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 "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 "TBuffer.h"
#include "TMath.h"
#include "THLimitsFinder.h"
#include "strlcpy.h"
#include "snprintf.h"
 
#include <iostream>
#include <cmath>
#include <ctime>
#include <cassert>
 
 
////////////////////////////////////////////////////////////////////////////////
/** \class TAxis
    \ingroup Histograms
    \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()
{
   fNbins   = 1;
   fXmin    = 0;
   fXmax    = 1;
   fFirst   = 0;
   fLast    = 0;
   fBits2   = 0;
   fTimeDisplay = false;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Axis constructor for axis with fix bin size
 
TAxis::TAxis(Int_t nbins,Double_t xlow,Double_t xup)
{
   Set(nbins,xlow,xup);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Axis constructor for variable bin size
 
TAxis::TAxis(Int_t nbins,const Double_t *xbins)
{
   Set(nbins,xbins);
}
 
TAxis::TAxis(std::vector<double> const &bins):
  TAxis(bins.size()-1, bins.data())
{}
 
////////////////////////////////////////////////////////////////////////////////
/// Destructor.
 
TAxis::~TAxis()
{
   if (fLabels) {
      fLabels->Delete();
      delete fLabels;
      fLabels = nullptr;
   }
   if (fModLabs) {
      fModLabs->Delete();
      delete fModLabs;
      fModLabs = nullptr;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Copy constructor.
 
TAxis::TAxis(const TAxis &axis) : TNamed(axis), TAttAxis(axis)
{
   fParent  = nullptr;
   fLabels  = nullptr;
   fModLabs = nullptr;
 
   axis.TAxis::Copy(*this);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Assignment operator.
 
TAxis& TAxis::operator=(const TAxis &axis)
{
   if (this != &axis)
      axis.TAxis::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
{
   TAxis &axis = static_cast<TAxis &>(obj);
   TNamed::Copy(axis);
   TAttAxis::Copy(axis);
   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 = nullptr;
   }
   if (fLabels) {
      //Properly handle case where not all bins have labels
      axis.fLabels = new THashList(axis.fNbins, 3);
      TIter next(fLabels);
      while(auto 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 = nullptr;
   }
   if (fModLabs) {
      axis.fModLabs = new TList();
      TIter next(fModLabs);
      while(auto modlabel = (TAxisModLab *)next()) {
         TAxisModLab *copyModLabel = new TAxisModLab(*modlabel);
         axis.fModLabs->Add(copyModLabel);
         copyModLabel->SetUniqueID(modlabel->GetUniqueID());
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// 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`.
///
/// @note The underflow bin (`0`) is for any `x` strictly smaller than `fXmin`,
/// whereas the overflow bin (`nbins+1`) is for any `x` greater or equal than `fXmax`,
/// as well as for `NaN`. The first regular bin (`1`) is for any `x`
/// greater or equal than `fXmin` and strictly smaller than `fXmin + binwidth`, and so on.
 
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 == nullptr) 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 == nullptr) return bin;
      if (!CanExtend() || IsAlphanumeric() ) return bin;
      ((TH1*)fParent)->ExtendAxis(x,this);
      return FindFixBin(x);
   } else {
      if (!fXbins.fN) {        //*-* fix bins
         const double width = (fXmax-fXmin)/fNbins;
         const int approxBin = (x-fXmin) / width; // Might be one unit too small/large due to limited precision of subtraction
         bin = 1 + approxBin - (x < fXmin + width*approxBin) + (fXmin + width*(approxBin+1) <= x);
      } 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 does 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.
/// @see TAxis::FindBin
 
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
         const double width = (fXmax-fXmin)/fNbins;
         const int approxBin = (x-fXmin) / width; // Might be one unit too small/large due to limited precision of subtraction
         bin = 1 + approxBin - (x < fXmin + width*approxBin) + (fXmin + width*(approxBin+1) <= x);
      } else {                  //*-* variable bin sizes
         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 - 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
///
/// If `bin > fNbins` (overflow bin) or `bin < 1` (underflow bin), the returned bin width is `(fXmax - fXmin) / fNbins`.
 
Double_t TAxis::GetBinWidth(Int_t bin) const
{
   if (fNbins <= 0) return 0;
   if (fXbins.fN <= 0 || bin >fNbins || bin <1)
      return (fXmax - fXmin) / Double_t(fNbins);
   return fXbins.fArray[bin] - fXbins.fArray[bin-1];
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Return an array with the center of all bins
 
void TAxis::GetCenter(Double_t *center) const
{
   for (Int_t bin = 1; bin <= fNbins; bin++)
      *(center + bin - 1) = GetBinCenter(bin);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Return an array with the low edge of all bins
 
void TAxis::GetLowEdge(Double_t *edge) const
{
   for (Int_t bin = 1; bin <= fNbins; bin++)
      *(edge + bin - 1) = GetBinLowEdge(bin);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Return the number of axis labels.
///
/// It is sometimes useful to know the number of labels on an axis. For instance
/// when changing the labels with TAxis::ChangeLabel. The number of labels is equal
/// to `the_number_of_divisions + 1`. By default the number of divisions is
/// optimised to show a coherent labeling of the main tick marks. After optimisation the
/// real number of divisions will be smaller or equal to number of divisions requested.
/// In order to turn off the labeling optimization, it is enough to give a negative
/// number of divisions to TAttAxis::SetNdivisions. The absolute value of this number will be use as
/// the exact number of divisions. This method takes the two cases (optimised or not) into
/// account.
 
Int_t TAxis::GetNlabels() const
{
   if (fNdivisions > 0) {
      Int_t divxo  = 0;
      Double_t x1o = 0.;
      Double_t x2o = 0.;
      Double_t bwx = 0.;
      THLimitsFinder::Optimize(fXmin, fXmax,fNdivisions%100,x1o,x2o,divxo,bwx,"");
      return divxo+1;
   } else {
      Int_t divx  = -fNdivisions;
      return divx%100+1;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// 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 time offset in GMT.
 
UInt_t TAxis::GetTimeOffset() {
 
  Int_t idF = fTimeFormat.Index("%F")+2;
  if (idF<2) {
    Warning("GetGMTimeOffset","Time format is not set!");
    return 0;
  }
  TString stime=fTimeFormat(idF,19);
  if (stime.Length() != 19) {
    Warning("GetGMTimeOffset","Bad time format!");
    return 0;
  }
 
  TDatime datime(stime.Data());
  return datime.Convert(kTRUE);  // Convert to unix gmt time
}
 
////////////////////////////////////////////////////////////////////////////////
/// Return the ticks option (see SetTicks)
 
const char *TAxis::GetTicks() const
{
   if (TestBit(kTickPlus) && TestBit(kTickMinus)) return "+-";
   if (TestBit(kTickMinus)) return "-";
   if (TestBit(kTickPlus)) 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)
{
   auto prefix = TString::Format("   %s%s->", name, subname);
 
   if (strlen(GetTitle()))
      out << prefix << "SetTitle(\"" << TString(GetTitle()).ReplaceSpecialCppChars() << "\");\n";
   if (fTimeDisplay) {
      out << prefix << "SetTimeDisplay(1);\n";
      out << prefix << "SetTimeFormat(\"" << GetTimeFormat() << "\");\n";
   }
   if (fLabels) {
      TIter next(fLabels);
      while (auto obj = static_cast<TObjString *>(next())) {
         out << prefix << "SetBinLabel(" << obj->GetUniqueID() << ", \""
             << TString(obj->GetName()).ReplaceSpecialCppChars() << "\");\n";
      }
   }
 
   if (fFirst || fLast)
      out << prefix << "SetRange(" << fFirst << ", " << fLast << ");\n";
 
   if (TestBit(kLabelsHori))
      out << prefix << "SetBit(TAxis::kLabelsHori);\n";
 
   if (TestBit(kLabelsVert))
      out << prefix << "SetBit(TAxis::kLabelsVert);\n";
 
   if (TestBit(kLabelsDown))
      out << prefix << "SetBit(TAxis::kLabelsDown);\n";
 
   if (TestBit(kLabelsUp))
      out << prefix << "SetBit(TAxis::kLabelsUp);\n";
 
   if (TestBit(kCenterLabels))
      out << prefix << "CenterLabels(true);\n";
 
   if (TestBit(kCenterTitle))
      out << prefix << "CenterTitle(true);\n";
 
   if (TestBit(kRotateTitle))
      out << prefix << "RotateTitle(true);\n";
 
   if (TestBit(kDecimals))
      out << prefix << "SetDecimals();\n";
 
   if (TestBit(kMoreLogLabels))
      out << prefix << "SetMoreLogLabels();\n";
 
   if (TestBit(kNoExponent))
      out << prefix << "SetNoExponent();\n";
 
   if (fModLabs) {
      TIter next(fModLabs);
      while (auto ml = static_cast<TAxisModLab *>(next())) {
         if (ml->GetLabNum() == 0)
            out << prefix << "ChangeLabelByValue(" << ml->GetLabValue();
         else
            out << prefix << "ChangeLabel(" << ml->GetLabNum();
         out << ", " << ml->GetAngle() << ", " << ml->GetSize() << ", " << ml->GetAlign() << ", "
             << TColor::SavePrimitiveColor(ml->GetColor()) << ", " << ml->GetFont() << ", \""
             << TString(ml->GetText()).ReplaceSpecialCppChars() << "\");\n";
      }
   }
   TAttAxis::SaveAttributes(out, name, subname);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Initialize axis with fix bins
///
/// An error is printed if xup or xlow are infinite/nan
/// (due to resulting undefined fixed bin width)
///
/// Set xup <= xlow to force the axis range and number of bins to be automatically
/// deduced after buffer is full or BufferEmpty is called
 
void TAxis::Set(Int_t nbins, Double_t xlow, Double_t xup)
{
   fNbins   = nbins;
   if (!std::isfinite(xlow) || !std::isfinite(xup))
      Error("TAxis::Set", "Axis limits need to be finite numbers");
   fXmin    = xlow;
   fXmax    = xup;
   if (!fParent) SetDefaults();
   if (fXbins.fN > 0) fXbins.Set(0);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Initialize axis with variable bins
///
/// An error is printed if bin edges are not in strictly increasing order
/// or if any of them is infinite or nan
 
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++) {
      if (!std::isfinite(xbins[bin])) {
         Error("TAxis::Set", "Bin edges need to be finite numbers. Use a large number instead.");
      }
      fXbins.fArray[bin] = xbins[bin];
   }
   for (bin=1; bin<= fNbins; bin++)
      if (fXbins.fArray[bin] <= fXbins.fArray[bin - 1])
         Error("TAxis::Set", "bin edges 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", "bin edges 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","Cannot switch axis %s of histogram %s to alphanumeric: it has non-zero content",GetName(),h->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 = false;
   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);
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Search for axis modifier by index or value
 
TAxisModLab *TAxis::FindModLab(Int_t num, Double_t v, Double_t eps) const
{
   if (!fModLabs)
      return nullptr;
 
   TIter next(fModLabs);
   while (auto ml = (TAxisModLab*)next()) {
      if (ml->GetLabNum() != num)
         continue;
 
      if ((num != 0) || (TMath::Abs(v - ml->GetLabValue()) <= eps))
         return ml;
   }
 
   return nullptr;
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// 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
///
///  #### Notes:
///
///  - If an attribute should not be changed just give the value "-1".
///  - If labnum=0 the list of modified labels is reset.
///  - To erase a label set labSize to 0.
///  - If labText is not specified or is an empty string, the text label is not changed.
///  - To retrieve the number of axis labels use TAxis::GetNlabels.
 
void TAxis::ChangeLabel(Int_t labNum, Double_t labAngle, Double_t labSize,
                        Int_t labAlign, Int_t labColor, Int_t labFont,
                        const TString &labText)
{
   // Reset the list of modified labels.
   if (labNum == 0) {
      SafeDelete(fModLabs);
      return;
   }
 
   if (!fModLabs) fModLabs = new TList();
 
   TAxisModLab *ml = FindModLab(labNum);
   if (!ml) {
      ml = new TAxisModLab();
      ml->SetLabNum(labNum);
      fModLabs->Add(ml);
   }
 
   ml->SetAngle(labAngle);
   ml->SetSize(labSize);
   ml->SetAlign(labAlign);
   ml->SetColor(labColor);
   ml->SetFont(labFont);
   ml->SetText(labText);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Define new text attributes for the label value "labValue". It allows to do a
/// fine tuning of the labels. All the attributes can be changed, even the
/// label text itself.
///
/// \param[in] labValue  Axis value to be changed
/// \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
///
///  #### Notes:
///
///  - If an attribute should not be changed just give the value "-1".
///  - If labnum=0 the list of modified labels is reset.
///  - To erase a label set labSize to 0.
///  - If labText is not specified or is an empty string, the text label is not changed.
///  - To retrieve the number of axis labels use TAxis::GetNlabels.
 
void TAxis::ChangeLabelByValue(Double_t labValue, Double_t labAngle, Double_t labSize,
                             Int_t labAlign, Int_t labColor, Int_t labFont,
                             const TString &labText)
{
   if (!fModLabs) fModLabs = new TList();
 
   TAxisModLab *ml = FindModLab(0, labValue, 0.);
   if (!ml) {
      ml = new TAxisModLab();
      ml->SetLabValue(labValue);
      fModLabs->Add(ml);
   }
 
   ml->SetAngle(labAngle);
   ml->SetSize(labSize);
   ml->SetAlign(labAlign);
   ml->SetColor(labColor);
   ml->SetFont(labFont);
   ml->SetText(labText);
}
 
////////////////////////////////////////////////////////////////////////////////
///  Set the viewing range for the axis using bin numbers.
///
///  \param first First bin of the range.
///  \param last  Last bin of the range.
///
///  To set a range using the axis coordinates, use TAxis::SetRangeUser.
///
///  If `first == last == 0` or if `first > last` or if the range specified does
///  not intersect at all with the maximum available range `[0, fNbins + 1]`,
///  then the viewing 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 with `[0, fNbins + 1]`, then the
///  intersection range is accepted. For instance, if `first == -2` and `last == fNbins`,
///  the accepted range will be `[0, fNbins]` (`fFirst = 0` and `fLast = fNbins`).
///
///  If `last > fNbins`, the overflow bin is included in the range and will be displayed during drawing.
///  If `first < 1`, the underflow bin is included in the range and will be displayed during drawing.
///
///  \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(-1,0)`.
///  \note This function will also restrict the fitting range
 
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, false);
   } else {
      fFirst = std::max(first, 0);
      fLast = std::min(last, nCells);
      SetBit(kAxisRange, true);
   }
}
 
////////////////////////////////////////////////////////////////////////////////
///  Set the viewing range for the axis from `ufirst` to `ulast` (in user coordinates,
///  that is, the "natural" axis coordinates).
///  To set a range using the axis bin numbers, use TAxis::SetRange.
///
///  If `ulast > fXmax`, the overflow bin is included in the range and will be displayed during drawing.
///  If `ufirst < fXmin`, the underflow bin is included in the range and will be displayed during drawing.
///
///  \note This function will also restrict the fitting range
 
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
///  option = ""   ticks will be drawn as whatever is defined as default. No bit is set internally.
 
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 = nullptr;
         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,false);
      }
      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) {
      Warning("TAxis::UnZoom","Cannot UnZoom if gPad does not exist. Did you mean to draw the TAxis first?");
      return;
   }
   gPad->SetView();
 
   //unzoom object owning this axis
   SetRange(0,0);
   TH1 *hobj1 = dynamic_cast<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->GetMinimumStored() && fXmax == hobj1->GetMaximumStored()) {
            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);
}