SiPixelTemplateReco.cc

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//
//  SiPixelTemplateReco.cc (Version 10.01)
//
//  Add goodness-of-fit to algorithm, include single pixel clusters in chi2 calculation
//  Try "decapitation" of large single pixels
//  Add correction for (Q_F-Q_L)/(Q_F+Q_L) bias
//  Add cot(beta) reflection to reduce y-entries and more sophisticated x-interpolation
//  Fix small double pixel bug with decapitation (2.41 5-Mar-2007).
//  Fix pseudopixel bug causing possible memory overwrite (2.42 12-Mar-2007)
//  Adjust template binning to span 3 (or 4) central pixels and implement improved (faster) chi2min search
//  Replace internal containers with static arrays
//  Add external threshold to calls to ysigma2 and xsigma2, use sorted signal heights to guarrantee min clust size = 2
//  Use denser search over larger bin range for clusters with big pixels.
//  Use single calls to template object to load template arrays (had been many)
//  Add speed switch to trade-off speed and robustness
//  Add qmin and re-define qbin to flag low-q clusters
//  Add qscale to match charge scales
//  Return error if no pixels in cluster
//  Replace 4 cout's with LogError's
//  Add LogDebug I/O to report various common errors
//  Incorporate "cluster repair" to handle dead pixels
//  Take truncation size from new pixmax information
//  Change to allow template sizes to be changed at compile time
//  Move interpolation range error to LogDebug
//  Add qbin = 5 and change 1-pixel probability to use new template info
//  Add floor for probabilities (no exact zeros)
//  Replace asserts with exceptions in CMSSW
//  Change calling sequence to handle cot(beta)<0 for FPix cosmics
//
//  V7.00 - Decouple BPix and FPix information into separate templates
//  Pass all containers by alias to prevent excessive cpu-usage (V7.01)
//  Slightly modify search bin range to avoid problem with single pixel clusters + large Lorentz drift (V7.02)
//
//  V8.00 - Add 2D probabilities, take pixel sizes from the template
//  V8.05 - Shift 2-D cluster to center on the buffer
//  V8.06 - Add locBz to the 2-D template (causes failover to the simple template when the cotbeta-locBz correlation is incorrect ... ie for non-IP tracks)
//        - include minimum value for prob2D (1.e-30)
//  V8.07 - Tune 2-d probability: consider only pixels above threshold and use threshold value for zero signal pixels (non-zero template)
//  V8.10 - Remove 2-d probability for ineffectiveness and replace with simple cluster charge probability
//  V8.11 - Change probQ to upper tail probability always (rather than two-sided tail probability)
//  V8.20 - Use template cytemp/cxtemp methods to center the data cluster in the right place when the template becomes asymmetric after irradiation
//  V8.25 - Incorporate VIs speed improvements
//  V8.26 - Fix centering problem for small signals
//  V9.00 - Set QProb = Q/Q_avg when calcultion is turned off, use fbin definitions of Qbin
//  V10.00 - Use new template object to reco Phase 1 FPix hits
//  V10.01 - Fix memory overwriting bug
//
//
//  Created by Morris Swartz on 10/27/06.
//
//

#ifndef SI_PIXEL_TEMPLATE_STANDALONE
//#include <cmath.h>
#else
#include <math.h>
#endif
#include <algorithm>
#include <vector>
#include <utility>
#include <iostream>
// ROOT::Math has a c++ function that does the probability calc, but only in v5.12 and later
#include "TMath.h"
#include "Math/DistFunc.h"
// Use current version of gsl instead of ROOT::Math
//#include <gsl/gsl_cdf.h>

static const int theVerboseLevel = 2;
#ifndef SI_PIXEL_TEMPLATE_STANDALONE
#include "RecoLocalTracker/SiPixelRecHits/interface/SiPixelTemplateReco.h"
#include "RecoLocalTracker/SiPixelRecHits/interface/VVIObjF.h"
#include "FWCore/MessageLogger/interface/MessageLogger.h"
#define LOGERROR(x) edm::LogError(x)
#define LOGDEBUG(x) LogDebug(x)
#define ENDL " "
#include "FWCore/Utilities/interface/Exception.h"
#else
#include "SiPixelTemplateReco.h"
#include "VVIObjF.h"
#define LOGERROR(x) std::cout << x << ": "
#define LOGDEBUG(x) std::cout << x << ": "
#define ENDL std::endl
#endif

using namespace SiPixelTemplateReco;

// *************************************************************************************************************************************
// *************************************************************************************************************************************
int SiPixelTemplateReco::PixelTempReco1D(int id,
                                         float cotalpha,
                                         float cotbeta,
                                         float locBz,
                                         float locBx,
                                         ClusMatrix& cluster,
                                         SiPixelTemplate& templ,
                                         float& yrec,
                                         float& sigmay,
                                         float& proby,
                                         float& xrec,
                                         float& sigmax,
                                         float& probx,
                                         int& qbin,
                                         int speed,
                                         bool deadpix,
                                         std::vector<std::pair<int, int> >& zeropix,
                                         float& probQ,
                                         int& nypix,
                                         int& nxpix)

{
  // Local variables
  int i, j, k, minbin, binl, binh, binq, midpix, fypix, lypix, logypx;
  int fxpix, lxpix, logxpx, shifty, shiftx, nyzero[TYSIZE];
  int nclusx, nclusy;
  int deltaj, jmin, jmax, fxbin, lxbin, fybin, lybin, djy, djx;
  //int fypix2D, lypix2D, fxpix2D, lxpix2D;
  float sythr, sxthr, rnorm, delta, sigma, sigavg, pseudopix, qscale, q50;
  float ss2, ssa, sa2, ssba, saba, sba2, rat, fq, qtotal, qpixel, fbin[3];
  float originx, originy, qfy, qly, qfx, qlx, bias, maxpix, minmax;
  double chi2x, meanx, chi2y, meany, chi2ymin, chi2xmin, chi21max;
  double hchi2, hndof, prvav, mpv, sigmaQ, kappa, xvav, beta2;
  float ytemp[41][BYSIZE], xtemp[41][BXSIZE], ysum[BYSIZE], xsum[BXSIZE], ysort[BYSIZE], xsort[BXSIZE];
  float chi2ybin[41], chi2xbin[41], ysig2[BYSIZE], xsig2[BXSIZE];
  float yw2[BYSIZE], xw2[BXSIZE], ysw[BYSIZE], xsw[BXSIZE];
  bool yd[BYSIZE], xd[BXSIZE], anyyd, anyxd, calc_probQ, use_VVIObj;
  float ysize, xsize;
  const float probmin = {1.110223e-16};
  const float probQmin = {1.e-5};

  // The minimum chi2 for a valid one pixel cluster = pseudopixel contribution only

  const double mean1pix = {0.100};
#ifdef SI_PIXEL_TEMPLATE_STANDALONE
  const double chi21min = {0.};
#else
  const double chi21min = {0.160};
#endif

  // First, interpolate the template needed to analyze this cluster
  // check to see of the track direction is in the physical range of the loaded template

  if (id >= 0) {  //if id < 0 bypass interpolation (used in calibration)
    if (!templ.interpolate(id, cotalpha, cotbeta, locBz, locBx)) {
      if (theVerboseLevel > 2) {
        LOGDEBUG("SiPixelTemplateReco") << "input cluster direction cot(alpha) = " << cotalpha
                                        << ", cot(beta) = " << cotbeta << ", local B_z = " << locBz
                                        << ", local B_x = " << locBx << ", template ID = " << id
                                        << ", no reconstruction performed" << ENDL;
      }
      return 20;
    }
  }

  // Check to see if Q probability is selected

  calc_probQ = false;
  use_VVIObj = false;
  if (speed < 0) {
    calc_probQ = true;
    if (speed < -1)
      use_VVIObj = true;
    speed = 0;
  }

  if (speed > 3) {
    calc_probQ = true;
    if (speed < 5)
      use_VVIObj = true;
    speed = 3;
  }

  // Get pixel dimensions from the template (to allow multiple detectors in the future)

  xsize = templ.xsize();
  ysize = templ.ysize();

  // Allow Qbin Q/Q_avg fractions to vary to optimize error estimation

  for (i = 0; i < 3; ++i) {
    fbin[i] = templ.fbin(i);
  }

  // Define size of pseudopixel

  q50 = templ.s50();
  pseudopix = 0.2f * q50;

  // Get charge scaling factor

  qscale = templ.qscale();

  // Check that the cluster container is (up to) a 7x21 matrix and matches the dimensions of the double pixel flags

  nclusx = cluster.mrow;
  nclusy = (int)cluster.mcol;
  auto const xdouble = cluster.xdouble;
  auto const ydouble = cluster.ydouble;

  // First, rescale all pixel charges and compute total charge
  qtotal = 0.f;
  for (i = 0; i < nclusx * nclusy; ++i) {
    cluster.matrix[i] *= qscale;
    qtotal += cluster.matrix[i];
  }
  // Next, sum the total charge and "decapitate" big pixels
  minmax = templ.pixmax();
  for (j = 0; j < nclusx; ++j)
    for (i = 0; i < nclusy; ++i) {
      maxpix = minmax;
      if (ydouble[i]) {
        maxpix *= 2.f;
      }
      if (cluster(j, i) > maxpix) {
        cluster(j, i) = maxpix;
      }
    }

  // Do the cluster repair here

  if (deadpix) {
    fypix = BYM3;
    lypix = -1;
    memset(nyzero, 0, TYSIZE * sizeof(int));
    memset(ysum, 0, BYSIZE * sizeof(float));
    for (i = 0; i < nclusy; ++i) {
      // Do preliminary cluster projection in y
      for (j = 0; j < nclusx; ++j) {
        ysum[i] += cluster(j, i);
      }
      if (ysum[i] > 0.f) {
        // identify ends of cluster to determine what the missing charge should be
        if (i < fypix) {
          fypix = i;
        }
        if (i > lypix) {
          lypix = i;
        }
      }
    }

    // Now loop over dead pixel list and "fix" everything

    //First see if the cluster ends are redefined and that we have only one dead pixel per column

    std::vector<std::pair<int, int> >::const_iterator zeroIter = zeropix.begin(), zeroEnd = zeropix.end();
    for (; zeroIter != zeroEnd; ++zeroIter) {
      i = zeroIter->second;
      if (i < 0 || i > TYSIZE - 1) {
        LOGERROR("SiPixelTemplateReco") << "dead pixel column y-index " << i << ", no reconstruction performed" << ENDL;
        return 11;
      }

      // count the number of dead pixels in each column
      ++nyzero[i];
      // allow them to redefine the cluster ends
      if (i < fypix) {
        fypix = i;
      }
      if (i > lypix) {
        lypix = i;
      }
    }

    nypix = lypix - fypix + 1;

    // Now adjust the charge in the dead pixels to sum to 0.5*truncation value in the end columns and the truncation value in the interior columns

    for (zeroIter = zeropix.begin(); zeroIter != zeroEnd; ++zeroIter) {
      i = zeroIter->second;
      j = zeroIter->first;
      if (j < 0 || j > TXSIZE - 1) {
        LOGERROR("SiPixelTemplateReco") << "dead pixel column x-index " << j << ", no reconstruction performed" << ENDL;
        return 12;
      }
      if ((i == fypix || i == lypix) && nypix > 1) {
        maxpix = templ.symax() / 2.;
      } else {
        maxpix = templ.symax();
      }
      if (ydouble[i]) {
        maxpix *= 2.;
      }
      if (nyzero[i] > 0 && nyzero[i] < 3) {
        qpixel = (maxpix - ysum[i]) / (float)nyzero[i];
      } else {
        qpixel = 1.;
      }
      if (qpixel < 1.) {
        qpixel = 1.;
      }
      cluster(j, i) = qpixel;
      // Adjust the total cluster charge to reflect the charge of the "repaired" cluster
      qtotal += qpixel;
    }
    // End of cluster repair section
  }

  // Next, make y-projection of the cluster and copy the double pixel flags into a 25 element container

  for (i = 0; i < BYSIZE; ++i) {
    ysum[i] = 0.f;
    yd[i] = false;
  }
  k = 0;
  anyyd = false;
  for (i = 0; i < nclusy; ++i) {
    for (j = 0; j < nclusx; ++j) {
      ysum[k] += cluster(j, i);
    }

    // If this is a double pixel, put 1/2 of the charge in 2 consective single pixels

    if (ydouble[i]) {
      ysum[k] /= 2.f;
      ysum[k + 1] = ysum[k];
      yd[k] = true;
      yd[k + 1] = false;
      k = k + 2;
      anyyd = true;
    } else {
      yd[k] = false;
      ++k;
    }
    if (k > BYM1) {
      break;
    }
  }

  // Next, make x-projection of the cluster and copy the double pixel flags into an 11 element container

  for (i = 0; i < BXSIZE; ++i) {
    xsum[i] = 0.f;
    xd[i] = false;
  }
  k = 0;
  anyxd = false;
  for (j = 0; j < nclusx; ++j) {
    for (i = 0; i < nclusy; ++i) {
      xsum[k] += cluster(j, i);
    }

    // If this is a double pixel, put 1/2 of the charge in 2 consective single pixels

    if (xdouble[j]) {
      xsum[k] /= 2.;
      xsum[k + 1] = xsum[k];
      xd[k] = true;
      xd[k + 1] = false;
      k = k + 2;
      anyxd = true;
    } else {
      xd[k] = false;
      ++k;
    }
    if (k > BXM1) {
      break;
    }
  }

  // next, identify the y-cluster ends, count total pixels, nypix, and logical pixels, logypx

  fypix = -1;
  nypix = 0;
  lypix = 0;
  logypx = 0;
  for (i = 0; i < BYSIZE; ++i) {
    if (ysum[i] > 0.f) {
      if (fypix == -1) {
        fypix = i;
      }
      if (!yd[i]) {
        ysort[logypx] = ysum[i];
        ++logypx;
      }
      ++nypix;
      lypix = i;
    }
  }

  //    dlengthy = (float)nypix - templ.clsleny();

  // Make sure cluster is continuous

  if ((lypix - fypix + 1) != nypix || nypix == 0) {
    LOGDEBUG("SiPixelTemplateReco") << "y-length of pixel cluster doesn't agree with number of pixels above threshold"
                                    << ENDL;
    if (theVerboseLevel > 2) {
      LOGDEBUG("SiPixelTemplateReco") << "ysum[] = ";
      for (i = 0; i < BYSIZE - 1; ++i) {
        LOGDEBUG("SiPixelTemplateReco") << ysum[i] << ", ";
      }
      LOGDEBUG("SiPixelTemplateReco") << ysum[BYSIZE - 1] << ENDL;
    }

    return 1;
  }

  // If cluster is longer than max template size, technique fails

  if (nypix > TYSIZE) {
    LOGDEBUG("SiPixelTemplateReco") << "y-length of pixel cluster is larger than maximum template size" << ENDL;
    if (theVerboseLevel > 2) {
      LOGDEBUG("SiPixelTemplateReco") << "ysum[] = ";
      for (i = 0; i < BYSIZE - 1; ++i) {
        LOGDEBUG("SiPixelTemplateReco") << ysum[i] << ", ";
      }
      LOGDEBUG("SiPixelTemplateReco") << ysum[BYSIZE - 1] << ENDL;
    }

    return 6;
  }

  // Remember these numbers for later

  //fypix2D = fypix;
  //lypix2D = lypix;

  // next, center the cluster on template center if necessary

  midpix = (fypix + lypix) / 2;
  shifty = templ.cytemp() - midpix;

  // calculate new cluster boundaries

  int lytmp = lypix + shifty;
  int fytmp = fypix + shifty;

  // Check the boundaries

  if (fytmp <= 1) {
    return 8;
  }
  if (lytmp >= BYM2) {
    return 8;
  }

  //  If OK, shift everything

  if (shifty > 0) {
    for (i = lypix; i >= fypix; --i) {
      ysum[i + shifty] = ysum[i];
      ysum[i] = 0.;
      yd[i + shifty] = yd[i];
      yd[i] = false;
    }
  } else if (shifty < 0) {
    for (i = fypix; i <= lypix; ++i) {
      ysum[i + shifty] = ysum[i];
      ysum[i] = 0.;
      yd[i + shifty] = yd[i];
      yd[i] = false;
    }
  }

  lypix = lytmp;
  fypix = fytmp;

  // add pseudopixels

  ysum[fypix - 1] = pseudopix;
  ysum[fypix - 2] = pseudopix;
  ysum[lypix + 1] = pseudopix;
  ysum[lypix + 2] = pseudopix;

  // finally, determine if pixel[0] is a double pixel and make an origin correction if it is

  if (ydouble[0]) {
    originy = -0.5f;
  } else {
    originy = 0.f;
  }

  // next, identify the x-cluster ends, count total pixels, nxpix, and logical pixels, logxpx

  fxpix = -1;
  nxpix = 0;
  lxpix = 0;
  logxpx = 0;
  for (i = 0; i < BXSIZE; ++i) {
    if (xsum[i] > 0.) {
      if (fxpix == -1) {
        fxpix = i;
      }
      if (!xd[i]) {
        xsort[logxpx] = xsum[i];
        ++logxpx;
      }
      ++nxpix;
      lxpix = i;
    }
  }

  //    dlengthx = (float)nxpix - templ.clslenx();

  // Make sure cluster is continuous

  if ((lxpix - fxpix + 1) != nxpix) {
    LOGDEBUG("SiPixelTemplateReco") << "x-length of pixel cluster doesn't agree with number of pixels above threshold"
                                    << ENDL;
    if (theVerboseLevel > 2) {
      LOGDEBUG("SiPixelTemplateReco") << "xsum[] = ";
      for (i = 0; i < BXSIZE - 1; ++i) {
        LOGDEBUG("SiPixelTemplateReco") << xsum[i] << ", ";
      }
      LOGDEBUG("SiPixelTemplateReco") << ysum[BXSIZE - 1] << ENDL;
    }

    return 2;
  }

  // If cluster is longer than max template size, technique fails

  if (nxpix > TXSIZE) {
    LOGDEBUG("SiPixelTemplateReco") << "x-length of pixel cluster is larger than maximum template size" << ENDL;
    if (theVerboseLevel > 2) {
      LOGDEBUG("SiPixelTemplateReco") << "xsum[] = ";
      for (i = 0; i < BXSIZE - 1; ++i) {
        LOGDEBUG("SiPixelTemplateReco") << xsum[i] << ", ";
      }
      LOGDEBUG("SiPixelTemplateReco") << ysum[BXSIZE - 1] << ENDL;
    }

    return 7;
  }

  // Remember these numbers for later

  //fxpix2D = fxpix;
  //lxpix2D = lxpix;

  // next, center the cluster on template center if necessary

  midpix = (fxpix + lxpix) / 2;
  shiftx = templ.cxtemp() - midpix;

  // calculate new cluster boundaries

  int lxtmp = lxpix + shiftx;
  int fxtmp = fxpix + shiftx;

  // Check the boundaries

  if (fxtmp <= 1) {
    return 9;
  }
  if (lxtmp >= BXM2) {
    return 9;
  }

  //  If OK, shift everything

  if (shiftx > 0) {
    for (i = lxpix; i >= fxpix; --i) {
      xsum[i + shiftx] = xsum[i];
      xsum[i] = 0.;
      xd[i + shiftx] = xd[i];
      xd[i] = false;
    }
  } else if (shiftx < 0) {
    for (i = fxpix; i <= lxpix; ++i) {
      xsum[i + shiftx] = xsum[i];
      xsum[i] = 0.;
      xd[i + shiftx] = xd[i];
      xd[i] = false;
    }
  }

  lxpix = lxtmp;
  fxpix = fxtmp;

  xsum[fxpix - 1] = pseudopix;
  xsum[fxpix - 2] = pseudopix;
  xsum[lxpix + 1] = pseudopix;
  xsum[lxpix + 2] = pseudopix;

  // finally, determine if pixel[0] is a double pixel and make an origin correction if it is

  if (xdouble[0]) {
    originx = -0.5f;
  } else {
    originx = 0.f;
  }

  // uncertainty and final corrections depend upon total charge bin

  fq = qtotal / templ.qavg();
  if (fq > fbin[0]) {
    binq = 0;
  } else {
    if (fq > fbin[1]) {
      binq = 1;
    } else {
      if (fq > fbin[2]) {
        binq = 2;
      } else {
        binq = 3;
      }
    }
  }

  // Return the charge bin via the parameter list unless the charge is too small (then flag it)

  qbin = binq;
  if (!deadpix && qtotal < 0.95f * templ.qmin()) {
    qbin = 5;
  } else {
    if (!deadpix && qtotal < 0.95f * templ.qmin(1)) {
      qbin = 4;
    }
  }
  if (theVerboseLevel > 9) {
    LOGDEBUG("SiPixelTemplateReco") << "ID = " << id << " cot(alpha) = " << cotalpha << " cot(beta) = " << cotbeta
                                    << " nclusx = " << nclusx << " nclusy = " << nclusy << ENDL;
  }

  // Next, copy the y- and x-templates to local arrays

  // First, decide on chi^2 min search parameters

#ifndef SI_PIXEL_TEMPLATE_STANDALONE
  if (speed < 0 || speed > 3) {
    throw cms::Exception("DataCorrupt") << "SiPixelTemplateReco::PixelTempReco1D called with illegal speed = " << speed
                                        << std::endl;
  }
#else
  assert(speed >= 0 && speed < 4);
#endif
  fybin = 3;
  lybin = 37;
  fxbin = 3;
  lxbin = 37;
  djy = 1;
  djx = 1;
  if (speed > 0) {
    fybin = 8;
    lybin = 32;
    if (yd[fypix]) {
      fybin = 4;
      lybin = 36;
    }
    if (lypix > fypix) {
      if (yd[lypix - 1]) {
        fybin = 4;
        lybin = 36;
      }
    }
    fxbin = 8;
    lxbin = 32;
    if (xd[fxpix]) {
      fxbin = 4;
      lxbin = 36;
    }
    if (lxpix > fxpix) {
      if (xd[lxpix - 1]) {
        fxbin = 4;
        lxbin = 36;
      }
    }
  }

  if (speed > 1) {
    djy = 2;
    djx = 2;
    if (speed > 2) {
      if (!anyyd) {
        djy = 4;
      }
      if (!anyxd) {
        djx = 4;
      }
    }
  }

  if (theVerboseLevel > 9) {
    LOGDEBUG("SiPixelTemplateReco") << "fypix " << fypix << " lypix = " << lypix << " fybin = " << fybin
                                    << " lybin = " << lybin << " djy = " << djy << " logypx = " << logypx << ENDL;
    LOGDEBUG("SiPixelTemplateReco") << "fxpix " << fxpix << " lxpix = " << lxpix << " fxbin = " << fxbin
                                    << " lxbin = " << lxbin << " djx = " << djx << " logxpx = " << logxpx << ENDL;
  }

  // Now do the copies

  templ.ytemp(fybin, lybin, ytemp);

  templ.xtemp(fxbin, lxbin, xtemp);

  // Do the y-reconstruction first

  // Apply the first-pass template algorithm to all clusters

  // Modify the template if double pixels are present

  if (nypix > logypx) {
    i = fypix;
    while (i < lypix) {
      if (yd[i] && !yd[i + 1]) {
        for (j = fybin; j <= lybin; ++j) {
          // Sum the adjacent cells and put the average signal in both

          sigavg = (ytemp[j][i] + ytemp[j][i + 1]) / 2.f;
          ytemp[j][i] = sigavg;
          ytemp[j][i + 1] = sigavg;
        }
        i += 2;
      } else {
        ++i;
      }
    }
  }

  // Define the maximum signal to allow before de-weighting a pixel

  sythr = 1.1 * (templ.symax());

  // Make sure that there will be at least two pixels that are not de-weighted

  std::sort(&ysort[0], &ysort[logypx]);
  if (logypx == 1) {
    sythr = 1.01f * ysort[0];
  } else {
    if (ysort[1] > sythr) {
      sythr = 1.01f * ysort[1];
    }
  }

  // Evaluate pixel-by-pixel uncertainties (weights) for the templ analysis

  //    for(i=0; i<BYSIZE; ++i) { ysig2[i] = 0.;}
  templ.ysigma2(fypix, lypix, sythr, ysum, ysig2);

  // Find the template bin that minimizes the Chi^2

  chi2ymin = 1.e15;
  for (i = fybin; i <= lybin; ++i) {
    chi2ybin[i] = -1.e15f;
  }
  ss2 = 0.f;
  for (i = fypix - 2; i <= lypix + 2; ++i) {
    yw2[i] = 1.f / ysig2[i];
    ysw[i] = ysum[i] * yw2[i];
    ss2 += ysum[i] * ysw[i];
  }

  minbin = -1;
  deltaj = djy;
  jmin = fybin;
  jmax = lybin;
  while (deltaj > 0) {
    for (j = jmin; j <= jmax; j += deltaj) {
      if (chi2ybin[j] < -100.f) {
        ssa = 0.f;
        sa2 = 0.f;
        for (i = fypix - 2; i <= lypix + 2; ++i) {
          ssa += ysw[i] * ytemp[j][i];
          sa2 += ytemp[j][i] * ytemp[j][i] * yw2[i];
        }
        rat = ssa / ss2;
        if (rat <= 0.f) {
          LOGERROR("SiPixelTemplateReco") << "illegal chi2ymin normalization (1) = " << rat << ENDL;
          rat = 1.;
        }
        chi2ybin[j] = ss2 - 2.f * ssa / rat + sa2 / (rat * rat);
      }
      if (chi2ybin[j] < chi2ymin) {
        chi2ymin = chi2ybin[j];
        minbin = j;
      }
    }
    deltaj /= 2;
    if (minbin > fybin) {
      jmin = minbin - deltaj;
    } else {
      jmin = fybin;
    }
    if (minbin < lybin) {
      jmax = minbin + deltaj;
    } else {
      jmax = lybin;
    }
  }

  if (theVerboseLevel > 9) {
    LOGDEBUG("SiPixelTemplateReco") << "minbin " << minbin << " chi2ymin = " << chi2ymin << ENDL;
  }

  // Do not apply final template pass to 1-pixel clusters (use calibrated offset)

  if (logypx == 1) {
    if (nypix == 1) {
      delta = templ.dyone();
      sigma = templ.syone();
    } else {
      delta = templ.dytwo();
      sigma = templ.sytwo();
    }

    yrec = 0.5f * (fypix + lypix - 2 * shifty + 2.f * originy) * ysize - delta;
    if (sigma <= 0.f) {
      sigmay = 43.3f;
    } else {
      sigmay = sigma;
    }

    // Do probability calculation for one-pixel clusters

    chi21max = fmax(chi21min, (double)templ.chi2yminone());
    chi2ymin -= chi21max;
    if (chi2ymin < 0.) {
      chi2ymin = 0.;
    }
    //     proby = gsl_cdf_chisq_Q(chi2ymin, mean1pix);
    meany = fmax(mean1pix, (double)templ.chi2yavgone());
    hchi2 = chi2ymin / 2.;
    hndof = meany / 2.;
    proby = 1. - TMath::Gamma(hndof, hchi2);

  } else {
    // For cluster > 1 pix, make the second, interpolating pass with the templates

    binl = minbin - 1;
    binh = binl + 2;
    if (binl < fybin) {
      binl = fybin;
    }
    if (binh > lybin) {
      binh = lybin;
    }
    ssa = 0.;
    sa2 = 0.;
    ssba = 0.;
    saba = 0.;
    sba2 = 0.;
    for (i = fypix - 2; i <= lypix + 2; ++i) {
      ssa += ysw[i] * ytemp[binl][i];
      sa2 += ytemp[binl][i] * ytemp[binl][i] * yw2[i];
      ssba += ysw[i] * (ytemp[binh][i] - ytemp[binl][i]);
      saba += ytemp[binl][i] * (ytemp[binh][i] - ytemp[binl][i]) * yw2[i];
      sba2 += (ytemp[binh][i] - ytemp[binl][i]) * (ytemp[binh][i] - ytemp[binl][i]) * yw2[i];
    }

    // rat is the fraction of the "distance" from template a to template b

    rat = (ssba * ssa - ss2 * saba) / (ss2 * sba2 - ssba * ssba);
    if (rat < 0.f) {
      rat = 0.f;
    }
    if (rat > 1.f) {
      rat = 1.0f;
    }
    rnorm = (ssa + rat * ssba) / ss2;

    // Calculate the charges in the first and last pixels

    qfy = ysum[fypix];
    if (yd[fypix]) {
      qfy += ysum[fypix + 1];
    }
    if (logypx > 1) {
      qly = ysum[lypix];
      if (yd[lypix - 1]) {
        qly += ysum[lypix - 1];
      }
    } else {
      qly = qfy;
    }

    //  Now calculate the mean bias correction and uncertainties

    float qyfrac = (qfy - qly) / (qfy + qly);
    bias = templ.yflcorr(binq, qyfrac) + templ.yavg(binq);

    // uncertainty and final correction depend upon charge bin

    yrec = (0.125f * binl + BHY - 2.5f + rat * (binh - binl) * 0.125f - (float)shifty + originy) * ysize - bias;
    sigmay = templ.yrms(binq);

    // Do goodness of fit test in y

    if (rnorm <= 0.) {
      LOGERROR("SiPixelTemplateReco") << "illegal chi2y normalization (2) = " << rnorm << ENDL;
      rnorm = 1.;
    }
    chi2y = ss2 - 2. / rnorm * ssa - 2. / rnorm * rat * ssba +
            (sa2 + 2. * rat * saba + rat * rat * sba2) / (rnorm * rnorm) - templ.chi2ymin(binq);
    if (chi2y < 0.0) {
      chi2y = 0.0;
    }
    meany = templ.chi2yavg(binq);
    if (meany < 0.01) {
      meany = 0.01;
    }
    // gsl function that calculates the chi^2 tail prob for non-integral dof
    //     proby = gsl_cdf_chisq_Q(chi2y, meany);
    //     proby = ROOT::Math::chisquared_cdf_c(chi2y, meany);
    hchi2 = chi2y / 2.;
    hndof = meany / 2.;
    proby = 1. - TMath::Gamma(hndof, hchi2);
  }

  // Do the x-reconstruction next

  // Apply the first-pass template algorithm to all clusters

  // Modify the template if double pixels are present

  if (nxpix > logxpx) {
    i = fxpix;
    while (i < lxpix) {
      if (xd[i] && !xd[i + 1]) {
        for (j = fxbin; j <= lxbin; ++j) {
          // Sum the adjacent cells and put the average signal in both

          sigavg = (xtemp[j][i] + xtemp[j][i + 1]) / 2.f;
          xtemp[j][i] = sigavg;
          xtemp[j][i + 1] = sigavg;
        }
        i += 2;
      } else {
        ++i;
      }
    }
  }

  // Define the maximum signal to allow before de-weighting a pixel

  sxthr = 1.1f * templ.sxmax();

  // Make sure that there will be at least two pixels that are not de-weighted
  std::sort(&xsort[0], &xsort[logxpx]);
  if (logxpx == 1) {
    sxthr = 1.01f * xsort[0];
  } else {
    if (xsort[1] > sxthr) {
      sxthr = 1.01f * xsort[1];
    }
  }

  // Evaluate pixel-by-pixel uncertainties (weights) for the templ analysis

  //    for(i=0; i<BXSIZE; ++i) { xsig2[i] = 0.; }
  templ.xsigma2(fxpix, lxpix, sxthr, xsum, xsig2);

  // Find the template bin that minimizes the Chi^2

  chi2xmin = 1.e15;
  for (i = fxbin; i <= lxbin; ++i) {
    chi2xbin[i] = -1.e15f;
  }
  ss2 = 0.f;
  for (i = fxpix - 2; i <= lxpix + 2; ++i) {
    xw2[i] = 1.f / xsig2[i];
    xsw[i] = xsum[i] * xw2[i];
    ss2 += xsum[i] * xsw[i];
  }
  minbin = -1;
  deltaj = djx;
  jmin = fxbin;
  jmax = lxbin;
  while (deltaj > 0) {
    for (j = jmin; j <= jmax; j += deltaj) {
      if (chi2xbin[j] < -100.f) {
        ssa = 0.f;
        sa2 = 0.f;
        //           std::cout << j << " ";
        for (i = fxpix - 2; i <= lxpix + 2; ++i) {
          //                std::cout << xtemp[j][i] << ", ";
          ssa += xsw[i] * xtemp[j][i];
          sa2 += xtemp[j][i] * xtemp[j][i] * xw2[i];
        }
        //           std::cout << std::endl;
        rat = ssa / ss2;
        if (rat <= 0.f) {
          LOGERROR("SiPixelTemplateReco") << "illegal chi2xmin normalization (1) = " << rat << ENDL;
          rat = 1.;
        }
        chi2xbin[j] = ss2 - 2.f * ssa / rat + sa2 / (rat * rat);
      }
      if (chi2xbin[j] < chi2xmin) {
        chi2xmin = chi2xbin[j];
        minbin = j;
      }
    }
    deltaj /= 2;
    if (minbin > fxbin) {
      jmin = minbin - deltaj;
    } else {
      jmin = fxbin;
    }
    if (minbin < lxbin) {
      jmax = minbin + deltaj;
    } else {
      jmax = lxbin;
    }
  }

  if (theVerboseLevel > 9) {
    LOGDEBUG("SiPixelTemplateReco") << "minbin " << minbin << " chi2xmin = " << chi2xmin << ENDL;
  }

  // Do not apply final template pass to 1-pixel clusters (use calibrated offset)

  if (logxpx == 1) {
    if (nxpix == 1) {
      delta = templ.dxone();
      sigma = templ.sxone();
    } else {
      delta = templ.dxtwo();
      sigma = templ.sxtwo();
    }
    xrec = 0.5 * (fxpix + lxpix - 2 * shiftx + 2. * originx) * xsize - delta;
    if (sigma <= 0.) {
      sigmax = 28.9;
    } else {
      sigmax = sigma;
    }

    // Do probability calculation for one-pixel clusters

    chi21max = fmax(chi21min, (double)templ.chi2xminone());
    chi2xmin -= chi21max;
    if (chi2xmin < 0.) {
      chi2xmin = 0.;
    }
    meanx = fmax(mean1pix, (double)templ.chi2xavgone());
    hchi2 = chi2xmin / 2.;
    hndof = meanx / 2.;
    probx = 1. - TMath::Gamma(hndof, hchi2);

  } else {
    // Now make the second, interpolating pass with the templates

    binl = minbin - 1;
    binh = binl + 2;
    if (binl < fxbin) {
      binl = fxbin;
    }
    if (binh > lxbin) {
      binh = lxbin;
    }
    ssa = 0.;
    sa2 = 0.;
    ssba = 0.;
    saba = 0.;
    sba2 = 0.;
    for (i = fxpix - 2; i <= lxpix + 2; ++i) {
      ssa += xsw[i] * xtemp[binl][i];
      sa2 += xtemp[binl][i] * xtemp[binl][i] * xw2[i];
      ssba += xsw[i] * (xtemp[binh][i] - xtemp[binl][i]);
      saba += xtemp[binl][i] * (xtemp[binh][i] - xtemp[binl][i]) * xw2[i];
      sba2 += (xtemp[binh][i] - xtemp[binl][i]) * (xtemp[binh][i] - xtemp[binl][i]) * xw2[i];
    }

    // rat is the fraction of the "distance" from template a to template b

    rat = (ssba * ssa - ss2 * saba) / (ss2 * sba2 - ssba * ssba);
    if (rat < 0.f) {
      rat = 0.f;
    }
    if (rat > 1.f) {
      rat = 1.0f;
    }
    rnorm = (ssa + rat * ssba) / ss2;

    // Calculate the charges in the first and last pixels

    qfx = xsum[fxpix];
    if (xd[fxpix]) {
      qfx += xsum[fxpix + 1];
    }
    if (logxpx > 1) {
      qlx = xsum[lxpix];
      if (xd[lxpix - 1]) {
        qlx += xsum[lxpix - 1];
      }
    } else {
      qlx = qfx;
    }

    //  Now calculate the mean bias correction and uncertainties

    float qxfrac = (qfx - qlx) / (qfx + qlx);
    bias = templ.xflcorr(binq, qxfrac) + templ.xavg(binq);

    // uncertainty and final correction depend upon charge bin

    xrec = (0.125f * binl + BHX - 2.5f + rat * (binh - binl) * 0.125f - (float)shiftx + originx) * xsize - bias;
    sigmax = templ.xrms(binq);

    // Do goodness of fit test in x

    if (rnorm <= 0.) {
      LOGERROR("SiPixelTemplateReco") << "illegal chi2x normalization (2) = " << rnorm << ENDL;
      rnorm = 1.;
    }
    chi2x = ss2 - 2. / rnorm * ssa - 2. / rnorm * rat * ssba +
            (sa2 + 2. * rat * saba + rat * rat * sba2) / (rnorm * rnorm) - templ.chi2xmin(binq);
    if (chi2x < 0.0) {
      chi2x = 0.0;
    }
    meanx = templ.chi2xavg(binq);
    if (meanx < 0.01) {
      meanx = 0.01;
    }
    // gsl function that calculates the chi^2 tail prob for non-integral dof
    //     probx = gsl_cdf_chisq_Q(chi2x, meanx);
    //     probx = ROOT::Math::chisquared_cdf_c(chi2x, meanx, trx0);
    hchi2 = chi2x / 2.;
    hndof = meanx / 2.;
    probx = 1. - TMath::Gamma(hndof, hchi2);
  }

  //  Don't return exact zeros for the probability

  if (proby < probmin) {
    proby = probmin;
  }
  if (probx < probmin) {
    probx = probmin;
  }

  //  Decide whether to generate a cluster charge probability

  if (calc_probQ) {
    // Calculate the Vavilov probability that the cluster charge is OK

    templ.vavilov_pars(mpv, sigmaQ, kappa);
#ifndef SI_PIXEL_TEMPLATE_STANDALONE
    if ((sigmaQ <= 0.) || (mpv <= 0.) || (kappa < 0.01) || (kappa > 9.9)) {
      throw cms::Exception("DataCorrupt") << "SiPixelTemplateReco::Vavilov parameters mpv/sigmaQ/kappa = " << mpv << "/"
                                          << sigmaQ << "/" << kappa << std::endl;
    }
#else
    assert((sigmaQ > 0.) && (mpv > 0.) && (kappa > 0.01) && (kappa < 10.));
#endif
    xvav = ((double)qtotal - mpv) / sigmaQ;
    beta2 = 1.;
    if (use_VVIObj) {
      //  VVIObj is a private port of CERNLIB VVIDIS
      VVIObjF vvidist(kappa, beta2, 1);
      prvav = vvidist.fcn(xvav);
    } else {
      //  Use faster but less accurate TMath Vavilov distribution function
      prvav = TMath::VavilovI(xvav, kappa, beta2);
    }
    //  Change to upper tail probability
    //      if(prvav > 0.5) prvav = 1. - prvav;
    //      probQ = (float)(2.*prvav);
    probQ = 1. - prvav;
    if (probQ < probQmin) {
      probQ = probQmin;
    }
  } else {
    probQ = -1;
  }

  return 0;
}  // PixelTempReco1D

// *************************************************************************************************************************************
//  Overload parameter list for compatibility with older versions
// *************************************************************************************************************************************
int SiPixelTemplateReco::PixelTempReco1D(int id,
                                         float cotalpha,
                                         float cotbeta,
                                         float locBz,
                                         float locBx,
                                         ClusMatrix& cluster,
                                         SiPixelTemplate& templ,
                                         float& yrec,
                                         float& sigmay,
                                         float& proby,
                                         float& xrec,
                                         float& sigmax,
                                         float& probx,
                                         int& qbin,
                                         int speed,
                                         float& probQ)

{
  // Local variables
  const bool deadpix = false;
  std::vector<std::pair<int, int> > zeropix;
  int nypix, nxpix;

  return SiPixelTemplateReco::PixelTempReco1D(id,
                                              cotalpha,
                                              cotbeta,
                                              locBz,
                                              locBx,
                                              cluster,
                                              templ,
                                              yrec,
                                              sigmay,
                                              proby,
                                              xrec,
                                              sigmax,
                                              probx,
                                              qbin,
                                              speed,
                                              deadpix,
                                              zeropix,
                                              probQ,
                                              nypix,
                                              nxpix);

}  // PixelTempReco1D

// *************************************************************************************************************************************
//  Overload parameter list for compatibility with older versions
// *************************************************************************************************************************************
int SiPixelTemplateReco::PixelTempReco1D(int id,
                                         float cotalpha,
                                         float cotbeta,
                                         ClusMatrix& cluster,
                                         SiPixelTemplate& templ,
                                         float& yrec,
                                         float& sigmay,
                                         float& proby,
                                         float& xrec,
                                         float& sigmax,
                                         float& probx,
                                         int& qbin,
                                         int speed,
                                         float& probQ)

{
  // Local variables
  const bool deadpix = false;
  std::vector<std::pair<int, int> > zeropix;
  int nypix, nxpix;
  float locBx, locBz;
  locBx = 1.f;
  if (cotbeta < 0.f) {
    locBx = -1.f;
  }
  locBz = locBx;
  if (cotalpha < 0.f) {
    locBz = -locBx;
  }

  return SiPixelTemplateReco::PixelTempReco1D(id,
                                              cotalpha,
                                              cotbeta,
                                              locBz,
                                              locBx,
                                              cluster,
                                              templ,
                                              yrec,
                                              sigmay,
                                              proby,
                                              xrec,
                                              sigmax,
                                              probx,
                                              qbin,
                                              speed,
                                              deadpix,
                                              zeropix,
                                              probQ,
                                              nypix,
                                              nxpix);

}  // PixelTempReco1D

// *************************************************************************************************************************************
//  Overload parameter list for compatibility with older versions
// *************************************************************************************************************************************
int SiPixelTemplateReco::PixelTempReco1D(int id,
                                         float cotalpha,
                                         float cotbeta,
                                         ClusMatrix& cluster,
                                         SiPixelTemplate& templ,
                                         float& yrec,
                                         float& sigmay,
                                         float& proby,
                                         float& xrec,
                                         float& sigmax,
                                         float& probx,
                                         int& qbin,
                                         int speed)

{
  // Local variables
  const bool deadpix = false;
  std::vector<std::pair<int, int> > zeropix;
  int nypix, nxpix;
  float locBx, locBz;
  locBx = 1.f;
  if (cotbeta < 0.f) {
    locBx = -1.f;
  }
  locBz = locBx;
  if (cotalpha < 0.f) {
    locBz = -locBx;
  }
  float probQ;
  if (speed < 0)
    speed = 0;
  if (speed > 3)
    speed = 3;

  return SiPixelTemplateReco::PixelTempReco1D(id,
                                              cotalpha,
                                              cotbeta,
                                              locBz,
                                              locBx,
                                              cluster,
                                              templ,
                                              yrec,
                                              sigmay,
                                              proby,
                                              xrec,
                                              sigmax,
                                              probx,
                                              qbin,
                                              speed,
                                              deadpix,
                                              zeropix,
                                              probQ,
                                              nypix,
                                              nxpix);

}  // PixelTempReco1D