PulseFitWithFunction.cc

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/* 
 *  \class PulseFitWithFunction
 *
 *  \author: Patrick Jarry - CEA/Saclay
 */

// File PulseFitWithFunction.cxx
// ===========================================================
// ==                                                       ==
// ==     Class for a function fit method                   ==
// ==                                                       ==
// ==  Date:   July 17th 2003                               ==
// ==  Author: Patrick Jarry                                ==
// ==                                                       ==
// ==                                                       ==
// ===========================================================

#include "CalibCalorimetry/EcalLaserAnalyzer/interface/PulseFitWithFunction.h"

#include <iostream>
#include "TMath.h"

//ClassImp(PulseFitWithFunction)

// Constructor...
PulseFitWithFunction::PulseFitWithFunction() {
  fNsamples = 0;
  fNum_samp_bef_max = 0;
  fNum_samp_after_max = 0;
}

// Destructor
PulseFitWithFunction::~PulseFitWithFunction() {}

// Initialisation

void PulseFitWithFunction::init(int n_samples, int samplb, int sampla, int niter, double alfa, double beta) {
  //printf("\n");
  //printf(" =========================================================\n");
  //printf(" ==     Initialising the function fit method            ==\n");
  //printf(" ==          PulseFitWithFunction::init                 ==\n");
  //printf(" ==                                                     ==\n");

  fNsamples = n_samples;
  fAlpha_laser = alfa;
  fBeta_laser = beta;
  fAlpha_beam = 0.98;
  fBeta_beam = 2.04;
  fNb_iter = niter;
  fNum_samp_bef_max = samplb;
  fNum_samp_after_max = sampla;
  //printf(" ==  # samples used = %3d                               ==\n",fNsamples);
  //printf(" ==  #sample before max= %1d and #sample after maximum= %1d ==\n",fNum_samp_bef_max,fNum_samp_after_max);
  //printf(" ==           alpha= %5.4f       beta= %5.4f          ==\n",fAlpha_laser,fBeta_laser);
  //printf(" =========================================================\n\n");
  return;
}

// Compute the amplitude using as input the Crystaldata
double PulseFitWithFunction::doFit(double *adc) {
  double parout[4];  // amp_max ;
                     //double amp_parab , tim_parab ;
  double chi2;
  //int imax ;
  //
  // first  one has to get starting point first with parabolic fun// //
  Fit_parab(&adc[0], 3, fNsamples, parout);
  amp_parab = parout[0];
  tim_parab = parout[1];
  imax = (int)parout[2];
  amp_max = parout[3];
  //printf("amp_parab= %f tim_parab=%f amp_max=%f imax=%d\n",amp_parab,tim_parab,amp_max,imax);
  fNumber_samp_max = imax;
  //

  if (amp_parab < 1.) {
    tim_parab = (double)imax;
    amp_parab = amp_max;
  }
  //
  fValue_tim_max = tim_parab;
  fFunc_max = amp_parab;
  fTim_max = tim_parab;

  //  here to fit maximum amplitude and time of arrival ...

  chi2 = Fit_electronic(0, &adc[0], 8.);
  // adc is an array to be filled with samples
  // 0 is for Laser (1 for electron)
  // 8 is for sigma of pedestals
  // which (can be computed)

  //  double amplitude = fAmp_fitted_max ; // amplitude fitted
  // double time = fTim_fitted_max ; // time fitted

  return chi2;  // return amplitude fitted
}

//-----------------------------------------------------------------------
//----------------------------------------------------------------------

/*************************************************/
double PulseFitWithFunction::Fit_electronic(int data, double *adc_to_fit, double sigmas_sample) {
  // fit electronic function from simulation
  // parameters fAlpha and fBeta are fixed and fit is providing
  // the maximum amplitude ( fAmp_fitted_max ) and the time of
  // the maximum amplitude ( fTim_fitted_max)
  // initialization of parameters
  double chi2 = 0;
  double d_alpha, d_beta;
  // first initialize parameters fAlpha and fBeta ( depending of beam or laser)
  fAlpha = fAlpha_laser;
  fBeta = fBeta_laser;
  if (data == 1) {
    fAlpha = fAlpha_beam;
    fBeta = fBeta_beam;
  }
  //
  fAmp_fitted_max = 0.;
  fTim_fitted_max = 0.;
  double un_sur_sigma = 1.;
  double variation_func_max = 0.;
  double variation_tim_max = 0.;
  //
  if (fValue_tim_max > 20. || fValue_tim_max < 3.) {
    fValue_tim_max = fNumber_samp_max;
  }
  int num_fit_min = (int)(fValue_tim_max - fNum_samp_bef_max);
  int num_fit_max = (int)(fValue_tim_max + fNum_samp_after_max);
  //

  if (sigmas_sample > 0.)
    un_sur_sigma = 1. / sigmas_sample;

  double func, delta;
  //          Loop on iterations
  for (int iter = 0; iter < fNb_iter; iter++) {
    //          initialization inside iteration loop !
    chi2 = 0.;
    double d11 = 0.;
    double d12 = 0.;
    double d22 = 0.;
    double z1 = 0.;
    double z2 = 0.;
    fFunc_max += variation_func_max;
    fTim_max += variation_tim_max;
    int nsamp_used = 0;
    //

    // Then we loop on samples to be fitted

    for (int i = num_fit_min; i < num_fit_max + 1; i++) {
      // calculate function to be fitted

      func = Electronic_shape((double)i);

      // then calculate derivatives of function to be fitted
      double dt = (double)i - fTim_max;
      double alpha_beta = fAlpha * fBeta;

      if (dt > -alpha_beta) {
        double dt_sur_beta = dt / fBeta;

        double variable = (double)1. + dt / alpha_beta;
        double expo = TMath::Exp(-dt_sur_beta);

        double puissance = TMath::Power(variable, fAlpha);
        d_alpha = un_sur_sigma * puissance * expo;
        d_beta = fFunc_max * d_alpha * dt_sur_beta / (alpha_beta * variable);
      } else {
        continue;
      }

      nsamp_used++;  // number of samples used inside the fit
      // compute matrix elements D (symetric --> d12 = d21 )
      d11 += d_alpha * d_alpha;
      d12 += d_alpha * d_beta;
      d22 += d_beta * d_beta;
      // compute delta
      delta = (adc_to_fit[i] - func) * un_sur_sigma;
      // compute vector elements Z
      z1 += delta * d_alpha;
      z2 += delta * d_beta;
      chi2 += delta * delta;
    }  //             end of loop on samples
    double denom = d11 * d22 - d12 * d12;
    if (denom == 0.) {
      //printf( "attention denom = 0 signal pas fitte \n") ;
      return 101;
    }
    if (nsamp_used < 3) {
      //printf( "Attention nsamp = %d ---> no function fit provided \n",nsamp_used) ;
      return 102;
    }
    // compute variations of parameters fAmp_max and fTim_max
    variation_func_max = (z1 * d22 - z2 * d12) / denom;
    variation_tim_max = (-z1 * d12 + z2 * d11) / denom;
    chi2 = chi2 / ((double)nsamp_used - 2.);
  }  //      end of loop on iterations
  // results of the fit are calculated
  fAmp_fitted_max = fFunc_max + variation_func_max;
  fTim_fitted_max = fTim_max + variation_tim_max;
  //
  return chi2;
}

//-----------------------------------------------------------------------
//----------------------------------------------------------------------

double PulseFitWithFunction::Electronic_shape(double tim) {
  // electronic function (from simulation) to fit ECAL pulse shape
  double func_electronic, dtsbeta, variable, puiss;
  double albet = fAlpha * fBeta;
  if (albet <= 0)
    return ((Double_t)0.);
  double dt = tim - fTim_max;
  if (dt > -albet) {
    dtsbeta = dt / fBeta;
    variable = 1. + dt / albet;
    puiss = TMath::Power(variable, fAlpha);
    func_electronic = fFunc_max * puiss * TMath::Exp(-dtsbeta);
  } else
    func_electronic = 0.;
  //
  return func_electronic;
}
void PulseFitWithFunction::Fit_parab(Double_t *ampl, Int_t nmin, Int_t nmax, Double_t *parout) {
  /* Now we calculate the parabolic adjustement in order to get        */
  /*    maximum and time max                                           */

  double denom, dt, amp1, amp2, amp3;
  double ampmax = 0.;
  int imax = 0;
  int k;
  /*
                                                                   */
  for (k = nmin; k < nmax; k++) {
    //printf("ampl[%d]=%f\n",k,ampl[k]);
    if (ampl[k] > ampmax) {
      ampmax = ampl[k];
      imax = k;
    }
  }
  amp1 = ampl[imax - 1];
  amp2 = ampl[imax];
  amp3 = ampl[imax + 1];
  denom = 2. * amp2 - amp1 - amp3;
  /*                                         */
  if (denom > 0.) {
    dt = 0.5 * (amp3 - amp1) / denom;
  } else {
    //printf("denom =%f\n",denom)  ;
    dt = 0.5;
  }
  /*                                             */
  /* ampmax correspond au maximum d'amplitude parabolique et dt        */
  /* decalage en temps par rapport au sample maximum soit k + dt       */

  parout[0] = amp2 + (amp3 - amp1) * dt * 0.25;
  parout[1] = (double)imax + dt;
  parout[2] = (double)imax;
  parout[3] = ampmax;
  return;
}