(*^ ::[paletteColors = 128; currentKernel; fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, L3, e8, 24, "New York"; ; fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e6, 18, "New York"; ; fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e6, 14, "New York"; ; fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, a20, 14, "New York"; ; fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, a15, 12, "New York"; ; fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, a12, 10, "New York"; ; fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 10, "New York"; ; fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 9, "New York"; ; fontset = input, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeInput, M18, N23, bold, 10, "Courier"; ; fontset = output, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M18, N23, 10, "Courier"; ; fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M18, N23, R65535, 10, "Courier"; ; fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M18, N23, 10, "Courier"; ; fontset = info, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M18, N23, 10, "Courier"; ; fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M18, l34, w373, h379, 12, "Courier"; ; fontset = name, inactive, nowordwrap, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic, B65535, 10, "Geneva"; ; fontset = header, inactive, noKeepOnOnePage, preserveAspect, M7, 10, "Times"; ; fontset = Left Header, inactive, 10, "Times"; ; fontset = footer, inactive, noKeepOnOnePage, preserveAspect, center, M7, 12, "Times"; ; fontset = Left Footer, inactive, center, 12, "Times"; ; fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 10, "Geneva"; ; fontset = clipboard, inactive, noKeepOnOnePage, preserveAspect, M7, 12, "New York"; ; fontset = completions, inactive, nowordwrap, noKeepOnOnePage, preserveAspect, M7, 12, "New York"; ; fontset = special1, inactive, nowordwrap, noKeepOnOnePage, preserveAspect, M7, 12, "New York"; ; fontset = special2, inactive, nowordwrap, noKeepOnOnePage, preserveAspect, center, M7, 12, "New York"; ; fontset = special3, inactive, nowordwrap, noKeepOnOnePage, preserveAspect, right, M7, 12, "New York"; ; fontset = special4, inactive, nowordwrap, noKeepOnOnePage, preserveAspect, M7, 12, "New York"; ; fontset = special5, inactive, nowordwrap, noKeepOnOnePage, preserveAspect, M7, 12, "New York"; ;] :[font = section; inactive; dontPreserveAspect; ] Test file for NonlinearFit.m :[font = input; dontPreserveAspect; startGroup; ] << NonlinearFit.m :[font = print; inactive; dontPreserveAspect; endGroup; ] {NonlinearFit} :[font = input; dontPreserveAspect; startGroup; ] ?NonlinearFit :[font = info; inactive; dontPreserveAspect; endGroup; ] NonlinearFit[data,model,params,vars{,options...}] finds values of params such that the expression model fits to data using the Levenberg - Marquardt method. The result is returned as a list of transformation rules analogous to Solve. Error estimates appear in the result,too. The meaning of the arguments data and vars is the same as in Fit. The argument model is any real-valued expression depending on params and vars. params must be a list of symbols. Supported options: Errors, MaxIterations, InitialGuess, Simplifier, ErrorNotation, ProgressTrace; help is available on each. :[font = subsection; inactive; dontPreserveAspect; ] Create a model with two Gaussian peaks :[font = input; dontPreserveAspect; startGroup; ] pars = {I1,w1,x1,I2,w2,x2}; pars0 = {1.,0.6,0.,1.5,0.4,1.2}; f[x_,{I1_,w1_,x1_,I2_,w2_,x2_}]= I1 Exp[-((x-x1)/w1)^2] + I2 Exp[-((x-x2)/w2)^2] :[font = output; output; inactive; dontPreserveAspect; endGroup; ] I1/E^((x - x1)^2/w1^2) + I2/E^((x - x2)^2/w2^2) ;[o] I1 I2 -------------- + -------------- 2 2 2 2 (x - x1) /w1 (x - x2) /w2 E E :[font = input; dontPreserveAspect; ] plot1 = Plot[f[x,pars0],{x,-1,3},DisplayFunction->Identity]; :[font = subsection; inactive; dontPreserveAspect; ] Data: perturb the original model a little :[font = input; dontPreserveAspect; ] X = Table[x,{x,-1.,3.,0.1}]; data = {#,f[#,pars0]+Random[Real,{-0.1,0.1}]}& /@ X; :[font = input; dontPreserveAspect; startGroup; ] plot2 = ListPlot[data,DisplayFunction->Identity]; :[font = subsection; inactive; dontPreserveAspect; ] Do the actual fitting: :[font = input; dontPreserveAspect; startGroup; ] fitted = NonlinearFit\ [data,f[x,pars], pars,x,Errors->0.1, InitialGuess->pars0+Table[Random[Real,{-0.2,0.2}]], (* give not too easy initial values! *) ProgressTrace->True] :[font = print; inactive; preserveAspect; ] NonlinearFit::trace params = {0.958898, 0.558898, -0.0411024, 1.4589, 0.358898, 1.1589}, lambda = -1. :[font = print; inactive; preserveAspect; ] NonlinearFit::trace params = {1.00189, 0.577392, -0.0405739, 1.49175, 0.422129, 1.19585} , lambda = 0.0001. :[font = print; inactive; preserveAspect; ] NonlinearFit::trace params = {1.00033, 0.577557, -0.0415344, 1.51069, 0.42212, 1.19966}, lambda = 0.00001. :[font = print; inactive; preserveAspect; ] NonlinearFit::trace params = {1.00036, 0.577431, -0.0416322, 1.51053, 0.42229, 1.19958}, lambda = -6 1. 10 . :[font = output; output; inactive; dontPreserveAspect; endGroup; endGroup; ] {I1 -> 1.00035667151675667, w1 -> 0.5774345036133173473, x1 -> -0.04162859448061922178, I2 -> 1.510521699089093066, w2 -> 0.4222917487662714442, x2 -> 1.199587866794528972, Sigma[I1] -> 0.04694842481599783768, Sigma[w1] -> 0.03853726361338434678, Sigma[x1] -> 0.02451818886703575865, Sigma[I2] -> 0.05343671691042377278, Sigma[w2] -> 0.02057349567089029599, Sigma[x2] -> 0.0141461502090203651} ;[o] {I1 -> 1.00036, w1 -> 0.577435, x1 -> -0.0416286, I2 -> 1.51052, w2 -> 0.422292, x2 -> 1.19959, Sigma[I1] -> 0.0469484, Sigma[w1] -> 0.0385373, Sigma[x1] -> 0.0245182, Sigma[I2] -> 0.0534367, Sigma[w2] -> 0.0205735, Sigma[x2] -> 0.0141462} :[font = input; dontPreserveAspect; ] plot3 = Plot[Release[f[x,pars]/.fitted],{x,-1,3}, DisplayFunction->Identity, PlotStyle->Dashing[{0.01,0.01}]]; :[font = subsection; inactive; dontPreserveAspect; ] and plot it all together: :[font = input; dontPreserveAspect; startGroup; ] Show[plot1,plot2,plot3, DisplayFunction->$DisplayFunction, 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