# NonlinearModelFit with multiple parameters

I am now trying a slightly more complicated model which actually consists of finding the parameters of 2 particles in an Image (I attached an Plot of an image). Although I put very good initial values and constrains Mathematica wasn’t able to produce a result. Note at the final stage I will need to decompose the location of 4 particles...

J[i_, j_, α_, β_, xpos_, ypos_, clip_] := N[Clip[(β α^2*π)/ 4*((Erf[(j - xpos)/α ] - Erf[(j + 1 - xpos)/α ])*(Erf[(i - ypos)/α ] - Erf[(i + 1 - ypos)/α ])), {0, clip}]];
PixelImage[mat_]:=ArrayPlot[Rescale[mat,{0,Max[mat]},{Max[mat],0}],Epilog->{Red,MapIndexed[Text[#1,Reverse[#2-1/2]]&,Reverse[mat],{2}]},Mesh->True];
MyThreshold = 4043;
model1 = Clip[N[(β1 α1^2*π)/4*((Erf[(j - xpos1)/α1 ] - Erf[(j + 1 - xpos1)/α1 ])*(Erf[(i-ypos1)/α1 ] - Erf[(i + 1 - ypos1)/α1]))], {0,MyThreshold}];
model2 = Clip[N[(β2 α2^2*π)/4*((Erf[(j - xpos2)/α2 ] - Erf[(j + 1 - xpos2)/α2 ])*(Erf[(i -ypos2)/α2 ] - Erf[(i + 1 - ypos2)/α2]))], {0, MyThreshold}];
Model = Clip[(model1 + model2), {0, MyThreshold}];
data1 = Flatten[Table[{i, j, J[i, j, 0.7, 500, 6.5, 6.5, MyThreshold]}, {i, 1, 14}, {j, 1, 14}], 1];
data2 = Flatten[Table[{i, j, J[i, j, 0.6, 300, 4.5, 4.2, MyThreshold]}, {i, 1, 14}, {j, 1, 14}], 1];
Data = Transpose[{data1[[All, 1]], data1[[All, 2]], Clip[data1[[All, 3]] + data2[[All, 3]], {0, MyThreshold}]}];
PixelImage[Round[Partition[Data[[All, 3]], 14]]]

nlm = NonlinearModelFit[Data, {Model,
{0.4 <= α1 <= 0.8, 0 <= β1 <= 6000, 0 <= xpos1 <= 8,
0 <= ypos1 <= 8, 0.4 <= α2 <= 0.8, 0 <= β2 <= 6000,
0 <= xpos2 <= 8, 0 <= ypos2 <= 8}}, {{α1, 0.6}, {β1,
300}, {xpos1, 6.5}, {ypos1, 6.5}, {α2, 0.6}, {β2,
300}, {xpos2, 4.5}, {ypos2, 4}}, {i, j}, Method -> "NMinimize"];
nlm["BestFitParameters"]

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This is your 5th question here, so: 1. please make sure you use the formatting tools to make the question readable. 2. try to make the question self contained and intelligible, don't rely on some other post you made that people may or may not have seen. I don't even see a question in your post. You can't expect any better answers than the quality of your question. – Szabolcs Dec 14 '13 at 16:38
Dear Szablocs. i wasnt tring to be rude. The moment i realised the format mistake you already fixed it and dint have the chance to do it my self. My question was about not being able to get a result from this model. (I tried to related this question to previus ones but there were too many charachters and i passes the limit.) I guess too many questions in the same subjeuct are not welcome. Sorry – Doron Dec 14 '13 at 16:42