SiPixelTemplateReco.cc

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//
//  SiPixelTemplateReco.cc (Version 10.00)
//
//  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
//
//
//  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>

#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)
static const int theVerboseLevel = 2;
#define ENDL " "
#include "FWCore/Utilities/interface/Exception.h"
#else
#include "SiPixelTemplateReco.h"
#include "VVIObjF.h"
//static int theVerboseLevel = {2};
#define LOGERROR(x) std::cout << x << ": "
#define LOGDEBUG(x) std::cout << x << ": "
#define ENDL std::endl
#endif

using namespace SiPixelTemplateReco;

// *************************************************************************************************************************************
// *************************************************************************************************************************************
int SiPixelTemplateReco::PixelTempReco2D(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}, chi21min={0.160};
   
   // 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(!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;
   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 +=shifty;
   fypix +=shifty;
   
   // If the cluster boundaries are OK, add pesudopixels, otherwise quit
   
   if(fypix > 1 && fypix < BYM2) {
      ysum[fypix-1] = pseudopix;
      ysum[fypix-2] = pseudopix;
   } else {return 8;}
   if(lypix > 1 && lypix < BYM2) {
      ysum[lypix+1] = pseudopix;
      ysum[lypix+2] = pseudopix;
   } else {return 8;}
   
   // 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;
   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 +=shiftx;
   fxpix +=shiftx;
   
   // If the cluster boundaries are OK, add pesudopixels, otherwise quit
   
   if(fxpix > 1 && fxpix < BXM2) {
      xsum[fxpix-1] = pseudopix;
      xsum[fxpix-2] = pseudopix;
   } else {return 9;}
   if(lxpix > 1 && lxpix < BXM2) {
      xsum[lxpix+1] = pseudopix;
      xsum[lxpix+2] = pseudopix;
   } else {return 9;}
   
   // 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::PixelTempReco2D 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;
} // PixelTempReco2D

// *************************************************************************************************************************************
//  Overload parameter list for compatibility with older versions
// *************************************************************************************************************************************
int SiPixelTemplateReco::PixelTempReco2D(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::PixelTempReco2D(id, cotalpha, cotbeta, locBz, locBx, cluster, templ,
                                               yrec, sigmay, proby, xrec, sigmax, probx, qbin, speed, deadpix, zeropix, probQ, nypix, nxpix);
   
} // PixelTempReco2D


// *************************************************************************************************************************************
//  Overload parameter list for compatibility with older versions
// *************************************************************************************************************************************
int SiPixelTemplateReco::PixelTempReco2D(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::PixelTempReco2D(id, cotalpha, cotbeta, locBz, locBx, cluster, templ,
                                               yrec, sigmay, proby, xrec, sigmax, probx, qbin, speed, deadpix, zeropix, probQ, nypix, nxpix);
   
} // PixelTempReco2D


// *************************************************************************************************************************************
//  Overload parameter list for compatibility with older versions
// *************************************************************************************************************************************
int SiPixelTemplateReco::PixelTempReco2D(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::PixelTempReco2D(id, cotalpha, cotbeta, locBz, locBx, cluster, templ, 
                                               yrec, sigmay, proby, xrec, sigmax, probx, qbin, speed, deadpix, zeropix, probQ, nypix, nxpix);
   
} // PixelTempReco2D