source: trunk/MagicSoft/Mars/mhbase/MH.cc@ 3602

/* ======================================================================== *\
!
! *
! * This file is part of MARS, the MAGIC Analysis and Reconstruction
! * Software. It is distributed to you in the hope that it can be a useful
! * and timesaving tool in analysing Data of imaging Cerenkov telescopes.
! * It is distributed WITHOUT ANY WARRANTY.
! *
! * Permission to use, copy, modify and distribute this software and its
! * documentation for any purpose is hereby granted without fee,
! * provided that the above copyright notice appear in all copies and
! * that both that copyright notice and this permission notice appear
! * in supporting documentation. It is provided "as is" without express
! * or implied warranty.
! *
!
!
!   Author(s): Thomas Bretz  07/2001 <mailto:tbretz@astro.uni-wuerzburg.de>
!
!   Copyright: MAGIC Software Development, 2000-2002
!
!
\* ======================================================================== */

//////////////////////////////////////////////////////////////////////////////
//                                                                          //
//  MH                                                                      //
//                                                                          //
//  This is a base tasks for mars histograms. It defines a common interface //
//  for filling the histograms with events (MH::Fill) which is used by a    //
//  common 'filler' And a SetupFill member function which may be used       //
//  by MFillH. The idea is:                                                 //
//   1) If your Histogram can become filled by one single container         //
//      (like MHHillas) you overload MH::Fill and it gets called with       //
//      a pointer to the container with which it should be filled.          //
//                                                                          //
//   2) You histogram needs several containers to get filled. Than you      //
//      have to overload MH::SetupFill and get the necessary objects from   //
//      the parameter list. Use this objects in Fill to fill your           //
//      histogram.                                                          //
//                                                                          //
//  If you want to create your own histogram class the new class must be    //
//  derived from MH (instead of the base MParContainer) and you must        //
//  the fill function of MH. This is the function which is called to fill   //
//  the histogram(s) by the data of a corresponding parameter container.    //
//                                                                          //
//  Remark: the static member function (eg MakeDefCanvas) can be called     //
//          from everywhere using: MH::MakeDefCanvas(...)                   //
//                                                                          //
//////////////////////////////////////////////////////////////////////////////

#include "MH.h"

#include <TH1.h>
#include <TH2.h>
#include <TH3.h>
#include <TStyle.h>       // TStyle::GetScreenFactor
#include <TGaxis.h>
#include <TCanvas.h>
#include <TLegend.h>
#include <TPaveStats.h>
#include <TBaseClass.h>
#if ROOT_VERSION_CODE > ROOT_VERSION(3,04,01)
#include <THLimitsFinder.h>
#endif

#include "MLog.h"
#include "MLogManip.h"

#include "MParList.h"
#include "MParContainer.h"

#include "MBinning.h"

ClassImp(MH);

using namespace std;

// --------------------------------------------------------------------------
//
// Default Constructor. It sets name and title only. Typically you won't
// need to change this.
//
MH::MH(const char *name, const char *title)
{
    //
    //   set the name and title of this object
    //
    fName  = name  ? name  : "MH";
    fTitle = title ? title : "Base class for Mars histograms";
}

// --------------------------------------------------------------------------
//
// If you want to use the automatic filling of your derived class you
// must overload this function. If it is not overloaded you cannot use
// FillH with this class. The argument is a pointer to a container
// in your paremeter list which is specified in the MFillH constructor.
// If you are not going to use it you should at least add
//   Bool_t MH::Fill(const MParContainer *) { return kTRUE; }
// to your class definition.
//
Bool_t MH::Fill(const MParContainer *par, const Stat_t w)
{
    *fLog << warn << GetDescriptor() << ": Fill not overloaded! Can't be used!" << endl;
    return kFALSE;
}

// --------------------------------------------------------------------------
//
// This virtual function is ment as a generalized interface to retrieve
// a pointer to a root histogram from the MH-derived class.
//
TH1 *MH::GetHistByName(const TString name)
{
    *fLog << warn << GetDescriptor() << ": GetHistByName not overloaded! Can't be used!" << endl;
    return NULL;
}

// --------------------------------------------------------------------------
//
// This is a function which should replace the creation of default
// canvases like root does. Because this is inconvinient in some aspects.
// need to change this.
// You can specify a name for the default canvas and a title. Also
// width and height can be given.
// MakeDefCanvas looks for a canvas with the given name. If now name is
// given the DefCanvasName of root is used. If no such canvas is existing
// it is created and returned. If such a canvas already exists a new canvas
// with a name plus anumber is created (the number is calculated by the
// number of all existing canvases plus one)
//
// Normally the canvas size is scaled with gStyle->GetScreenFactor() so
// that on all screens it looks like the same part of the screen.
// To suppress this scaling use usescreenfactor=kFALSE. In this case
// you specify directly the size of the embedded pad.
//
TCanvas *MH::MakeDefCanvas(TString name, const char *title,
                           UInt_t w, UInt_t h, Bool_t usescreenfactor)
{
    const TList *list = (TList*)gROOT->GetListOfCanvases();

    if (name.IsNull())
        name = gROOT->GetDefCanvasName();

    if (list->FindObject(name))
        name += Form(" <%d>", list->GetSize()+1);

    if (!usescreenfactor)
    {
        const Float_t cx = gStyle->GetScreenFactor();
        w += 4;
        h += 28;
        w = (int)(w/cx+1);
        h = (int)(h/cx+1);
    }

    return new TCanvas(name, title, w, h);
}

// --------------------------------------------------------------------------
//
// This function works like MakeDefCanvas(name, title, w, h) but name
// and title are retrieved from the given TObject.
//
// Normally the canvas size is scaled with gStyle->GetScreenFactor() so
// that on all screens it looks like the same part of the screen.
// To suppress this scaling use usescreenfactor=kFALSE. In this case
// you specify directly the size of the embedded pad.
//
TCanvas *MH::MakeDefCanvas(const TObject *obj,
                           UInt_t w, UInt_t h, Bool_t usescreenfactor)
{
    if (!usescreenfactor)
    {
        const Float_t cx = gStyle->GetScreenFactor();
        w += 4;
        h += 28;
        h = (int)(h/cx+1);
        w = (int)(w/cx+1);
    }

    return MakeDefCanvas(obj->GetName(), obj->GetTitle(), w, h);
}

// --------------------------------------------------------------------------
//
// Applies a given binning to a 1D-histogram
//
void MH::SetBinning(TH1 *h, const MBinning *binsx)
{
    //
    // Another strange behaviour: TAxis::Set deletes the axis title!
    //
    TAxis &x = *h->GetXaxis();

#if ROOT_VERSION_CODE < ROOT_VERSION(3,03,03)
    TString xtitle = x.GetTitle();
#endif

    //
    // This is a necessary workaround if one wants to set
    // non-equidistant bins after the initialization
    // TH1D::fNcells must be set correctly.
    //
    h->SetBins(binsx->GetNumBins(), 0, 1);

    //
    // Set the binning of the current histogram to the binning
    // in one of the two given histograms
    //
    x.Set(binsx->GetNumBins(), binsx->GetEdges());
#if ROOT_VERSION_CODE < ROOT_VERSION(3,03,03)
    x.SetTitle(xtitle);
#endif
}

// --------------------------------------------------------------------------
//
// Applies given binnings to the two axis of a 2D-histogram
//
void MH::SetBinning(TH2 *h, const MBinning *binsx, const MBinning *binsy)
{
    TAxis &x = *h->GetXaxis();
    TAxis &y = *h->GetYaxis();

    //
    // Another strange behaviour: TAxis::Set deletes the axis title!
    //
#if ROOT_VERSION_CODE < ROOT_VERSION(3,03,03)
    TString xtitle = x.GetTitle();
    TString ytitle = y.GetTitle();
#endif

    //
    // This is a necessary workaround if one wants to set
    // non-equidistant bins after the initialization
    // TH1D::fNcells must be set correctly.
    //
    h->SetBins(binsx->GetNumBins(), 0, 1,
               binsy->GetNumBins(), 0, 1);

    //
    // Set the binning of the current histogram to the binning
    // in one of the two given histograms
    //
    x.Set(binsx->GetNumBins(), binsx->GetEdges());
    y.Set(binsy->GetNumBins(), binsy->GetEdges());
#if ROOT_VERSION_CODE < ROOT_VERSION(3,03,03)
    x.SetTitle(xtitle);
    y.SetTitle(ytitle);
#endif
}

// --------------------------------------------------------------------------
//
// Applies given binnings to the three axis of a 3D-histogram
//
void MH::SetBinning(TH3 *h, const MBinning *binsx, const MBinning *binsy, const MBinning *binsz)
{
    //
    // Another strange behaviour: TAxis::Set deletes the axis title!
    //
    TAxis &x = *h->GetXaxis();
    TAxis &y = *h->GetYaxis();
    TAxis &z = *h->GetZaxis();

#if ROOT_VERSION_CODE < ROOT_VERSION(3,03,03)
    TString xtitle = x.GetTitle();
    TString ytitle = y.GetTitle();
    TString ztitle = z.GetTitle();
#endif

    //
    // This is a necessary workaround if one wants to set
    // non-equidistant bins after the initialization
    // TH1D::fNcells must be set correctly.
    //
    h->SetBins(binsx->GetNumBins(), 0, 1,
               binsy->GetNumBins(), 0, 1,
               binsz->GetNumBins(), 0, 1);

    //
    // Set the binning of the current histogram to the binning
    // in one of the two given histograms
    //
    x.Set(binsx->GetNumBins(), binsx->GetEdges());
    y.Set(binsy->GetNumBins(), binsy->GetEdges());
    z.Set(binsz->GetNumBins(), binsz->GetEdges());
#if ROOT_VERSION_CODE < ROOT_VERSION(3,03,03)
    x.SetTitle(xtitle);
    y.SetTitle(ytitle);
    z.SetTitle(ztitle);
#endif
}

// --------------------------------------------------------------------------
//
// Applies given binning (the n+1 edges)  to the axis of a 1D-histogram
//
void MH::SetBinning(TH1 *h, const TArrayD &binsx)
{
    MBinning bx;
    bx.SetEdges(binsx);
    SetBinning(h, &bx);
}

// --------------------------------------------------------------------------
//
// Applies given binning (the n+1 edges) to the two axis of a
// 2D-histogram
//
void MH::SetBinning(TH2 *h, const TArrayD &binsx, const TArrayD &binsy)
{
    MBinning bx;
    MBinning by;
    bx.SetEdges(binsx);
    by.SetEdges(binsy);
    SetBinning(h, &bx, &by);
}

// --------------------------------------------------------------------------
//
// Applies given binning (the n+1 edges) to the three axis of a
// 3D-histogram
//
void MH::SetBinning(TH3 *h, const TArrayD &binsx, const TArrayD &binsy, const TArrayD &binsz)
{
    MBinning bx;
    MBinning by;
    MBinning bz;
    bx.SetEdges(binsx);
    by.SetEdges(binsy);
    bz.SetEdges(binsz);
    SetBinning(h, &bx, &by, &bz);
}

// --------------------------------------------------------------------------
//
// Applies the binning of a TAxis (eg from a root histogram) to the axis
// of a 1D-histogram
//
void MH::SetBinning(TH1 *h, const TAxis *binsx)
{
    const Int_t nx = binsx->GetNbins();

    TArrayD bx(nx+1);
    for (int i=0; i<nx; i++) bx[i] = binsx->GetBinLowEdge(i+1);
    bx[nx] = binsx->GetXmax();

    SetBinning(h, bx);
}

// --------------------------------------------------------------------------
//
// Applies the binnings of the TAxis' (eg from a root histogram) to the
// two axis' of a 2D-histogram
//
void MH::SetBinning(TH2 *h, const TAxis *binsx, const TAxis *binsy)
{
    const Int_t nx = binsx->GetNbins();
    const Int_t ny = binsy->GetNbins();

    TArrayD bx(nx+1);
    TArrayD by(ny+1);
    for (int i=0; i<nx; i++) bx[i] = binsx->GetBinLowEdge(i+1);
    for (int i=0; i<ny; i++) by[i] = binsy->GetBinLowEdge(i+1);
    bx[nx] = binsx->GetXmax();
    by[ny] = binsy->GetXmax();

    SetBinning(h, bx, by);
}

// --------------------------------------------------------------------------
//
// Applies the binnings of the TAxis' (eg from a root histogram) to the
// three axis' of a 3D-histogram
//
void MH::SetBinning(TH3 *h, const TAxis *binsx, const TAxis *binsy, const TAxis *binsz)
{
    const Int_t nx = binsx->GetNbins();
    const Int_t ny = binsy->GetNbins();
    const Int_t nz = binsz->GetNbins();

    TArrayD bx(nx+1);
    TArrayD by(ny+1);
    TArrayD bz(nz+1);
    for (int i=0; i<nx; i++) bx[i] = binsx->GetBinLowEdge(i+1);
    for (int i=0; i<ny; i++) by[i] = binsy->GetBinLowEdge(i+1);
    for (int i=0; i<nz; i++) bz[i] = binsz->GetBinLowEdge(i+1);
    bx[nx] = binsx->GetXmax();
    by[ny] = binsy->GetXmax();
    bz[nz] = binsz->GetXmax();

    SetBinning(h, bx, by, bz);
}

// --------------------------------------------------------------------------
//
// Applies the binnings of one root-histogram x to another one h
// Both histograms must be of the same type: TH1, TH2 or TH3
//
void MH::SetBinning(TH1 *h, const TH1 *x)
{
    if (h->InheritsFrom(TH3::Class()) && x->InheritsFrom(TH3::Class()))
    {
        SetBinning((TH3*)h, ((TH1*)x)->GetXaxis(), ((TH1*)x)->GetYaxis(), ((TH1*)x)->GetZaxis());
        return;
    }
    if (h->InheritsFrom(TH3::Class()) || x->InheritsFrom(TH3::Class()))
        return;
    if (h->InheritsFrom(TH2::Class()) && x->InheritsFrom(TH2::Class()))
    {
        SetBinning((TH2*)h, ((TH1*)x)->GetXaxis(), ((TH1*)x)->GetYaxis());
        return;
    }
    if (h->InheritsFrom(TH2::Class()) || x->InheritsFrom(TH2::Class()))
        return;
    if (h->InheritsFrom(TH1::Class()) && x->InheritsFrom(TH1::Class()))
    {
        SetBinning(h, ((TH1*)x)->GetXaxis());
        return;
    }
}

// --------------------------------------------------------------------------
//
// Multiplies all entries in a TArrayD by a float f
//
void MH::ScaleArray(TArrayD &bins, Double_t f)
{
    for (int i=0; i<bins.GetSize(); i++)
        bins[i] *= f;
}

// --------------------------------------------------------------------------
//
// Scales the binning of a TAxis by a float f
//
TArrayD MH::ScaleAxis(TAxis &axe, Double_t f)
{
    TArrayD arr(axe.GetNbins()+1);

    for (int i=1; i<=axe.GetNbins()+1; i++)
        arr[i-1] = axe.GetBinLowEdge(i);

    ScaleArray(arr, f);

    return arr;
}

// --------------------------------------------------------------------------
//
// Scales the binning of one, two or three axis of a histogram by a float f
//
void MH::ScaleAxis(TH1 *h, Double_t fx, Double_t fy, Double_t fz)
{
    if (h->InheritsFrom(TH3::Class()))
    {
        SetBinning((TH3*)h,
                   ScaleAxis(*h->GetXaxis(), fx),
                   ScaleAxis(*h->GetYaxis(), fy),
                   ScaleAxis(*h->GetZaxis(), fz));
        return;
    }

    if (h->InheritsFrom(TH2::Class()))
    {
        SetBinning((TH2*)h,
                   ScaleAxis(*h->GetXaxis(), fx),
                   ScaleAxis(*h->GetYaxis(), fy));
        return;
    }

    if (h->InheritsFrom(TH1::Class()))
        SetBinning(h, ScaleAxis(*h->GetXaxis(), fx));
}

// --------------------------------------------------------------------------
//
// Tries to find a MBinning container with the name "Binning"+name
// in the given parameter list. If it was found it is applied to the
// given histogram. This is only valid for 1D-histograms
//
Bool_t MH::ApplyBinning(const MParList &plist, TString name, TH1 *h)
{
    if (h->InheritsFrom(TH2::Class()) || h->InheritsFrom(TH3::Class()))
    {
        gLog << warn << "MH::ApplyBinning: '" << h->GetName() << "' is not a basic TH1 object... no binning applied." << endl;
        return kFALSE;
    }

    const MBinning *bins = (MBinning*)plist.FindObject("Binning"+name);
    if (!bins)
    {
        gLog << inf << "Object 'Binning" << name << "' [MBinning] not found... no binning applied." << endl;
        return kFALSE;
    }

    SetBinning(h, bins);
    return kTRUE;
}

void MH::FindGoodLimits(Int_t nbins, Int_t &newbins, Double_t &xmin, Double_t &xmax, Bool_t isInteger)
{
#if ROOT_VERSION_CODE > ROOT_VERSION(3,04,01)
    THLimitsFinder::OptimizeLimits(nbins, newbins, xmin, xmax, isInteger);
#else
//*-*-*-*-*-*-*-*-*Find reasonable bin values*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
//*-*              ==========================

    Double_t dx = 0.1*(xmax-xmin);
    Double_t umin = xmin - dx;
    Double_t umax = xmax + dx;

    if (umin < 0 && xmin >= 0)
        umin = 0;

    if (umax > 0 && xmax <= 0)
        umax = 0;

    Double_t binlow  =0;
    Double_t binhigh =0;
    Double_t binwidth=0;

    TGaxis::Optimize(umin, umax, nbins, binlow, binhigh, nbins, binwidth, "");

    if (binwidth <= 0 || binwidth > 1.e+39)
    {
        xmin = -1;
        xmax = 1;
    }
    else
    {
        xmin = binlow;
        xmax = binhigh;
    }

    if (isInteger)
    {
        Int_t ixmin = (Int_t)xmin;
        Int_t ixmax = (Int_t)xmax;
        Double_t dxmin = (Double_t)ixmin;
        Double_t dxmax = (Double_t)ixmax;

        xmin = xmin<0 && xmin!=dxmin ? dxmin - 1 : dxmin;
        xmax = xmax>0 && xmax!=dxmax ? dxmax + 1 : dxmax;

        if (xmin>=xmax)
            xmax = xmin+1;

        Int_t bw = 1 + (Int_t)((xmax-xmin)/nbins);

        nbins = (Int_t)((xmax-xmin)/bw);

        if (xmin+nbins*bw < xmax)
        {
            nbins++;
            xmax = xmin +nbins*bw;
        }
    }

    newbins = nbins;
#endif
}

// --------------------------------------------------------------------------
//
//  Returns the lowest entry in a histogram which is greater than gt (eg >0)
//
Double_t MH::GetMinimumGT(const TH1 &h, Double_t gt)
{
    Double_t min = FLT_MAX;

    const TAxis &axex = *((TH1&)h).GetXaxis();
    const TAxis &axey = *((TH1&)h).GetYaxis();
    const TAxis &axez = *((TH1&)h).GetZaxis();

    for (int iz=1; iz<=axez.GetNbins(); iz++)
        for (int iy=1; iy<=axey.GetNbins(); iy++)
            for (int ix=1; ix<=axex.GetNbins(); ix++)
            {
                const Double_t v = h.GetBinContent(h.GetBin(ix, iy, iz));
                if (gt<v && v<min)
                    min = v;
            }
    return min;
}

// --------------------------------------------------------------------------
//
//  Returns the bin center in a logarithmic scale. If the given bin
//  number is <1 it is set to 1. If it is =GetNbins() it is set to
//  GetNbins()
//
Double_t MH::GetBinCenterLog(const TAxis &axe, Int_t nbin)
{
    if (nbin>axe.GetNbins())
        nbin = axe.GetNbins();

    if (nbin<1)
        nbin = 1;

    const Double_t lo = axe.GetBinLowEdge(nbin);
    const Double_t hi = axe.GetBinUpEdge(nbin);

    const Double_t val = log10(lo) + log10(hi);

    return pow(10, val/2);
}

// --------------------------------------------------------------------------
//
// Draws a copy of the two given histograms. Uses title as the pad title.
// Also layout the two statistic boxes and a legend.
//
void MH::DrawSameCopy(const TH1 &hist1, const TH1 &hist2, const TString title)
{
    //
    // Draw first histogram
    //
    TH1 *h1 = ((TH1&)hist1).DrawCopy();
    gPad->SetBorderMode(0);
    gPad->Update();

    // FIXME: Also align max/min with set Maximum/Minimum
    const Double_t maxbin1 = hist1.GetBinContent(hist1.GetMaximumBin());
    const Double_t maxbin2 = hist2.GetBinContent(hist2.GetMaximumBin());
    const Double_t minbin1 = hist1.GetBinContent(hist1.GetMinimumBin());
    const Double_t minbin2 = hist2.GetBinContent(hist2.GetMinimumBin());

    const Double_t max = TMath::Max(maxbin1, maxbin2);
    const Double_t min = TMath::Min(minbin1, minbin2);

    h1->SetMaximum(max>0?max*1.05:max*0.95);
    h1->SetMinimum(max>0?min*0.95:min*1.05);

    TPaveText *t = (TPaveText*)gPad->FindObject("title");
    if (t)
    {
        t->SetName((TString)"MHTitle");     // rename object
        t->Clear();                         // clear old lines
        t->AddText((TString)" "+title+" "); // add the new title
        t->SetBit(kCanDelete);              // make sure object is deleted

        //
        // FIXME: This is a stupid workaround to hide the redrawn
        // (see THistPainter::PaintTitle) title
        //
        gPad->Modified();  // indicates a change
        gPad->Update();    // recreates the original title
        t->Pop();          // bring our title on top
    }

    //
    // Rename first statistics box
    //
    TPaveStats *s1 = (TPaveStats*)gPad->FindObject("stats");
    if (!s1)
        s1 = (TPaveStats*)hist1.GetListOfFunctions()->FindObject("stats");
    else
        s1->SetName((TString)"Stat"+hist1.GetTitle());

    if (s1 && s1->GetX2NDC()>0.95)
    {
        const Double_t x1 = s1->GetX1NDC()-0.01;
        s1->SetX1NDC(x1-(s1->GetX2NDC()-s1->GetX1NDC()));
        s1->SetX2NDC(x1);
    }

    //
    // Draw second histogram
    //
    TH1 *h2 = ((TH1&)hist2).DrawCopy("sames");
    gPad->Update();

    //
    // Draw Legend
    //
    TPaveStats *s2 = (TPaveStats*)gPad->FindObject("stats");
    if (!s2)
        s2 = (TPaveStats*)hist2.GetListOfFunctions()->FindObject("stats");

    if (s2)
    {
        TLegend &l = *new TLegend(s2->GetX1NDC(),
                                  s2->GetY1NDC()-0.015-(s2->GetY2NDC()-s2->GetY1NDC())/2,
                                  s2->GetX2NDC(),
                                  s2->GetY1NDC()-0.01
                                 );
        l.AddEntry(h1, h1->GetTitle());
        l.AddEntry(h2, h2->GetTitle());
        l.SetTextSize(s2->GetTextSize());
        l.SetTextFont(s2->GetTextFont());
        l.SetBorderSize(s2->GetBorderSize());
        l.SetBit(kCanDelete);
        l.Draw();
    }
}

// --------------------------------------------------------------------------
//
// Draws the two given histograms. Uses title as the pad title.
// Also layout the two statistic boxes and a legend.
//
void MH::DrawSame(TH1 &hist1, TH1 &hist2, const TString title)
{
    //
    // Draw first histogram
    //
    hist1.Draw();
    gPad->SetBorderMode(0);
    gPad->Update();

    if (hist1.GetEntries()>0 && hist2.GetEntries()>0)
    {
        const Double_t maxbin1 = hist1.GetBinContent(hist1.GetMaximumBin());
        const Double_t maxbin2 = hist2.GetBinContent(hist2.GetMaximumBin());
        const Double_t minbin1 = hist1.GetBinContent(hist1.GetMinimumBin());
        const Double_t minbin2 = hist2.GetBinContent(hist2.GetMinimumBin());

        const Double_t max = TMath::Max(maxbin1, maxbin2);
        const Double_t min = TMath::Min(minbin1, minbin2);

        if (max!=min)
        {
            hist1.SetMaximum(max>0?max*1.05:max*0.95);
            hist1.SetMinimum(max>0?min*0.95:min*1.05);
        }
    }

    TPaveText *t = (TPaveText*)gPad->FindObject("title");
    if (t)
    {
        t->SetName((TString)"MHTitle");     // rename object
        t->Clear();                         // clear old lines
        t->AddText((TString)" "+title+" "); // add the new title
        t->SetBit(kCanDelete);              // make sure object is deleted

        //
        // FIXME: This is a stupid workaround to hide the redrawn
        // (see THistPainter::PaintTitle) title
        //
        gPad->Modified();  // indicates a change
        gPad->Update();    // recreates the original title
        t->Pop();          // bring our title on top
    }

    //
    // Rename first statistics box
    //
    // Where to get the TPaveStats depends on the root version
    TPaveStats *s1 = (TPaveStats*)gPad->FindObject("stats");
    if (!s1)
        s1 = (TPaveStats*)hist1.GetListOfFunctions()->FindObject("stats");
    else
        s1->SetName((TString)"Stat"+hist1.GetTitle());

    if (s1 && s1->GetX2NDC()>0.95)
    {
        const Double_t x1 = s1->GetX1NDC()-0.01;
        s1->SetX1NDC(x1-(s1->GetX2NDC()-s1->GetX1NDC()));
        s1->SetX2NDC(x1);
    }

    //
    // Draw second histogram
    //
    hist2.Draw("sames");
    gPad->Update();

    //
    // Draw Legend
    //
    // Where to get the TPaveStats depends on the root version
    TPaveStats *s2 = (TPaveStats*)gPad->FindObject("stats");
    if (!s2)
        s2 = (TPaveStats*)hist2.GetListOfFunctions()->FindObject("stats");

    if (s2)
    {
        TLegend &l = *new TLegend(s2->GetX1NDC(),
                                  s2->GetY1NDC()-0.015-(s2->GetY2NDC()-s2->GetY1NDC())/2,
                                  s2->GetX2NDC(),
                                  s2->GetY1NDC()-0.01
                                 );
        l.AddEntry(&hist1, hist1.GetTitle());
        l.AddEntry(&hist2, hist2.GetTitle());
        l.SetTextSize(s2->GetTextSize());
        l.SetTextFont(s2->GetTextFont());
        l.SetBorderSize(s2->GetBorderSize());
        l.SetBit(kCanDelete);
        l.Draw();
    }
}

// --------------------------------------------------------------------------
//
// If the opt string contains 'nonew' or gPad is not given NULL is returned.
// Otherwise the present gPad is returned.
//
TVirtualPad *MH::GetNewPad(TString &opt)
{
    opt.ToLower();

    if (!opt.Contains("nonew"))
        return NULL;

    opt.ReplaceAll("nonew", "");

    return gPad;
}

// --------------------------------------------------------------------------
//
// Encapsulate the TObject::Clone such, that a cloned TH1 (or derived)
// object is not added to the current directory, when cloned.
//
TObject *MH::Clone(const char *name) const
{
    const Bool_t store = TH1::AddDirectoryStatus();

    TH1::AddDirectory(kFALSE);
    TObject *o = MParContainer::Clone(name);
    TH1::AddDirectory(store);

    return o;
}

// --------------------------------------------------------------------------
//
// If the opt string contains 'nonew' or gPad is not given a new canvas
// with size w/h is created. Otherwise the object is cloned and drawn
// to the present pad. The kCanDelete bit is set for the clone.
//
TObject *MH::DrawClone(Option_t *opt, Int_t w, Int_t h) const
{
    TString option(opt);

    TVirtualPad *p = GetNewPad(option);
    if (!p)
        p = MakeDefCanvas(this, w, h);
    else
        if (!option.Contains("same", TString::kIgnoreCase))
            p->Clear();

    gROOT->SetSelectedPad(NULL);

    TObject *o = MParContainer::DrawClone(option);
    o->SetBit(kCanDelete);
    return o;
}

// --------------------------------------------------------------------------
//
// Check whether a class inheriting from MH overwrites the Draw function
//
Bool_t MH::OverwritesDraw(TClass *cls) const
{
    if (!cls)
        cls = IsA();

    //
    // Check whether we reached the base class MTask
    //
    if (TString(cls->GetName())=="MH")
        return kFALSE;

    //
    // Check whether the class cls overwrites Draw
    //
    if (cls->GetMethodAny("Draw"))
        return kTRUE;

    //
    // If the class itself doesn't overload it check all it's base classes
    //
    TBaseClass *base=NULL;
    TIter NextBase(cls->GetListOfBases());
    while ((base=(TBaseClass*)NextBase()))
    {
        if (OverwritesDraw(base->GetClassPointer()))
            return kTRUE;
    }

    return kFALSE;
}

// --------------------------------------------------------------------------
//
//  Cuts the bins containing only zeros at the edges.
//
//  A new number of bins can be defined with nbins != 0
//        In the case of nbins == 0, no rebinning will take place
//
//  Returns the new (real) number of bins
//
Int_t MH::StripZeros(TH1 *h, Int_t nbins)
{
    TAxis &axe = *h->GetXaxis();

    const Int_t min1   = axe.GetFirst();
    const Int_t max1   = axe.GetLast();
    const Int_t range1 = max1-min1;

    //
    // Check for useless zeros
    //
    if (range1 == 0)
        return 0;

    Int_t min2 = 0;
    for (int i=min1; i<=max1; i++)
        if (h->GetBinContent(i) != 0)
        {
            min2 = i;
            break;
        }

    //
    // If the histogram consists of zeros only
    //
    if (min2 == max1)
        return 0;

    Int_t max2 = 0;
    for (int i=max1; i>=min2; i--)
        if (h->GetBinContent(i) != 0)
        {
            max2 = i;
            break;
        }

    //
    // Appying TAxis->SetRange before ReBin does not work ...
    // But this workaround helps quite fine
    //
    Axis_t min = h->GetBinLowEdge(min2);
    Axis_t max = h->GetBinLowEdge(max2)+h->GetBinWidth(max2);

    Int_t nbins2 = max2-min2;
    //
    // Check for rebinning
    //
    if (nbins > 0)
      {
        const Int_t ngroup = (Int_t)(nbins2*h->GetNbinsX()/nbins/(max1-min1));
        if (ngroup > 1)
          {
            h->Rebin(ngroup);
            nbins2 /= ngroup;
          }
      }
    
    Int_t newbins = 0;
    FindGoodLimits(nbins2, newbins, min, max, kFALSE);
    axe.SetRangeUser(min,max);
    return axe.GetLast()-axe.GetFirst();
}

void MH::ProjectionX(TH1D &dest, const TH2 &src, Int_t firstybin, Int_t lastybin)
{
    //*-*-*-*-*Project a 2-D histogram into a 1-D histogram along X*-*-*-*-*-*-*
    //*-*      ====================================================
    //
    //   The projection dest is always of the type TH1D.
    //   The projection is made from the channels along the Y axis
    //   ranging from firstybin to lastybin included.
    //   By default, bins 1 to ny are included
    //   When all bins are included, the number of entries in the projection
    //   is set to the number of entries of the 2-D histogram, otherwise
    //   the number of entries is incremented by 1 for all non empty cells.
    //
    //   if Sumw2() was called for dest, the errors are computed.
    //
    TAxis &axex = *((TH2&)src).GetXaxis();
    TAxis &axey = *((TH2&)src).GetYaxis();

    const Int_t nx = axex.GetNbins();
    const Int_t ny = axey.GetNbins();
    if (firstybin < 0)
        firstybin = 1;
    if (lastybin > ny)
        lastybin = ny;

    dest.Reset();
    SetBinning(&dest, &axex);

    // Create the projection histogram
    const Bool_t computeErrors = dest.GetSumw2N() ? 1 : 0;

    // Fill the projected histogram
    for (Int_t binx=0; binx<=nx+1; binx++)
    {
        Double_t err2 = 0;
        for (Int_t biny=firstybin; biny<=lastybin; biny++)
        {
            const Double_t cont = src.GetCellContent(binx,biny);
            const Double_t err1 = src.GetCellError(binx,biny);
            err2 += err1*err1;
            if (cont)
                dest.Fill(axex.GetBinCenter(binx), cont);
        }
        if (computeErrors)
            dest.SetBinError(binx, TMath::Sqrt(err2));
    }
    if (firstybin <=1 && lastybin >= ny)
        dest.SetEntries(src.GetEntries());
}

void MH::ProjectionY(TH1D &dest, const TH2 &src, Int_t firstxbin, Int_t lastxbin)
{
    //*-*-*-*-*Project a 2-D histogram into a 1-D histogram along X*-*-*-*-*-*-*
    //*-*      ====================================================
    //
    //   The projection dest is always of the type TH1D.
    //   The projection is made from the channels along the Y axis
    //   ranging from firstybin to lastybin included.
    //   By default, bins 1 to ny are included
    //   When all bins are included, the number of entries in the projection
    //   is set to the number of entries of the 2-D histogram, otherwise
    //   the number of entries is incremented by 1 for all non empty cells.
    //
    //   if Sumw2() was called for dest, the errors are computed.
    //
    TAxis &axex = *((TH2&)src).GetXaxis();
    TAxis &axey = *((TH2&)src).GetYaxis();

    const Int_t nx = axex.GetNbins();
    const Int_t ny = axey.GetNbins();
    if (firstxbin < 0)
        firstxbin = 1;
    if (lastxbin > nx)
        lastxbin = nx;

    dest.Reset();
    SetBinning(&dest, &axey);

    // Create the projection histogram
    const Bool_t computeErrors = dest.GetSumw2N() ? 1 : 0;

    // Fill the projected histogram
    for (Int_t biny=0; biny<=ny+1; biny++)
    {
        Double_t err2 = 0;
        for (Int_t binx=firstxbin; binx<=lastxbin; binx++)
        {
            const Double_t cont = src.GetCellContent(binx,biny);
            const Double_t err1 = src.GetCellError(binx,biny);
            err2 += err1*err1;
            if (cont)
                dest.Fill(axey.GetBinCenter(biny), cont);
        }
        if (computeErrors)
            dest.SetBinError(biny, TMath::Sqrt(err2));
    }
    if (firstxbin <=1 && lastxbin >= nx)
        dest.SetEntries(src.GetEntries());
}

// --------------------------------------------------------------------------
//
// In contradiction to TPad::FindObject this function searches recursively
// in a pad for an object. gPad is the default.
//
TObject *MH::FindObjectInPad(const char *name, TVirtualPad *pad)
{
    if (!pad)
        pad = gPad;

    if (!pad)
        return NULL;

    TObject *o;

    TIter Next(pad->GetListOfPrimitives());
    while ((o=Next()))
    {
        if (!strcmp(o->GetName(), name))
            return o;

        if (o->InheritsFrom("TPad"))
            if ((o = FindObjectInPad(name, (TVirtualPad*)o)))
                return o;
    }
    return NULL;
}

// --------------------------------------------------------------------------
//
// M.Gaug added this withouz Documentation
//
TH1I* MH::ProjectArray(const TArrayF &array, Int_t nbins, const char* name, const char* title)
{
    const Int_t size = array.GetSize();

    TH1I *h1=0;

    //check if histogram with identical name exist
    TObject *h1obj = gROOT->FindObject(name);
    if (h1obj && h1obj->InheritsFrom("TH1I"))
    {
        h1 = (TH1I*)h1obj;
        h1->Reset();
    }

    Double_t min = size>0 ? array[0] : 0;
    Double_t max = size>0 ? array[0] : 1;

    // first loop over array to find the min and max
    for (Int_t i=1; i<size;i++)
    {
        max = TMath::Max((Double_t)array[i], max);
        min = TMath::Min((Double_t)array[i], min);
    }

    Int_t newbins = 0;
    FindGoodLimits(nbins, newbins, min, max, kFALSE);

    if (!h1)
    {
        h1 = new TH1I(name, title, nbins, min, max);
        h1->SetXTitle("");
        h1->SetYTitle("Counts");
        h1->SetDirectory(gROOT);
    }

    // Second loop to fill the histogram
    for (Int_t i=0;i<size;i++)
        h1->Fill(array[i]);

    return h1;
}

// --------------------------------------------------------------------------
//
// M.Gaug added this withouz Documentation
//
TH1I* MH::ProjectArray(const TArrayD &array, Int_t nbins, const char* name, const char* title)
{
    const Int_t size = array.GetSize();
    TH1I *h1=0;

    //check if histogram with identical name exist
    TObject *h1obj = gROOT->FindObject(name);
    if (h1obj && h1obj->InheritsFrom("TH1I"))
    {
        h1 = (TH1I*)h1obj;
        h1->Reset();
    }

    Double_t min = size>0 ? array[0] : 0;
    Double_t max = size>0 ? array[0] : 1;

    // first loop over array to find the min and max
    for (Int_t i=1; i<size;i++)
    {
        max = TMath::Max(array[i], max);
        min = TMath::Min(array[i], min);
    }

    Int_t newbins = 0;
    FindGoodLimits(nbins, newbins, min, max, kFALSE);

    if (!h1)
    {
        h1 = new TH1I(name, title, newbins, min, max);
        h1->SetXTitle("");
        h1->SetYTitle("Counts");
        h1->SetDirectory(gROOT);
    }

    // Second loop to fill the histogram
    for (Int_t i=0;i<size;i++)
        h1->Fill(array[i]);

    return h1;
}