Re: NonlinearFit works not so good

*To*: mathgroup at smc.vnet.net*Subject*: [mg49587] Re: NonlinearFit works not so good*From*: "Kevin J. McCann" <kmccann at umbc.edu>*Date*: Sat, 24 Jul 2004 03:47:17 -0400 (EDT)*Organization*: University of Maryland, Baltimore County*References*: <cdqqa4$kkd$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

I am a simple kinda guy; so, I tend to use a "roll-your-own" LSQ whenever possible. I do this especially when I have a multivariate fit. The real problem is that it is that there is no single answer due to the periodicity of the sine. This makes a numerical search complicated. Anyway, here is my version. \!\(\* RowBox[{\(p1 = Plot[100\ Sin[3\ x + 1] + 2, {x, 0, 5}];\), "\n", \(data = p1[\([\)\(1, 1, 1, 1\)\(]\)];\), "\n", \(p2 = ListPlot[data];\), "\n", RowBox[{\(f[a_, b_, c_, d_, x_]\), ":=", StyleBox[\(a\ Sin[b\ \ x + c] + d\), FormatType->StandardForm]}], "\n", \(lsfit[a_, b_, c_, d_]\ := \ Plus\ @@ Apply[\ \((f[a, b, c, d, #1] - #2)\)\^2 &, data, {1}]\), "\n", \(lsfit[100, 3, 0, 2]\), "\n", \(sol = FindMinimum[ lsfit[a, b, c, d], {a, 90, 91}, {b, 2.5, 2.6}, {c, 0, 1}, {d, 0, 1}, MaxIterations \[Rule] 1000]\), "\n", \(Plot[f[a, b, c, d, x] /. sol[\([\)\(2\)\(]\)], {x, 0, 5}, Epilog \[Rule] {AbsolutePointSize[4], p2[\([\)\(1\)\(]\)]}];\)}]\) Cheers, Kevin -- Kevin J. McCann Joint Center for Earth Systems Technology (JCET) Department of Physics UMBC Baltimore MD 21250 "Daohua Song" <ds2081 at columbia.edu> wrote in message news:cdqqa4$kkd$1 at smc.vnet.net... > Dear group, > I find the NonlinearFit give an answer far away from the truth; Here > is an example: > Plot[100 Sin[3 x+1]+2,{x,0,5}]; > data=Cases[Graphics[%],Line[x___]?x,Infinity]; > <<Statistics`NonlinearFit` > NonlinearFit[data//First,A Sin[B x+C]+D,{x},{A,B,C,D}]; > Plot[%,{x,0,5}] > ListPlot[data//First] > > If i chop the +2 from above, it works fine. but The whole thing gives > bad fit again if you change {x,0,5}->{x,0,10} > So NonlinearFit also is not stable! > I hope it should be improved > Daohua >

**Follow-Ups**:**Re: Re: NonlinearFit works not so good***From:*stephen layland <layland@wolfram.com>

**Re: Re: NonlinearFit works not so good***From:*DrBob <drbob@bigfoot.com>