Hi All,
I modified the langaus.C example (under $ROOTSYS/tutorials) so that it does a breit-wigner convoluted with a gaussian (see code bellow). The problem is that I happen to be missing a normalisation factor somewhere, but I just can't see it. Perhaps you can spot it right away.
The following macro defines a gaussian convoluted breit-wigner function, fills a histogram out of it with 1000 entries, and the does the fit. I would expect the par[2] variable to be ~1000 but...rather I get ~3K. I would appretiate any help!
/*--------------------------------------------------------------------*/Double_t breitgausfun(Double_t *x, Double_t *par)
/*--------------------------------------------------------------------*/{
//Fit parameters:
//par[0]=Width (scale) Breit-Wigner
//par[1]=Most Probable (MP, location) Breit mean
//par[2]=Total area (integral -inf to inf, normalization constant)
//par[3]=Width (sigma) of convoluted Gaussian function
//
//In the Landau distribution (represented by the CERNLIB approximation),
//the maximum is located at x=-0.22278298 with the location parameter=0.
//This shift is corrected within this function, so that the actual
//maximum is identical to the MP parameter.
// Numeric constants Double_t invsq2pi = 0.3989422804014; // (2 pi)^(-1/2) Double_t twoPi = 6.2831853071795;//2Pi // Control constants Double_t np = 100.0; // number of convolution steps Double_t sc = .4; // convolution extends to +-sc Gaussian sigmas // Variables Double_t xx; Double_t fland; Double_t sum = 0.0; Double_t xlow,xupp; Double_t step; Double_t i; // Range of convolution integral xlow = x[0] - sc * par[3]; xupp = x[0] + sc * par[3]; step = (xupp-xlow) / np; // Convolution integral of Breit and Gaussian by sum for(i=1.0; i<=np/2; i++) { xx = xlow + (i-.5) * step; fland = TMath::BreitWigner(xx,par[1],par[0]); sum += fland * TMath::Gaus(x[0],xx,par[3]); xx = xupp - (i-.5) * step; fland = TMath::BreitWigner(xx,par[1],par[0]); sum += fland * TMath::Gaus(x[0],xx,par[3]); } return (par[2] * step * sum * invsq2pi / par[3]);}
/*--------------------------------------------*/Double_t Genbreitgaus()
/*--------------------------------------------*/{
Double_t par[4];
par[0] = 2.495; par[1] = 80.0; par[2] = 1000.0; par[3] = 10.0; f->SetParameters(par); f->FixParameter(0, 2.495);
brgauss->FillRandom("f", 1000);
brgauss->Fit(f, "RBO");
}
//////////////////////////////////////////////////////////////////////
Cheers
Manuel
Received on Fri Apr 29 2005 - 15:24:54 MEST
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