JGandalfFitToGauss.cc

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#include <string>
#include <iostream>
#include <iomanip>
#include <vector>
#include <cmath>

#include "TROOT.h"
#include "TFile.h"
#include "TF1.h"
#include "TH1D.h"
#include "TMath.h"

#include "JFit/JGandalf.hh"
#include "JTools/JElement.hh"
#include "JTools/JQuantile.hh"
#include "JROOT/JRootToolkit.hh"
#include "JMath/JGauss.hh"
#include "JMath/JConstants.hh"

#include "Jeep/JTimer.hh"
#include "Jeep/JPrint.hh"
#include "Jeep/JParser.hh"
#include "Jeep/JMessage.hh"


namespace {

  using namespace JPP;
  using TMath::PoissonI;

  typedef JElement2D<double, double>     JElement_t;
  typedef JGandalf<JGauss>::result_type  result_type;

  /**
   * Fit function.
   *
   * \param  gauss              gauss
   * \param  point              point
   * \return                    chi2
   */
  inline result_type g1(const JGauss& gauss, const JElement_t& point) 
  {
    result_type result;

    const double u  = (point.getX() - gauss.mean) / gauss.sigma;
    const double fs =  gauss.signal * exp(-0.5*u*u) / (sqrt(2.0*PI) * gauss.sigma);
    const double fb =  gauss.background;
    const double f1 =  fs + fb;

    const double p  =  PoissonI(point.getY(), f1);

    result.chi2 = -log(p);

    result.gradient.mean       = fs * u   / gauss.sigma;                           // d(f)/d(mean)
    result.gradient.sigma      = fs * u*u / gauss.sigma  -  fs / gauss.sigma;      // d(f)/d(sigma)
    result.gradient.signal     = fs       / gauss.signal;                          // d(f)/d(signal)
    result.gradient.background = 1.0;                                              // d(f)/d(background)

    result.gradient *= 1.0 - point.getY()/f1;                                      // d(chi2)/d(f)

    return result;
  }
}


/**
 * \file
 *
 * Program to test JFIT::JGandalf algorithm.
 * \author mdejong
 */
int main(int argc, char **argv)
{
  using namespace std;
  using namespace JPP;

  string   outputFile;
  int      numberOfEvents;
  JGauss   gauss;
  JGauss   precision;
  int      debug;

  try {

    JParser<> zap("Program to test JGandalf algorithm.");

    zap['o'] = make_field(outputFile)          = "";
    zap['n'] = make_field(numberOfEvents)      = 100;
    zap['@'] = make_field(gauss)               = JGauss(0.0,  1.0,  1000.0, 100.0);
    zap['e'] = make_field(precision)           = JGauss(0.05, 0.05,   25.0,  25.0);
    zap['d'] = make_field(debug)               = 3;

    zap(argc, argv);
  }
  catch(const exception& error) {
    FATAL(error.what() << endl);
  }

  using namespace JFIT;

  ASSERT(numberOfEvents > 0);

  JGandalf<JGauss>::debug = debug;

  TF1 fs("fs", "exp(-0.5 * (x-[0])*(x-[0]) / ([1]*[1]))");
  TF1 fb("fb", "1.0");

  fs.FixParameter(0, gauss.mean);
  fs.FixParameter(1, gauss.sigma);

  const Int_t    nx   = 21;
  const Double_t xmin = -5.0;
  const Double_t xmax = +5.0;

  JQuantile Q[] = { JQuantile("mean      "),
                    JQuantile("sigma     "),
                    JQuantile("signal    "),
                    JQuantile("background") };

  TH1D      H[] = { TH1D("ha", "", 101,   -0.1,    +0.1),
                    TH1D("hb", "", 101,   -0.1,    +0.1),
                    TH1D("hc", "", 101, -100.0,  +100.0),
                    TH1D("hd", "", 101, -100.0,  +100.0) };

  JTimer timer;

  for (int i = 0; i != numberOfEvents; ++i) {
    
    STATUS("event: " << setw(10) << i << '\r'); DEBUG(endl);

    TH1D h0("h0", NULL, nx, xmin, xmax);

    h0.Sumw2();
     
    h0.FillRandom("fs", (Int_t) gauss.signal);
    h0.FillRandom("fb", (Int_t) gauss.background);

    vector<JElement_t> data;

    for (Int_t i = 1; i <= h0.GetNbinsX(); ++i) {
      data.push_back(JElement_t(h0.GetBinCenter (i),
                                h0.GetBinContent(i)));
    }

    JGandalf<JGauss> fit;

    fit.parameters.resize(4);

    fit.parameters[0] = &JGauss::mean;
    fit.parameters[1] = &JGauss::sigma;
    fit.parameters[2] = &JGauss::signal;
    fit.parameters[3] = &JGauss::background;

    fit.value = JGauss(h0.GetMean(),
                       h0.GetRMS(),
                       h0.GetEntries() * (xmax - xmin) / nx - h0.GetMinimum(),
                       h0.GetMinimum());
    
    DEBUG("Start value " << fit.value << endl);

    timer.start();
    
    const double chi2 = fit(g1, data.begin(), data.end());

    timer.stop();

    DEBUG("Final value " << fit.value << endl);
    DEBUG("Chi2 " << chi2 << endl);
    
    const double Y[] = { fit.value.mean                             - gauss.mean,
                         fit.value.sigma                            - gauss.sigma,
                         fit.value.signal     * nx / (xmax - xmin)  - gauss.signal,
                         fit.value.background * nx                  - gauss.background };

    for (int i = 0; i != sizeof(Q)/sizeof(Q[0]); ++i) {
      Q[i].put (Y[i]);
      H[i].Fill(Y[i]);
    }
  }

  for (int i = 0; i != sizeof(Q)/sizeof(Q[0]); ++i) {
    NOTICE((i == 0 ? longprint : shortprint) << Q[i]);
  }

  if (debug >= notice_t) {
    timer.print(cout, true, micro_t);
  }

  if (outputFile != "") {

    TFile out(outputFile.c_str(), "recreate");
    
    for (int i = 0; i != sizeof(H)/sizeof(H[0]); ++i) {
      out << H[i];
    }
    
    out.Write();
    out.Close();
  }
  
  for (int i = 0; i != sizeof(Q)/sizeof(Q[0]); ++i) {
    ASSERT(fabs(Q[i].getMean()) < Q[i].getSTDev());
  }

  ASSERT(Q[0].getSTDev() < precision.mean);
  ASSERT(Q[1].getSTDev() < precision.sigma);
  ASSERT(Q[2].getSTDev() < precision.signal);
  ASSERT(Q[3].getSTDev() < precision.background);

  return 0;
}