TutorialFindPeaks.C

// 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.
//
// To execute this example, do
//  root > .x peaks.C  (generate 10 peaks by default)
//  root > .x peaks.C++ (use the compiler)
//  root > .x peaks.C++(30) (generates 30 peaks)
//
// 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)
//
//Author: Rene Brun

#include "TCanvas.h"
#include "TF1.h"
#include "TH1.h"
#include "TMath.h"
#include "TRandom.h"
#include "TSpectrum.h"
#include "TVirtualFitter.h"

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];
    Double_t mean  = par[3 * p + 3];
    Double_t sigma = par[3 * p + 4];
    result += norm * TMath::Gaus(x[0], mean, sigma);
  }
  return result;
}

void TutorialFindPeaks(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;
    par[3 * p + 3] = 10 + gRandom->Rndm() * 980;
    par[3 * p + 4] = 3 + 2 * gRandom->Rndm();
  }
  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 = 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;
    par[3 * npeaks + 3] = xp;
    par[3 * npeaks + 4] = 3;
    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");
}