SiPixelTemplateSplit.cc

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//
//  SiPixelTemplateSplit.cc (Version 2.30)
//
//  Procedure to fit two templates (same angle hypotheses) to a single cluster
//  Return two x- and two y-coordinates for the cluster
//
//  Created by Morris Swartz on 04/10/08.
//
//  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 q2bin = 5 and change 1-pixel probability to use new template info
//  Add floor for probabilities (no exact zeros)
//  Add ambiguity resolution with crude 2-D templates (v2.00)
//  Pass all containers by alias to prevent excessive cpu-usage (v2.01)
//  Add ambiguity resolution with fancy 2-D templates (v2.10)
//  Make small change to indices for ambiguity resolution (v2.11)
//  Tune x and y errors separately (v2.12)
//  Use template cytemp/cxtemp methods to center the data cluster in the right place when the templates become asymmetric after irradiation (v2.20)
//  Add charge probability to the splitter [tests consistency with a two-hit merged cluster hypothesis]  (v2.20)
//  Improve likelihood normalization slightly (v2.21)
//  Replace hardwired pixel size derived errors with ones from templated pixel sizes (v2.22)
//  Add shape and charge probabilities for the merged cluster hypothesis (v2.23)
//  Incorporate VI-like speed improvements (v2.25)
//  Improve speed by eliminating the triple index boost::multiarray objects and add speed switch to optimize the algorithm (v2.30)
//

#ifndef SI_PIXEL_TEMPLATE_STANDALONE
//#include <cmath.h>
#else
#include <math.h>
#endif
#include <algorithm>
#include <vector>
#include <list>
#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/SiPixelTemplateSplit.h"
#include "RecoLocalTracker/SiPixelRecHits/interface/VVIObj.h"
#include "FWCore/MessageLogger/interface/MessageLogger.h"
#define LOGERROR(x) edm::LogError(x)
#define LOGDEBUG(x) LogDebug(x)
static constexpr int theVerboseLevel = 2;
#define ENDL " "
#else
#include "SiPixelTemplateSplit.h"
#include "VVIObj.h"
//#include "SiPixelTemplate2D.h"
//#include "SimpleTemplate2D.h"
//static int theVerboseLevel = {2};
#define LOGERROR(x) std::cout << x << ": "
#define LOGDEBUG(x) std::cout << x << ": "
#define ENDL std::endl
#endif

using namespace SiPixelTemplateSplit;

// *************************************************************************************************************************************
// *************************************************************************************************************************************
int SiPixelTemplateSplit::PixelTempSplit(int id, float cotalpha, float cotbeta, array_2d& clust, 
            std::vector<bool>& ydouble, std::vector<bool>& xdouble, 
            SiPixelTemplate& templ, 
            float& yrec1, float& yrec2, float& sigmay, float& prob2y,
            float& xrec1, float& xrec2, float& sigmax, float& prob2x, int& q2bin, float& prob2Q, bool resolve, int speed, float& dchisq, bool deadpix, std::vector<std::pair<int, int> >& zeropix, SiPixelTemplate2D& templ2D)
            
{
    // Local variables 
    int i, j, k, binq, midpix, fypix, nypix, lypix, logypx, lparm;
    int fxpix, nxpix, lxpix, logxpx, shifty, shiftx;
    int nclusx, nclusy;
    int nybin, ycbin, nxbin, xcbin, minbinj, minbink;
    int deltaj, jmin, jmax, kmin, kmax, km, fxbin, lxbin, fybin, lybin, djy, djx;
    float sythr, sxthr, delta, sigma, sigavg, pseudopix, xsize, ysize, qscale, lanpar[2][5];
    float ss2, ssa, sa2, rat, fq, qtotal, qpixel, qavg;
    float x1p, x2p, y1p, y2p, deltachi2;
    float originx, originy, bias, maxpix, minmax;
    double chi2x, meanx, chi2y, meany, chi2ymin, chi2xmin, chi21max;
    double hchi2, hndof, sigmal1, sigmal2, mpv1, mpv2, arg1, arg2, q05, like, loglike1, loglike2;
    double prvav, mpv, sigmaQ, kappa, xvav, beta2;
    float ysum[BYSIZE], xsum[BXSIZE], ysort[BYSIZE], xsort[BXSIZE];
    float ysig2[BYSIZE], xsig2[BXSIZE];
    float yw2[BYSIZE], xw2[BXSIZE],  ysw[BYSIZE], xsw[BXSIZE];
    float cluster2[BXM2][BYM2], temp2d1[BXM2][BYM2], temp2d2[BXM2][BYM2];
    bool yd[BYSIZE], xd[BXSIZE], anyyd, anyxd, any2dfail;
    const float sqrt2x={3.0000}, sqrt2y={1.7000};
    const float sqrt12={3.4641};
    const float probmin={1.110223e-16};
    const float prob2Qmin={1.e-5};
    std::pair<int, int> pixel;
    
//  bool SiPixelTemplateSplit::SimpleTemplate2D(float cotalpha, float cotbeta, float xhit, float yhit, float thick, float lorxwidth, float lorywidth, 
//                        float qavg, std::vector<bool> ydouble, std::vector<bool> xdouble, float template2d[BXM2][BYM2]);
    
// 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)) {
       LOGDEBUG("SiPixelTemplateReco") << "input cluster direction cot(alpha) = " << cotalpha << ", cot(beta) = " << cotbeta 
       << " is not within the acceptance of template ID = " << id << ", no reconstruction performed" << ENDL;   
       return 20;
    }
              
// Get pixel dimensions from the template (to allow multiple detectors in the future)
    
    xsize = templ.xsize();
    ysize = templ.ysize();
    
// Define size of pseudopixel

    pseudopix = templ.s50();
//  q05 = 0.28*pseudopix;
    q05 = 0.05f*pseudopix;
    
// Get charge scaling factor

    qscale = templ.qscale();
    
// Make a local copy of the cluster container so that we can muck with it
    
    array_2d cluster = clust;
    
// 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 = (int)cluster.shape()[0];
    nclusy = (int)cluster.shape()[1];
    if(nclusx != (int)xdouble.size()) {
       LOGERROR("SiPixelTemplateReco") << "input cluster container x-size is not equal to double pixel flag container size" << ENDL;    
       return 4;
    }
    if(nclusy != (int)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.f;
    minmax = 2.0f*templ.pixmax();
    for(i=0; i<nclusy; ++i) {
       maxpix = minmax;
       if(ydouble[i]) {maxpix *=2.f;}
       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.f;
// 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
       int nyzero[TYSIZE]{};
       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.f) {qpixel = 1.f;}
          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.f;
          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;
        }
    }
    
// 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 template center if necessary   

    midpix = (fypix+lypix)/2;
//  shifty = BHY - midpix;
    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] = 0.2f*pseudopix;
    } else {return 8;}
    if(lypix > 1 && lypix < BYM2) {
       ysum[lypix+1] = pseudopix;   
       ysum[lypix+2] = 0.2f*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;
        }
    }
    
// 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 template center if necessary   

    midpix = (fxpix+lxpix)/2;
//  shiftx = BHX - midpix;
    shiftx = templ.cxtemp() - midpix;
    if(shiftx > 0) {
       for(i=lxpix; i>=fxpix; --i) {
          xsum[i+shiftx] = xsum[i];
          xsum[i] = 0.f;
          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.f;
          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] = 0.2f*pseudopix;
    } else {return 9;}
    if(lxpix > 1 && lxpix < BXM2) {
       xsum[lxpix+1] = pseudopix;
       xsum[lxpix+2] = 0.2f*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      
       
    qavg = templ.qavg();
    fq = qtotal/qavg;
    if(fq > 3.0f) {
       binq=0;
    } else {
       if(fq > 2.0f) {
          binq=1;
       } else {
          if(fq > 1.70f) {
             binq=2;
          } else {
             binq=3;
          }
       }
    }
    
        
// Calculate the Vavilov probability that the cluster charge is consistent with a merged cluster
    
    if(speed < 0) {
       templ.vavilov2_pars(mpv, sigmaQ, kappa);
#ifndef SI_PIXEL_TEMPLATE_STANDALONE
       if((sigmaQ <=0.) || (mpv <= 0.) || (kappa < 0.01) || (kappa > 9.9)) {
            throw cms::Exception("DataCorrupt") << "SiPixelTemplateSplit::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.;
//  VVIObj is a private port of CERNLIB VVIDIS
       VVIObj vvidist(kappa, beta2, 1);
       prvav = vvidist.fcn(xvav);           
       prob2Q = 1. - prvav;
       if(prob2Q < prob2Qmin) {prob2Q = prob2Qmin;}
    } else {
        prob2Q = -1.f;
    }
    
    
// Return the charge bin via the parameter list unless the charge is too small (then flag it)
    
    q2bin = binq;
    if(!deadpix && qtotal < 1.9f*templ.qmin()) {q2bin = 5;} else {
        if(!deadpix && qtotal < 1.9f*templ.qmin(1)) {q2bin = 4;}
    }
    
    if (theVerboseLevel > 9) {
       LOGDEBUG("SiPixelTemplateSplit") <<
        "ID = " << id << 
         " cot(alpha) = " << cotalpha << " cot(beta) = " << cotbeta << 
         " nclusx = " << nclusx << " nclusy = " << nclusy << ENDL;
    }

    
// Next, generate the 3d y- and x-templates
   
    templ.ytemp3d_int(nypix, nybin);
    
    ycbin = nybin/2;    
   
    templ.xtemp3d_int(nxpix, nxbin);
    
// retrieve the number of x-bins 
    
    xcbin = nxbin/2;
        
    
// First, decide on chi^2 min search parameters
    
#ifndef SI_PIXEL_TEMPLATE_STANDALONE
    if(speed < -1 || speed > 2) {
        throw cms::Exception("DataCorrupt") << "SiPixelTemplateReco::PixelTempReco2D called with illegal speed = " << speed << std::endl;
    }
#else
    assert(speed >= -1 && speed < 3);
#endif
    fybin = 0; lybin = nybin-1; fxbin = 0; lxbin = nxbin-1; djy = 1; djx = 1;
    if(speed > 0) {
       djy = 2; djx = 2;
       if(speed > 1) {
          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;
    }
    
    
    
// Do the y-reconstruction first 
         
// Define the maximum signal to allow before de-weighting a pixel 

    sythr = 2.1f*(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;
    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];
    }
    minbinj = -1; 
    minbink = -1;
    deltaj = djy;
    jmin = fybin;
    jmax = lybin;
    kmin = fybin;
    kmax = lybin;
    std::vector<float> ytemp(BYSIZE);
    while(deltaj > 0) {
       for(j=jmin; j<jmax; j+=deltaj) {
            km = std::min(kmax, j);
            for(k=kmin; k<=km; k+=deltaj) {
                
// Get the template for this set of indices
                
               templ.ytemp3d(j, k, ytemp);
                
// Modify the template if double pixels are present   
                
                if(nypix > logypx) {
                    i=fypix;
                    while(i < lypix) {
                       if(yd[i] && !yd[i+1]) {
                                    
// Sum the adjacent cells and put the average signal in both   
                                    
                           sigavg = (ytemp[i] +  ytemp[i+1])/2.f;
                           ytemp[i] = sigavg;
                           ytemp[i+1] = sigavg;
                           i += 2;
                        } else {
                            ++i;
                        }
                    }
                }   
              ssa = 0.f;
              sa2 = 0.f;
              for(i=fypix-2; i<=lypix+2; ++i) {
                  ssa += ysw[i]*ytemp[i];
                  sa2 += ytemp[i]*ytemp[i]*yw2[i];
              }
              rat=ssa/ss2;
              if(rat <= 0.) {LOGERROR("SiPixelTemplateSplit") << "illegal chi2ymin normalization = " << rat << ENDL; rat = 1.;}
              chi2y=ss2-2.f*ssa/rat+sa2/(rat*rat);
              if(chi2y < chi2ymin) {
                  chi2ymin = chi2y;
                  minbinj = j;
                  minbink = k;
              }
          } 
       }
       deltaj /= 2;
       if(minbinj > fybin) {jmin = minbinj - deltaj;} else {jmin = fybin;}
       if(minbinj < lybin) {jmax = minbinj + deltaj;} else {jmax = lybin;}
       if(minbink > fybin) {kmin = minbink - deltaj;} else {kmin = fybin;}
       if(minbink < lybin) {kmax = minbink + deltaj;} else {kmax = lybin;}      
    }
    
    if (theVerboseLevel > 9) {
       LOGDEBUG("SiPixelTemplateReco") <<
        "minbins " << minbinj << "," << minbink << " 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();
       }
       
       yrec1 = 0.5f*(fypix+lypix-2*shifty+2.f*originy)*ysize-delta;
       yrec2 = yrec1;
       
       if(sigma <= 0.) {
          sigmay = ysize/sqrt12;
       } else {
          sigmay = sigma;
       }
       
// Do probability calculation for one-pixel clusters

        chi21max = fmax(chi21min, (double)templ.chi2yminone());
        chi2ymin -=chi21max;
        if(chi2ymin < 0.) {chi2ymin = 0.;}
        //     prob2y = gsl_cdf_chisq_Q(chi2ymin, mean1pix);
        meany = fmax(mean1pix, (double)templ.chi2yavgone());
        hchi2 = chi2ymin/2.; hndof = meany/2.;
        prob2y = 1. - TMath::Gamma(hndof, hchi2);
       
    } else {
       
// For cluster > 1 pix, use chi^2 minimm to recontruct the two y-positions

// at small eta, the templates won't actually work on two pixel y-clusters so just return the pixel centers    

       if(logypx == 2 && fabsf(cotbeta) < 0.25f) {
           switch(nypix) {
              case 2:
//  Both pixels are small
                 yrec1 = (fypix-shifty+originy)*ysize;
                 yrec2 = (lypix-shifty+originy)*ysize;
                 sigmay = ysize/sqrt12;
                 break;
              case 3:
//  One big pixel and one small pixel
                if(yd[fypix]) {
                   yrec1 = (fypix+0.5f-shifty+originy)*ysize;
                   yrec2 = (lypix-shifty+originy)*ysize;
                   sigmay = ysize/sqrt12;
                } else {
                   yrec1 = (fypix-shifty+originy)*ysize;
                   yrec2 = (lypix-0.5f-shifty+originy)*ysize;
                   sigmay = 1.5f*ysize/sqrt12;
                }
                break;
             case 4:
//  Two big pixels
                yrec1 = (fypix+0.5f-shifty+originy)*ysize;
                yrec2 = (lypix-0.5f-shifty+originy)*ysize;
                sigmay = 2.f*ysize/sqrt12;
                break;
             default:
//  Something is screwy ...
                LOGERROR("SiPixelTemplateReco") << "weird problem: logical y-pixels = " << logypx << ", total ysize in normal pixels = " << nypix << ENDL;  
                return 10;
          }
       } else {
       
// uncertainty and final correction depend upon charge bin   
  
          bias = templ.yavgc2m(binq);
          yrec1 = (0.125f*(minbink-ycbin)+BHY-(float)shifty+originy)*ysize - bias;
          yrec2 = (0.125f*(minbinj-ycbin)+BHY-(float)shifty+originy)*ysize - bias;
          sigmay = sqrt2y*templ.yrmsc2m(binq);
          
       }
       
// Do goodness of fit test in y  
       
       if(chi2ymin < 0.0) {chi2ymin = 0.0;}
       meany = templ.chi2yavgc2m(binq);
       if(meany < 0.01) {meany = 0.01;}
// gsl function that calculates the chi^2 tail prob for non-integral dof
//     prob2y = gsl_cdf_chisq_Q(chi2y, meany);
//     prob2y = ROOT::Math::chisquared_cdf_c(chi2y, meany);
       hchi2 = chi2ymin/2.; hndof = meany/2.;
       prob2y = 1. - TMath::Gamma(hndof, hchi2);
    }
    
// Do the x-reconstruction next 
              
                  
// Define the maximum signal to allow before de-weighting a pixel 

    sxthr = 2.1f*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<BYSIZE; ++i) { xsig2[i] = 0.; }
    templ.xsigma2(fxpix, lxpix, sxthr, xsum, xsig2);
              
// Find the template bin that minimizes the Chi^2 

    chi2xmin = 1.e15;
    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];
    }
    minbinj = -1; 
    minbink = -1;
    deltaj = djx;
    jmin = fxbin;
    jmax = lxbin;
    kmin = fxbin;
    kmax = lxbin;
    std::vector<float> xtemp(BXSIZE);
    while(deltaj > 0) {
       for(j=jmin; j<jmax; j+=deltaj) {
            km = std::min(kmax, j);
          for(k=kmin; k<=km; k+=deltaj) {
              
// Get the template for this set of indices
              
              templ.xtemp3d(j, k, xtemp);
              
// Modify the template if double pixels are present   
              
              if(nxpix > logxpx) {
                  i=fxpix;
                  while(i < lxpix) {
                     if(xd[i] && !xd[i+1]) {
                                  
// Sum the adjacent cells and put the average signal in both   
                                  
                        sigavg = (xtemp[i] +  xtemp[i+1])/2.f;
                        xtemp[i] = sigavg;
                        xtemp[i+1] = sigavg;
                          i += 2;
                      } else {
                          ++i;
                      }
                  }
              } 
              ssa = 0.f;
              sa2 = 0.f;
              for(i=fxpix-2; i<=lxpix+2; ++i) {
                  ssa += xsw[i]*xtemp[i];
                  sa2 += xtemp[i]*xtemp[i]*xw2[i];
              }
              rat=ssa/ss2;
              if(rat <= 0.f) {LOGERROR("SiPixelTemplateSplit") << "illegal chi2xmin normalization = " << rat << ENDL; rat = 1.;}
              chi2x=ss2-2.f*ssa/rat+sa2/(rat*rat);
              if(chi2x < chi2xmin) {
                  chi2xmin = chi2x;
                  minbinj = j;
                  minbink = k;
                }
           }
       } 
       deltaj /= 2;
       if(minbinj > fxbin) {jmin = minbinj - deltaj;} else {jmin = fxbin;}
       if(minbinj < lxbin) {jmax = minbinj + deltaj;} else {jmax = lxbin;}
       if(minbink > fxbin) {kmin = minbink - deltaj;} else {kmin = fxbin;}
       if(minbink < lxbin) {kmax = minbink + deltaj;} else {kmax = lxbin;}      
    }
    
    if (theVerboseLevel > 9) {
       LOGDEBUG("SiPixelTemplateSplit") <<
        "minbinj/minbink " << minbinj<< "/" << minbink << " 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();
       }
       xrec1 = 0.5f*(fxpix+lxpix-2*shiftx+2.f*originx)*xsize-delta;
       xrec2 = xrec1;
       if(sigma <= 0.f) {
          sigmax = xsize/sqrt12;
       } 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.;
        prob2x = 1. - TMath::Gamma(hndof, hchi2);
       
    } else {
       
// For cluster > 1 pix, use chi^2 minimm to recontruct the two x-positions

// uncertainty and final correction depend upon charge bin     
       
       bias = templ.xavgc2m(binq);
       xrec1 = (0.125f*(minbink-xcbin)+BHX-(float)shiftx+originx)*xsize - bias;
       xrec2 = (0.125f*(minbinj-xcbin)+BHX-(float)shiftx+originx)*xsize - bias;
       sigmax = sqrt2x*templ.xrmsc2m(binq);
       
// Do goodness of fit test in y  
       
       if(chi2xmin < 0.0) {chi2xmin = 0.0;}
       meanx = templ.chi2xavgc2m(binq);
       if(meanx < 0.01) {meanx = 0.01;}
       hchi2 = chi2xmin/2.; hndof = meanx/2.;
       prob2x = 1. - TMath::Gamma(hndof, hchi2);
    }
    
    //  Don't return exact zeros for the probability
    
    if(prob2y < probmin) {prob2y = probmin;}
    if(prob2x < probmin) {prob2x = probmin;}
    
//  New code: resolve the ambiguity if resolve is set to true
    
    dchisq = 0.;
    if(resolve) {
        
//  First copy the unexpanded cluster into a new working buffer
        
        for(i=0; i<BYM2; ++i) {
            for(j=0; j<BXM2; ++j) {
                if((i>0 && i<BYM3)&&(j>0 && j<BXM3)) {
                    cluster2[j][i] = qscale*clust[j-1][i-1];
                } else {
                    cluster2[j][i] = 0.f;
                }
            }
        }
        
//  Next, redefine the local coordinates to start at the lower LH corner of pixel[1][1];
        
        if(xdouble[0]) {
            x1p = xrec1+xsize;
            x2p = xrec2+xsize;
        } else {
            x1p = xrec1+xsize/2.f;
            x2p = xrec2+xsize/2.f;  
        }
        
        if(ydouble[0]) {
            y1p = yrec1+ysize;
            y2p = yrec2+ysize;
        } else {
            y1p = yrec1+ysize/2.f;
            y2p = yrec2+ysize/2.f;  
        }
        
// Next, calculate 2-d templates for the (x1,y1)+(x2,y2) and the (x1,y2)+(x2,y1) hypotheses
        
//  First zero the two 2-d hypotheses
        
        for(i=0; i<BYM2; ++i) {
            for(j=0; j<BXM2; ++j) {
                temp2d1[j][i] = 0.f;
                temp2d2[j][i] = 0.f;
            }
        }
        
        
// Add the two hits in the first hypothesis
        
        any2dfail = templ2D.xytemp(id, cotalpha, cotbeta, x1p, y1p, xdouble, ydouble, temp2d1) && templ2D.xytemp(id, cotalpha, cotbeta, x2p, y2p, xdouble, ydouble, temp2d1);
        
// And then the second hypothesis
        
        any2dfail = any2dfail && templ2D.xytemp(id, cotalpha, cotbeta, x1p, y2p, xdouble, ydouble, temp2d2);
        
        any2dfail = any2dfail && templ2D.xytemp(id, cotalpha, cotbeta, x2p, y1p, xdouble, ydouble, temp2d2);
        
// If any of these have failed, use the simple templates instead
        
        if(!any2dfail) {
            
//  Rezero the two 2-d hypotheses
            
            for(i=0; i<BYM2; ++i) {
                for(j=0; j<BXM2; ++j) {
                    temp2d1[j][i] = 0.f;
                    temp2d2[j][i] = 0.f;
                }
            }
            
// Add the two hits in the first hypothesis
            
            if(!templ.simpletemplate2D(x1p, y1p, xdouble, ydouble, temp2d1)) {return 1;}
            
            if(!templ.simpletemplate2D(x2p, y2p, xdouble, ydouble, temp2d1)) {return 1;}
            
// And then the second hypothesis
            
            if(!templ.simpletemplate2D(x1p, y2p, xdouble, ydouble, temp2d2)) {return 1;}
            
            if(!templ.simpletemplate2D(x2p, y1p, xdouble, ydouble, temp2d2)) {return 1;}
        }
        
// Keep lists of pixels and nearest neighbors   
        
        std::list<std::pair<int, int> > pixellst;
        
// Loop through the array and find non-zero elements
        
        for(i=0; i<BYM2; ++i) {
            for(j=0; j<BXM2; ++j) {
                if(cluster2[j][i] > 0.f || temp2d1[j][i] > 0.f || temp2d2[j][i] > 0.f) {
                    pixel.first = j; pixel.second = i;
                    pixellst.push_back(pixel);
                }
            }
        }
        
        // Now calculate the product of Landau probabilities (alpha probability)
        
      templ2D.landau_par(lanpar);       
        loglike1 = 0.; loglike2 = 0.;
        
        // Now, for each neighbor, match it again the pixel list.
        // If found, delete it from the neighbor list
        
        std::list<std::pair<int, int> >::const_iterator pixIter, pixEnd;
        pixIter = pixellst.begin();
        pixEnd = pixellst.end();
        for( ; pixIter != pixEnd; ++pixIter ) {
            j = pixIter->first; i = pixIter->second;
            if((i < BHY && cotbeta > 0.) || (i >= BHY && cotbeta < 0.)) {lparm = 0;} else {lparm = 1;}
            mpv1 = lanpar[lparm][0] + lanpar[lparm][1]*temp2d1[j][i];
            sigmal1 = lanpar[lparm][2]*mpv1;
            sigmal1 = sqrt(sigmal1*sigmal1+lanpar[lparm][3]*lanpar[lparm][3]);
            if(sigmal1 < q05) sigmal1 = q05;
            arg1 = (cluster2[j][i]-mpv1)/sigmal1-0.22278;
            mpv2 = lanpar[lparm][0] + lanpar[lparm][1]*temp2d2[j][i];
            sigmal2 = lanpar[lparm][2]*mpv2;
            sigmal2 = sqrt(sigmal2*sigmal2+lanpar[lparm][3]*lanpar[lparm][3]);
            if(sigmal2 < q05) sigmal2 = q05;
            arg2 = (cluster2[j][i]-mpv2)/sigmal2-0.22278;
//          like = ROOT::Math::landau_pdf(arg1)/sigmal1;
            like = ROOT::Math::landau_pdf(arg1);
            if(like < 1.e-30) like = 1.e-30;
            loglike1 += log(like);
//          like = ROOT::Math::landau_pdf(arg2)/sigmal2;
            like = ROOT::Math::landau_pdf(arg2);
            if(like < 1.e-30) like = 1.e-30;
            loglike2 += log(like);
        }
        
// Calculate chisquare difference for the two hypotheses 9don't multiply by 2 for less inconvenient scaling
        
        deltachi2 = loglike1 - loglike2;
                
        if(deltachi2 < 0.) {
            
            // Flip the x1 and x2
            
            x1p = xrec1;
            xrec1 = xrec2;
            xrec2 = x1p;
        }
        
        // Return a positive definite value
        
        dchisq = fabs(deltachi2);       
    }
    
    return 0;
} // PixelTempSplit 


// *************************************************************************************************************************************
// *************************************************************************************************************************************

int SiPixelTemplateSplit::PixelTempSplit(int id, float cotalpha, float cotbeta, array_2d& cluster, 
            std::vector<bool>& ydouble, std::vector<bool>& xdouble, 
            SiPixelTemplate& templ, 
            float& yrec1, float& yrec2, float& sigmay, float& prob2y,
            float& xrec1, float& xrec2, float& sigmax, float& prob2x, int& q2bin, float& prob2Q, bool resolve, int speed, float& dchisq, SiPixelTemplate2D& templ2D)
{
    // Local variables 
    const bool deadpix = false;
    std::vector<std::pair<int, int> > zeropix;
    
    return SiPixelTemplateSplit::PixelTempSplit(id, cotalpha, cotbeta, cluster, ydouble, xdouble, templ, 
            yrec1, yrec2, sigmay, prob2y, xrec1, xrec2, sigmax, prob2x, q2bin, prob2Q, resolve, speed, dchisq, deadpix, zeropix, templ2D);

} // PixelTempSplit


// *************************************************************************************************************************************
// *************************************************************************************************************************************

int SiPixelTemplateSplit::PixelTempSplit(int id, float cotalpha, float cotbeta, array_2d& cluster, 
                                         std::vector<bool>& ydouble, std::vector<bool>& xdouble, 
                                         SiPixelTemplate& templ, 
                                         float& yrec1, float& yrec2, float& sigmay, float& prob2y,
                                         float& xrec1, float& xrec2, float& sigmax, float& prob2x, int& q2bin, float& prob2Q, bool resolve, float& dchisq, SiPixelTemplate2D& templ2D)
{
    // Local variables 
    const bool deadpix = false;
    std::vector<std::pair<int, int> > zeropix;
    const int speed = 1;
    
    return SiPixelTemplateSplit::PixelTempSplit(id, cotalpha, cotbeta, cluster, ydouble, xdouble, templ, 
                                                yrec1, yrec2, sigmay, prob2y, xrec1, xrec2, sigmax, prob2x, q2bin, prob2Q, resolve, speed, dchisq, deadpix, zeropix, templ2D);
    
} // PixelTempSplit

// *************************************************************************************************************************************
// *************************************************************************************************************************************

int SiPixelTemplateSplit::PixelTempSplit(int id, float cotalpha, float cotbeta, array_2d& cluster, 
                                        std::vector<bool>& ydouble, std::vector<bool>& xdouble, 
                                        SiPixelTemplate& templ, 
                                        float& yrec1, float& yrec2, float& sigmay, float& prob2y,
                                        float& xrec1, float& xrec2, float& sigmax, float& prob2x, int& q2bin, float& prob2Q, SiPixelTemplate2D& templ2D)
{
    // Local variables 
    const bool deadpix = false;
    const bool resolve = true;
    float dchisq;
    std::vector<std::pair<int, int> > zeropix;
    const int speed = 1;
    
    return SiPixelTemplateSplit::PixelTempSplit(id, cotalpha, cotbeta, cluster, ydouble, xdouble, templ, 
                                               yrec1, yrec2, sigmay, prob2y, xrec1, xrec2, sigmax, prob2x, q2bin, prob2Q, resolve, speed, dchisq, deadpix, zeropix, templ2D);
    
} // PixelTempSplit



// *************************************************************************************************************************************
// *************************************************************************************************************************************

int SiPixelTemplateSplit::PixelTempSplit(int id, float cotalpha, float cotbeta, array_2d& cluster, 
                                                     std::vector<bool>& ydouble, std::vector<bool>& xdouble, 
                                                     SiPixelTemplate& templ, 
                                                     float& yrec1, float& yrec2, float& sigmay, float& prob2y,
                                                     float& xrec1, float& xrec2, float& sigmax, float& prob2x, int& q2bin, SiPixelTemplate2D& templ2D)
{
    // Local variables 
    const bool deadpix = false;
    const bool resolve = true;
    float dchisq, prob2Q;
    std::vector<std::pair<int, int> > zeropix;
    const int speed = 1;
    
    return SiPixelTemplateSplit::PixelTempSplit(id, cotalpha, cotbeta, cluster, ydouble, xdouble, templ, 
                                                             yrec1, yrec2, sigmay, prob2y, xrec1, xrec2, sigmax, prob2x, q2bin, prob2Q, resolve, speed, dchisq, deadpix, zeropix, templ2D);
    
} // PixelTempSplit