Logo ROOT  
Reference Guide
 
Loading...
Searching...
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

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->SetLabelSize(0.03,"x");
gStyle->SetLabelSize(0.03,"y");
hSNR->GetXaxis()->SetRange(0,70);
hSNR->Draw();
fitsnr->Draw("lsame");
}
winID h TVirtualViewer3D TVirtualGLPainter p
Option_t Option_t TPoint TPoint const char GetTextMagnitude GetFillStyle GetLineColor GetLineWidth GetMarkerStyle GetTextAlign GetTextColor GetTextSize void data
Option_t Option_t TPoint TPoint const char GetTextMagnitude GetFillStyle GetLineColor GetLineWidth GetMarkerStyle GetTextAlign GetTextColor GetTextSize void char Point_t Rectangle_t WindowAttributes_t Float_t Float_t Float_t Int_t Int_t UInt_t UInt_t Rectangle_t Int_t Int_t Window_t TString Int_t GCValues_t GetPrimarySelectionOwner GetDisplay GetScreen GetColormap GetNativeEvent const char const char dpyName wid window const char font_name cursor keysym reg const char only_if_exist regb h Point_t np
#define gROOT
Definition TROOT.h:407
R__EXTERN TStyle * gStyle
Definition TStyle.h:433
virtual void SetRange(Int_t first=0, Int_t last=0)
Set the viewing range for the axis using bin numbers.
Definition TAxis.cxx:1052
1-Dim function class
Definition TF1.h:214
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:1891
virtual Double_t GetParError(Int_t ipar) const
Return value of parameter number ipar.
Definition TF1.cxx:1932
Double_t GetChisquare() const
Definition TF1.h:450
virtual Double_t * GetParameters() const
Definition TF1.h:526
void Draw(Option_t *option="") override
Draw this function with its current attributes.
Definition TF1.cxx:1335
virtual void SetParLimits(Int_t ipar, Double_t parmin, Double_t parmax)
Set lower and upper limits for parameter ipar.
Definition TF1.cxx:3501
virtual void SetParameters(const Double_t *params)
Definition TF1.h:650
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:3462
1-D histogram with a float per channel (see TH1 documentation)}
Definition TH1.h:577
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:7452
TAxis * GetXaxis()
Definition TH1.h:322
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:3901
virtual Int_t Fill(Double_t x)
Increment bin with abscissa X by 1.
Definition TH1.cxx:3345
void Draw(Option_t *option="") override
Draw this histogram with options.
Definition TH1.cxx:3067
const char * GetName() const override
Returns name of object.
Definition TNamed.h:47
virtual TObject * FindObject(const char *name) const
Must be redefined in derived classes.
Definition TObject.cxx:403
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:1636
void SetLabelSize(Float_t size=0.04, Option_t *axis="X")
Set size of axis labels.
Definition TStyle.cxx:1440
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:1589
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)
Calculates a gaussian function with mean and sigma.
Definition TMath.cxx:471
Double_t Landau(Double_t x, Double_t mpv=0, Double_t sigma=1, Bool_t norm=kFALSE)
The LANDAU function.
Definition TMath.cxx:492
Short_t Abs(Short_t d)
Returns the absolute value of parameter Short_t d.
Definition TMathBase.h:123
TLine l
Definition textangle.C:4
static uint64_t sum(uint64_t i)
Definition Factory.cxx:2345
Authors
H.Pernegger, Markus Friedl

Definition in file langaus.C.