> I can get a plot or of a table of values out of the function by:
> Plot[F(x),{x, minRange, maxRange}]
> Table[F(x),{x, minRange, maxRange, binWidth}]
>
> Is there a way to fit using a function like this? I would also like to error
> bars on the fit parameters.
>
> Thank you,
> Adam Dally
>
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