langaus.C File Reference

Detailed Description

Convoluted Landau and Gaussian Fitting Function (using ROOT's Landau and Gauss functions)

Based on a Fortran code by R.Fruehwirth (fruhw.nosp@m.irth.nosp@m.@heph.nosp@m.y.oe.nosp@m.aw.ac.nosp@m..at)

to execute this example, do:

root > .x langaus.C

or

root > .x langaus.C++

Fitting...
****************************************
Minimizer is Minuit2 / Migrad
Chi2                      =      5.25252
NDf                       =           64
Edm                       =  6.48548e-07
NCalls                    =          184
Width                     =      1.25725   +/-   0.304795       (limited)
MP                        =      20.8889   +/-   1.2821         (limited)
Area                      =      11552.8   +/-   2422.85        (limited)
GSigma                    =       4.0632   +/-   0.758575       (limited)
Fitting done
Plotting results...

 
#include "TH1.h"
#include "TF1.h"
#include "TROOT.h"
#include "TStyle.h"
#include "TMath.h"
 
double langaufun(double *x, double *par) {
 
   //Fit parameters:
   //par[0]=Width (scale) parameter of Landau density
   //par[1]=Most Probable (MP, location) parameter of Landau density
   //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 invsq2pi = 0.3989422804014;   // (2 pi)^(-1/2)
      double mpshift  = -0.22278298;       // Landau maximum location
 
      // Control constants
      double np = 100.0;      // number of convolution steps
      double sc =   5.0;      // convolution extends to +-sc Gaussian sigmas
 
      // Variables
      double xx;
      double mpc;
      double fland;
      double sum = 0.0;
      double xlow,xupp;
      double step;
      double i;
 
 
      // MP shift correction
      mpc = par[1] - mpshift * par[0];
 
      // Range of convolution integral
      xlow = x[0] - sc * par[3];
      xupp = x[0] + sc * par[3];
 
      step = (xupp-xlow) / np;
 
      // Convolution integral of Landau and Gaussian by sum
      for(i=1.0; i<=np/2; i++) {
         xx = xlow + (i-.5) * step;
         fland = TMath::Landau(xx,mpc,par[0]) / par[0];
         sum += fland * TMath::Gaus(x[0],xx,par[3]);
 
         xx = xupp - (i-.5) * step;
         fland = TMath::Landau(xx,mpc,par[0]) / par[0];
         sum += fland * TMath::Gaus(x[0],xx,par[3]);
      }
 
      return (par[2] * step * sum * invsq2pi / par[3]);
}
 
 
 
TF1 *langaufit(TH1F *his, double *fitrange, double *startvalues, double *parlimitslo, double *parlimitshi, double *fitparams, double *fiterrors, double *ChiSqr, int *NDF)
{
   // Once again, here are the Landau * Gaussian parameters:
   //   par[0]=Width (scale) parameter of Landau density
   //   par[1]=Most Probable (MP, location) parameter of Landau density
   //   par[2]=Total area (integral -inf to inf, normalization constant)
   //   par[3]=Width (sigma) of convoluted Gaussian function
   //
   // Variables for langaufit call:
   //   his             histogram to fit
   //   fitrange[2]     lo and hi boundaries of fit range
   //   startvalues[4]  reasonable start values for the fit
   //   parlimitslo[4]  lower parameter limits
   //   parlimitshi[4]  upper parameter limits
   //   fitparams[4]    returns the final fit parameters
   //   fiterrors[4]    returns the final fit errors
   //   ChiSqr          returns the chi square
   //   NDF             returns ndf
 
   int i;
   char FunName[100];
 
   sprintf(FunName,"Fitfcn_%s",his->GetName());
 
   TF1 *ffitold = (TF1*)gROOT->GetListOfFunctions()->FindObject(FunName);
   if (ffitold) delete ffitold;
 
   TF1 *ffit = new TF1(FunName,langaufun,fitrange[0],fitrange[1],4);
   ffit->SetParameters(startvalues);
   ffit->SetParNames("Width","MP","Area","GSigma");
 
   for (i=0; i<4; i++) {
      ffit->SetParLimits(i, parlimitslo[i], parlimitshi[i]);
   }
 
   his->Fit(FunName,"RB0");   // fit within specified range, use ParLimits, do not plot
 
   ffit->GetParameters(fitparams);    // obtain fit parameters
   for (i=0; i<4; i++) {
      fiterrors[i] = ffit->GetParError(i);     // obtain fit parameter errors
   }
   ChiSqr[0] = ffit->GetChisquare();  // obtain chi^2
   NDF[0] = ffit->GetNDF();           // obtain ndf
 
   return (ffit);              // return fit function
 
}
 
 
int langaupro(double *params, double &maxx, double &FWHM) {
 
   // Searches for the location (x value) at the maximum of the
   // Landau-Gaussian convolute and its full width at half-maximum.
   //
   // The search is probably not very efficient, but it's a first try.
 
   double p,x,fy,fxr,fxl;
   double step;
   double l,lold;
   int i = 0;
   int MAXCALLS = 10000;
 
 
   // Search for maximum
 
   p = params[1] - 0.1 * params[0];
   step = 0.05 * params[0];
   lold = -2.0;
   l    = -1.0;
 
 
   while ( (l != lold) && (i < MAXCALLS) ) {
      i++;
 
      lold = l;
      x = p + step;
      l = langaufun(&x,params);
 
      if (l < lold)
         step = -step/10;
 
      p += step;
   }
 
   if (i == MAXCALLS)
      return (-1);
 
   maxx = x;
 
   fy = l/2;
 
 
   // Search for right x location of fy
 
   p = maxx + params[0];
   step = params[0];
   lold = -2.0;
   l    = -1e300;
   i    = 0;
 
 
   while ( (l != lold) && (i < MAXCALLS) ) {
      i++;
 
      lold = l;
      x = p + step;
      l = TMath::Abs(langaufun(&x,params) - fy);
 
      if (l > lold)
         step = -step/10;
 
      p += step;
   }
 
   if (i == MAXCALLS)
      return (-2);
 
   fxr = x;
 
 
   // Search for left x location of fy
 
   p = maxx - 0.5 * params[0];
   step = -params[0];
   lold = -2.0;
   l    = -1e300;
   i    = 0;
 
   while ( (l != lold) && (i < MAXCALLS) ) {
      i++;
 
      lold = l;
      x = p + step;
      l = TMath::Abs(langaufun(&x,params) - fy);
 
      if (l > lold)
         step = -step/10;
 
      p += step;
   }
 
   if (i == MAXCALLS)
      return (-3);
 
 
   fxl = x;
 
   FWHM = fxr - fxl;
   return (0);
}
 
void langaus() {
   // Fill Histogram
   int data[100] = {0,0,0,0,0,0,2,6,11,18,18,55,90,141,255,323,454,563,681,
                    737,821,796,832,720,637,558,519,460,357,291,279,241,212,
                    153,164,139,106,95,91,76,80,80,59,58,51,30,49,23,35,28,23,
                    22,27,27,24,20,16,17,14,20,12,12,13,10,17,7,6,12,6,12,4,
                    9,9,10,3,4,5,2,4,1,5,5,1,7,1,6,3,3,3,4,5,4,4,2,2,7,2,4};
   TH1F *hSNR = new TH1F("snr","Signal-to-noise",400,0,400);
 
   for (int i=0; i<100; i++) hSNR->Fill(i,data[i]);
 
   // Fitting SNR histo
   printf("Fitting...\n");
 
   // Setting fit range and start values
   double fr[2];
   double sv[4], pllo[4], plhi[4], fp[4], fpe[4];
   fr[0]=0.3*hSNR->GetMean();
   fr[1]=3.0*hSNR->GetMean();
 
   pllo[0]=0.5; pllo[1]=5.0; pllo[2]=1.0; pllo[3]=0.4;
   plhi[0]=5.0; plhi[1]=50.0; plhi[2]=1000000.0; plhi[3]=5.0;
   sv[0]=1.8; sv[1]=20.0; sv[2]=50000.0; sv[3]=3.0;
 
   double chisqr;
   int    ndf;
   TF1 *fitsnr = langaufit(hSNR,fr,sv,pllo,plhi,fp,fpe,&chisqr,&ndf);
 
   double SNRPeak, SNRFWHM;
   langaupro(fp,SNRPeak,SNRFWHM);
 
   printf("Fitting done\nPlotting results...\n");
 
   // Global style settings
   gStyle->SetOptStat(1111);
   gStyle->SetOptFit(111);
   gStyle->SetLabelSize(0.03,"x");
   gStyle->SetLabelSize(0.03,"y");
 
   hSNR->GetXaxis()->SetRange(0,70);
   hSNR->Draw();
   fitsnr->Draw("lsame");
}
 

Authors

H.Pernegger, Markus Friedl

Definition in file langaus.C.