Problem with 2D fit

[marini]

Hello root users,
I’m trying to perform a 2D fit of a TH2F (or a TGraph2DErrors, I get the same results).
My points lie in a certain region in the x-y plane, around the bisector, so I have defined the limits of my function as a rectangle. I’m trying to fit my points with a plane but I always get an error matrix accurate at 50% and parameters value which are consistent with the xy plane, like if the fit is ignoring my points. I guess the problem is that I should tell to the function to fit just where the bin are not-zero, but I don’t know how to require it.
Here you have the main piece of my code:

void fit2D(){
TH2F *h=new TH2F(“h”,“h”,23,0,22,18,0,17);
h->SetMinimum(-5);
h->SetBinContent(0,1,-0.487812);
h->SetBinError(0,1,0.00771375);
h->SetBinContent(1,1,0.0114149);
h->SetBinError(1,1,0.0123048);
h->SetBinContent(2,1,0.540351);
h->SetBinError(2,1,0.0182454);
h->SetBinContent(1,2,-0.614683);
h->SetBinError(1,2,0.0256728);
h->SetBinContent(2,2,-0.0707187);
h->SetBinError(2,2,0.00701989);
…
h->Draw(“CONTZ”);
Double_t delta=0.0427394;

TF2 f2d=new TF2(“f2d”,"[0]([1]x+[2]y)",“cutg”);//,0,22,0,17);
f2d->SetParName(1,“alfa”);
f2d->SetParName(2,“beta”);
f2d->SetParLimits(1,0,100delta);
f2d->SetParLimits(2,-100delta,0.);
h->Fit(f2d,“M”);
}

The expected values of my parameters are alpha ~ -beta and alpha ~ 0.7
Where is the mistake?

Thank you very much for your help
Cheers
Paola

[brun]

Paola,

Could you post a short running script reproducing your problem?
In your code snippet the call to the TF2 constructor is wrong.

Rene

[marini]

Hi Rene,
sorry, I was trying to define my function in a limited region and I forgot to paste here the previuos version.
Now it should work:

#include <stdio.h>
#include <Riostream.h>
#include <iostream.h>
#include <TF2.h>
#include <TH2.h>
void fit2D(){
TH2F *h=new TH2F(“h”,“h”,23,0,22,18,0,17);
h->SetMinimum(-5);
h->SetBinContent(0,1,-0.487812);
h->SetBinError(0,1,0.00771375);
h->SetBinContent(1,1,0.0114149);
h->SetBinError(1,1,0.0123048);
h->SetBinContent(2,1,0.540351);
h->SetBinError(2,1,0.0182454);
h->SetBinContent(1,2,-0.614683);
h->SetBinError(1,2,0.0256728);
h->SetBinContent(2,2,-0.0707187);
h->SetBinError(2,2,0.00701989);
h->SetBinContent(4,2,1.32414);
h->SetBinError(4,2,0.0663372);
h->SetBinContent(3,3,-0.107608);
h->SetBinError(3,3,0.0428034);
h->SetBinContent(4,3,0.335772);
h->SetBinError(4,3,0.0395426);
h->SetBinContent(3,4,-0.765134);
h->SetBinError(3,4,0.0580094);
h->SetBinContent(6,2,2.92252);
h->SetBinError(6,2,0.391068);
h->SetBinContent(5,3,0.950505);
h->SetBinError(5,3,0.0780463);
h->SetBinContent(6,3,1.60981);
h->SetBinError(6,3,0.232201);
h->SetBinContent(5,4,0.393094);
h->SetBinError(5,4,0.0565881);
h->SetBinContent(4,5,-0.902492);
h->SetBinError(4,5,0.655065);
h->SetBinContent(6,4,0.932567);
h->SetBinError(6,4,0.0754298);
h->SetBinContent(5,5,-0.163799);
h->SetBinError(5,5,0.0525497);
h->SetBinContent(7,4,1.62972);
h->SetBinError(7,4,0.297529);
h->SetBinContent(6,5,0.334462);
h->SetBinError(6,5,0.0416216);
h->SetBinContent(5,6,-0.840158);
h->SetBinError(5,6,0.0714593);
h->SetBinContent(7,5,0.935788);
h->SetBinError(7,5,0.096568);
h->SetBinContent(6,6,-0.271717);
h->SetBinError(6,6,0.0389002);
h->SetBinContent(8,5,1.50752);
h->SetBinError(8,5,0.211056);
h->SetBinContent(7,6,0.192132);
h->SetBinError(7,6,0.0458492);
h->SetBinContent(6,7,-1.32007);
h->SetBinError(6,7,0.121486);
h->SetBinContent(8,6,0.90872);
h->SetBinError(8,6,0.0751261);
h->SetBinContent(7,7,-0.271307);
h->SetBinError(7,7,0.0501235);
h->SetBinContent(9,6,2.96722);
h->SetBinError(9,6,0.441983);
h->SetBinContent(8,7,0.314563);
h->SetBinError(8,7,0.0437325);
h->SetBinContent(7,8,-1.20055);
h->SetBinError(7,8,0.0993301);
h->SetBinContent(9,7,0.835046);
h->SetBinError(9,7,0.099458);
h->SetBinContent(8,8,-0.482027);
h->SetBinError(8,8,0.0438957);
h->SetBinContent(10,7,1.38831);
h->SetBinError(10,7,0.171625);
h->SetBinContent(9,8,0.114414);
h->SetBinError(9,8,0.0586271);
h->SetBinContent(8,9,-1.47435);
h->SetBinError(8,9,0.185775);
h->SetBinContent(10,8,0.751375);
h->SetBinError(10,8,0.0773047);
h->SetBinContent(9,9,-0.380347);
h->SetBinError(9,9,0.0796451);
h->SetBinContent(11,8,1.62519);
h->SetBinError(11,8,0.196295);
h->SetBinContent(10,9,0.200471);
h->SetBinError(10,9,0.0647798);
h->SetBinContent(9,10,-1.30316);
h->SetBinError(9,10,0.147234);
h->SetBinContent(12,8,2.20917);
h->SetBinError(12,8,0.509264);
h->SetBinContent(11,9,0.910363);
h->SetBinError(11,9,0.0850836);
h->SetBinContent(10,10,-0.505681);
h->SetBinError(10,10,0.0684179);
h->SetBinContent(12,9,1.48823);
h->SetBinError(12,9,0.132217);
h->SetBinContent(11,10,0.0306258);
h->SetBinError(11,10,0.0584673);
h->SetBinContent(10,11,-2.27044);
h->SetBinError(10,11,0.226155);
h->SetBinContent(13,9,1.58311);
h->SetBinError(13,9,0.345569);
h->SetBinContent(12,10,0.689927);
h->SetBinError(12,10,0.0670461);
h->SetBinContent(11,11,-0.799846);
h->SetBinError(11,11,0.0773451);
h->SetBinContent(13,10,1.06345);
h->SetBinError(13,10,0.112009);
h->SetBinContent(12,11,-0.163768);
h->SetBinError(12,11,0.0564672);
h->SetBinContent(11,12,-1.81676);
h->SetBinError(11,12,0.18148);
h->SetBinContent(14,10,2.06685);
h->SetBinError(14,10,0.298325);
h->SetBinContent(13,11,0.59586);
h->SetBinError(13,11,0.0746976);
h->SetBinContent(12,12,-0.58803);
h->SetBinError(12,12,0.0729569);
h->SetBinContent(14,11,1.41698);
h->SetBinError(14,11,0.126987);
h->SetBinContent(13,12,-0.137893);
h->SetBinError(13,12,0.0619973);
h->SetBinContent(12,13,-1.57219);
h->SetBinError(12,13,0.225464);
h->SetBinContent(15,11,1.88218);
h->SetBinError(15,11,0.248527);
h->SetBinContent(14,12,0.413951);
h->SetBinError(14,12,0.0664471);
h->SetBinContent(13,13,-0.612643);
h->SetBinError(13,13,0.0938202);
h->SetBinContent(15,12,0.844641);
h->SetBinError(15,12,0.111332);
h->SetBinContent(14,13,-0.169116);
h->SetBinError(14,13,0.0612087);
h->SetBinContent(13,14,-1.74719);
h->SetBinError(13,14,0.402536);
h->SetBinContent(16,12,2.52204);
h->SetBinError(16,12,0.34976);
h->SetBinContent(15,13,0.409126);
h->SetBinError(15,13,0.0782132);
h->SetBinContent(14,14,-1.0863);
h->SetBinError(14,14,0.101803);
h->SetBinContent(16,13,1.01496);
h->SetBinError(16,13,0.116808);
h->SetBinContent(15,14,-0.515689);
h->SetBinError(15,14,0.0788456);
h->SetBinContent(14,15,-2.05038);
h->SetBinError(14,15,0.8547);
h->SetBinContent(17,13,1.78754);
h->SetBinError(17,13,0.246717);
h->SetBinContent(16,14,0.127458);
h->SetBinError(16,14,0.0793795);
h->SetBinContent(15,15,-1.94501);
h->SetBinError(15,15,0.476356);
h->SetBinContent(17,14,0.73143);
h->SetBinError(17,14,0.140341);
h->SetBinContent(16,15,-0.837697);
h->SetBinError(16,15,0.15784);
h->SetBinContent(15,16,-2.96667);
h->SetBinError(15,16,0.532283);
h->SetBinContent(18,14,1.85347);
h->SetBinError(18,14,0.305376);
h->SetBinContent(17,15,0.279087);
h->SetBinError(17,15,0.117522);
h->SetBinContent(16,16,-1.54247);
h->SetBinError(16,16,0.182182);
h->SetBinContent(18,15,0.859294);
h->SetBinError(18,15,0.138565);
h->SetBinContent(17,16,-0.821997);
h->SetBinError(17,16,0.133157);
h->SetBinContent(19,15,1.74161);
h->SetBinError(19,15,0.239647);
h->SetBinContent(18,16,-0.0585065);
h->SetBinError(18,16,0.13898);
h->SetBinContent(17,17,-1.50033);
h->SetBinError(17,17,0.57716);
h->SetBinContent(20,15,2.35285);
h->SetBinError(20,15,0.465003);
h->SetBinContent(19,16,0.797616);
h->SetBinError(19,16,0.204282);
h->SetBinContent(18,17,-0.7238);
h->SetBinError(18,17,0.216061);
h->SetBinContent(20,16,1.40079);
h->SetBinError(20,16,0.323073);
h->SetBinContent(19,17,0.316748);
h->SetBinError(19,17,0.203092);
h->SetBinContent(20,17,0.997748);
h->SetBinError(20,17,0.309874);
h->SetBinContent(21,17,1.62698);
h->SetBinError(21,17,0.470594);

h->Draw(“CONTZ”);
Double_t delta=0.0427394;

TF2 f2d=new TF2(“f2d”,"[0]([1]x+[2]y)",0,22,0,17);
f2d->SetParName(1,“alfa”);
f2d->SetParName(2,“beta”);
f2d->SetParLimits(1,0,100delta);
f2d->SetParLimits(2,-100delta,0.);
// h->Fit(f2d,“VBMRF”);
h->Fit(f2d,“M”);
}

These are all my points.
Thank you very much for your help

Cheers
Paola

[brun]

Paola,

Lorenzo will follow your problem. Meanwhile I suggest
-calling f2d->SetParameters(with the 3 initial guess values);
-calling h->Fit(f2d"); //ie without option “m”

Rene

[marini]

Ok, thank you very much Rene.

When I call
f2d->SetParameters(with the 3 initial guess values);
the fit results strongly depend on the guess. It seems like that the fit ends in local minima:
I have tried
f2d->SetParameters(0.7, 0.7, -0.7)
and I get:
FCN=283.174 FROM MIGRAD STATUS=CONVERGED 85 CALLS 86 TOTAL
EDM=4.9826e-10 STRATEGY= 1 ERR MATRIX NOT POS-DEF
EXT PARAMETER APPROXIMATE STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 p0 9.30977e-01 2.67026e-02 9.72406e-05 8.25749e-04
2 alfa 6.71283e-01 1.73045e-02 5.79094e-06 -4.06335e-02
3 beta -7.51119e-01 1.93627e-02 6.24364e-06 -3.96546e-02

and f2d->SetParameters(0.6, -0.9, -0.9)
FCN=283.174 FROM MIGRAD STATUS=CONVERGED 84 CALLS 85 TOTAL
EDM=7.16911e-10 STRATEGY= 1 ERR MATRIX NOT POS-DEF
EXT PARAMETER APPROXIMATE STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 p0 7.26141e-01 2.08274e-02 7.58450e-05 -3.13154e-03
2 alfa 8.60644e-01 2.21857e-02 6.73533e-06 2.53756e-02
3 beta -9.63000e-01 2.48245e-02 7.29114e-06 2.78393e-02

I know that the expected value for alfa should be around 0.7, but it could be 0.6 or 0.8…

Thank you very much
Cheers
Paola

[moneta]

Hi,

the fit converges to the minimum, but your 3 parameters are not uniquely defined. The function is not written correctly. In this case, you should define your TF2 with only two parameters as:

TF2 *f2d=new TF2("f2d","[0]*x+[1]*y",0,22,0,17);

Best Regards

Lorenzo

[marini]

Thank you very much Lorenzo!
I didn’t notice that letting the constant as a free parameter would have let my other two parameters free.

Best regards
Paola