Fitting a three-Gaussian model on data

Questions
, ,
1

Hi!
I want to fit a three-Gaussian model on a given data (download-link: http://sharesend.com/6yhykztt).
I’ve tried different inital Number to get the fit to converge. Either the left peak doesn’t converge or the peak in the middle doesn’t converge.

Would be grateful if somebody has some hint or solution for this problem!

Best regards,

Tohu

data = Import["$path/data.txt", "Table"];
Block[{$DisplayFunction = Identity}, 
  dataPlot = 
    ListPlot[data, PlotStyle -> {AbsolutePointSize[4], Hue[.7]}, 
     PlotRange -> {{0, 400}, {0, 65000}}];
  ];
Show[dataPlot]

data.png
data.png445×275 7.05 KB

model = (amp1 E^(-((-mu1 + x)^2/(2 sigma1^2)))) + (amp2 E^(-((-mu2 + 
             x)^2/(2 sigma2^2)))) + (amp3 E^(-((-mu3 + 
             x)^2/(2 sigma3^2))));


vars = {{amp1, 63000}, {mu1, 100}, {sigma1, 8}, {amp2, 6000}, {mu2, 
    210}, {sigma2}, {amp3, 40000}, {mu3, 310}, {sigma3}};
cons = And @@ Thread[{amp1, sigma1, amp2, sigma2, amp3, sigma3} > 0];
fit = NonlinearModelFit[data, {model, cons}, vars, x, 
  MaxIterations -> 100]


Show[Plot[fit[x], {x, 0, 500}, PlotRange -> All, 
  PlotStyle -> {Thick, Red}], 
 ListPlot[data, PlotStyle -> Opacity[0.5]]]
fit["ParameterTable"]

datafit.png
datafit.png833×507 24.5 KB

2

Hi,

Is it some kind of photon distribution? If you split your problem into parts result will look slightly better.

model1 = (amp1 E^(-((-mu1 + x)^2/(2 sigma1^2))));

model2 = (amp2 E^(-((-mu2 + x)^2/(2 sigma2^2))));
model3 = (amp3 E^(-((-mu3 + x)^2/(2 sigma3^2))));

vars1 = {{amp1, 63000}, {mu1, 100}, {sigma1}};
vars2 = {{amp2, 6000}, {mu2, 210}, {sigma2}};
vars3 = {{amp3, 40000}, {mu3, 310}, {sigma3}};

fit1 = NonlinearModelFit[data1, {model1, amp1 > 0 && sigma1 > 0}, vars1, x, MaxIterations -> 100];
fit2 = NonlinearModelFit[data2, {model2, amp2 > 0 && sigma2 > 0}, vars2, x, MaxIterations -> 100];
fit3 = NonlinearModelFit[data3, {model3, amp3 > 0 && sigma3 > 0}, vars3, x, MaxIterations -> 100];

Show[
 Plot[{fit1[x] + fit2[x] + fit3[x]}, {x, 0, 500}, PlotRange -> All],
 ListPlot[data, PlotStyle -> {AbsolutePointSize[4], Hue[.7]}, 
  PlotRange -> {{0, 400}, {0, 65000}}]
 ]

3g.png
3g.png360×218 7.06 KB

Sorry, I forgot to add definitions for data1,data2 and data3,
each of them in fact something like Take[data,{n,m}] where n&m are chosen so that data looks like gaussian in that range.
I’ve already removed exact ranges, but I still have them loaded into memory, so here are the files

http://sharesend.com/h35pjd31 - d3.txt
http://sharesend.com/0faxgkcx - d2.txt
http://sharesend.com/att5y5vc - d1.txt

I.M.

3

Hello I´m having a similar problem , i want to fit a Gaussian for this set of data (which is normalized) but i dont have notting

data = Import["$/normref.txt", 

   "Table"];

dataPlot = ListPlot[data, PlotRange -> All];

Show[dataPlot]



model1 = ( E^(-((-a + x)^2/(2 b^2))));

fit1 = NonlinearModelFit[data, {model1, b > 0}, {a, b}, x, 

  MaxIterations -> 100]

Show[Plot[fit1[x], {x, 0, 1000}, PlotRange -> All, 

  PlotStyle -> {Orange}], 

 ListPlot[data, PlotRange -> {{0, 400}, {0, 1.2}}]]

gaussianfit.png
gaussianfit.png360×231 2.04 KB

I add the code and the data file

I hope you could helpme

Regards