# Re: Breit-Wigner convoluted with a gaussian

From: Jan Friedrich <friedric_at_ph.tum.de>
Date: Mon, 02 May 2005 09:45:45 +0200

Hi Manuel,

if you need that specific function (and don't want to do numerical integration on your own), TMath::Voigt() may be an option for you.

Greetings Jan

Rene Brun wrote:

>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 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=Width (scale) Breit-Wigner
>> //par=Most Probable (MP, location) Breit mean
>> //par=Total area (integral -inf to inf, normalization constant)
>> //par=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 - sc * par;
>> xupp = x + sc * par;
>>
>> 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,par);
>> sum += fland * TMath::Gaus(x,xx,par);
>>
>> xx = xupp - (i-.5) * step;
>> fland = TMath::BreitWigner(xx,par,par);
>> sum += fland * TMath::Gaus(x,xx,par);
>> }
>>
>> return (par * step * sum * invsq2pi / par);
>>}
>>
>>/*--------------------------------------------*/
>>Double_t Genbreitgaus()
>>/*--------------------------------------------*/
>>{
>> TH1F *brgauss = new TH1F("breitg","", 131, 0, 130);
>> TF1 *f = new TF1("f",breitgausfun, 0, 130 ,4);
>>
>> Double_t par;
>> par = 2.495;
>> par = 80.0;
>> par = 1000.0;
>> par = 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 - 09:45:54 MEST

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