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peaks.C File Reference
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Detailed Description

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Illustrates how to find peaks in histograms.

This script generates a random number of gaussian peaks on top of a linear background. The position of the peaks is found via TSpectrum and injected as initial values of parameters to make a global fit. The background is computed and drawn on top of the original histogram.

This script can fit "peaks' heights" or "peaks' areas" (comment out or uncomment the line which defines __PEAKS_C_FIT_AREAS__).

To execute this example, do (in ROOT 5 or ROOT 6):

root > .x peaks.C (generate 10 peaks by default)
root > .x peaks.C++ (use the compiler)
root > .x peaks.C++(30) (generates 30 peaks)
x
Double_t x[n]
Definition: legend1.C:17

To execute only the first part of the script (without fitting) specify a negative value for the number of peaks, eg

root > .x peaks.C(-20)
Found 9 candidate peaks to fit
Found 9 useful peaks to fit
Now fitting: Be patient
FCN=596.686 FROM MIGRAD STATUS=CONVERGED 1343 CALLS 1344 TOTAL
EDM=3.92392e-07 STRATEGY= 1 ERROR MATRIX UNCERTAINTY 4.1 per cent
EXT PARAMETER STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 p0 5.27684e+02 2.01895e+00 1.61337e-04 1.75611e-05
2 p1 -3.95030e-01 3.04733e-03 -2.24976e-07 9.00273e-03
3 p2 6.34691e+02 2.03922e+01 6.11343e-03 8.34700e-06
4 p3 5.19331e+02 9.71873e-02 -3.36434e-05 5.32034e-03
5 p4 3.49850e+00 1.08256e-01 -2.36209e-05 1.49297e-03
6 p5 6.64734e+02 1.64194e+01 -1.21344e-03 3.63148e-06
7 p6 3.19147e+02 1.05478e-01 7.08426e-06 2.00939e-04
8 p7 4.69148e+00 9.07160e-02 1.69389e-06 -1.62399e-03
9 p8 6.70930e+02 1.64206e+01 3.50063e-03 -9.49091e-06
10 p9 7.54806e+02 9.99565e-02 1.99123e-05 -2.47890e-03
11 p10 4.29726e+00 7.99677e-02 -3.50356e-05 -3.01094e-03
12 p11 6.69618e+02 1.73089e+01 -7.16995e-03 1.61496e-05
13 p12 4.75964e+02 9.46541e-02 -1.85498e-05 -6.93464e-04
14 p13 3.89327e+00 8.40808e-02 2.51847e-05 -4.75462e-03
15 p14 6.48094e+02 1.48388e+01 1.51648e-02 1.40873e-05
16 p15 9.89666e+02 7.93960e-02 2.05426e-08 5.80091e-03
17 p16 3.34529e+00 5.62112e-02 6.45922e-06 6.69573e-03
18 p17 6.62565e+02 1.83711e+01 9.37344e-03 1.71791e-05
19 p18 5.39268e+02 1.17175e-01 -4.07242e-05 2.90506e-04
20 p19 4.56057e+00 9.79810e-02 -3.17654e-05 1.67849e-03
21 p20 6.59405e+02 1.56865e+01 -5.02844e-03 1.33136e-05
22 p21 9.48476e+02 1.01997e-01 -2.38534e-05 -2.87561e-03
23 p22 4.41169e+00 8.80653e-02 3.30904e-05 -1.55483e-04
24 p23 7.53519e+02 1.46208e+01 -1.21918e-03 -1.58005e-05
25 p24 2.32585e+02 1.49583e-01 4.30086e-05 2.06782e-03
26 p25 6.95026e+00 1.18485e-01 1.79213e-05 3.79338e-04
27 p26 6.45490e+02 1.58541e+01 5.23845e-03 8.39699e-06
28 p27 2.86948e+02 1.20789e-01 7.08536e-05 -1.98488e-04
29 p28 4.98698e+00 9.92605e-02 -3.61574e-05 3.47101e-03
#include "TCanvas.h"
#include "TMath.h"
#include "TH1.h"
#include "TF1.h"
#include "TRandom.h"
#include "TSpectrum.h"
#include "TVirtualFitter.h"
//
// Comment out the line below, if you want "peaks' heights".
// Uncomment the line below, if you want "peaks' areas".
//
// #define __PEAKS_C_FIT_AREAS__ 1 /* fit peaks' areas */
Int_t npeaks = 30;
Double_t fpeaks(Double_t *x, Double_t *par) {
Double_t result = par[0] + par[1]*x[0];
for (Int_t p=0;p<npeaks;p++) {
Double_t norm = par[3*p+2]; // "height" or "area"
Double_t mean = par[3*p+3];
Double_t sigma = par[3*p+4];
#if defined(__PEAKS_C_FIT_AREAS__)
norm /= sigma * (TMath::Sqrt(TMath::TwoPi())); // "area"
#endif /* defined(__PEAKS_C_FIT_AREAS__) */
result += norm*TMath::Gaus(x[0],mean,sigma);
}
return result;
}
void peaks(Int_t np=10) {
npeaks = TMath::Abs(np);
TH1F *h = new TH1F("h","test",500,0,1000);
// Generate n peaks at random
Double_t par[3000];
par[0] = 0.8;
par[1] = -0.6/1000;
Int_t p;
for (p=0;p<npeaks;p++) {
par[3*p+2] = 1; // "height"
par[3*p+3] = 10+gRandom->Rndm()*980; // "mean"
par[3*p+4] = 3+2*gRandom->Rndm(); // "sigma"
#if defined(__PEAKS_C_FIT_AREAS__)
par[3*p+2] *= par[3*p+4] * (TMath::Sqrt(TMath::TwoPi())); // "area"
#endif /* defined(__PEAKS_C_FIT_AREAS__) */
}
TF1 *f = new TF1("f",fpeaks,0,1000,2+3*npeaks);
f->SetNpx(1000);
f->SetParameters(par);
TCanvas *c1 = new TCanvas("c1","c1",10,10,1000,900);
c1->Divide(1,2);
c1->cd(1);
h->FillRandom("f",200000);
h->Draw();
TH1F *h2 = (TH1F*)h->Clone("h2");
// Use TSpectrum to find the peak candidates
TSpectrum *s = new TSpectrum(2*npeaks);
Int_t nfound = s->Search(h,2,"",0.10);
printf("Found %d candidate peaks to fit\n",nfound);
// Estimate background using TSpectrum::Background
TH1 *hb = s->Background(h,20,"same");
if (hb) c1->Update();
if (np <0) return;
//estimate linear background using a fitting method
c1->cd(2);
TF1 *fline = new TF1("fline","pol1",0,1000);
h->Fit("fline","qn");
// Loop on all found peaks. Eliminate peaks at the background level
par[0] = fline->GetParameter(0);
par[1] = fline->GetParameter(1);
npeaks = 0;
Double_t *xpeaks;
xpeaks = s->GetPositionX();
for (p=0;p<nfound;p++) {
Double_t xp = xpeaks[p];
Int_t bin = h->GetXaxis()->FindBin(xp);
Double_t yp = h->GetBinContent(bin);
if (yp-TMath::Sqrt(yp) < fline->Eval(xp)) continue;
par[3*npeaks+2] = yp; // "height"
par[3*npeaks+3] = xp; // "mean"
par[3*npeaks+4] = 3; // "sigma"
#if defined(__PEAKS_C_FIT_AREAS__)
par[3*npeaks+2] *= par[3*npeaks+4] * (TMath::Sqrt(TMath::TwoPi())); // "area"
#endif /* defined(__PEAKS_C_FIT_AREAS__) */
npeaks++;
}
printf("Found %d useful peaks to fit\n",npeaks);
printf("Now fitting: Be patient\n");
TF1 *fit = new TF1("fit",fpeaks,0,1000,2+3*npeaks);
// We may have more than the default 25 parameters
TVirtualFitter::Fitter(h2,10+3*npeaks);
fit->SetParameters(par);
fit->SetNpx(1000);
h2->Fit("fit");
}
f
#define f(i)
Definition: RSha256.hxx:104
h
#define h(i)
Definition: RSha256.hxx:106
Int_t
int Int_t
Definition: RtypesCore.h:45
Double_t
double Double_t
Definition: RtypesCore.h:59
p
winID h TVirtualViewer3D TVirtualGLPainter p
Definition: TGWin32VirtualGLProxy.cxx:51
np
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
Definition: TGWin32VirtualXProxy.cxx:222
result
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 result
Definition: TGWin32VirtualXProxy.cxx:174
gRandom
R__EXTERN TRandom * gRandom
Definition: TRandom.h:62
TCanvas
The Canvas class.
Definition: TCanvas.h:23
TF1
1-Dim function class
Definition: TF1.h:213
TF1::Eval
virtual Double_t Eval(Double_t x, Double_t y=0, Double_t z=0, Double_t t=0) const
Evaluate this function.
Definition: TF1.cxx:1440
TF1::GetParameter
virtual Double_t GetParameter(Int_t ipar) const
Definition: TF1.h:517
TH1F
1-D histogram with a float per channel (see TH1 documentation)}
Definition: TH1.h:577
TH1
TH1 is the base class of all histogram classes in ROOT.
Definition: TH1.h:58
TH1::Fit
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:3894
TRandom::Rndm
Double_t Rndm() override
Machine independent random number generator.
Definition: TRandom.cxx:552
TSpectrum
Advanced Spectra Processing.
Definition: TSpectrum.h:18
TVirtualFitter::Fitter
static TVirtualFitter * Fitter(TObject *obj, Int_t maxpar=25)
Static function returning a pointer to the current fitter.
Definition: TVirtualFitter.cxx:159
sigma
const Double_t sigma
Definition: h1analysisProxy.h:11
c1
return c1
Definition: legend1.C:41
PyTorch_Generate_CNN_Model.fit
def fit(model, train_loader, val_loader, num_epochs, batch_size, optimizer, criterion, save_best, scheduler)
Definition: PyTorch_Generate_CNN_Model.py:34
TGeant4Unit::s
static constexpr double s
Definition: TGeant4SystemOfUnits.h:162
TMath::Gaus
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
TMath::Sqrt
Double_t Sqrt(Double_t x)
Returns the square root of x.
Definition: TMath.h:662
TMath::Abs
Short_t Abs(Short_t d)
Returns the absolute value of parameter Short_t d.
Definition: TMathBase.h:123
TMath::TwoPi
constexpr Double_t TwoPi()
Definition: TMath.h:44
Author
Rene Brun

Definition in file peaks.C.