th1fmorph.cc File Reference

#include "../interface/th1fmorph.h"
#include "TROOT.h"
#include "TAxis.h"
#include "TArrayD.h"
#include <iostream>
#include <cmath>
#include <set>

Go to the source code of this file.

Functions
TH1F *	th1fmorph (const char *chname, const char *chtitle, TH1F *hist1, TH1F *hist2, Double_t par1, Double_t par2, Double_t parinterp, Double_t morphedhistnorm, Int_t idebug)
TH1D *	th1fmorph (const char *chname, const char *chtitle, TH1D *hist1, TH1D *hist2, Double_t par1, Double_t par2, Double_t parinterp, Double_t morphedhistnorm, Int_t idebug)
template<typename TH1_t , typename Value_t >
TH1_t *	th1fmorph_ (const char *chname, const char *chtitle, TH1_t *hist1, TH1_t *hist2, Double_t par1, Double_t par2, Double_t parinterp, Double_t morphedhistnorm, Int_t idebug)

Function Documentation

TH1F* th1fmorph	(	const char *	chname,
		const char *	chtitle,
		TH1F *	hist1,
		TH1F *	hist2,
		Double_t	par1,
		Double_t	par2,
		Double_t	parinterp,
		Double_t	morphedhistnorm,
		Int_t	idebug
	)

Definition at line 489 of file th1fmorph.cc.

{ return th1fmorph_<TH1F, Float_t>(chname, chtitle, hist1, hist2, par1, par2, parinterp, morphedhistnorm, idebug); }

TH1D* th1fmorph	(	const char *	chname,
		const char *	chtitle,
		TH1D *	hist1,
		TH1D *	hist2,
		Double_t	par1,
		Double_t	par2,
		Double_t	parinterp,
		Double_t	morphedhistnorm,
		Int_t	idebug
	)

Definition at line 497 of file th1fmorph.cc.

{ return th1fmorph_<TH1D, Double_t>(chname, chtitle, hist1, hist2, par1, par2, parinterp, morphedhistnorm, idebug); }

template<typename TH1_t , typename Value_t >

TH1_t* th1fmorph_	(	const char *	chname,
		const char *	chtitle,
		TH1_t *	hist1,
		TH1_t *	hist2,
		Double_t	par1,
		Double_t	par2,
		Double_t	parinterp,
		Double_t	morphedhistnorm,
		Int_t	idebug
	)

Definition at line 13 of file th1fmorph.cc.

References gather_cfg::cout, alignCSCRings::e, i, pileupDistInMC::total, x, and detailsBasic3DVector::y.

{
  //--------------------------------------------------------------------------
  // Author           : Alex Read 
  // Version 0.2 of ROOT implementation, 08.05.2011
  // *
  // *      Perform a linear interpolation between two histograms as a function
  // *      of the characteristic parameter of the distribution.
  // *
  // *      The algorithm is described in Read, A. L., "Linear Interpolation
  // *      of Histograms", NIM A 425 (1999) 357-360.
  // *      
  // *      This ROOT-based CINT implementation is based on the FORTRAN77
  // *      implementation used by the DELPHI experiment at LEP (d_pvmorph.f).
  // *      The use of double precision allows pdf's to be accurately 
  // *      interpolated down to something like 10**-15.
  // *
  // *      The input histograms don't have to be identical, the binning is also
  // *      interpolated.
  // *
  // *      Extrapolation is allowed (a warning is given) but the extrapolation 
  // *      is not as well-defined as the interpolation and the results should 
  // *      be used with great care.
  // *
  // *      Data in the underflow and overflow bins are completely ignored. 
  // *      They are neither interpolated nor do they contribute to the 
  // *      normalization of the histograms.
  // *
  // * Input arguments:
  // * ================
  // * chname, chtitle : The ROOT name and title of the interpolated histogram.
  // *                   Defaults for the name and title are "THF1-interpolated"
  // *                   and "Interpolated histogram", respectively.
  // *
  // * hist1, hist2    : The two input histograms.
  // *
  // * par1,par2       : The values of the linear parameter that characterises
  // *                   the histograms (e.g. a particle mass).
  // *
  // * parinterp       : The value of the linear parameter we wish to 
  // *                   interpolate to. 
  // * 
  // * morphedhistnorm : The normalization of the interpolated histogram 
  // *                   (default is 1.0).  
  // * 
  // * idebug          : Default is zero, no internal information displayed. 
  // *                   Values between 1 and increase the verbosity of 
  // *                   informational output which may prove helpful to
  // *                   understand errors and pathalogical results.
  // * 
  // * The routine returns a pointer (TH1_t *) to a new histogram which is
  // * the interpolated result.
  // *
  // *------------------------------------------------------------------------
  // Changes from 0.1 to 0.2:
  // o Treatment of empty and non-existing histograms now well-defined.
  // o The tricky regions of the first and last bins are improved (and
  //   well-tested).
  // *------------------------------------------------------------------------

  // Return right away if one of the input histograms doesn't exist.
  if(!hist1) {
    cout << "ERROR! th1morph says first input histogram doesn't exist." << endl;
    return(0);
  }
  if(!hist2) {
    cout << "ERROR! th1morph says second input histogram doesn't exist." << endl;
    return(0);
  }
  
  // Extract bin parameters of input histograms 1 and 2. 
  // Supports the cases of non-equidistant as well as equidistant binning
  // and also the case that binning of histograms 1 and 2 is different.
  TAxis* axis1 = hist1->GetXaxis();
  Int_t nb1 = axis1->GetNbins();
  TAxis* axis2 = hist2->GetXaxis();
  Int_t nb2 = axis2->GetNbins();

  std::set<Double_t> bedgesn_tmp;
  for(Int_t i = 1; i <= nb1; ++i){
    bedgesn_tmp.insert(axis1->GetBinLowEdge(i));
    bedgesn_tmp.insert(axis1->GetBinUpEdge(i));
  }
  for(Int_t i = 1; i <= nb2; ++i){
    bedgesn_tmp.insert(axis2->GetBinLowEdge(i));
    bedgesn_tmp.insert(axis2->GetBinUpEdge(i));
  }
  Int_t nbn = bedgesn_tmp.size() - 1;
  TArrayD bedgesn(nbn+1);
  Int_t idx = 0;
  for (std::set<Double_t>::const_iterator bedge = bedgesn_tmp.begin();
       bedge != bedgesn_tmp.end(); ++bedge){
    bedgesn[idx]=(*bedge);
    ++idx;
  }
  Double_t xminn = bedgesn[0];
  Double_t xmaxn = bedgesn[nbn];

  // ......The weights (wt1,wt2) are the complements of the "distances" between 
  //       the values of the parameters at the histograms and the desired 
  //       interpolation point. For example, wt1=0, wt2=1 means that the 
  //       interpolated histogram should be identical to input histogram 2.
  //       Check that they make sense. If par1=par2 then we can choose any
  //       valid set of wt1,wt2 so why not take the average?

  Double_t wt1,wt2;
  if (par2 != par1) {
    wt1 = 1. - (parinterp-par1)/(par2-par1);
    wt2 = 1. + (parinterp-par2)/(par2-par1);
  }
  else { 
    wt1 = 0.5;
    wt2 = 0.5;
  }

  //......Give a warning if this is an extrapolation.

  if (wt1 < 0 || wt1 > 1. || wt2 < 0. || wt2 > 1. || fabs(1-(wt1+wt2)) 
      > 1.0e-4) {
    cout << "Warning! th1fmorph: This is an extrapolation!! Weights are "
         << wt1 << " and " << wt2 << " (sum=" << wt1+wt2 << ")" << endl;
  }
  if (idebug >= 1) cout << "th1morph - Weights: " << wt1 << " " << wt2 << endl;

  if (idebug >= 1) cout << "New hist: " << nbn << " " << xminn << " " 
                        << xmaxn << endl;

  // Treatment for empty histograms: Return an empty histogram
  // with interpolated bins.

  if (hist1->GetSum() <= 0 || hist2->GetSum() <=0 ) {
    cout << "Warning! th1morph detects an empty input histogram. Empty interpolated histogram returned: " 
         <<endl << "         " << chname << " - " << chtitle << endl;
    TH1_t *morphedhist = (TH1_t *)gROOT->FindObject(chname);
    if (morphedhist) delete morphedhist;
    morphedhist = new TH1_t(chname,chtitle,nbn,xminn,xmaxn);
    return(morphedhist);
  }
  if (idebug >= 1) cout << "Input histogram content sums: " 
                        << hist1->GetSum() << " " << hist2->GetSum() << endl;
  // *         
  // *......Extract the single precision histograms into double precision arrays
  // *      for the interpolation computation. The offset is because sigdis(i)
  // *      describes edge i (there are nbins+1 of them) while dist1/2
  // *      describe bin i. Be careful, ROOT does not use C++ convention to
  // *      number bins: dist1[ibin] is content of bin ibin where ibin runs from
  // *      1 to nbins. We allocate some extra space for the derived distributions
  // *      because there may be as many as nb1+nb2+2 edges in the intermediate 
  // *      interpolated cdf described by xdisn[i] (position of edge i) and 
  // *      sigdisn[i] (cummulative probability up this edge) before we project 
  // *      into the final binning.

  Value_t *dist1=hist1->GetArray(); 
  Value_t *dist2=hist2->GetArray();
  Double_t *sigdis1 = new Double_t[1+nb1];
  Double_t *sigdis2 = new Double_t[1+nb2];
  Double_t *sigdisn = new Double_t[2+nb1+nb2];
  Double_t *xdisn = new Double_t[2+nb1+nb2];
  Double_t *sigdisf = new Double_t[nbn+1];

  for(Int_t i=0;i<2+nb1+nb2;i++) xdisn[i] = 0; // Start with empty edges
  sigdis1[0] = 0; sigdis2[0] = 0; // Start with cdf=0 at left edge

  for(Int_t i=1;i<nb1+1;i++) {   // Remember, bin i has edges at i-1 and 
    sigdis1[i] = dist1[i];       // i and i runs from 1 to nb.
  }
  for(Int_t i=1;i<nb2+1;i++) {
    sigdis2[i] = dist2[i];
  }

  if (idebug >= 3) {
    for(Int_t i=0;i<nb1+1;i++) {
      cout << i << " dist1" << dist1[i] << endl;
    }
    for(Int_t i=0;i<nb2+1;i++) {
      cout << i << " dist2" << dist2[i] << endl;
    }
  }
  
  //......Normalize the distributions to 1 to obtain pdf's and integrate 
  //      (sum) to obtain cdf's.

  Double_t total = 0;
  for(Int_t i=0;i<nb1+1;i++) {
    total += sigdis1[i];
  }
  if (idebug >=1) cout << "Total histogram 1: " <<  total << endl;
  for(Int_t i=1;i<nb1+1;i++) {
    sigdis1[i] = sigdis1[i]/total + sigdis1[i-1];
  }
  
  total = 0.;
  for(Int_t i=0;i<nb2+1;i++) {
    total += sigdis2[i];
  }
  if (idebug >=1) cout << "Total histogram 22: " <<  total << endl;
  for(Int_t i=1;i<nb2+1;i++) {
    sigdis2[i] = sigdis2[i]/total + sigdis2[i-1];
  }

  // *
  // *......We are going to step through all the edges of both input
  // *      cdf's ordered by increasing value of y. We start at the
  // *      lower edge, but first we should identify the upper ends of the
  // *      curves. These (ixl1, ixl2) are the first point in each cdf from 
  // *      above that has the same integral as the last edge.
  // *

  Int_t ix1l = nb1;
  Int_t ix2l = nb2;
  while(sigdis1[ix1l-1] >= sigdis1[ix1l]) {
    ix1l = ix1l - 1;
  }
  while(sigdis2[ix2l-1] >= sigdis2[ix2l]) {
    ix2l = ix2l - 1;
  }

  // *
  // *......Step up to the beginnings of the curves. These (ix1, ix2) are the
  // *      first non-zero points from below.

  Int_t ix1 = -1;
  do {
    ix1 = ix1 + 1;
  } while(sigdis1[ix1+1] <= sigdis1[0]);

  Int_t ix2 = -1;
  do {
    ix2 = ix2 + 1;
  } while(sigdis2[ix2+1] <= sigdis2[0]);

  if (idebug >= 1) {
    cout << "First and last edge of hist1: " << ix1 << " " << ix1l << endl;
    cout << "   " << sigdis1[ix1] << " " << sigdis1[ix1+1] << endl;
    cout << "First and last edge of hist2: " << ix2 << " " << ix2l << endl;
    cout << "   " << sigdis2[ix2] << " " << sigdis2[ix2+1] << endl;
  }

  //......The first interpolated point should be computed now.

  Int_t nx3 = 0;
  Double_t x1,x2,x;
  x1 = axis1->GetBinLowEdge(ix1+1); 
  x2 = axis2->GetBinLowEdge(ix2+1); 
  x = wt1*x1 + wt2*x2;
  xdisn[nx3] = x;
  sigdisn[nx3] = 0;
  if(idebug >= 1) {
    cout << "First interpolated point: " << xdisn[nx3] << " " 
         << sigdisn[nx3] << endl;
    cout << "                          " << x1 << " <= " << x << " <= " 
         << x2 << endl;
  }

  //......Loop over the remaining point in both curves. Getting the last
  //      points may be a bit tricky due to limited floating point 
  //      precision.

  if (idebug >= 1) {
    cout << "----BEFORE while with ix1=" << ix1 << ", ix1l=" << ix1l 
         << ", ix2=" << ix2 << ", ix2l=" << ix2l << endl;
  }

  Double_t yprev = -1; // The probability y of the previous point, it will 
                       //get updated and used in the loop.
  Double_t y = 0;
  while((ix1 < ix1l) | (ix2 < ix2l)) {
    if (idebug >= 1 ) cout << "----Top of while with ix1=" << ix1 
                           << ", ix1l=" << ix1l << ", ix2=" << ix2 
                           << ", ix2l=" << ix2l << endl;

    //......Increment to the next lowest point. Step up to the next
    //      kink in case there are several empty (flat in the integral)
    //      bins.

    Int_t i12type = -1; // Tells which input distribution we need to 
                        // see next point of.
    if ((sigdis1[ix1+1] <= sigdis2[ix2+1] || ix2 == ix2l) && ix1 < ix1l) {
      ix1 = ix1 + 1;
      while(sigdis1[ix1+1] <= sigdis1[ix1] && ix1 < ix1l) {
        ix1 = ix1 + 1;
      }
      i12type = 1;
    } else if (ix2 < ix2l) {
      ix2 = ix2 + 1;
      while(sigdis2[ix2+1] <= sigdis2[ix2] && ix2 < ix2l) {
        ix2 = ix2 + 1;
      }
      i12type = 2;
    }
    if (i12type == 1) {
      if (idebug >= 3) {
        cout << "Pair for i12type=1: " << sigdis2[ix2] << " " 
             << sigdis1[ix1] << " " << sigdis2[ix2+1] << endl;
      }
      x1 = axis1->GetBinLowEdge(ix1+1);
      y = sigdis1[ix1];
      Double_t x20 = axis2->GetBinLowEdge(ix2+1);
      Double_t x21 = axis2->GetBinUpEdge(ix2+1);
      Double_t y20 = sigdis2[ix2];
      Double_t y21 = sigdis2[ix2+1];

      //......Calculate where the cummulative probability y in distribution 1
      //      intersects between the 2 points from distribution 2 which 
      //      bracket it.

      if (y21 > y20) {
        x2 = x20 + (x21-x20)*(y-y20)/(y21-y20);
      } 
      else {
        x2 = x20;
      }
    } else {
      if (idebug >= 3) {
        cout << "Pair for i12type=2: " << sigdis1[ix1] << " " << sigdis2[ix2] 
             << " " << sigdis1[ix1+1] << endl;
      }
      x2 = axis2->GetBinLowEdge(ix2+1);
      y = sigdis2[ix2];
      Double_t x10 = axis1->GetBinLowEdge(ix1+1);
      Double_t x11 = axis1->GetBinUpEdge(ix1+1);
      Double_t y10 = sigdis1[ix1];
      Double_t y11 = sigdis1[ix1+1];

      //......Calculate where the cummulative probability y in distribution 2
      //      intersects between the 2 points from distribution 1 which 
      //      brackets it.

      if (y11 > y10) {
        x1 = x10 + (x11-x10)*(y-y10)/(y11-y10);
      } else {
        x1 = x10;
      }
    }

    //......Interpolate between the x's in the 2 distributions at the 
    //      cummulative probability y. Store the (x,y) for provisional 
    //      edge nx3 in (xdisn[nx3],sigdisn[nx3]). nx3 grows for each point
    //      we add the the arrays. Note: Should probably turn the pair into 
    //      a structure to make the code more object-oriented and readable.

    x = wt1*x1 + wt2*x2;
    if (y > yprev) {
      nx3 = nx3+1;
      if (idebug >= 1) {
        cout << " ---> y > yprev: i12type=" << i12type << ", nx3=" 
             << nx3 << ", x= " << x << ", y=" << y << ", yprev=" << yprev 
             << endl;
      }
      yprev = y;
      xdisn[nx3] = x;
      sigdisn[nx3] = y;
      if(idebug >= 1) {
        cout << "    ix1=" << ix1 << ", ix2= " << ix2 << ", i12type= " 
             << i12type << ", sigdis1[ix1]=" << sigdis1[ix1] << endl;
        cout << "        " << ", nx3=" << nx3 << ", x=" << x << ", y= " 
             << sigdisn[nx3] << endl;
      }
    }
  }
  if (idebug >=3) for (Int_t i=0;i<nx3;i++) {
    cout << " nx " << i << " " << xdisn[i] << " " << sigdisn[i] << endl;
  }

  // *......Now we loop over the edges of the bins of the interpolated
  // *      histogram and find out where the interpolated cdf 3
  // *      crosses them. This projection defines the result and will
  // *      be stored (after differention and renormalization) in the
  // *      output histogram.
  // *
  // *......We set all the bins following the final edge to the value
  // *      of the final edge.

  x = xmaxn;
  Int_t ix = nbn;

  if (idebug >= 1) cout << "------> Any final bins to set? " << x << " " 
                        << xdisn[nx3] << endl;
  while(x >= xdisn[nx3]) {
    sigdisf[ix] = sigdisn[nx3];
    if (idebug >= 2) cout << "   Setting final bins" << ix << " " << x 
                          << " " << sigdisf[ix] << endl;
    ix = ix-1;
    x = bedgesn[ix];
  }
  Int_t ixl = ix + 1;
  if (idebug >= 1) cout << " Now ixl=" << ixl << " ix=" << ix << endl;

  // *
  // *......The beginning may be empty, so we have to step up to the first
  // *      edge where the result is nonzero. We zero the bins which have
  // *      and upper (!) edge which is below the first point of the
  // *      cummulative distribution we are going to project to this
  // *      output histogram binning.
  // *

  ix = 0;
  x = bedgesn[ix+1];
  if (idebug >= 1) cout << "Start setting initial bins at x=" << x << endl;
  while(x <= xdisn[0]) {
    sigdisf[ix] = sigdisn[0];
    if (idebug >= 1) cout << "   Setting initial bins " << ix << " " << x 
                          << " " << xdisn[1] << " " << sigdisf[ix] << endl;
    ix = ix+1;
    x = bedgesn[ix+1];
  }
  Int_t ixf = ix;

  if (idebug >= 1)
    cout << "Bins left to loop over:" << ixf << "-" << ixl << endl;

  // *......Also the end (from y to 1.0) often comes before the last edge
  // *      so we have to set the following to 1.0 as well.

  Int_t ix3 = 0; // Problems with initial edge!!!
  for(ix=ixf;ix<ixl;ix++) {
    x = bedgesn[ix];
    if (x < xdisn[0]) {
      y = 0;
    } else if (x > xdisn[nx3]) {
      y = 1.;
    } else {
      while(xdisn[ix3+1] <= x && ix3 < 2*nbn) {
        ix3 = ix3 + 1;
      }
      Double_t dx2=axis2->GetBinWidth(axis2->FindBin(x));
      if (xdisn[ix3+1]-x > 1.1*dx2) { // Empty bin treatment
        y = sigdisn[ix3+1];
      }
      else if (xdisn[ix3+1] > xdisn[ix3]) { // Normal bins
        y = sigdisn[ix3] + (sigdisn[ix3+1]-sigdisn[ix3])
          *(x-xdisn[ix3])/(xdisn[ix3+1]-xdisn[ix3]);
      } else {  // Is this ever used?
        y = 0;
        cout << "Warning - th1fmorph: This probably shoudn't happen! " 
             << endl;
        cout << "Warning - th1fmorph: Zero slope solving x(y)" << endl;
      }
    }
    sigdisf[ix] = y;
    if (idebug >= 3) {
      cout << ix << ", ix3=" << ix3 << ", xdisn=" << xdisn[ix3] << ", x=" 
           << x << ", next xdisn=" << xdisn[ix3+1] << endl;
      cout << "   cdf n=" << sigdisn[ix3] << ", y=" << y << ", next point=" 
           << sigdisn[ix3+1] << endl;
    }
  }

  //......Differentiate interpolated cdf and return renormalized result in 
  //      new histogram. 

  TH1_t *morphedhist = (TH1_t *)gROOT->FindObject(chname);
  if (morphedhist) delete morphedhist;
  morphedhist = new TH1_t(chname,chtitle,nbn,bedgesn.GetArray());

  for(ix=nbn-1;ix>-1;ix--) {
    y = sigdisf[ix+1]-sigdisf[ix];
    morphedhist->SetBinContent(ix+1,y*morphedhistnorm);
  }
  
  //......Clean up the temporary arrays we allocated.

  delete sigdis1; delete sigdis2; 
  delete sigdisn; delete xdisn; delete sigdisf;

  //......All done, return the result.

  return(morphedhist);
}