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Re: FindFit bug
*To*: mathgroup at smc.vnet.net
*Subject*: [mg116093] Re: FindFit bug
*From*: Daniel Lichtblau <danl at wolfram.com>
*Date*: Tue, 1 Feb 2011 06:56:01 -0500 (EST)
Igor wrote:
> Hello,
> It seems that FindFit cannot fit a sine function.
> It produces no warnings and gives a totally
> wrong answer:
>
> dat = Table[{t, 3 Sin[3 t + 1]}, {t, -3, 3, 0.1}];
>
> fit = FindFit[dat, a Sin[w t + f], {a, w, f}, t]
>
> Show[ListPlot[dat], Plot[a Sin[w t + f] /. fit, {t, -3, 3}]]
>
> Output: {a -> 0.599211, w -> 1.51494, f -> 3.80421}
>
> At the same time it fits Sin[3t+1] just fine.
Very likely has trouble when not given reasonable starting points. Can
get around this by using a global method. That would be "NMinimize"
since the other possibilities are local optimization methods.
In[47]:= fit =
FindFit[dat, a Sin[w t + f], {a, w, f}, t, Method -> "NMinimize"]
Out[47]= {a -> -3., w -> -3., f -> -1.}
I notice that several methods give a result equivalent to yours, so I
would guess it is a local minimizer, in the {a,w,f} parameter space, for
a sums of squares approximation.
Daniel Lichtblau
Wolfram Research
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