Problems fitting

Chris Jillings (chris@sno.phy.queensu.ca)
Fri, 6 Mar 1998 09:56:02 -0500 (EST)

Hi Rooters,
I have found a pathological fit and I am trying to understand why root
failed to fit properly.
I have a macro below that starts the fit at a particular set of
parameter values close to the correct answer. I calcuated the chi square
two ways. First I looped over the histogram bins and calculated it myself
in the macro (Answer: 5233). Second, I set very tight bounds on the
paremeters, effectively forcing migrad not to change them, and then looked
at the value of FCN from migrad( Answer 5E8!).

The output of the macro is
(bin #) data model (model-data)**2 total chiSq
---------------
data

:
:

70 2138.000000 2790.239235 198.978494 1390.020928
71 2547.000000 3419.200307 298.678200 1688.699128
72 3267.000000 4196.629537 264.527418 1953.226546
73 4010.000000 5158.748900 329.083300 2282.309846
74 4942.000000 6350.814741 401.610477 2683.920323
75 6087.000000 7829.403125 498.762715 3182.683039
76 7695.000000 9665.278362 504.483018 3687.166056
77 9704.000000 11946.994351 518.448440 4205.614496
78 12155.000000 14785.416850 569.238404 4774.852900
79 15641.000000 18319.403236 458.656345 5233.509246
**********
** 1 **SET ERR 1
**********
FCN=5.16288e+08 FROM MIGRAD STATUS=CONVERGED 48 CALLS 49
TOTAL
EDM=1.25522e-06 STRATEGY= 1 ERROR MATRIX
ACCURATE
EXT PARAMETER STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 1st slope 9.20000e+00 9.23121e-08 2.13212e-02** at limit **
2 2nd Amp 2.00000e-01 1.20541e-09 7.70472e-03** at limit **
3 2nd slope 5.70000e+00 4.82292e-07 4.87308e-02** at limit **
4 scale fac 1.70000e+04 1.64631e-05 9.00421e-03** at limit **

So FCN, which from the docs is a chi square, is 5E8, whereas my
loop calculates 5233.

Any ideas? Thanks once again for your help. The full macro follows.

Chris

{
gROOT->Reset();
gStyle->SetOptFit(1);
gStyle->SetStatX(0.45);
gStyle->SetStatY(0.85);

TCanvas* c1 = new TCanvas("c1","Ntuple Plots",1); // create canvas
c1->SetFillColor(kWhite);

TFile* f1 = new TFile("cjj_g10.root","READ");
TH1F* hi1 = new TH1F("hi1","Angular Resolution: Gamma Energy = 10 MeV
",80,-1.0,1.0);
hi1->SetXTitle("Cos`q#");
// h509->Draw("Angres>>hi1","Egen>4&&Rfitt<600","goff");
h503->Draw("(Ue*Uf+Ve*Vf+We*Wf)>>hi1","Rfit<600","goff");
c1->SetLogy(1);
TF1* expExp = new TF1("expExp",expExp,-1,1,4);
expExp->SetParameters(9.2,0.2,5.7,17000);
expExp->SetParNames("1st slope","2nd Amp","2nd slope","scale fac");
Double_t x;
Double_t y;
Double_t dChiSq;
Double_t chiSq = 0..0;
Double_t data;
Double_t sigSq;
printf("Hello\n");
for( Int_t i=0 ; i<80 ; i++) {
x = -0.9875+i*0.025;
// printf("%d\t%f\n",i,x);
y = expExp->Eval(x);
data = hi1->GetBinContent(i);
if (data==0.0) sigSq = y;
else sigSq = data;
dChiSq = (data-y)*(data-y)/sigSq;
chiSq += dChiSq;
printf("%d\t%f\t%f\t%f\t%f\n",i,data,y,dChiSq,chiSq);
}
// expExp->Draw();
expExp->SetParLimits(0,9.2,9.3);
expExp->SetParLimits(1,0.2,0.21);
expExp->SetParLimits(2,5.7,5.8);
expExp->SetParLimits(3,17000.0,17100.0);

TPostScript ps("cjj_g10.eps",114);
hi1->Fit("expExp","RB");
// expExp->Draw();
// hi1->Draw("same");
c1->Update();
ps.Close();

}

=================================================================
= =
= Chris Jillings =
= Department of Physics phone/voice mail: (613) 545-6000x4805 =
= Queen's University fax: (613) 545-6813 =
= Kingston, Ontario email: chris@sno.phy.queensu.ca =
= Canada, K7L 3N6 web: http://snodaq.phy.queensu.ca =
= =
=================================================================