EcalUncalibRecHitRatioMethodAlgo.h

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#ifndef RecoLocalCalo_EcalRecAlgos_EcalUncalibRecHitRatioMethodAlgo_HH
#define RecoLocalCalo_EcalRecAlgos_EcalUncalibRecHitRatioMethodAlgo_HH
 
#include "Math/SVector.h"
#include "Math/SMatrix.h"
#include "RecoLocalCalo/EcalRecAlgos/interface/EcalUncalibRecHitRecAbsAlgo.h"
#include "CondFormats/EcalObjects/interface/EcalSampleMask.h"
#include <vector>
#include <array>
 
//#include "vdt/vdtMath.h"
#include "DataFormats/Math/interface/approx_exp.h"
#include "DataFormats/Math/interface/approx_log.h"
 
#define RANDOM_MAGIC
 
#include <random>
 
namespace myMath {
  inline float fast_expf(float x) { return unsafe_expf<6>(x); }
  inline float fast_logf(float x) { return unsafe_logf<7>(x); }
}  // namespace myMath
 
template <class C>
class EcalUncalibRecHitRatioMethodAlgo {
public:
  struct Ratio {
    unsigned int index;
    unsigned int step;
    double value;
    double error;
  };
  struct Tmax {
    unsigned int index;
    unsigned int step;
    double value;
    double error;
    double amplitude;
    double chi2;
  };
  struct CalculatedRecHit {
    double amplitudeMax;
    double timeMax;
    double timeError;
    double chi2;
  };
 
  EcalUncalibratedRecHit makeRecHit(const C &dataFrame,
                                    const EcalSampleMask &sampleMask,
                                    const double *pedestals,
                                    const double *pedestalRMSes,
                                    const double *gainRatios,
                                    std::vector<double> &timeFitParameters,
                                    std::vector<double> &amplitudeFitParameters,
                                    std::pair<double, double> &timeFitLimits);
 
  // more function to be able to compute
  // amplitude and time separately
  void init(const C &dataFrame,
            const EcalSampleMask &sampleMask,
            const double *pedestals,
            const double *pedestalRMSes,
            const double *gainRatios);
  void computeTime(std::vector<double> &timeFitParameters,
                   std::pair<double, double> &timeFitLimits,
                   std::vector<double> &amplitudeFitParameters);
  void computeAmplitude(std::vector<double> &amplitudeFitParameters);
  CalculatedRecHit getCalculatedRecHit() { return calculatedRechit_; }
  bool fixMGPAslew(const C &dataFrame);
 
  double computeAmplitudeImpl(std::vector<double> &amplitudeFitParameters, double, double);
 
protected:
  EcalSampleMask sampleMask_;
  DetId theDetId_;
  std::array<double, C::MAXSAMPLES> amplitudes_;
  std::array<double, C::MAXSAMPLES> amplitudeErrors_;
  std::array<double, C::MAXSAMPLES> amplitudeIE2_;
  std::array<bool, C::MAXSAMPLES> useless_;
 
  double pedestal_;
  int num_;
  double ampMaxError_;
 
  CalculatedRecHit calculatedRechit_;
};
 
template <class C>
void EcalUncalibRecHitRatioMethodAlgo<C>::init(const C &dataFrame,
                                               const EcalSampleMask &sampleMask,
                                               const double *pedestals,
                                               const double *pedestalRMSes,
                                               const double *gainRatios) {
  sampleMask_ = sampleMask;
  theDetId_ = DetId(dataFrame.id().rawId());
 
  calculatedRechit_.timeMax = 5;
  calculatedRechit_.amplitudeMax = 0;
  calculatedRechit_.timeError = -999;
 
  // to obtain gain 12 pedestal:
  // -> if it's in gain 12, use first sample
  // --> average it with second sample if in gain 12 and 3-sigma-noise
  // compatible (better LF noise cancellation)
  // -> else use pedestal from database
  pedestal_ = 0;
  num_ = 0;
  if (dataFrame.sample(0).gainId() == 1 && sampleMask_.useSample(0, theDetId_)) {
    pedestal_ += double(dataFrame.sample(0).adc());
    num_++;
  }
  if (num_ != 0 && dataFrame.sample(1).gainId() == 1 && sampleMask_.useSample(1, theDetId_) &&
      std::abs(dataFrame.sample(1).adc() - dataFrame.sample(0).adc()) < 3 * pedestalRMSes[0]) {
    pedestal_ += double(dataFrame.sample(1).adc());
    num_++;
  }
  if (num_ != 0)
    pedestal_ /= num_;
  else
    pedestal_ = pedestals[0];
 
  // fill vector of amplitudes, pedestal subtracted and vector
  // of amplitude uncertainties Also, find the uncertainty of a
  // sample with max amplitude. We will use it later.
 
  ampMaxError_ = 0;
  double ampMaxValue = -1000;
 
  // ped-subtracted and gain-renormalized samples. It is VERY
  // IMPORTANT to have samples one clock apart which means to
  // have vector size equal to MAXSAMPLES
  double sample;
  double sampleError;
  int GainId;
  for (int iSample = 0; iSample < C::MAXSAMPLES; iSample++) {
    GainId = dataFrame.sample(iSample).gainId();
 
    bool bad = false;
    // only use normally samples which are desired; if sample not to be used
    // inflate error so won't generate ratio considered for the measurement
    if (!sampleMask_.useSample(iSample, theDetId_)) {
      sample = 0;
      sampleError = 0;
      bad = true;
    } else if (GainId == 1) {
      sample = double(dataFrame.sample(iSample).adc() - pedestal_);
      sampleError = pedestalRMSes[0];
    } else if (GainId == 2 || GainId == 3) {
      sample = (double(dataFrame.sample(iSample).adc() - pedestals[GainId - 1])) * gainRatios[GainId - 1];
      sampleError = pedestalRMSes[GainId - 1] * gainRatios[GainId - 1];
    } else {
      sample = 0;       // GainId=0 case falls here, from saturation
      sampleError = 0;  // inflate error so won't generate ratio considered for
                        // the measurement
      bad = true;
    }
 
    useless_[iSample] = (sampleError <= 0) | bad;
    amplitudes_[iSample] = sample;
    // inflate error for useless samples
    amplitudeErrors_[iSample] = useless_[iSample] ? 1e+9 : sampleError;
    amplitudeIE2_[iSample] = useless_[iSample] ? 0 : 1 / (amplitudeErrors_[iSample] * amplitudeErrors_[iSample]);
    if (sampleError > 0) {
      if (ampMaxValue < sample) {
        ampMaxValue = sample;
        ampMaxError_ = sampleError;
      }
    }
  }
}
template <class C>
bool EcalUncalibRecHitRatioMethodAlgo<C>::fixMGPAslew(const C &dataFrame) {
  // This fuction finds sample(s) preceeding gain switching and
  // inflates errors on this sample, therefore, making this sample
  // invisible for Ratio Method. Only gain switching DOWN is
  // considered Only gainID=1,2,3 are considered. In case of the
  // saturation (gainID=0), we keep "distorted" sample because it is
  // the only chance to make time measurement; the qualilty of it will
  // be bad anyway.
 
  bool result = false;
 
  int GainIdPrev;
  int GainIdNext;
  for (int iSample = 1; iSample < C::MAXSAMPLES; iSample++) {
    // only use samples which are desired
    if (!sampleMask_.useSample(iSample, theDetId_))
      continue;
 
    GainIdPrev = dataFrame.sample(iSample - 1).gainId();
    GainIdNext = dataFrame.sample(iSample).gainId();
    if (GainIdPrev >= 1 && GainIdPrev <= 3 && GainIdNext >= 1 && GainIdNext <= 3 && GainIdPrev < GainIdNext) {
      amplitudes_[iSample - 1] = 0;
      amplitudeErrors_[iSample - 1] = 1e+9;
      amplitudeIE2_[iSample - 1] = 0;
      useless_[iSample - 1] = true;
      result = true;
    }
  }
  return result;
}
 
template <class C>
void EcalUncalibRecHitRatioMethodAlgo<C>::computeTime(std::vector<double> &timeFitParameters,
                                                      std::pair<double, double> &timeFitLimits,
                                                      std::vector<double> &amplitudeFitParameters) {
  //                                                          //
  //              RATIO METHOD FOR TIME STARTS HERE           //
  //                                                          //
  double ampMaxAlphaBeta = 0;
  double tMaxAlphaBeta = 5;
  double tMaxErrorAlphaBeta = 999;
  double tMaxRatio = 5;
  double tMaxErrorRatio = 999;
 
  double sumAA = 0;
  double sumA = 0;
  double sum1 = 0;
  double sum0 = 0;
  double sumAf = 0;
  double sumff = 0;
  double NullChi2 = 0;
 
  // null hypothesis = no pulse, pedestal only
  for (unsigned int i = 0; i < amplitudes_.size(); i++) {
    if (useless_[i])
      continue;
    double inverr2 = amplitudeIE2_[i];
    sum0 += 1;
    sum1 += inverr2;
    sumA += amplitudes_[i] * inverr2;
    sumAA += amplitudes_[i] * (amplitudes_[i] * inverr2);
  }
  if (sum0 > 0) {
    NullChi2 = (sumAA - sumA * sumA / sum1) / sum0;
  } else {
    // not enough samples to reconstruct the pulse
    return;
  }
 
  // Make all possible Ratio's based on any pair of samples i and j
  // (j>i) with positive amplitudes_
  //
  //       Ratio[k] = Amp[i]/Amp[j]
  //       where Amp[i] is pedestal subtracted ADC value in a time sample [i]
  //
  double alphabeta = amplitudeFitParameters[0] * amplitudeFitParameters[1];
  double invalphabeta = 1. / alphabeta;
  double alpha = amplitudeFitParameters[0];
  double beta = amplitudeFitParameters[1];
 
  Ratio ratios_[C::MAXSAMPLES * (C::MAXSAMPLES - 1) / 2];
  unsigned int ratios_size = 0;
 
  double Rlim[amplitudes_.size()];
  for (unsigned int k = 1; k != amplitudes_.size(); ++k)
    Rlim[k] = myMath::fast_expf(double(k) / beta) - 0.001;
 
  double relErr2[amplitudes_.size()];
  double invampl[amplitudes_.size()];
  for (unsigned int i = 0; i < amplitudes_.size(); i++) {
    invampl[i] = (useless_[i]) ? 0 : 1. / amplitudes_[i];
    relErr2[i] = (useless_[i]) ? 0 : (amplitudeErrors_[i] * invampl[i]) * (amplitudeErrors_[i] * invampl[i]);
  }
 
  for (unsigned int i = 0; i < amplitudes_.size() - 1; i++) {
    if (useless_[i])
      continue;
    for (unsigned int j = i + 1; j < amplitudes_.size(); j++) {
      if (useless_[j])
        continue;
 
      if (amplitudes_[i] > 1 && amplitudes_[j] > 1) {
        // ratio
        double Rtmp = amplitudes_[i] / amplitudes_[j];
 
        // error^2 due to stat fluctuations of time samples
        // (uncorrelated for both samples)
 
        double err1 = Rtmp * Rtmp * (relErr2[i] + relErr2[j]);
 
        // error due to fluctuations of pedestal (common to both samples)
        double stat;
        if (num_ > 0)
          stat = num_;  // num presampeles used to compute pedestal
        else
          stat = 1;  // pedestal from db
        double err2 =
            amplitudeErrors_[j] * (amplitudes_[i] - amplitudes_[j]) * (invampl[j] * invampl[j]);  // /sqrt(stat);
        err2 *= err2 / stat;
 
        //error due to integer round-down. It is relevant to low
        //amplitudes_ in gainID=1 and negligible otherwise.
        double err3 = (0.289 * 0.289) * (invampl[j] * invampl[j]);
 
        double totalError = std::sqrt(err1 + err2 + err3);
 
        // don't include useless ratios
        if (totalError < 1.0 && Rtmp > 0.001 && Rtmp < Rlim[j - i]) {
          Ratio currentRatio = {i, (j - i), Rtmp, totalError};
          ratios_[ratios_size++] = currentRatio;
        }
      }
    }
  }
 
  // No useful ratios, return zero amplitude and no time measurement
  if (0 == ratios_size)
    return;
 
  //  std::array < Tmax, C::MAXSAMPLES*(C::MAXSAMPLES-1)/2 > times_;
  Tmax timesAB_[C::MAXSAMPLES * (C::MAXSAMPLES - 1) / 2];
  unsigned int timesAB_size = 0;
 
  // make a vector of Tmax measurements that correspond to each ratio
  // and based on Alpha-Beta parameterization of the pulse shape
 
  for (unsigned int i = 0; i < ratios_size; i++) {
    double stepOverBeta = double(ratios_[i].step) / beta;
    double offset = double(ratios_[i].index) + alphabeta;
 
    double Rmin = ratios_[i].value - ratios_[i].error;
    if (Rmin < 0.001)
      Rmin = 0.001;
 
    double Rmax = ratios_[i].value + ratios_[i].error;
    double RLimit = Rlim[ratios_[i].step];
    if (Rmax > RLimit)
      Rmax = RLimit;
 
    double time1 =
        offset - ratios_[i].step / (myMath::fast_expf((stepOverBeta - myMath::fast_logf(Rmin)) / alpha) - 1.0);
    double time2 =
        offset - ratios_[i].step / (myMath::fast_expf((stepOverBeta - myMath::fast_logf(Rmax)) / alpha) - 1.0);
 
    // this is the time measurement based on the ratios[i]
    double tmax = 0.5 * (time1 + time2);
    double tmaxerr = 0.5 * std::sqrt((time1 - time2) * (time1 - time2));
 
    // calculate chi2
    sumAf = 0;
    sumff = 0;
    int itmin = std::max(-1, int(std::floor(tmax - alphabeta)));
    double loffset = (double(itmin) - tmax) * invalphabeta;
    for (unsigned int it = itmin + 1; it < amplitudes_.size(); it++) {
      loffset += invalphabeta;
      if (useless_[it])
        continue;
      double inverr2 = amplitudeIE2_[it];
      //      double offset = (double(it) - tmax)/alphabeta;
      double term1 = 1.0 + loffset;
      // assert(term1>1e-6);
      double f = (term1 > 1e-6) ? myMath::fast_expf(alpha * (myMath::fast_logf(term1) - loffset)) : 0;
      sumAf += amplitudes_[it] * (f * inverr2);
      sumff += f * (f * inverr2);
    }
 
    double chi2 = sumAA;
    double amp = 0;
    if (sumff > 0) {
      chi2 = sumAA - sumAf * (sumAf / sumff);
      amp = (sumAf / sumff);
    }
    chi2 /= sum0;
 
    // choose reasonable measurements. One might argue what is
    // reasonable and what is not.
    if (chi2 > 0 && tmaxerr > 0 && tmax > 0) {
      Tmax currentTmax = {ratios_[i].index, ratios_[i].step, tmax, tmaxerr, amp, chi2};
      timesAB_[timesAB_size++] = currentTmax;
    }
  }
 
  // no reasonable time measurements!
  if (0 == timesAB_size)
    return;
 
  // find minimum chi2
  double chi2min = 1.0e+9;
  //double timeMinimum = 5;
  //double errorMinimum = 999;
  for (unsigned int i = 0; i < timesAB_size; i++) {
    if (timesAB_[i].chi2 < chi2min) {
      chi2min = timesAB_[i].chi2;
      //timeMinimum = timesAB_[i].value;
      //errorMinimum = timesAB_[i].error;
    }
  }
 
  // make a weighted average of tmax measurements with "small" chi2
  // (within 1 sigma of statistical uncertainty :-)
  double chi2Limit = chi2min + 1.0;
  double time_max = 0;
  double time_wgt = 0;
  for (unsigned int i = 0; i < timesAB_size; i++) {
    if (timesAB_[i].chi2 < chi2Limit) {
      double inverseSigmaSquared = 1.0 / (timesAB_[i].error * timesAB_[i].error);
      time_wgt += inverseSigmaSquared;
      time_max += timesAB_[i].value * inverseSigmaSquared;
    }
  }
 
  tMaxAlphaBeta = time_max / time_wgt;
  tMaxErrorAlphaBeta = 1.0 / sqrt(time_wgt);
 
  // find amplitude and chi2
  sumAf = 0;
  sumff = 0;
  for (unsigned int i = 0; i < amplitudes_.size(); i++) {
    if (useless_[i])
      continue;
    double inverr2 = amplitudeIE2_[i];
    double offset = (double(i) - tMaxAlphaBeta) * invalphabeta;
    double term1 = 1.0 + offset;
    if (term1 > 1e-6) {
      double f = myMath::fast_expf(alpha * (myMath::fast_logf(term1) - offset));
      sumAf += amplitudes_[i] * (f * inverr2);
      sumff += f * (f * inverr2);
    }
  }
 
  if (sumff > 0) {
    ampMaxAlphaBeta = sumAf / sumff;
    double chi2AlphaBeta = (sumAA - sumAf * sumAf / sumff) / sum0;
    if (chi2AlphaBeta > NullChi2) {
      // null hypothesis is better
      return;
    }
 
  } else {
    // no visible pulse here
    return;
  }
 
  // if we got to this point, we have a reconstructied Tmax
  // using RatioAlphaBeta Method. To summarize:
  //
  //     tMaxAlphaBeta      - Tmax value
  //     tMaxErrorAlphaBeta - error on Tmax, but I would not trust it
  //     ampMaxAlphaBeta    - amplitude of the pulse
  //     ampMaxError_        - uncertainty of the time sample with max amplitude
  //
 
  // Do Ratio's Method with "large" pulses
  if (ampMaxAlphaBeta / ampMaxError_ > 5.0) {
    // make a vector of Tmax measurements that correspond to each
    // ratio. Each measurement have it's value and the error
 
    double time_max = 0;
    double time_wgt = 0;
 
    for (unsigned int i = 0; i < ratios_size; i++) {
      if (ratios_[i].step == 1 && ratios_[i].value >= timeFitLimits.first && ratios_[i].value <= timeFitLimits.second) {
        double time_max_i = ratios_[i].index;
 
        // calculate polynomial for Tmax
 
        double u = timeFitParameters[timeFitParameters.size() - 1];
        for (int k = timeFitParameters.size() - 2; k >= 0; k--) {
          u = u * ratios_[i].value + timeFitParameters[k];
        }
 
        // calculate derivative for Tmax error
        double du = (timeFitParameters.size() - 1) * timeFitParameters[timeFitParameters.size() - 1];
        for (int k = timeFitParameters.size() - 2; k >= 1; k--) {
          du = du * ratios_[i].value + k * timeFitParameters[k];
        }
 
        // running sums for weighted average
        double errorsquared = ratios_[i].error * ratios_[i].error * du * du;
        if (errorsquared > 0) {
          time_max += (time_max_i - u) / errorsquared;
          time_wgt += 1.0 / errorsquared;
          //            Tmax currentTmax =
          //  { ratios_[i].index, 1, (time_max_i - u),
          //sqrt(errorsquared),0,1 };
          // times_.push_back(currentTmax);
        }
      }
    }
 
    // calculate weighted average of all Tmax measurements
    if (time_wgt > 0) {
      tMaxRatio = time_max / time_wgt;
      tMaxErrorRatio = 1.0 / sqrt(time_wgt);
 
      // combine RatioAlphaBeta and Ratio Methods
 
      if (ampMaxAlphaBeta / ampMaxError_ > 10.0) {
        // use pure Ratio Method
        calculatedRechit_.timeMax = tMaxRatio;
        calculatedRechit_.timeError = tMaxErrorRatio;
 
      } else {
        // combine two methods
        calculatedRechit_.timeMax = (tMaxAlphaBeta * (10.0 - ampMaxAlphaBeta / ampMaxError_) +
                                     tMaxRatio * (ampMaxAlphaBeta / ampMaxError_ - 5.0)) /
                                    5.0;
        calculatedRechit_.timeError = (tMaxErrorAlphaBeta * (10.0 - ampMaxAlphaBeta / ampMaxError_) +
                                       tMaxErrorRatio * (ampMaxAlphaBeta / ampMaxError_ - 5.0)) /
                                      5.0;
      }
 
    } else {
      // use RatioAlphaBeta Method
      calculatedRechit_.timeMax = tMaxAlphaBeta;
      calculatedRechit_.timeError = tMaxErrorAlphaBeta;
    }
 
  } else {
    // use RatioAlphaBeta Method
    calculatedRechit_.timeMax = tMaxAlphaBeta;
    calculatedRechit_.timeError = tMaxErrorAlphaBeta;
  }
}
 
template <class C>
void EcalUncalibRecHitRatioMethodAlgo<C>::computeAmplitude(std::vector<double> &amplitudeFitParameters) {
  calculatedRechit_.amplitudeMax = computeAmplitudeImpl(amplitudeFitParameters, 1., 1.);
}
 
template <class C>
double EcalUncalibRecHitRatioMethodAlgo<C>::computeAmplitudeImpl(std::vector<double> &amplitudeFitParameters,
                                                                 double corr4,
                                                                 double corr6) {
  //                                                            //
  //             CALCULATE AMPLITUDE                            //
  //                                                            //
 
  double alpha = amplitudeFitParameters[0];
  double beta = amplitudeFitParameters[1];
 
  // calculate pedestal, again
 
  double pedestalLimit = calculatedRechit_.timeMax - (alpha * beta) - 1.0;
  double sumA = 0;
  double sumF = 0;
  double sumAF = 0;
  double sumFF = 0;
  double sum1 = 0;
  for (unsigned int i = 0; i < amplitudes_.size(); i++) {
    if (useless_[i])
      continue;
    double inverr2 = amplitudeIE2_[i];
    double f = 0;
    double termOne = 1 + (i - calculatedRechit_.timeMax) / (alpha * beta);
    if (termOne > 1.e-5)
      f = myMath::fast_expf(alpha * myMath::fast_logf(termOne) - (i - calculatedRechit_.timeMax) / beta);
 
    // apply range of interesting samples
 
    if ((i < pedestalLimit) || (f > 0.6 * corr6 && i <= calculatedRechit_.timeMax) ||
        (f > 0.4 * corr4 && i >= calculatedRechit_.timeMax)) {
      sum1 += inverr2;
      sumA += amplitudes_[i] * inverr2;
      sumF += f * inverr2;
      sumAF += (f * inverr2) * amplitudes_[i];
      sumFF += f * (f * inverr2);
    }
  }
 
  double amplitudeMax = 0;
  if (sum1 > 0) {
    double denom = sumFF * sum1 - sumF * sumF;
    if (std::abs(denom) > 1.0e-20) {
      amplitudeMax = (sumAF * sum1 - sumA * sumF) / denom;
    }
  }
  return amplitudeMax;
}
 
template <class C>
EcalUncalibratedRecHit EcalUncalibRecHitRatioMethodAlgo<C>::makeRecHit(const C &dataFrame,
                                                                       const EcalSampleMask &sampleMask,
                                                                       const double *pedestals,
                                                                       const double *pedestalRMSes,
                                                                       const double *gainRatios,
                                                                       std::vector<double> &timeFitParameters,
                                                                       std::vector<double> &amplitudeFitParameters,
                                                                       std::pair<double, double> &timeFitLimits) {
  init(dataFrame, sampleMask, pedestals, pedestalRMSes, gainRatios);
  computeTime(timeFitParameters, timeFitLimits, amplitudeFitParameters);
  computeAmplitude(amplitudeFitParameters);
 
  // 1st parameters is id
  //
  // 2nd parameters is amplitude. It is calculated by this method.
  //
  // 3rd parameter is pedestal. It is not calculated. This method
  // relies on input parameters for pedestals and gain ratio. Return
  // zero.
  //
  // 4th parameter is jitter which is a bad choice to call Tmax. It is
  // calculated by this method (in 25 nsec clock units)
  //
  // GF subtract 5 so that jitter==0 corresponds to synchronous hit
  //
  //
  // 5th parameter is chi2. It is possible to calculate chi2 for
  // Tmax. It is possible to calculate chi2 for Amax. However, these
  // values are not very useful without TmaxErr and AmaxErr. This
  // method can return one value for chi2 but there are 4 different
  // parameters that have useful information about the quality of Amax
  // ans Tmax. For now we can return TmaxErr. The quality of Tmax and
  // Amax can be judged from the magnitude of TmaxErr
 
  return EcalUncalibratedRecHit(dataFrame.id(),
                                calculatedRechit_.amplitudeMax,
                                pedestal_,
                                calculatedRechit_.timeMax - 5,
                                calculatedRechit_.timeError);
}
#endif