       Re: FindFit bug

• To: mathgroup at smc.vnet.net
• Subject: [mg116095] Re: FindFit bug
• From: "Kevin J. McCann" <Kevin.McCann at umbc.edu>
• Date: Wed, 2 Feb 2011 06:06:51 -0500 (EST)
• References: <ii5rhr\$fh4\$1@smc.vnet.net> <ii8s9u\$2ok\$1@smc.vnet.net>

```A more curious result.

I was considering using a simulated annealing approach (for fun) to
this, and in order to make the graphics easy, I reduced the number of
parameters to two, viz. 3 Sin[w t + f] with parameters w and f. Before
trying SA on this, I thought I would just do FindFit. Here are some results:

1) FindFit with no help
fit=FindFit[dat,3 Sin[w t+f],{w,f},t]
{w->0.6865385392552121`,f->1.3319574051344707`}

2) FindFit with some initial guess
fit=FindFit[dat,3 Sin[w t+f],{{w,2},{f,.5}},t]
{w->3.`,f->1.0000000000000002`}

3) FindFit with NMinimize, but no initial guess
fit=FindFit[dat,3 Sin[w t+f],{{w,2},{f,.5}},t,Method->"NMinimize"]
{w->0.05770388710750852`,f->0.025226415829465294`}

4) The surprise, FindFit with NMinimize and the above initial guesses
fit=FindFit[dat,3 Sin[w t+f],{{w,2},{f,.5}},t,Method->"NMinimize"]
{w->0.05770388710750852`,f->0.025226415829465294`}

It seems that the use of NMinimize does not help all the time.

Next, I will try SA, but that will be for another post.

Kevin

On 2/1/2011 6:54 AM, Albert Retey wrote:
> Hi,
>
>> It seems that FindFit cannot fit a sine function.
>> It produces no warnings and gives a totally
>>
>> 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.
>
> Which version are you using? For me it gives a warning with version 8
> but not with version 7. In both cases using Method "NMinimize" yields a
> correct result:
>
> fit = FindFit[dat, a Sin[w t + f], {a, w, f}, t,
>    Method ->  "NMinimize"]
>
> It is interesting to see that version 8 finds the parameters with
> negative signs when no additional constraints are given (which is of
> course also a correct result and you can enforce the positive signs with