SiPixelTemplateReco.cc

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//
//  SiPixelTemplateReco.cc (Version 8.25)
//
//  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
//
//
//  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/VVIObj.h"
#include "FWCore/MessageLogger/interface/MessageLogger.h"
#define LOGERROR(x) edm::LogError(x)
#define LOGDEBUG(x) LogDebug(x)
static int theVerboseLevel = 2;
#define ENDL " "
#include "FWCore/Utilities/interface/Exception.h"
#else
#include "SiPixelTemplateReco.h"
#include "VVIObj.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, array_2d& clust, 
            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,
             float& probQ)
            
{
    // Local variables 
    int i, j, k, minbin, binl, binh, binq, midpix, fypix, nypix, lypix, logypx;
    int fxpix, nxpix, 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;
    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)) {
       if (theVerboseLevel > 2) {LOGDEBUG("SiPixelTemplateReco") << "input cluster direction cot(alpha) = " << cotalpha << ", cot(beta) = " << cotbeta<< ", local B_z = " << locBz << ", template ID = " << id << ", no reconstruction performed" << ENDL;} 
       return 20;
    }
    
// Make a local copy of the cluster container so that we can muck with it
    
    array_2d cluster = clust;
    
// 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();
   
// 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

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

    qtotal = 0.f;
    minmax = 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; nyzero[i] = 0;
// 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 > 1.5f) {
       binq=0;
    } else {
       if(fq > 1.0f) {
          binq=1;
       } else {
          if(fq > 0.85f) {
             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 = 2; lybin = 38; fxbin = 2; lxbin = 38; 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;
             for(i=fxpix-2; i<=lxpix+2; ++i) {
                 ssa += xsw[i]*xtemp[j][i];
                  sa2 += xtemp[j][i]*xtemp[j][i]*xw2[i];
             }
             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
           VVIObj 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, 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,
             float& probQ)
            
{
    // Local variables 
    const bool deadpix = false;
    std::vector<std::pair<int, int> > zeropix;
    
    return SiPixelTemplateReco::PixelTempReco2D(id, cotalpha, cotbeta, locBz, cluster, ydouble, xdouble, templ, 
        yrec, sigmay, proby, xrec, sigmax, probx, qbin, speed, deadpix, zeropix, probQ);

} // PixelTempReco2D

// *************************************************************************************************************************************
//  Overload parameter list for compatibility with older versions
// *************************************************************************************************************************************
int SiPixelTemplateReco::PixelTempReco2D(int id, 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,
                                         float& probQ)

{
    // Local variables 
    const bool deadpix = false;
    std::vector<std::pair<int, int> > zeropix;
    float locBz = -1.f;
    if(cotbeta < 0.) {locBz = -locBz;}
    
    return SiPixelTemplateReco::PixelTempReco2D(id, cotalpha, cotbeta, locBz, cluster, ydouble, xdouble, templ, 
                                                yrec, sigmay, proby, xrec, sigmax, probx, qbin, speed, deadpix, zeropix, probQ);
    
} // PixelTempReco2D


// *************************************************************************************************************************************
//  Overload parameter list for compatibility with older versions
// *************************************************************************************************************************************
int SiPixelTemplateReco::PixelTempReco2D(int id, 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;
    float locBz = -1.f;
    if(cotbeta < 0.) {locBz = -locBz;}
    float probQ;
    if(speed < 0) speed = 0;
   if(speed > 3) speed = 3;
    
    return SiPixelTemplateReco::PixelTempReco2D(id, cotalpha, cotbeta, locBz, cluster, ydouble, xdouble, templ, 
                                                              yrec, sigmay, proby, xrec, sigmax, probx, qbin, speed, deadpix, zeropix, probQ);
    
} // PixelTempReco2D