Re: Why this function does not return a single value

*To*: mathgroup at smc.vnet.net*Subject*: [mg60342] Re: Why this function does not return a single value*From*: Marek Bromberek <marekbr at gmail.com>*Date*: Wed, 14 Sep 2005 03:27:11 -0400 (EDT)*References*: <dg696f$a2u$1@smc.vnet.net>*Reply-to*: marekbr at gmail.com*Sender*: owner-wri-mathgroup at wolfram.com

Hi Bill If You run the code from my previous post You will see how my data looks like because I adjusted the parameters in the lists a, b, \[Delta]L and \[Delta]G so that it represents my data quite well. However I want to use NonlinearFit (or FindFit) to find the values of those parameters which best represent my data. Regards Marek Bill Rowe wrote: > On 9/10/05 at 10:36 PM, marekbr at gmail.com (Marek Bromberek) wrote: > > >>Thanks Bill for Your reply. It makes a few things clear. > > Glad to help. > >>Let me explain what I want to do (probably it was not entirely >>clear from my original post). I want to fit a sum of 15 Voight >>functions to a dataset. Initially I thought that by making all the >>parameters as an array I would be able to use Sum function so that >>a[i], b[i] and c[i] would refer to the parameters of i-th peak in >>the sum. However I could not get this to work. (see my original >>post). Following Paul's suggestions I did the following > >>I defined the Voigt function > >>Voigt[x_, (a_)?NumericQ, (b_)?NumericQ, (\[Delta]L_)?NumericQ, >>(\[Delta]G_)?NumericQ] := >>(a*(2.*Log[2.]*\[Delta]L)*NIntegrate[1/(E^t^2*(((Sqrt[Log[2.]]*\[ >>Delta]L)/\[Delta]G)^2 + ((Sqrt[4.*Log[2.]]*(x - b))/\[Delta]G - >>t)^2)), {t, -Infinity, Infinity}])/(Pi^(3/2)*\[Delta]G) > >>then I defined lists of parameters > >>a = {6224., 2122., 1936., 4261., 7275., 19059., 5057., 3209., >>3586., 3792., >>6182., 1993., 1615., 737., 3114.}; >>b = {5.49, 9.87, 11.17, 13.91, 14.83, 16.92, 17.91, 19.44, 21.91, >>22.8, 23.9, 26.0, 29.75, 30.97, 33.99}; \[Delta]L = {0.5, 0.5, 0.5, >>0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5}; >>\[Delta]G = {0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, >>0.5, 0.5, 0.5, 0.5}; > >>Then I defined another function for plotting purposes like so: > >>Fu[x_] := Plus @@ Thread[Voigt[x, a, b, \[Delta]L, \[Delta]G]] > >>And that allows me to plot what I want > >>Plot[Fu[x] + 4680.*Exp[(-Log[2.])*((x - 27.4)^2/15^2)] + >>6569*Exp[-x/2.57], {x, 0, 40}, ImageSize -> {600, 400}, PlotRange >>-> All] > >>But I have no idea how to do the NonlinearFit with that function. >>Any help would be greatly appreciated > > It still isn't clear to me what it is you want to do. Your code defines > parameters for 15 instances of your function which you sum. You say you > are trying to fit this sum to a data set using NonlinearFit. But you don't > really explain what you mean by fitting this sum to a data set. What does > your data set look like? What unknown parameters are you trying to > esitmate? > > As an aside, I will mentiion the functionality of NonlinearFit is fully > contained in the built in function FindFit. I suspect (but haven't > verified) FindFit will be faster than NonlinearFit. Also, FindFit has a > bit more flexibility in that it provides for a mechanism to monitor > convergence and allows for different norms. > > -- > To reply via email subtract one hundred and four