---

SiPixelTemplateReco.cc

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//
//  SiPixelTemplateReco.cc (Version 5.01)
//
//  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
//
//  Created by Morris Swartz on 10/27/06.
//  Copyright 2006 __TheJohnsHopkinsUniversity__. All rights reserved.
//
//

#include <math.h>
#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 "Math/DistFunc.h"
#include "TMath.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 "FWCore/MessageLogger/interface/MessageLogger.h"
#define LOGERROR(x) edm::LogError(x)
#define LOGDEBUG(x) LogDebug(x)
#define ENDL " "
#else
#include "SiPixelTemplateReco.h"
//static int theVerboseLevel = {2};
#define LOGERROR(x) std::cout << x << ": "
#define LOGDEBUG(x) std::cout << x << ": "
#define ENDL std::endl
#endif

static int theVerboseLevel = {2};

using namespace SiPixelTemplateReco;

// *************************************************************************************************************************************
// *************************************************************************************************************************************
int SiPixelTemplateReco::PixelTempReco2D(int id, bool fpix, float cotalpha, float cotbeta, array_2d cluster, 
                    std::vector<bool> ydouble, std::vector<bool> xdouble, 
                    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)
                        
{
    // Local variables 
        static int i, j, k, minbin, binl, binh, binq, midpix, fypix, nypix, lypix, logypx;
    static int fxpix, nxpix, lxpix, logxpx, shifty, shiftx, nyzero[TYSIZE];
        static unsigned int nclusx, nclusy;
        static int deltaj, jmin, jmax, fxbin, lxbin, fybin, lybin, djy, djx;
        static float sythr, sxthr, rnorm, delta, sigma, sigavg, pseudopix, qscale;
        static float ss2, ssa, sa2, ssba, saba, sba2, rat, fq, qtotal, qpixel;
        static float originx, originy, qfy, qly, qfx, qlx, bias, err, maxpix, minmax;
        static double chi2x, meanx, chi2y, meany, chi2ymin, chi2xmin, chi2;
        static double hchi2, hndof;
        static float ytemp[41][BYSIZE], xtemp[41][BXSIZE], ysum[BYSIZE], xsum[BXSIZE], ysort[BYSIZE], xsort[BXSIZE];
        static float chi2ybin[41], chi2xbin[41], ysig2[BYSIZE], xsig2[BXSIZE];
        static bool yd[BYSIZE], xd[BXSIZE], anyyd, anyxd;
        const float ysize={150.}, xsize={100.};
        
// 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, fpix, cotalpha, cotbeta)) {
           LOGDEBUG("SiPixelTemplateReco") << "input cluster direction cot(alpha) = " << cotalpha << ", cot(beta) = " << cotbeta << " is not within the acceptance of fpix = "
           << fpix << ", template ID = " << id << ", no reconstruction performed" << ENDL;      
           return 20;
        }
   
// Define size of pseudopixel

    pseudopix = 0.2*templ.s50();
        
// 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

        if(cluster.num_dimensions() != 2) {
           LOGERROR("SiPixelTemplateReco") << "input cluster container (BOOST Multiarray) has wrong number of dimensions" << ENDL;      
           return 3;
        }
        nclusx = cluster.shape()[0];
        nclusy = cluster.shape()[1];
        if(nclusx != xdouble.size()) {
           LOGERROR("SiPixelTemplateReco") << "input cluster container x-size is not equal to double pixel flag container size" << ENDL;        
           return 4;
        }
        if(nclusy != ydouble.size()) {
           LOGERROR("SiPixelTemplateReco") << "input cluster container y-size is not equal to double pixel flag container size" << ENDL;        
           return 5;
        }
        
// enforce maximum size 
        
        if(nclusx > TXSIZE) {nclusx = TXSIZE;}
        if(nclusy > TYSIZE) {nclusy = TYSIZE;}
        
// First, rescale all pixel charges       

    for(i=0; i<nclusy; ++i) {
           for(j=0; j<nclusx; ++j) {
                  if(cluster[j][i] > 0) {cluster[j][i] *= qscale;}
           }
        }
        
// Next, sum the total charge and "decapitate" big pixels         

        qtotal = 0.;
        minmax = templ.pixmax();
        for(i=0; i<nclusy; ++i) {
           maxpix = minmax;
           if(ydouble[i]) {maxpix *=2.;}
           for(j=0; j<nclusx; ++j) {
                  qtotal += cluster[j][i];
                  if(cluster[j][i] > maxpix) {cluster[j][i] = maxpix;}
           }
        }
        
// Do the cluster repair here   
        
    if(deadpix) {
           fypix = BYM3; lypix = -1;
       for(i=0; i<nclusy; ++i) {
              ysum[i] = 0.; nyzero[i] = 0;
// Do preliminary cluster projection in y
              for(j=0; j<nclusx; ++j) {
                     ysum[i] += cluster[j][i];
                  }
                  if(ysum[i] > 0.) {
// 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.; 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.;
                  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.; 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.) {
              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; 
        }
        
// next, center the cluster on pixel 12 if necessary   

        midpix = (fypix+lypix)/2;
        shifty = BHY - 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 = -0.5;
        } else {
           originy = 0.;
        }
        
// 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; 
        }
        
// next, center the cluster on pixel 5 if necessary   

        midpix = (fxpix+lxpix)/2;
        shiftx = BHX - 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 = -0.5;
        } else {
           originx = 0.;
        }
        
// uncertainty and final corrections depend upon total charge bin          
           
        fq = qtotal/templ.qavg();
        if(fq > 1.5) {
           binq=0;
        } else {
           if(fq > 1.0) {
              binq=1;
           } else {
                  if(fq > 0.85) {
                         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 < 0.95*templ.qmin()) {qbin = 4;} else {qbin = binq;}

        if (theVerboseLevel > 9) {
       LOGDEBUG("SiPixelTemplateReco") <<
        "ID = " << id << " FPix = " << fpix << 
         " 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
    
    assert(speed >= 0 && speed < 4);
        fybin = 0; lybin = 40; fxbin = 0; lxbin = 40; 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.;
                                 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 = 1.01*ysort[0];} else {
           if (ysort[1] > sythr) { sythr = 1.01*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.e15;}
        minbin = -1;
        deltaj = djy;
        jmin = fybin;
        jmax = lybin;
        while(deltaj > 0) {
           for(j=jmin; j<=jmax; j+=deltaj) {
              if(chi2ybin[j] < -100.) {
                     ss2 = 0.;
                     ssa = 0.;
                     sa2 = 0.;
                     for(i=fypix-2; i<=lypix+2; ++i) {
                             ss2 += ysum[i]*ysum[i]/ysig2[i];
                             ssa += ysum[i]*ytemp[j][i]/ysig2[i];
                             sa2 += ytemp[j][i]*ytemp[j][i]/ysig2[i];
                     }
                     rat=ssa/ss2;
                     if(rat <= 0.) {LOGERROR("SiPixelTemplateReco") << "illegal chi2ymin normalization = " << rat << ENDL; rat = 1.;}
                     chi2ybin[j]=ss2-2.*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 = 0.5*(fypix+lypix-2*shifty+2.*originy)*ysize-delta;
           
           if(sigma <= 0.) {
              sigmay = 43.3;
           } else {
          sigmay = sigma;
           }
           
// Do probability calculation for one-pixel clusters

       chi2ymin -=chi21min;
           if(chi2ymin < 0.) {chi2ymin = 0.;}
//         proby = gsl_cdf_chisq_Q(chi2ymin, mean1pix);
       hchi2 = chi2ymin/2.; hndof = mean1pix/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;}      
           ss2 = 0.;
           ssa = 0.;
           sa2 = 0.;
           ssba = 0.;
           saba = 0.;
           sba2 = 0.;
           for(i=fypix-2; i<=lypix+2; ++i) {
                  ss2 += ysum[i]*ysum[i]/ysig2[i];
                  ssa += ysum[i]*ytemp[binl][i]/ysig2[i];
                  sa2 += ytemp[binl][i]*ytemp[binl][i]/ysig2[i];
                  ssba += ysum[i]*(ytemp[binh][i] - ytemp[binl][i])/ysig2[i];
                  saba += ytemp[binl][i]*(ytemp[binh][i] - ytemp[binl][i])/ysig2[i];
                  sba2 += (ytemp[binh][i] - ytemp[binl][i])*(ytemp[binh][i] - ytemp[binl][i])/ysig2[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.) {rat=0.;}
           if(rat > 1.) {rat=1.0;}
           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 = (0.125*binl+BHY-2.5+rat*(binh-binl)*0.125-(float)shifty+originy)*ysize - bias;
           sigmay = templ.yrms(binq);
           
// Do goodness of fit test in y  
           
           if(rnorm <= 0.) {LOGERROR("SiPixelTemplateReco") << "illegal chi2y normalization = " << 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.;
                                   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 = 1.1*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 = 1.01*xsort[0];} else {
           if (xsort[1] > sxthr) { sxthr = 1.01*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.e15;}
        minbin = -1;
        deltaj = djx;
        jmin = fxbin;
        jmax = lxbin;
        while(deltaj > 0) {
           for(j=jmin; j<=jmax; j+=deltaj) {
              if(chi2xbin[j] < -100.) {
                     ss2 = 0.;
                     ssa = 0.;
                     sa2 = 0.;
                     for(i=fxpix-2; i<=lxpix+2; ++i) {
                             ss2 += xsum[i]*xsum[i]/xsig2[i];
                             ssa += xsum[i]*xtemp[j][i]/xsig2[i];
                             sa2 += xtemp[j][i]*xtemp[j][i]/xsig2[i];
                         }
                     rat=ssa/ss2;
                     if(rat <= 0.) {LOGERROR("SiPixelTemplateReco") << "illegal chi2ymin normalization = " << rat << ENDL; rat = 1.;}
                     chi2xbin[j]=ss2-2.*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

       chi2xmin -=chi21min;
           if(chi2xmin < 0.) {chi2xmin = 0.;}
//         probx = gsl_cdf_chisq_Q(chi2xmin, mean1pix);
       hchi2 = chi2xmin/2.; hndof = mean1pix/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;}      
           ss2 = 0.;
           ssa = 0.;
           sa2 = 0.;
           ssba = 0.;
           saba = 0.;
           sba2 = 0.;
           for(i=fxpix-2; i<=lxpix+2; ++i) {
                  ss2 += xsum[i]*xsum[i]/xsig2[i];
                  ssa += xsum[i]*xtemp[binl][i]/xsig2[i];
                  sa2 += xtemp[binl][i]*xtemp[binl][i]/xsig2[i];
                  ssba += xsum[i]*(xtemp[binh][i] - xtemp[binl][i])/xsig2[i];
                  saba += xtemp[binl][i]*(xtemp[binh][i] - xtemp[binl][i])/xsig2[i];
                  sba2 += (xtemp[binh][i] - xtemp[binl][i])*(xtemp[binh][i] - xtemp[binl][i])/xsig2[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.) {rat=0.;}
           if(rat > 1.) {rat=1.0;}
           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 = (0.125*binl+BHX-2.5+rat*(binh-binl)*0.125-(float)shiftx+originx)*xsize - bias;
           sigmax = templ.xrms(binq);
           
// Do goodness of fit test in x  
           
           if(rnorm <= 0.) {LOGERROR("SiPixelTemplateReco") << "illegal chi2x normalization = " << 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);
        }
        
    return 0;
} // PixelTempReco2D 

// *************************************************************************************************************************************
//  Overload parameter list for compatibility with older versions
// *************************************************************************************************************************************
int SiPixelTemplateReco::PixelTempReco2D(int id, bool fpix, float cotalpha, float cotbeta, array_2d cluster, 
                    std::vector<bool> ydouble, std::vector<bool> xdouble, 
                    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;
    
        return SiPixelTemplateReco::PixelTempReco2D(id, fpix, cotalpha, cotbeta, cluster, ydouble, xdouble, templ, 
                yrec, sigmay, proby, xrec, sigmax, probx, qbin, speed, deadpix, zeropix);

} // PixelTempReco2D

---