SiStripTemplateReco Namespace Reference

Functions
int	StripTempReco1D (int id, float cotalpha, float cotbeta, float locBy, std::vector< float > &cluster, SiStripTemplate &templ, float &xrec, float &sigmax, float &probx, int &qbin, int speed, float &probQ)

Function Documentation

int SiStripTemplateReco::StripTempReco1D	(	int	id,
		float	cotalpha,
		float	cotbeta,
		float	locBy,
		std::vector< float > &	cluster,
		SiStripTemplate &	templ,
		float &	xrec,
		float &	sigmax,
		float &	probx,
		int &	qbin,
		int	speed,
		float &	probQ
	)

Reconstruct the best estimate of the hit position for strip clusters, includes autoswitching to barycenter when that technique is more accurate.

Parameters

id	- (input) identifier of the template to use
cotalpha	- (input) the cotangent of the alpha track angle (see CMS IN 2004/014)
cotbeta	- (input) the cotangent of the beta track angle (see CMS IN 2004/014)
locBy	- (input) the sign of the local B_y field to specify the Lorentz drift direction
cluster	- (input) boost multi_array container array of 13 pixel signals, origin of local coords (0,0) at center of pixel cluster[0].
templ	- (input) the template used in the reconstruction
xrec	- (output) best estimate of x-coordinate of hit in microns
sigmax	- (output) best estimate of uncertainty on xrec in microns
probx	- (output) probability describing goodness-of-fit for x-reco
qbin	- (output) index (0-4) describing the charge of the cluster qbin = 0 Q/Q_avg > 1.5 [few % of all hits] 1 1.5 > Q/Q_avg > 1.0 [~30% of all hits] 2 1.0 > Q/Q_avg > 0.85 [~30% of all hits] 3 0.85 > Q/Q_avg > min1 [~30% of all hits] 4 min1 > Q/Q_avg > min2 [~0.1% of all hits] 5 min2 > Q/Q_avg [~0.1% of all hits]
speed	- (input) switch (-2->5) trading speed vs robustness -2 totally bombproof, searches the entire 41 bin range at full density (equiv to V2_4), calculates Q probability w/ VVIObj (better but slower) -1 totally bombproof, searches the entire 41 bin range at full density (equiv to V2_4), calculates Q probability w/ TMath::VavilovI (poorer but faster) 0 totally bombproof, searches the entire 41 bin range at full density (equiv to V2_4) 1 faster, searches reduced 25 bin range (no big pix) + 33 bins (big pix at ends) at full density 2 faster yet, searches same range as 1 but at 1/2 density 3 fastest, searches same range as 1 but at 1/4 density (no big pix) and 1/2 density (big pix in cluster) 4 fastest w/ Q prob, searches same range as 1 but at 1/4 density (no big pix) and 1/2 density (big pix in cluster), calculates Q probability w/ VVIObj (better but slower) 5 fastest w/ Q prob, searches same range as 1 but at 1/4 density (no big pix) and 1/2 density (big pix in cluster), calculates Q probability w/ TMath::VavilovI (poorer but faster)
probQ	- (output) the Vavilov-distribution-based cluster charge probability

Definition at line 84 of file SiStripTemplateReco.cc.

References assert(), BSHX, BSXM2, BSXSIZE, SiStripTemplate::chi2xavg(), SiStripTemplate::chi2xavgone(), SiStripTemplate::chi2xmin(), SiStripTemplate::chi2xminone(), SiStripTemplate::cxtemp(), delta, SiStripTemplate::dxone(), ENDL, Exception, f, sistripvvi::VVIObj::fcn(), Gamma, i, SiStripTemplate::interpolate(), j, kappa, LOGDEBUG, LOGERROR, SiStripTemplate::lorxwidth(), maxpix, SiStripTemplate::qavg(), SiStripTemplate::qmin(), SiStripTemplate::qscale(), SiStripTemplate::s50(), SiStripTemplate::sxmax(), SiStripTemplate::sxone(), theVerboseLevel, TSXSIZE, SiStripTemplate::vavilov_pars(), SiStripTemplate::xavg(), SiStripTemplate::xavgbcn(), SiStripTemplate::xflcorr(), SiStripTemplate::xrms(), SiStripTemplate::xrmsbcn(), SiStripTemplate::xsigma2(), xsize, SiStripTemplate::xsize(), and SiStripTemplate::xtemp().

Referenced by StripCPEfromTemplate::localParameters().

{
    // Local variables 
    int i, j, minbin, binl, binh, binq, midpix;
    int fxpix, nxpix, lxpix, logxpx, shiftx, ftpix, ltpix;
    int nclusx;
    int deltaj, jmin, jmax, fxbin, lxbin, djx;
    float sxthr, rnorm, delta, sigma, pseudopix, qscale, q50, q100;
    float ss2, ssa, sa2, ssba, saba, sba2, rat, fq, qtotal, barycenter, sigmaxbcn;
    float originx, qfx, qlx, bias, biasbcn, maxpix;
    double chi2x, meanx, chi2xmin, chi21max;
    double hchi2, hndof, prvav, mpv, sigmaQ, kappa, xvav, beta2;
    float xtemp[41][BSXSIZE], xsum[BSXSIZE];
    float chi2xbin[41], xsig2[BSXSIZE];
    float xw2[BSXSIZE],  xsw[BSXSIZE];
    bool calc_probQ, use_VVIObj;
    float 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, locBy)) {
       if (theVerboseLevel > 2) {LOGDEBUG("SiStripTemplateReco") << "input cluster direction cot(alpha) = " << cotalpha << ", cot(beta) = " << cotbeta << ", local B_y = " << locBy << ", template ID = " << id << ", no reconstruction performed" << ENDL;}    
       return 20;
    }
    
// Check to see if Q probability is selected
    
    calc_probQ = false;
    use_VVIObj = false;
    if(speed < 0) {
        calc_probQ = true;
        if(speed < -1) use_VVIObj = true;
        speed = 0;
    }
    
    if(speed > 3) {
        calc_probQ = true;
        if(speed < 5) use_VVIObj = true;
        speed = 3;
    }
    
// Get pixel dimensions from the template (to allow multiple detectors in the future)
    
    xsize = templ.xsize();
   
// Define size of pseudopixel
    
    q50 = templ.s50();
    q100 = 2.f * q50;
    pseudopix = q50;
    
// Get charge scaling factor

    qscale = templ.qscale();
        
// enforce maximum size 
    
    nclusx = (int)cluster.size();
    
    if(nclusx > TSXSIZE) {nclusx = TSXSIZE;}
    
// First, rescale all strip charges, sum them and trunate the strip charges      

    qtotal = 0.;
    for(i=0; i<BSXSIZE; ++i) {xsum[i] = 0.f;}
    maxpix = templ.sxmax();
    barycenter = 0.f;
    for(j=0; j<nclusx; ++j) {
        xsum[j] = qscale*cluster[j];
        qtotal += xsum[j];
        barycenter += j*xsize*xsum[j];
       if(xsum[j] > maxpix) {xsum[j] = maxpix;}
   }
    
    barycenter = barycenter/qtotal - 0.5f*templ.lorxwidth();
            
// next, identify the x-cluster ends, count total pixels, nxpix, and logical pixels, logxpx   

    fxpix = -1;
    ftpix = -1;
    nxpix=0;
    lxpix=0;
    ltpix=0;
    logxpx=0;
    for(i=0; i<BSXSIZE; ++i) {
       if(xsum[i] > 0.f) {
          if(fxpix == -1) {fxpix = i;}
          ++logxpx;
          ++nxpix;
          lxpix = i;
            if(xsum[i] > q100) {
                if(ftpix == -1) {ftpix = i;}
                ltpix = i;
         }              
        }
    }

    
//  dlengthx = (float)nxpix - templ.clslenx();
    
// Make sure cluster is continuous

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

       return 2; 
    }

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

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

       return 7; 
    }
    
// next, center the cluster on template center if necessary   

    midpix = (ftpix+ltpix)/2;
    shiftx = templ.cxtemp() - midpix;
        
    if(shiftx > 0) {
       for(i=lxpix; i>=fxpix; --i) {
           xsum[i+shiftx] = xsum[i];
           xsum[i] = 0.f;
       }
    } else if (shiftx < 0) {
       for(i=fxpix; i<=lxpix; ++i) {
          xsum[i+shiftx] = xsum[i];
           xsum[i] = 0.f;
       }
    }
    lxpix +=shiftx;
    fxpix +=shiftx;
    
// If the cluster boundaries are OK, add pesudopixels, otherwise quit
    
    if(fxpix > 1 && fxpix < BSXM2) {
       xsum[fxpix-1] = pseudopix;
       xsum[fxpix-2] = 0.2f*pseudopix;
    } else {return 9;}
    if(lxpix > 1 && lxpix < BSXM2) {
       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   

       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(qtotal < 0.95f*templ.qmin()) {qbin = 5;} else {
        if(qtotal < 0.95f*templ.qmin(1)) {qbin = 4;}
    }
    if (theVerboseLevel > 9) {
       LOGDEBUG("SiStripTemplateReco") <<
        "ID = " << id <<  
         " cot(alpha) = " << cotalpha << " cot(beta) = " << cotbeta << 
         " nclusx = " << nclusx << 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") << "SiStripTemplateReco::StripTempReco2D called with illegal speed = " << speed << std::endl;
    }
#else
    assert(speed >= 0 && speed < 4);
#endif
    fxbin = 2; lxbin = 38; djx = 1;
    if(speed > 0) {
       fxbin = 8; lxbin = 32;
     }
    
    if(speed > 1) { 
       djx = 2;
       if(speed > 2) {
          djx = 4;
       }
    }
    
    if (theVerboseLevel > 9) {
       LOGDEBUG("SiStripTemplateReco") <<
        "fxpix " << fxpix << " lxpix = " << lxpix << 
         " fxbin = " << fxbin << " lxbin = " << lxbin << 
         " djx = " << djx << " logxpx = " << logxpx << ENDL;
    }
        
// Now do the copies
        
    templ.xtemp(fxbin, lxbin, xtemp);
    
// Do the x-reconstruction next 
              
// Apply the first-pass template algorithm to all clusters

// Modify the template if double pixels are present 
                  
// Define the maximum signal to allow before de-weighting a pixel 

    sxthr = 1.1f*maxpix;
              
// Evaluate pixel-by-pixel uncertainties (weights) for the templ analysis 

//  for(i=0; i<BSXSIZE; ++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("SiStripTemplateReco") << "illegal chi2xmin normalization (1) = " << 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("SiStripTemplateReco") <<
        "minbin " << minbin << " chi2xmin = " << chi2xmin << ENDL;
    }

// Do not apply final template pass to 1-pixel clusters (use calibrated offset)
    
    if(nxpix == 1) {
    
        delta = templ.dxone();
        sigma = templ.sxone();
       xrec = 0.5f*(fxpix+lxpix-2*shiftx+2.f*originx)*xsize-delta;
       if(sigma <= 0.f) {
          sigmax = 28.9f;
       } 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(logxpx > 1) {
            qlx=xsum[lxpix];
        } 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+BSHX-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.f) {LOGERROR("SiStripTemplateReco") << "illegal chi2x normalization (2) = " << rnorm << ENDL; rnorm = 1.;}
        chi2x=ss2-2.f/rnorm*ssa-2.f/rnorm*rat*ssba+(sa2+2.f*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);
               
// Now choose the better result

        bias = templ.xavg(binq);
        biasbcn = templ.xavgbcn(binq);
        sigmaxbcn = templ.xrmsbcn(binq);
        
        if((bias*bias+sigmax*sigmax) > (biasbcn*biasbcn+sigmaxbcn*sigmaxbcn)) {
                
            xrec = barycenter - biasbcn;
            sigmax = sigmaxbcn;
            
        }   
       
    }
    
//  Don't return exact zeros for the probability
    
    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") << "SiStripTemplateReco::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
                  sistripvvi::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;
} // StripTempReco2D