TAxis.cxx

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// @(#)root/hist:$Id$
// Author: Rene Brun   12/12/94

/*************************************************************************
 * Copyright (C) 1995-2000, Rene Brun and Fons Rademakers.               *
 * All rights reserved.                                                  *
 *                                                                       *
 * For the licensing terms see $ROOTSYS/LICENSE.                         *
 * For the list of contributors see $ROOTSYS/README/CREDITS.             *
 *************************************************************************/

#include "Riostream.h"
#include "TAxis.h"
#include "TVirtualPad.h"
#include "TStyle.h"
#include "TError.h"
#include "THashList.h"
#include "TList.h"
#include "TAxisModLab.h"
#include "TH1.h"
#include "TObjString.h"
#include "TDatime.h"
#include "TTimeStamp.h"
#include "TROOT.h"
#include "TClass.h"
#include "TMath.h"
#include <time.h>
#include <cassert>

ClassImp(TAxis);

////////////////////////////////////////////////////////////////////////////////
/** \class TAxis
    \ingroup Hist
    \brief Class to manage histogram axis

This class manages histogram axis. It is referenced by TH1 and TGraph.
To make a graphical representation of an histogram axis, this class
references the TGaxis class. TAxis supports axis with fixed or variable bin sizes.
Labels may be associated to individual bins.
See examples of various axis representations drawn by class TGaxis.
*///////////////////////////////////////////////////////////////////////////////

////////////////////////////////////////////////////////////////////////////////
/// Default constructor.

TAxis::TAxis(): TNamed(), TAttAxis()
{
   fNbins   = 1;
   fXmin    = 0;
   fXmax    = 1;
   fFirst   = 0;
   fLast    = 0;
   fParent  = 0;
   fLabels  = 0;
   fModLabs = 0;
   fBits2   = 0;
   fTimeDisplay = 0;
}

////////////////////////////////////////////////////////////////////////////////
/// Axis constructor for axis with fix bin size

TAxis::TAxis(Int_t nbins,Double_t xlow,Double_t xup): TNamed(), TAttAxis()
{
   fParent  = 0;
   fLabels  = 0;
   fModLabs = 0;
   Set(nbins,xlow,xup);
}

////////////////////////////////////////////////////////////////////////////////
/// Axis constructor for variable bin size

TAxis::TAxis(Int_t nbins,const Double_t *xbins): TNamed(), TAttAxis()
{
   fParent  = 0;
   fLabels  = 0;
   fModLabs = 0;
   Set(nbins,xbins);
}

////////////////////////////////////////////////////////////////////////////////
/// Destructor.

TAxis::~TAxis()
{
   if (fLabels) {
      fLabels->Delete();
      delete fLabels;
      fLabels = 0;
   }
   if (fModLabs) {
      fModLabs->Delete();
      delete fModLabs;
      fModLabs = 0;
   }
}

////////////////////////////////////////////////////////////////////////////////
/// Copy constructor.

TAxis::TAxis(const TAxis &axis) : TNamed(axis), TAttAxis(axis), fLabels(0), fModLabs(0)
{
   axis.Copy(*this);
}

////////////////////////////////////////////////////////////////////////////////
/// Assignment operator.

TAxis& TAxis::operator=(const TAxis &orig)
{
   orig.Copy( *this );
   return *this;
}


////////////////////////////////////////////////////////////////////////////////
/// Choose a reasonable time format from the coordinates in the active pad
/// and the number of divisions in this axis
/// If orientation = "X", the horizontal axis of the pad will be used for ref.
/// If orientation = "Y", the vertical axis of the pad will be used for ref.

const char *TAxis::ChooseTimeFormat(Double_t axislength)
{
   const char *formatstr = nullptr;
   Int_t reasformat = 0;
   Int_t ndiv,nx1,nx2,n;
   Double_t awidth;
   Double_t length;

   if (!axislength) {
      length = gPad->GetUxmax() - gPad->GetUxmin();
   } else {
      length = axislength;
   }

   ndiv = GetNdivisions();
   if (ndiv > 1000) {
      nx2   = ndiv/100;
      nx1   = TMath::Max(1, ndiv%100);
      ndiv = 100*nx2 + Int_t(Double_t(nx1)*gPad->GetAbsWNDC());
   }
   ndiv = TMath::Abs(ndiv);
   n = ndiv - (ndiv/100)*100;
   awidth = length/n;

//  width in seconds ?
   if (awidth>=.5) {
      reasformat = 1;
//  width in minutes ?
      if (awidth>=30) {
         awidth /= 60; reasformat = 2;
//   width in hours ?
         if (awidth>=30) {
            awidth /=60; reasformat = 3;
//   width in days ?
            if (awidth>=12) {
               awidth /= 24; reasformat = 4;
//   width in months ?
               if (awidth>=15.218425) {
                  awidth /= 30.43685; reasformat = 5;
//   width in years ?
                  if (awidth>=6) {
                     awidth /= 12; reasformat = 6;
                     if (awidth>=2) {
                        awidth /= 12; reasformat = 7;
                     }
                  }
               }
            }
         }
      }
   }
//   set reasonable format
   switch (reasformat) {
      case 0:
        formatstr = "%S";
        break;
      case 1:
        formatstr = "%Mm%S";
        break;
      case 2:
        formatstr = "%Hh%M";
        break;
      case 3:
        formatstr = "%d-%Hh";
        break;
      case 4:
        formatstr = "%d/%m";
        break;
      case 5:
        formatstr = "%d/%m/%y";
        break;
      case 6:
        formatstr = "%d/%m/%y";
        break;
      case 7:
        formatstr = "%m/%y";
        break;
   }
   return formatstr;
}

////////////////////////////////////////////////////////////////////////////////
/// Copy axis structure to another axis

void TAxis::Copy(TObject &obj) const
{
   TNamed::Copy(obj);
   TAttAxis::Copy(((TAxis&)obj));
   TAxis &axis( ((TAxis&)obj) );
   axis.fNbins  = fNbins;
   axis.fXmin   = fXmin;
   axis.fXmax   = fXmax;
   axis.fFirst  = fFirst;
   axis.fLast   = fLast;
   axis.fBits2  = fBits2;
   fXbins.Copy(axis.fXbins);
   axis.fTimeFormat   = fTimeFormat;
   axis.fTimeDisplay  = fTimeDisplay;
   axis.fParent       = fParent;
   if (axis.fLabels) {
      axis.fLabels->Delete();
      delete axis.fLabels;
      axis.fLabels = 0;
   }
   if (fLabels) {
      //Properly handle case where not all bins have labels
      TIter next(fLabels);
      TObjString *label;
      if(! axis.fLabels) {
         axis.fLabels = new THashList(axis.fNbins, 3);
      }
      while( (label=(TObjString*)next()) ) {
         TObjString *copyLabel = new TObjString(*label);
         axis.fLabels->Add(copyLabel);
         copyLabel->SetUniqueID(label->GetUniqueID());
      }
   }
   if (axis.fModLabs) {
      axis.fModLabs->Delete();
      delete axis.fModLabs;
      axis.fModLabs = 0;
   }
}

////////////////////////////////////////////////////////////////////////////////
/// Compute distance from point px,py to an axis

Int_t TAxis::DistancetoPrimitive(Int_t, Int_t)
{
   return 9999;
}

////////////////////////////////////////////////////////////////////////////////
/// Execute action corresponding to one event
///
///  This member function is called when an axis is clicked with the locator.
///  The axis range is set between the position where the mouse is pressed
///  and the position where it is released.
///  If the mouse position is outside the current axis range when it is released
///  the axis is unzoomed with the corresponding proportions.
///  Note that the mouse does not need to be in the pad or even canvas
///  when it is released.

void TAxis::ExecuteEvent(Int_t event, Int_t px, Int_t py)
{
   if (!gPad) return;
   gPad->ExecuteEventAxis(event,px,py,this);
}

////////////////////////////////////////////////////////////////////////////////
/// Find bin number corresponding to abscissa x. NOTE: this method does not work with alphanumeric bins !!!
///
/// If x is underflow or overflow, attempt to extend the axis if TAxis::kCanExtend is true.
/// Otherwise, return 0 or fNbins+1.

Int_t TAxis::FindBin(Double_t x)
{
   Int_t bin;
   // NOTE: This should not be allowed for Alphanumeric histograms,
   // but it is heavily used (legacy) in the TTreePlayer to fill alphanumeric histograms.
   // but in case of alphanumeric do-not extend the axis. It makes no sense
   if (IsAlphanumeric() && gDebug) Info("FindBin","Numeric query on alphanumeric axis - Sorting the bins or extending the axes / rebinning can alter the correspondence between the label and the bin interval.");
   if (x < fXmin) {              //*-* underflow
      bin = 0;
      if (fParent == 0) return bin;
      if (!CanExtend() || IsAlphanumeric() ) return bin;
      ((TH1*)fParent)->ExtendAxis(x,this);
      return FindFixBin(x);
   } else  if ( !(x < fXmax)) {     //*-* overflow  (note the way to catch NaN)
      bin = fNbins+1;
      if (fParent == 0) return bin;
      if (!CanExtend() || IsAlphanumeric() ) return bin;
      ((TH1*)fParent)->ExtendAxis(x,this);
      return FindFixBin(x);
   } else {
      if (!fXbins.fN) {        //*-* fix bins
         bin = 1 + int (fNbins*(x-fXmin)/(fXmax-fXmin) );
      } else {                  //*-* variable bin sizes
         //for (bin =1; x >= fXbins.fArray[bin]; bin++);
         bin = 1 + TMath::BinarySearch(fXbins.fN,fXbins.fArray,x);
      }
   }
   return bin;
}

////////////////////////////////////////////////////////////////////////////////
/// Find bin number with label.
/// If the List of labels does not exist create it and make the axis alphanumeric
/// If one wants just to add a single label- just call TAxis::SetBinLabel
/// If label is not in the list of labels do the following depending on the
/// bit TAxis::kCanExtend; of the axis.
///   - if the bit is set add the new label and if the number of labels exceeds
///      the number of bins, double the number of bins via TH1::LabelsInflate
///   - if the bit is not set and the histogram has labels in each bin
///        set the bit automatically and consider the histogram as alphanumeric
///     if histogram has only some bins with labels then the histogram is not
///     consider alphanumeric and return -1
///
/// -1 is returned only when the Axis has no parent histogram

Int_t TAxis::FindBin(const char *label)
{
   //create list of labels if it does not exist yet
   if (!fLabels) {
      if (!fParent) return -1;
      fLabels = new THashList(fNbins,3);
      // we set the axis alphanumeric
      // when list of labels does not exist
      // do we want to do this also when histogram is not empty ?????
      if (CanBeAlphanumeric() ) {
         SetCanExtend(kTRUE);
         SetAlphanumeric(kTRUE);
         if (fXmax <= fXmin) {
            //L.M. Dec 2010 in case of no min and max specified use 0 ->NBINS
            fXmin = 0;
            fXmax = fNbins;
         }
      }
   }

   // search for label in the existing list and return it if it exists
   TObjString *obj = (TObjString*)fLabels->FindObject(label);
   if (obj) return (Int_t)obj->GetUniqueID();

   // if labels is not in the list and we have already labels
   if (!IsAlphanumeric()) {
      // if bins without labels exist or if the axis cannot be set to alphanumeric
      if (HasBinWithoutLabel() || !CanBeAlphanumeric() ) {
         Info("FindBin","Label %s is not in the list and the axis is not alphanumeric - ignore it",label);
         return -1;
      }
      else {
         Info("FindBin","Label %s not in the list. It will be added to the histogram",label);
         SetCanExtend(kTRUE);
         SetAlphanumeric(kTRUE);
      }
   }

   //Not yet in the list. Can we extend the axis ?
   assert ( CanExtend() && IsAlphanumeric() );
   // {
   //    if (gDebug>0)
   //       Info("FindBin","Label %s is not in the list and the axis cannot be extended - the entry will be added in the underflow bin",label);
   //    return 0;
   // }

   Int_t n = fLabels->GetEntries();

   //may be we have to resize the histogram (doubling number of channels)
   if (n >= fNbins) ((TH1*)fParent)->LabelsInflate(GetName());

   //add new label to the list: assign bin number
   obj = new TObjString(label);
   fLabels->Add(obj);
   obj->SetUniqueID(n+1);
   return n+1;
}

////////////////////////////////////////////////////////////////////////////////
/// Find bin number with label.
/// If the List of labels does not exist or the label doe not exist just return -1 .
/// Do not attempt to modify the axis. This is different than FindBin

Int_t TAxis::FindFixBin(const char *label) const
{
   //create list of labels if it does not exist yet
   if (!fLabels) return -1;

   // search for label in the existing list and return it if it exists
   TObjString *obj = (TObjString*)fLabels->FindObject(label);
   if (obj) return (Int_t)obj->GetUniqueID();
   return -1;
}


////////////////////////////////////////////////////////////////////////////////
/// Find bin number corresponding to abscissa x
///
/// Identical to TAxis::FindBin except that if x is an underflow/overflow
/// no attempt is made to extend the axis.

Int_t TAxis::FindFixBin(Double_t x) const
{
   Int_t bin;
   if (x < fXmin) {              //*-* underflow
      bin = 0;
   } else  if ( !(x < fXmax)) {     //*-* overflow  (note the way to catch NaN
      bin = fNbins+1;
   } else {
      if (!fXbins.fN) {        //*-* fix bins
         bin = 1 + int (fNbins*(x-fXmin)/(fXmax-fXmin) );
      } else {                  //*-* variable bin sizes
//         for (bin =1; x >= fXbins.fArray[bin]; bin++);
         bin = 1 + TMath::BinarySearch(fXbins.fN,fXbins.fArray,x);
      }
   }
   return bin;
}

////////////////////////////////////////////////////////////////////////////////
/// Return label for bin

const char *TAxis::GetBinLabel(Int_t bin) const
{
   if (!fLabels) return "";
   if (bin <= 0 || bin > fNbins) return "";
   TIter next(fLabels);
   TObjString *obj;
   while ((obj=(TObjString*)next())) {
      Int_t binid = (Int_t)obj->GetUniqueID();
      if (binid == bin) return obj->GetName();
   }
   return "";
}

////////////////////////////////////////////////////////////////////////////////
/// Return first bin on the axis
/// i.e. 1 if no range defined
/// NOTE: in some cases a zero is returned (see TAxis::SetRange)

Int_t TAxis::GetFirst() const
{
   if (!TestBit(kAxisRange)) return 1;
   return fFirst;
}

////////////////////////////////////////////////////////////////////////////////
/// Return last bin on the axis
/// i.e. fNbins if no range defined
/// NOTE: in some cases a zero is returned (see TAxis::SetRange)

Int_t TAxis::GetLast() const
{
   if (!TestBit(kAxisRange)) return fNbins;
   return fLast;
}

////////////////////////////////////////////////////////////////////////////////
/// Return center of bin

Double_t TAxis::GetBinCenter(Int_t bin) const
{
   Double_t binwidth;
   if (!fXbins.fN || bin<1 || bin>fNbins) {
      binwidth = (fXmax - fXmin) / Double_t(fNbins);
      return fXmin + (bin-1) * binwidth + 0.5*binwidth;
   } else {
      binwidth = fXbins.fArray[bin] - fXbins.fArray[bin-1];
      return fXbins.fArray[bin-1] + 0.5*binwidth;
   }
}

////////////////////////////////////////////////////////////////////////////////
/// Return center of bin in log
/// With a log-equidistant binning for a bin with low and up edges, the mean is :
/// 0.5*(ln low + ln up) i.e. sqrt(low*up) in logx (e.g. sqrt(10^0*10^2) = 10).
/// Imagine a bin with low=1 and up=100 :
/// - the center in lin is (100-1)/2=50.5
/// - the center in log would be sqrt(1*100)=10 (!=log(50.5))
///
/// NB: if the low edge of the bin is negative, the function returns the bin center
///     as computed by TAxis::GetBinCenter

Double_t TAxis::GetBinCenterLog(Int_t bin) const
{
   Double_t low,up;
   if (!fXbins.fN || bin<1 || bin>fNbins) {
      Double_t binwidth = (fXmax - fXmin) / Double_t(fNbins);
      low = fXmin + (bin-1) * binwidth;
      up  = low+binwidth;
   } else {
      low = fXbins.fArray[bin-1];
      up  = fXbins.fArray[bin];
   }
   if (low <=0 ) return GetBinCenter(bin);
   return TMath::Sqrt(low*up);
}
////////////////////////////////////////////////////////////////////////////////
/// Return low edge of bin

Double_t TAxis::GetBinLowEdge(Int_t bin) const
{
   if (fXbins.fN && bin > 0 && bin <=fNbins) return fXbins.fArray[bin-1];
   Double_t binwidth = (fXmax - fXmin) / Double_t(fNbins);
   return fXmin + (bin-1) * binwidth;
}

////////////////////////////////////////////////////////////////////////////////
/// Return up edge of bin

Double_t TAxis::GetBinUpEdge(Int_t bin) const
{
   if (!fXbins.fN || bin < 1 || bin>fNbins) {
      Double_t binwidth = (fXmax - fXmin) / Double_t(fNbins);
      return fXmin + bin*binwidth;
   }
   return fXbins.fArray[bin];
}

////////////////////////////////////////////////////////////////////////////////
/// Return bin width

Double_t TAxis::GetBinWidth(Int_t bin) const
{
   if (fNbins <= 0) return 0;
   if (fXbins.fN <= 0)  return (fXmax - fXmin) / Double_t(fNbins);
   if (bin >fNbins) bin = fNbins;
   if (bin <1 ) bin = 1;
   return fXbins.fArray[bin] - fXbins.fArray[bin-1];
}


////////////////////////////////////////////////////////////////////////////////
/// Return an array with the center of all bins

void TAxis::GetCenter(Double_t *center) const
{
   Int_t bin;
   for (bin=1; bin<=fNbins; bin++) *(center + bin-1) = GetBinCenter(bin);
}

////////////////////////////////////////////////////////////////////////////////
/// Return an array with the lod edge of all bins

void TAxis::GetLowEdge(Double_t *edge) const
{
   Int_t bin;
   for (bin=1; bin<=fNbins; bin++) *(edge + bin-1) = GetBinLowEdge(bin);
}

////////////////////////////////////////////////////////////////////////////////
/// Return *only* the time format from the string fTimeFormat

const char *TAxis::GetTimeFormatOnly() const
{
   static TString timeformat;
   Int_t idF = fTimeFormat.Index("%F");
   if (idF>=0) {
      timeformat = fTimeFormat(0,idF);
   } else {
      timeformat = fTimeFormat;
   }
   return timeformat.Data();
}

////////////////////////////////////////////////////////////////////////////////
/// Return the ticks option (see SetTicks)

const char *TAxis::GetTicks() const
{
   if (TestBit(kTickPlus) && TestBit(kTickMinus)) return "+-";
   if (TestBit(kTickMinus)) return "-";
   return "+";
}

////////////////////////////////////////////////////////////////////////////////
/// this helper function checks if there is a bin without a label
/// if all bins have labels, the axis can / will become alphanumeric

Bool_t TAxis::HasBinWithoutLabel() const
{
   return fLabels->GetSize() != fNbins;
}

////////////////////////////////////////////////////////////////////////////////
///  Set option(s) to draw axis with labels
///  option can be:
///   - "a" sort by alphabetic order
///   - ">" sort by decreasing values
///   - "<" sort by increasing values
///   - "h" draw labels horizontal
///   - "v" draw labels vertical
///   - "u" draw labels up (end of label right adjusted)
///   - "d" draw labels down (start of label left adjusted)

void TAxis::LabelsOption(Option_t *option)
{
   if (!fLabels) {
      Warning("Sort","Cannot sort. No labels");
      return;
   }
   TH1 *h = (TH1*)GetParent();
   if (!h) {
      Error("Sort","Axis has no parent");
      return;
   }

   h->LabelsOption(option,GetName());
}

////////////////////////////////////////////////////////////////////////////////
/// Copy axis attributes to this

void TAxis::ImportAttributes(const TAxis *axis)
{
   SetTitle(axis->GetTitle());
   SetNdivisions(axis->GetNdivisions());
   SetAxisColor(axis->GetAxisColor());
   SetLabelColor(axis->GetLabelColor());
   SetLabelFont(axis->GetLabelFont());
   SetLabelOffset(axis->GetLabelOffset());
   SetLabelSize(axis->GetLabelSize());
   SetTickLength(axis->GetTickLength());
   SetTitleOffset(axis->GetTitleOffset());
   SetTitleSize(axis->GetTitleSize());
   SetTitleColor(axis->GetTitleColor());
   SetTitleFont(axis->GetTitleFont());
   SetBit(TAxis::kCenterTitle,   axis->TestBit(TAxis::kCenterTitle));
   SetBit(TAxis::kCenterLabels,  axis->TestBit(TAxis::kCenterLabels));
   SetBit(TAxis::kRotateTitle,   axis->TestBit(TAxis::kRotateTitle));
   SetBit(TAxis::kNoExponent,    axis->TestBit(TAxis::kNoExponent));
   SetBit(TAxis::kTickPlus,      axis->TestBit(TAxis::kTickPlus));
   SetBit(TAxis::kTickMinus,     axis->TestBit(TAxis::kTickMinus));
   SetBit(TAxis::kMoreLogLabels, axis->TestBit(TAxis::kMoreLogLabels));
   SetBit(TAxis::kDecimals,      axis->TestBit(TAxis::kDecimals));
   SetTimeFormat(axis->GetTimeFormat());
}



////////////////////////////////////////////////////////////////////////////////
/// Save axis attributes as C++ statement(s) on output stream out

void TAxis::SaveAttributes(std::ostream &out, const char *name, const char *subname)
{
   char quote = '"';
   if (strlen(GetTitle())) {
      TString t(GetTitle());
      t.ReplaceAll("\\","\\\\");
      out<<"   "<<name<<subname<<"->SetTitle("<<quote<<t.Data()<<quote<<");"<<std::endl;
   }
   if (fTimeDisplay) {
      out<<"   "<<name<<subname<<"->SetTimeDisplay(1);"<<std::endl;
      out<<"   "<<name<<subname<<"->SetTimeFormat("<<quote<<GetTimeFormat()<<quote<<");"<<std::endl;
   }
   if (fLabels) {
      TIter next(fLabels);
      TObjString *obj;
      while ((obj=(TObjString*)next())) {
         out<<"   "<<name<<subname<<"->SetBinLabel("<<obj->GetUniqueID()<<","<<quote<<obj->GetName()<<quote<<");"<<std::endl;
      }
   }

   if (fFirst || fLast) {
      out<<"   "<<name<<subname<<"->SetRange("<<fFirst<<","<<fLast<<");"<<std::endl;
   }

   if (TestBit(kLabelsHori)) {
      out<<"   "<<name<<subname<<"->SetBit(TAxis::kLabelsHori);"<<std::endl;
   }

   if (TestBit(kLabelsVert)) {
      out<<"   "<<name<<subname<<"->SetBit(TAxis::kLabelsVert);"<<std::endl;
   }

   if (TestBit(kLabelsDown)) {
      out<<"   "<<name<<subname<<"->SetBit(TAxis::kLabelsDown);"<<std::endl;
   }

   if (TestBit(kLabelsUp)) {
      out<<"   "<<name<<subname<<"->SetBit(TAxis::kLabelsUp);"<<std::endl;
   }

   if (TestBit(kCenterLabels)) {
      out<<"   "<<name<<subname<<"->CenterLabels(true);"<<std::endl;
   }

   if (TestBit(kCenterTitle)) {
      out<<"   "<<name<<subname<<"->CenterTitle(true);"<<std::endl;
   }

   if (TestBit(kRotateTitle)) {
      out<<"   "<<name<<subname<<"->RotateTitle(true);"<<std::endl;
   }

   if (TestBit(kDecimals)) {
      out<<"   "<<name<<subname<<"->SetDecimals();"<<std::endl;
   }

   if (TestBit(kMoreLogLabels)) {
      out<<"   "<<name<<subname<<"->SetMoreLogLabels();"<<std::endl;
   }

   if (TestBit(kNoExponent)) {
      out<<"   "<<name<<subname<<"->SetNoExponent();"<<std::endl;
   }

   TAttAxis::SaveAttributes(out,name,subname);
}

////////////////////////////////////////////////////////////////////////////////
/// Initialize axis with fix bins

void TAxis::Set(Int_t nbins, Double_t xlow, Double_t xup)
{
   fNbins   = nbins;
   fXmin    = xlow;
   fXmax    = xup;
   if (!fParent) SetDefaults();
   if (fXbins.fN > 0) fXbins.Set(0);
}

////////////////////////////////////////////////////////////////////////////////
/// Initialize axis with variable bins

void TAxis::Set(Int_t nbins, const Float_t *xbins)
{
   Int_t bin;
   fNbins  = nbins;
   fXbins.Set(fNbins+1);
   for (bin=0; bin<= fNbins; bin++)
      fXbins.fArray[bin] = xbins[bin];
   for (bin=1; bin<= fNbins; bin++)
      if (fXbins.fArray[bin] < fXbins.fArray[bin-1])
         Error("TAxis::Set", "bins must be in increasing order");
   fXmin      = fXbins.fArray[0];
   fXmax      = fXbins.fArray[fNbins];
   if (!fParent) SetDefaults();
}

////////////////////////////////////////////////////////////////////////////////
/// Initialize axis with variable bins

void TAxis::Set(Int_t nbins, const Double_t *xbins)
{
   Int_t bin;
   fNbins  = nbins;
   fXbins.Set(fNbins+1);
   for (bin=0; bin<= fNbins; bin++)
      fXbins.fArray[bin] = xbins[bin];
   for (bin=1; bin<= fNbins; bin++)
      if (fXbins.fArray[bin] < fXbins.fArray[bin-1])
         Error("TAxis::Set", "bins must be in increasing order");
   fXmin      = fXbins.fArray[0];
   fXmax      = fXbins.fArray[fNbins];
   if (!fParent) SetDefaults();
}

////////////////////////////////////////////////////////////////////////////////
/// Set axis alphanumeric

void TAxis::SetAlphanumeric(Bool_t alphanumeric)
{
   if (alphanumeric) fBits2 |= kAlphanumeric;
   else fBits2 &= ~kAlphanumeric;

   // clear underflow and overflow (in an alphanumeric situation they do not make sense)
   // NOTE: using AddBinContent instead of SetBinContent in order to not change
   //  the number of entries
   //((TH1 *)fParent)->ClearUnderflowAndOverflow();
   // L.M. 26.1.15 Keep underflow and overflows (see ROOT-7034)
   if (gDebug && fParent) {
      TH1 * h = dynamic_cast<TH1*>( fParent);
      if (!h) return;
      double s[TH1::kNstat];
      h->GetStats(s);
      if (s[0] != 0. && gDebug > 0)
         Info("SetAlphanumeric","Histogram %s is set alphanumeric but has non-zero content",GetName());
   }
}


////////////////////////////////////////////////////////////////////////////////
/// Set axis default values (from TStyle)

void TAxis::SetDefaults()
{
   fFirst   = 0;
   fLast    = 0;
   fBits2   = 0;
   char name[2];
   strlcpy(name,GetName(),2);
   name[1] = 0;
   TAttAxis::ResetAttAxis(name);
   fTimeDisplay = 0;
   SetTimeFormat();
}

////////////////////////////////////////////////////////////////////////////////
/// Set label for bin.
/// If no label list exists, it is created. If all the bins have labels, the
/// axis becomes alphanumeric and extendable.
/// New labels will not be added with the Fill method but will end-up in the
/// underflow bin. See documentation of TAxis::FindBin(const char*)

void TAxis::SetBinLabel(Int_t bin, const char *label)
{
   if (!fLabels) fLabels = new THashList(fNbins,3);

   if (bin <= 0 || bin > fNbins) {
      Error("SetBinLabel","Illegal bin number: %d",bin);
      return;
   }

   // Check whether this bin already has a label.
   TIter next(fLabels);
   TObjString *obj;
   while ((obj=(TObjString*)next())) {
      if ( obj->GetUniqueID()==(UInt_t)bin ) {
         // It does. Overwrite it.
         obj->SetString(label);
         // LM need to rehash the labels list (see ROOT-5025)
         fLabels->Rehash(fLabels->GetSize() );
         return;
      }
   }
   // It doesn't. Add this new label.
   obj = new TObjString(label);
   fLabels->Add(obj);
   obj->SetUniqueID((UInt_t)bin);

   // check for Alphanumeric case (labels for each bin)
   if (CanBeAlphanumeric() && fLabels->GetSize() == fNbins) {
      SetAlphanumeric(kTRUE);
      SetCanExtend(kTRUE);
   }
}

////////////////////////////////////////////////////////////////////////////////
/// Define new text attributes for the label number "labNum". It allows to do a
/// fine tuning of the labels. All the attributes can be changed, even the
/// label text itself.
///
/// \param[in] labNum    Number of the label to be changed, negative numbers start from the end
/// \param[in] labAngle  New angle value
/// \param[in] labSize   New size (0 erase the label)
/// \param[in] labAlign  New alignment value
/// \param[in] labColor  New label color
/// \param[in] labFont   New label font
/// \param[in] labText   New label text
///
/// If an attribute should not be changed just give the value "-1".
///
/// If labnum=0 the list of modified labels is reset.

void TAxis::ChangeLabel(Int_t labNum, Double_t labAngle, Double_t labSize,
                               Int_t labAlign, Int_t labColor, Int_t labFont,
                               TString labText)
{
   if (!fModLabs) fModLabs = new TList();

   // Reset the list of modified labels.
   if (labNum == 0) {
      delete fModLabs;
      fModLabs  = 0;
      return;
   }

   TAxisModLab *ml = new TAxisModLab();
   ml->SetLabNum(labNum);
   ml->SetAngle(labAngle);
   ml->SetSize(labSize);
   ml->SetAlign(labAlign);
   ml->SetColor(labColor);
   ml->SetFont(labFont);
   ml->SetText(labText);

   fModLabs->Add((TObject*)ml);
}


////////////////////////////////////////////////////////////////////////////////
///  Set the viewing range for the axis from bin first to last.
///  To set a range using the axis coordinates, use TAxis::SetRangeUser.
///
///  If first == last == 0 or if last < first or if the range specified does
///  not intersect at all with the maximum available range [0, fNbins + 1],
///  then the range is reset by removing the bit TAxis::kAxisRange. In this
///  case the functions TAxis::GetFirst() and TAxis::GetLast() will return 1
///  and fNbins.
///
///  If the range specified partially intersects [0, fNbins + 1], then the
///  intersection range is set. For instance, if first == -2 and last == fNbins,
///  then the set range is [0, fNbins] (fFirst = 0 and fLast = fNbins).
///
///  NOTE: for historical reasons, SetRange(0,0) resets the range even though Bin 0 is
///       technically reserved for the underflow; in order to set the range of the axis
///       so that it only includes the underflow, use SetRange(a,0), where a < 0

void TAxis::SetRange(Int_t first, Int_t last)
{

   Int_t nCells = fNbins + 1; // bins + overflow

   // special reset range cases
   if (last < first || (first < 0 && last < 0) ||
         (first > nCells && last > nCells) || (first == 0 && last == 0)
   ) {
      fFirst = 1;
      fLast = fNbins;
      SetBit(kAxisRange, 0);
   } else {
      fFirst = std::max(first, 0);
      fLast = std::min(last, nCells);
      SetBit(kAxisRange, 1);
   }

}


////////////////////////////////////////////////////////////////////////////////
///  Set the viewing range for the axis from ufirst to ulast (in user coordinates).
///  To set a range using the axis bin numbers, use TAxis::SetRange.

void TAxis::SetRangeUser(Double_t ufirst, Double_t ulast)
{
   if (!strstr(GetName(),"xaxis")) {
      TH1 *hobj = (TH1*)GetParent();
      if (hobj &&
          ((hobj->GetDimension() == 2 && strstr(GetName(),"zaxis"))
           || (hobj->GetDimension() == 1 && strstr(GetName(),"yaxis")))) {
         hobj->SetMinimum(ufirst);
         hobj->SetMaximum(ulast);
         return;
      }
   }
   Int_t ifirst = FindFixBin(ufirst);
   Int_t ilast = FindFixBin(ulast);
   // fixes for numerical error and for https://savannah.cern.ch/bugs/index.php?99777
   if (GetBinUpEdge(ifirst) <= ufirst ) ifirst += 1;
   if (GetBinLowEdge(ilast) >= ulast ) ilast -= 1;
   SetRange(ifirst, ilast);
}

////////////////////////////////////////////////////////////////////////////////
///  Set ticks orientation.
///  option = "+"  ticks drawn on the "positive side" (default)
///  option = "-"  ticks drawn on the "negative side"
///  option = "+-" ticks drawn on both sides

void TAxis::SetTicks(Option_t *option)
{
   ResetBit(kTickPlus);
   ResetBit(kTickMinus);
   if (strchr(option,'+')) SetBit(kTickPlus);
   if (strchr(option,'-')) SetBit(kTickMinus);
}

////////////////////////////////////////////////////////////////////////////////
/// Change the format used for time plotting
///
/// The format string for date and time use the same options as the one used
/// in the standard strftime C function, i.e. :
/// for date :
///
///          %a abbreviated weekday name
///          %b abbreviated month name
///          %d day of the month (01-31)
///          %m month (01-12)
///          %y year without century
///
/// for time :
///
///          %H hour (24-hour clock)
///          %I hour (12-hour clock)
///          %p local equivalent of AM or PM
///          %M minute (00-59)
///          %S seconds (00-61)
///          %% %
///
/// This function allows also to define the time offset. It is done via %F
/// which should be appended at the end of the format string. The time
/// offset has the following format: 'yyyy-mm-dd hh:mm:ss'
/// Example:
///
///          h = new TH1F("Test","h",3000,0.,200000.);
///          h->GetXaxis()->SetTimeDisplay(1);
///          h->GetXaxis()->SetTimeFormat("%d\/%m\/%y%F2000-02-28 13:00:01");
///
/// This defines the time format being "dd/mm/yy" and the time offset as the
/// February 28th 2003 at 13:00:01
///
/// If %F is not specified, the time offset used will be the one defined by:
/// gStyle->SetTimeOffset. For example like that:
///
///          TDatime da(2003,02,28,12,00,00);
///          gStyle->SetTimeOffset(da.Convert());

void TAxis::SetTimeFormat(const char *tformat)
{
   TString timeformat = tformat;

   if (timeformat.Index("%F")>=0 || timeformat.IsNull()) {
      fTimeFormat = timeformat;
      return;
   }

   Int_t idF = fTimeFormat.Index("%F");
   if (idF>=0) {
      Int_t lnF = fTimeFormat.Length();
      TString stringtimeoffset = fTimeFormat(idF,lnF);
      fTimeFormat = tformat;
      fTimeFormat.Append(stringtimeoffset);
   } else {
      fTimeFormat = tformat;
      SetTimeOffset(gStyle->GetTimeOffset());
   }
}


////////////////////////////////////////////////////////////////////////////////
/// Change the time offset
/// If option = "gmt", set display mode to GMT.

void TAxis::SetTimeOffset(Double_t toffset, Option_t *option)
{
   TString opt = option;
   opt.ToLower();

   char tmp[20];
   time_t timeoff;
   struct tm* utctis;
   Int_t idF = fTimeFormat.Index("%F");
   if (idF>=0) fTimeFormat.Remove(idF);
   fTimeFormat.Append("%F");

   timeoff = (time_t)((Long_t)(toffset));
   // offset is always saved in GMT to allow file transport
   // to different time zones
   utctis = gmtime(&timeoff);

   strftime(tmp,20,"%Y-%m-%d %H:%M:%S",utctis);
   fTimeFormat.Append(tmp);

   // append the decimal part of the time offset
   Double_t ds = toffset-(Int_t)toffset;
   snprintf(tmp,20,"s%g",ds);
   fTimeFormat.Append(tmp);

   // add GMT/local option
   if (opt.Contains("gmt")) fTimeFormat.Append(" GMT");
}


////////////////////////////////////////////////////////////////////////////////
/// Stream an object of class TAxis.

void TAxis::Streamer(TBuffer &R__b)
{
   if (R__b.IsReading()) {
      UInt_t R__s, R__c;
      Version_t R__v = R__b.ReadVersion(&R__s, &R__c);
      if (R__v > 5) {
         R__b.ReadClassBuffer(TAxis::Class(), this, R__v, R__s, R__c);
         return;
      }
      //====process old versions before automatic schema evolution
      TNamed::Streamer(R__b);
      TAttAxis::Streamer(R__b);
      R__b >> fNbins;
      if (R__v < 5) {
         Float_t xmin,xmax;
         R__b >> xmin; fXmin = xmin;
         R__b >> xmax; fXmax = xmax;
         Float_t *xbins = 0;
         Int_t n = R__b.ReadArray(xbins);
         fXbins.Set(n);
         for (Int_t i=0;i<n;i++) fXbins.fArray[i] = xbins[i];
         delete [] xbins;
      } else {
         R__b >> fXmin;
         R__b >> fXmax;
         fXbins.Streamer(R__b);
      }
      if (R__v > 2) {
         R__b >> fFirst;
         R__b >> fLast;
          // following lines required to repair for a bug in Root version 1.03
         if (fFirst < 0 || fFirst > fNbins) fFirst = 0;
         if (fLast  < 0 || fLast  > fNbins) fLast  = 0;
         if (fLast  < fFirst) { fFirst = 0; fLast = 0;}
         if (fFirst ==0 && fLast == 0) SetBit(kAxisRange,0);
      }
      if (R__v > 3) {
         R__b >> fTimeDisplay;
         fTimeFormat.Streamer(R__b);
      } else {
         SetTimeFormat();
      }
      R__b.CheckByteCount(R__s, R__c, TAxis::IsA());
      //====end of old versions

   } else {
      R__b.WriteClassBuffer(TAxis::Class(),this);
   }
}

////////////////////////////////////////////////////////////////////////////////
/// Reset first & last bin to the full range

void TAxis::UnZoom()
{
   if (!gPad) return;
   gPad->SetView();

   //unzoom object owning this axis
   SetRange(0,0);
   TH1 *hobj1 = (TH1*)GetParent();
   if (!strstr(GetName(),"xaxis")) {
      if (!hobj1) return;
      if (hobj1->GetDimension() == 2) {
         if (strstr(GetName(),"zaxis")) {
            hobj1->SetMinimum();
            hobj1->SetMaximum();
            hobj1->ResetBit(TH1::kIsZoomed);
         }
         return;
      }
      if (strcmp(hobj1->GetName(),"hframe") == 0 ) {
         hobj1->SetMinimum(fXmin);
         hobj1->SetMaximum(fXmax);
      } else {
         if (fXmin==hobj1->GetMinimum() && fXmax==hobj1->GetMaximum()) {
            hobj1->SetMinimum(fXmin);
            hobj1->SetMaximum(fXmax);
         } else {
            hobj1->SetMinimum();
            hobj1->SetMaximum();
         }
         hobj1->ResetBit(TH1::kIsZoomed);
      }
   }
   //must unzoom all histograms in the pad
   TIter next(gPad->GetListOfPrimitives());
   TObject *obj;
   while ((obj= next())) {
      if (!obj->InheritsFrom(TH1::Class())) continue;
      TH1 *hobj = (TH1*)obj;
      if (hobj == hobj1) continue;
      if (!strstr(GetName(),"xaxis")) {
         if (hobj->GetDimension() == 2) {
            if (strstr(GetName(),"zaxis")) {
               hobj->SetMinimum();
               hobj->SetMaximum();
               hobj->ResetBit(TH1::kIsZoomed);
            } else {
               hobj->GetYaxis()->SetRange(0,0);
            }
            return;
         }
         if (strcmp(hobj->GetName(),"hframe") == 0 ) {
            hobj->SetMinimum(fXmin);
            hobj->SetMaximum(fXmax);
         } else {
            hobj->SetMinimum();
            hobj->SetMaximum();
            hobj->ResetBit(TH1::kIsZoomed);
         }
      } else {
         hobj->GetXaxis()->SetRange(0,0);
      }
   }

   gPad->UnZoomed();
}

////////////////////////////////////////////////////////////////////////////////
/// Zoom out by a factor of 'factor' (default =2)
///   uses previous zoom factor by default
/// Keep center defined by 'offset' fixed
///   ie. -1 at left of current range, 0 in center, +1 at right

void TAxis::ZoomOut(Double_t factor, Double_t offset)
{

   if (factor <= 0) factor = 2;
   Double_t center = (GetFirst()*(1-offset) + GetLast()*(1+offset))/2.;
   Int_t first = int(TMath::Floor(center+(GetFirst()-center)*factor + 0.4999999));
   Int_t last  = int(TMath::Floor(center+(GetLast() -center)*factor + 0.5000001));
   if (first==GetFirst() && last==GetLast()) { first--; last++; }
   SetRange(first,last);
}