Re: Why this function does not return a single value

*To*: mathgroup at smc.vnet.net*Subject*: [mg60313] Re: Why this function does not return a single value*From*: Marek Bromberek <marekbr at gmail.com>*Date*: Sat, 10 Sep 2005 22:36:37 -0400 (EDT)*References*: <dfueac$1tf$1@smc.vnet.net>*Reply-to*: marekbr at gmail.com*Sender*: owner-wri-mathgroup at wolfram.com

Thanks Bill for Your reply. It makes a few things clear. I do understand that using a[1] in pattern matching probably does not make sense. Disregarding whether one thinks of it as a first element of an array or a function evaluated at 1. However I would expect Mathematica will return an error or a warning of some kind in this case. 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 Bill Rowe wrote: > On 9/9/05 at 4:07 AM, marekbr at gmail.com (Marek) wrote: > >>I know that Mathematica treats space as a multiplication sign. What >>happens here is that when I remove the multiplication signs in Input >>mode, convert to Standard mode and then back to Input mode the >>multiplication signs reappear. I just did the following experiment. >>Opened fresh Mathematica notebook and typed in (in Standard mode) >>g[x_,a[1]_]:=a*x (no spaces anywhere) Executed that Then converted to >>Input mode and there will be a star between a[1] and the blanc sign _ . > > In essence, g[x_,a[1]_]:= a*x is meaningless. This defines a function > named g having an arbitrary first arguement you are naming x, an arbitrary > second argument you are naming as the function a evaluated at 1 returning > the product of the function and the first argument. Is this really what > you want? > > Perhaps, you want to create a function that returns the product of > somehing and the first element of something else. That could be simply > done as > > g[x_, a_]:= x*First[a] > > Or perhaps you want to return the product of something an a function > evaluated at 1. That could be done as > > g[x_,a_]:= x*a[1] > -- > To reply via email subtract one hundred and four