Logo ROOT  
Reference Guide
No Matches
langaus.C File Reference

Detailed Description

View in nbviewer Open in SWAN 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


root > .x langaus.C++
1 Width 1.25740e+00 3.04846e-01 1.37307e-04 1.57021e-04
2 MP 2.08890e+01 1.28244e+00 3.40886e-05 8.22843e-04
3 Area 1.15515e+04 2.42312e+03 1.66644e-05 -1.66635e-03
4 GSigma 4.06350e+00 7.58845e-01 2.30703e-04 -2.48397e-04
Fitting done
Plotting results...
#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 mpc;
Double_t fland;
Double_t sum = 0.0;
Double_t xlow,xupp;
Double_t step;
// 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];
TF1 *ffitold = (TF1*)gROOT->GetListOfFunctions()->FindObject(FunName);
if (ffitold) delete ffitold;
TF1 *ffit = new TF1(FunName,langaufun,fitrange[0],fitrange[1],4);
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) ) {
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) ) {
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) ) {
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_t data[100] = {0,0,0,0,0,0,2,6,11,18,18,55,90,141,255,323,454,563,681,
TH1F *hSNR = new TH1F("snr","Signal-to-noise",400,0,400);
for (Int_t i=0; i<100; i++) hSNR->Fill(i,data[i]);
// Fitting SNR histo
// Setting fit range and start values
Double_t fr[2];
Double_t sv[4], pllo[4], plhi[4], fp[4], fpe[4];
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;
printf("Fitting done\nPlotting results...\n");
// Global style settings
int Int_t
Definition RtypesCore.h:45
char Char_t
Definition RtypesCore.h:37
double Double_t
Definition RtypesCore.h:59
#define gROOT
Definition TROOT.h:406
R__EXTERN TStyle * gStyle
Definition TStyle.h:412
virtual void SetRange(Int_t first=0, Int_t last=0)
Set the viewing range for the axis using bin numbers.
Definition TAxis.cxx:920
1-Dim function class
Definition TF1.h:213
virtual Int_t GetNDF() const
Return the number of degrees of freedom in the fit the fNDF parameter has been previously computed du...
Definition TF1.cxx:1879
virtual Double_t GetParError(Int_t ipar) const
Return value of parameter number ipar.
Definition TF1.cxx:1920
Double_t GetChisquare() const
Definition TF1.h:444
virtual Double_t * GetParameters() const
Definition TF1.h:520
virtual void SetParLimits(Int_t ipar, Double_t parmin, Double_t parmax)
Set limits for parameter ipar.
Definition TF1.cxx:3511
virtual void Draw(Option_t *option="")
Draw this function with its current attributes.
Definition TF1.cxx:1322
virtual void SetParameters(const Double_t *params)
Definition TF1.h:644
virtual void SetParNames(const char *name0="p0", const char *name1="p1", const char *name2="p2", const char *name3="p3", const char *name4="p4", const char *name5="p5", const char *name6="p6", const char *name7="p7", const char *name8="p8", const char *name9="p9", const char *name10="p10")
Set up to 10 parameter names.
Definition TF1.cxx:3475
1-D histogram with a float per channel (see TH1 documentation)}
Definition TH1.h:575
virtual Double_t GetMean(Int_t axis=1) const
For axis = 1,2 or 3 returns the mean value of the histogram along X,Y or Z axis.
Definition TH1.cxx:7428
TAxis * GetXaxis()
Get the behaviour adopted by the object about the statoverflows. See EStatOverflows for more informat...
Definition TH1.h:320
virtual TFitResultPtr Fit(const char *formula, Option_t *option="", Option_t *goption="", Double_t xmin=0, Double_t xmax=0)
Fit histogram with function fname.
Definition TH1.cxx:3892
virtual Int_t Fill(Double_t x)
Increment bin with abscissa X by 1.
Definition TH1.cxx:3350
virtual void Draw(Option_t *option="")
Draw this histogram with options.
Definition TH1.cxx:3073
virtual const char * GetName() const
Returns name of object.
Definition TNamed.h:47
virtual TObject * FindObject(const char *name) const
Must be redefined in derived classes.
Definition TObject.cxx:323
void SetOptStat(Int_t stat=1)
The type of information printed in the histogram statistics box can be selected via the parameter mod...
Definition TStyle.cxx:1589
void SetLabelSize(Float_t size=0.04, Option_t *axis="X")
Set size of axis labels.
Definition TStyle.cxx:1392
void SetOptFit(Int_t fit=1)
The type of information about fit parameters printed in the histogram statistics box can be selected ...
Definition TStyle.cxx:1541
Double_t x[n]
Definition legend1.C:17
Double_t Gaus(Double_t x, Double_t mean=0, Double_t sigma=1, Bool_t norm=kFALSE)
Calculate a gaussian function with mean and sigma.
Definition TMath.cxx:448
Double_t Landau(Double_t x, Double_t mpv=0, Double_t sigma=1, Bool_t norm=kFALSE)
The LANDAU function.
Definition TMath.cxx:469
Short_t Abs(Short_t d)
Definition TMathBase.h:120
auto * l
Definition textangle.C:4
static uint64_t sum(uint64_t i)
Definition Factory.cxx:2345
H.Pernegger, Markus Friedl

Definition in file langaus.C.