RE: Breit-Wigner convoluted with a gaussian

From: Manuel Diaz Gomez <Manuel.Maria.Diaz.Gomez_at_cern.ch>
Date: Mon, 2 May 2005 11:28:08 +0200

Thanks Rene,

Changing the convolution range solved the problem.

Cheers
Manuel

-----Original Message-----

From:	Rene Brun [mailto:brun_at_pcroot.cern.ch]
Sent:	Sat 4/30/2005 7:04 AM
To:	Manuel Diaz Gomez
Cc:	roottalk_at_pcroot.cern.ch
Subject:	Re: [ROOT] Breit-Wigner convoluted with a gaussian

Hi Manuel,

Change the convolution range from .4 sigma to 4 (as in langaus.C) ie:

   Double_t sc = 4; // convolution extends to +-sc Gaussian sigmas

Rene Brun

On Fri,
29 Apr 2005, Manuel Diaz Gomez wrote:

> 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()
> /*--------------------------------------------*/
> {
> TH1F *brgauss = new TH1F("breitg","", 131, 0, 130);
> TF1 *f = new TF1("f",breitgausfun, 0, 130 ,4);
>
> 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);
> f->FixParameter(1, 80.0);
> f->FixParameter(3, 10.0);
>
>
> brgauss->FillRandom("f", 1000);
> brgauss->Fit(f, "RBO");
>
> }
> //////////////////////////////////////////////////////////////////////
>
>
> Cheers
> Manuel
>
Received on Mon May 02 2005 - 11:28:14 MEST