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langaus.c
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//-----------------------------------------------------------------------
//
// Convoluted Landau and Gaussian Fitting Function
// (using ROOT's Landau and Gauss functions)
//
// Based on a Fortran code by R.Fruehwirth ([email protected])
// Adapted for C++/ROOT by H.Pernegger ([email protected]) and
// Markus Friedl ([email protected])
//
// to execute this example, do:
// root > .x langaus.C
// or
// root > .x langaus.C++
//
//-----------------------------------------------------------------------
#include "TH1.h"
#include "TF1.h"
#include "TROOT.h"
#include "TStyle.h"
#include "TMath.h"
Double_t langaufun(Double_t *x, Double_t *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_t invsq2pi = 0.3989422804014; // (2 pi)^(-1/2)
Double_t mpshift = -0.22278298; // Landau maximum location
// Control constants
Double_t np = 100.0; // number of convolution steps
Double_t sc = 5.0; // convolution extends to +-sc Gaussian sigmas
// Variables
Double_t xx;
Double_t mpc;
Double_t fland;
Double_t sum = 0.0;
Double_t xlow,xupp;
Double_t step;
Double_t 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_t *fitrange, Double_t *startvalues, Double_t *parlimitslo, Double_t *parlimitshi, Double_t *fitparams, Double_t *fiterrors, Double_t *ChiSqr, Int_t *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_t i;
Char_t 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_t langaupro(Double_t *params, Double_t &maxx, Double_t &FWHM) {
// Seaches 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_t p,x,fy,fxr,fxl;
Double_t step;
Double_t l,lold;
Int_t i = 0;
Int_t 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() {
Double_t x = 0;
TFile *file = new TFile("flat_scint3_box15_gap01_x_z_1.5_1.5mm_e200.root");
TH1F* hist = (TH1F *)file->Get("fCounterSipm");
Int_t nentries = (Int_t)hist->GetEntries();
Int_t 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};
for (Int_t i=0; i<nentries; i++)
x = hist->GetBinContent();
// Setting fit range and start values
Double_t fr[2];
Double_t sv[4], pllo[4], plhi[4], fp[4], fpe[4];
fr[0]=0.3*hist->GetMean();
fr[1]=3.0*hist->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_t chisqr;
Int_t ndf;
TF1 *fitsnr = langaufit(hSNR,fr,sv,pllo,plhi,fp,fpe,&chisqr,&ndf);
Double_t SNRPeak, SNRFWHM;
langaupro(fp,SNRPeak,SNRFWHM);
hSNR->Draw();
fitsnr->Draw("lsame");
}