base_histo

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// Copyright (C) 2010, Guy Barrand. All rights reserved.
// See the file tools.license for terms.
 
#ifndef tools_histo_base_histo
#define tools_histo_base_histo
 
#ifdef TOOLS_MEM
#include "../mem"
#endif
 
#include "histo_data"
 
#include <cmath>
#include <map> //for annotations
#include <ostream>
 
namespace tools {
namespace histo {
 
//TC is for a coordinate.
//TO is for an offset used to identify a bin.
//TN is for a number of entries.
//TW is for a weight.
//TH is for a height.
 
template <class TC,class TO,class TN,class TW,class TH>
class base_histo : protected histo_data<TC,TO,TN,TW> {
  typedef histo_data<TC,TO,TN,TW> parent;
private:
  static const std::string& s_class() {
    static const std::string s_v("tools::histo::base_histo");
    return s_v;
  }
public:
  typedef histo_data<TC,TO,TN,TW> hd_t;
  typedef axis<TC,TO> axis_t;
  typedef typename axis_t::bn_t bn_t;
  typedef unsigned int dim_t;
  typedef TC coordinate_t;
  typedef TO offset_t;
  typedef TN num_entries_t;
  typedef TW weight_t;
  typedef TH height_t;
protected:
  virtual TH get_bin_height(TO) const = 0;  //histo/profile
protected:
  void base_from_data(const hd_t& a_from) {parent::operator=(a_from);}
#ifdef tools_histo_base_histo //for backward compatibility with tools
  hd_t base_get_data() const {
    hd_t hd;
    hd = *this;
    return hd;
  }
#endif
public:
  const hd_t& dac() const {return *this;} //data accessor.
protected:
  base_histo():parent() {
#ifdef TOOLS_MEM
    mem::increment(s_class().c_str());
#endif
  }
protected:
  virtual ~base_histo() {
#ifdef TOOLS_MEM
    mem::decrement(s_class().c_str());
#endif
  }
protected:
  base_histo(const base_histo& a_from):parent(a_from) {
#ifdef TOOLS_MEM
    mem::increment(s_class().c_str());
#endif
  }
 
  base_histo& operator=(const base_histo& a_from) {
    if(&a_from==this) return *this;
    parent::operator=(a_from);
    return *this;
  }
 
public:
  bool equals(const base_histo& a_from,const TW& a_prec,TW(*a_fabs)(TW)) const {
    return parent::equals(a_from,a_prec,a_fabs);
  }
 
  const std::string& title() const {return parent::m_title;}
  bool set_title(const std::string& a_title){parent::m_title = a_title;return true;}
  dim_t dimension() const {return parent::m_dimension;}
  dim_t number_of_planes() const {return dim_planes(parent::m_dimension);}
 
  TN entries() const {
    return parent::m_in_range_entries; //not set if reading a TH from a CERN-ROOT file.
  }
  TN all_entries() const {
    return parent::m_all_entries; //works also is reading histo from a CERN-ROOT file.
  }
 
  TN extra_entries() const {
    return parent::m_all_entries-parent::m_in_range_entries; //works also is reading histo from a CERN-ROOT file.
  }
  TW equivalent_bin_entries() const {
    TW sw = 0;
    TW sw2 = 0;
    for(TO ibin=0;ibin<parent::m_bin_number;ibin++) {
      if(!histo::is_out(parent::m_axes,ibin)) {
        sw += parent::m_bin_Sw[ibin];
        sw2 += parent::m_bin_Sw2[ibin];
      }
    }
    if(sw2==0) return 0;
    return (sw * sw)/sw2;
  }
  TH sum_bin_heights() const {
    TH sh = 0;
    for(TO ibin=0;ibin<parent::m_bin_number;ibin++) {
      if(!histo::is_out(parent::m_axes,ibin)) {
        sh += get_bin_height(ibin);
      }
    }
    return sh;
  }
  TH sum_all_bin_heights() const {
    TH sh = 0;
    for(TO ibin=0;ibin<parent::m_bin_number;ibin++) {
      sh += get_bin_height(ibin);
    }
    return sh;
  }
 
  TH sum_extra_bin_heights() const {
    TH sh = 0;
    for(TO ibin=0;ibin<parent::m_bin_number;ibin++) {
      if(histo::is_out(parent::m_axes,ibin)) {
        sh += get_bin_height(ibin);
      }
    }
    return sh;
  }
 
  TH min_bin_height() const {
    TH value = 0;
    bool first = true;
    for(TO ibin=0;ibin<parent::m_bin_number;ibin++) {
      if(!histo::is_out(parent::m_axes,ibin)) {
        TH vbin = get_bin_height(ibin);
        if(first) {
          first = false;
          value = vbin;
        } else {
          if(vbin<=value) value = vbin;
        }
      }
    }
    return value;
  }
 
  TH max_bin_height() const {
    TH value = 0;
    bool first = true;
    for(TO ibin=0;ibin<parent::m_bin_number;ibin++) {
      if(!histo::is_out(parent::m_axes,ibin)) {
        TH vbin = get_bin_height(ibin);
        if(first) {
          first = false;
          value = vbin;
        } else {
          if(vbin>=value) value = vbin;
        }
      }
    }
    return value;
  }
 
  bool min_bin_height_with_entries(TH& a_value) const {
    TH value = 0;
    bool first = true;
    for(TO ibin=0;ibin<parent::m_bin_number;ibin++) {
      if(!histo::is_out(parent::m_axes,ibin) && (parent::m_bin_entries[ibin]>0) ) {
        TH vbin = get_bin_height(ibin);
        if(first) {
          first = false;
          value = vbin;
        } else {
          if(vbin<=value) value = vbin;
        }
      }
    }
    a_value = value;
    return first?false:true; //return true if at least one bin with entries processed.
  }
 
  bool max_bin_height_with_entries(TH& a_value) const {
    TH value = 0;
    bool first = true;
    for(TO ibin=0;ibin<parent::m_bin_number;ibin++) {
      if(!histo::is_out(parent::m_axes,ibin) && (parent::m_bin_entries[ibin]>0) ) {
        TH vbin = get_bin_height(ibin);
        if(first) {
          first = false;
          value = vbin;
        } else {
          if(vbin>=value) value = vbin;
        }
      }
    }
    a_value = value;
    return first?false:true; //return true if at least one bin with entries processed.
  }
 
  bool has_entries_per_bin() const { //to detect histos coming from TH streaming out of a root file.
    // it assumes that update_fast_getters() had been applied.
    if(parent::m_in_range_entries) return true;
    // may be a from-root histo :
    if(parent::m_in_range_Sw) return false;
    // no in range entries and weight :
    return true; //for exa not filled = ok.
  }
 
public: //histo_data
  bool get_ith_axis_Sxw(dim_t a_axis,TC& a_value) const {
    a_value = 0;
    if(a_axis>=parent::m_dimension) return false;
    for(TO ibin=0;ibin<parent::m_bin_number;ibin++) {
      if(!histo::is_out(parent::m_axes,ibin)) {
        a_value += parent::m_bin_Sxw[ibin][a_axis];
      }
    }
    return true;
  }
 
  bool get_ith_axis_Sx2w(dim_t a_axis,TC& a_value) const {
    a_value = 0;
    if(a_axis>=parent::m_dimension) return false;
    for(TO ibin=0;ibin<parent::m_bin_number;ibin++) {
      if(!histo::is_out(parent::m_axes,ibin)) {
        a_value += parent::m_bin_Sx2w[ibin][a_axis];
      }
    }
    return true;
  }
 
  TW get_in_range_Sw() const {return parent::m_in_range_Sw;}   //for CERN-ROOT file writing.
  TW get_in_range_Sw2() const {return parent::m_in_range_Sw2;} //for CERN-ROOT file writing.
 
  void get_Sw_Sw2(TW& a_sw,TW& a_sw2) const {
    a_sw = 0;
    a_sw2 = 0;
    for(TO ibin=0;ibin<parent::m_bin_number;ibin++) {
      if(!histo::is_out(parent::m_axes,ibin)) {
        a_sw += parent::m_bin_Sw[ibin];
        a_sw2 += parent::m_bin_Sw2[ibin];
      }
    }
  }
  void get_all_Sw_Sw2(TW& a_sw,TW& a_sw2) const {
    a_sw = 0;
    a_sw2 = 0;
    for(TO ibin=0;ibin<parent::m_bin_number;ibin++) {
      a_sw += parent::m_bin_Sw[ibin];
      a_sw2 += parent::m_bin_Sw2[ibin];
    }
  }
 
/*
  TW get_all_Sw() const {
    TW sw = 0;
    for(TO ibin=0;ibin<m_bin_number;ibin++) sw += m_bin_Sw[ibin];
    return sw;
  }
  TN get_all_entries() const {
    TN number = 0;
    for(TO ibin=0;ibin<m_bin_number;ibin++) {
      number += m_bin_entries[ibin];
    }
    return number;
  }
 
  // for inlib/wroot/streamers :
  TN get_entries() const {
    TN number = 0;
    for(TO ibin=0;ibin<m_bin_number;ibin++) {
      if(!histo::is_out(m_axes,ibin)) {
        number += m_bin_entries[ibin];
      }
    }
    return number;
  }
*/
protected:
  enum {AxisX=0,AxisY=1,AxisZ=2};
 
  bool configure(dim_t a_dim,
                 const std::vector<bn_t>& aNumbers,
                 const std::vector<TC>& aMins,
                 const std::vector<TC>& aMaxs) {
    // Clear :
    parent::m_bin_entries.clear();
    parent::m_bin_Sw.clear();
    parent::m_bin_Sw2.clear();
    parent::m_bin_Sxw.clear();
    parent::m_bin_Sx2w.clear();
    parent::m_in_range_Sxw.clear();
    parent::m_in_range_Sx2w.clear();
    parent::m_axes.clear();
    parent::m_in_range_plane_Sxyw.clear();
    parent::m_annotations.clear();
 
    parent::m_bin_number = 0;
    parent::m_dimension = 0;
    parent::m_all_entries = 0;
    parent::m_in_range_entries = 0;
    parent::m_in_range_Sw = 0;
    parent::m_in_range_Sw2 = 0;
    parent::m_in_range_Sxw.resize(a_dim,0);
    parent::m_in_range_Sx2w.resize(a_dim,0);
 
    // Some checks :
    if(!a_dim) return false;
    parent::m_axes.resize(a_dim);
    // Setup axes :
    for(dim_t iaxis=0;iaxis<a_dim;iaxis++) {
      if(!parent::m_axes[iaxis].configure(aNumbers[iaxis],aMins[iaxis],aMaxs[iaxis])) {
        // do not do :
        //   m_axes.clear()
        // so that :
        //   b1::axis(),b2::axis_[x,y]()
        // do not crash in case of a bad booking.
        //m_axes.clear();
        return false;
      }
    }
 
    parent::m_dimension = a_dim;
 
    base_allocate(); //set m_bin_number.
 
    return true;
  }
 
  bool configure(dim_t a_dim,const std::vector< std::vector<TC> >& a_edges) {
    // Clear :
    parent::m_bin_entries.clear();
    parent::m_bin_Sw.clear();
    parent::m_bin_Sw2.clear();
    parent::m_bin_Sxw.clear();
    parent::m_bin_Sx2w.clear();
    parent::m_in_range_Sxw.clear();
    parent::m_in_range_Sx2w.clear();
    parent::m_axes.clear();
    parent::m_in_range_plane_Sxyw.clear();
    parent::m_annotations.clear();
 
    parent::m_bin_number = 0;
    parent::m_dimension = 0;
    parent::m_all_entries = 0;
    parent::m_in_range_entries = 0;
    parent::m_in_range_Sw = 0;
    parent::m_in_range_Sw2 = 0;
    parent::m_in_range_Sxw.resize(a_dim,0);
    parent::m_in_range_Sx2w.resize(a_dim,0);
 
    // Some checks :
    if(!a_dim) return false;
    parent::m_axes.resize(a_dim);
    // Setup axes :
    for(dim_t iaxis=0;iaxis<a_dim;iaxis++) {
      if(!parent::m_axes[iaxis].configure(a_edges[iaxis])) {
        //m_axes.clear();
        return false;
      }
    }
 
    parent::m_dimension = a_dim;
 
    base_allocate(); //set m_bin_number.
 
    return true;
  }
 
  void base_reset() {
    // Reset content (different of clear that deallocate all internal things).
    for(TO ibin=0;ibin<parent::m_bin_number;ibin++) {
      parent::m_bin_entries[ibin] = 0;
      parent::m_bin_Sw[ibin] = 0;
      parent::m_bin_Sw2[ibin] = 0;
      for(dim_t iaxis=0;iaxis<parent::m_dimension;iaxis++) {
        parent::m_bin_Sxw[ibin][iaxis] = 0;
        parent::m_bin_Sx2w[ibin][iaxis] = 0;
      }
    }
    parent::m_in_range_plane_Sxyw.assign(dim_planes(parent::m_dimension),0);
    //profile not done here.
    parent::reset_fast_getters();
  }
 
protected:
  void base_allocate() {
    dim_t iaxis;
    // Add two bins for the [under,out]flow data.
    TO n_bin = 1;
    for(iaxis=0;iaxis<parent::m_dimension;iaxis++) {
      n_bin *= (parent::m_axes[iaxis].bins() + 2);
    }
 
    parent::m_bin_entries.resize(n_bin,0);
    parent::m_bin_Sw.resize(n_bin,0);
    parent::m_bin_Sw2.resize(n_bin,0);
 
    std::vector<TC> empty;
    empty.resize(parent::m_dimension,0);
    parent::m_bin_Sxw.resize(n_bin,empty);
    parent::m_bin_Sx2w.resize(n_bin,empty);
 
    parent::m_bin_number = n_bin; // All bins : [in-range, underflow, outflow] bins.
 
    parent::m_axes[0].m_offset = 1;
    for(iaxis=1;iaxis<parent::m_dimension;iaxis++) {
      parent::m_axes[iaxis].m_offset = parent::m_axes[iaxis-1].m_offset * (parent::m_axes[iaxis-1].bins()+2);
    }
 
    parent::m_in_range_plane_Sxyw.resize(dim_planes(parent::m_dimension),0);
  }
 
public:
  // to access data from methods :
  const std::vector<TN>& bins_entries() const {return parent::m_bin_entries;}
  const std::vector<TW>& bins_sum_w() const {return parent::m_bin_Sw;}
  const std::vector<TW>& bins_sum_w2() const {return parent::m_bin_Sw2;}
  const std::vector< std::vector<TC> >& bins_sum_xw() const {return parent::m_bin_Sxw;}
  const std::vector< std::vector<TC> >& bins_sum_x2w() const {return parent::m_bin_Sx2w;}
  const std::vector<TC>& in_range_planes_xyw() const {return parent::m_in_range_plane_Sxyw;}
 
public:
  const axis_t& get_axis(int a_index) const {return parent::m_axes[a_index];}
  offset_t get_bins() const {return parent::m_bin_number;}
  const std::string& get_title() const {return parent::m_title;}
  dim_t get_dimension() const {return parent::m_dimension;}
  bool is_valid() const {return (parent::m_dimension?true:false);}
 
public: //annotations :
  typedef std::map<std::string,std::string> annotations_t;
  const annotations_t& annotations() const {return parent::m_annotations;}
  annotations_t annotations() {return parent::m_annotations;}
 
  void add_annotation(const std::string& a_key,const std::string& a_value) {
    parent::m_annotations[a_key] = a_value; //override if a_key already exists.
  }
  bool annotation(const std::string& a_key,std::string& a_value) const {
    annotations_t::const_iterator it = parent::m_annotations.find(a_key);
    if(it==parent::m_annotations.end()) {a_value.clear();return false;}
    a_value = (*it).second;
    return true;
  }
 
  void set_annotations(const annotations_t& a_annotations) {parent::m_annotations = a_annotations;}
 
  void hprint_annotations(std::ostream& a_out) {
    a_out << " * ANNOTATIONS :" << std::endl;
    annotations_t::const_iterator it;
    for(it=parent::m_annotations.begin();it!=parent::m_annotations.end();++it) {
    //out << " * (" << index << ") "
      a_out << " *  " << (*it).first << " = " << (*it).second << std::endl;
    }
  }
 
protected:
  bool is_compatible(const base_histo& a_histo){
    if(parent::m_dimension!=a_histo.m_dimension) return false;
    for(dim_t iaxis=0;iaxis<parent::m_dimension;iaxis++) {
      if(!parent::m_axes[iaxis].is_compatible(a_histo.m_axes[iaxis])) return false;
    }
    return true;
  }
 
  void base_add(const base_histo& a_histo){
    // The only histogram operation that makes sense.
    for(TO ibin=0;ibin<parent::m_bin_number;ibin++) {
      parent::m_bin_entries[ibin] += a_histo.m_bin_entries[ibin];
      parent::m_bin_Sw[ibin] += a_histo.m_bin_Sw[ibin];
      parent::m_bin_Sw2[ibin] += a_histo.m_bin_Sw2[ibin];
      for(dim_t iaxis=0;iaxis<parent::m_dimension;iaxis++) {
        parent::m_bin_Sxw[ibin][iaxis] += a_histo.m_bin_Sxw[ibin][iaxis];
        parent::m_bin_Sx2w[ibin][iaxis] += a_histo.m_bin_Sx2w[ibin][iaxis];
      }
    }
   {size_t nplane = parent::m_in_range_plane_Sxyw.size();
    for(size_t iplane=0;iplane<nplane;iplane++)
      parent::m_in_range_plane_Sxyw[iplane] += a_histo.m_in_range_plane_Sxyw[iplane];}
    parent::update_fast_getters();
  }
 
  void base_subtract(const base_histo& a_histo) {
    //ill-defined operation. We keep that because of the "ill-defined past".
    // We build a new histo with one entry in each bin.
    for(TO ibin=0;ibin<parent::m_bin_number;ibin++) {
      parent::m_bin_entries[ibin] = 1;
 
      parent::m_bin_Sw[ibin] -= a_histo.m_bin_Sw[ibin];
      // Yes, it is a += in the below.
      parent::m_bin_Sw2[ibin] += a_histo.m_bin_Sw2[ibin];
      for(dim_t iaxis=0;iaxis<parent::m_dimension;iaxis++) {
        parent::m_bin_Sxw[ibin][iaxis] -= a_histo.m_bin_Sxw[ibin][iaxis];
        parent::m_bin_Sx2w[ibin][iaxis] -= a_histo.m_bin_Sx2w[ibin][iaxis];
      }
    }
 
 //{for(dim_t iplane=0;iplane<nplane;iplane++) parent::m_in_range_plane_Sxyw[iplane] ??? a_histo.m_in_range_plane_Sxyw[iplane];}
 
    parent::update_fast_getters();
  }
 
  bool base_multiply(const base_histo& a_histo) {
    //ill-defined operation. We keep that because of the "ill-defined past".
 
    // We build a new histo with one entry in each bin of weight :
    //   this.w * a_histo.w
    // The current histo is overriden with this new histo.
    // The m_bin_Sw2 computation is consistent with FreeHEP and CERN-ROOT.
 
    if(!is_compatible(a_histo)) return false;
 
    std::vector<int> is(parent::m_dimension);
    for(TO ibin=0;ibin<parent::m_bin_number;ibin++) {
      TW swa = parent::m_bin_Sw[ibin];
      TW sw2a = parent::m_bin_Sw2[ibin];
      TW swb = a_histo.m_bin_Sw[ibin];
      TW sw2b = a_histo.m_bin_Sw2[ibin];
      TW sw = swa * swb;
      parent::m_bin_entries[ibin] = 1;
      parent::m_bin_Sw[ibin] = sw;
      parent::m_bin_Sw2[ibin] = sw2a * swb * swb + sw2b * swa * swa;
      histo::get_indices(parent::m_axes,ibin,is);
      for(dim_t iaxis=0;iaxis<parent::m_dimension;iaxis++) {
        TC x = parent::m_axes[iaxis].bin_center(is[iaxis]);
        parent::m_bin_Sxw[ibin][iaxis] = x * sw;
        parent::m_bin_Sx2w[ibin][iaxis] = x * x * sw;
      }
    }
 
 //{for(dim_t iplane=0;iplane<nplane;iplane++) parent::m_in_range_plane_Sxyw[iplane] ??? a_histo.m_in_range_plane_Sxyw[iplane];}
 
    parent::update_fast_getters();
    return true;
  }
 
  bool base_divide(const base_histo& a_histo) {
    //ill-defined operation. We keep that because of the "ill-defined past".
 
    // We build a new histo with one entry in each bin of weight :
    //   this.w / a_histo.w
    // The current histo is overriden with this new histo.
    // The m_bin_Sw2 computation is consistent with FreeHEP and ROOT.
 
    if(!is_compatible(a_histo)) return false;
 
    std::vector<int> is(parent::m_dimension);
    for(TO ibin=0;ibin<parent::m_bin_number;ibin++) {
      histo::get_indices(parent::m_axes,ibin,is);
      TW swa = parent::m_bin_Sw[ibin];
      TW swb = a_histo.m_bin_Sw[ibin];
      TW sw2a = parent::m_bin_Sw2[ibin];
      TW sw2b = a_histo.m_bin_Sw2[ibin];
      if(swb!=0) {
        parent::m_bin_entries[ibin] = 1;
        TW sw = swa / swb;
        parent::m_bin_Sw[ibin] = sw;
        TW swb2 = swb * swb;
        parent::m_bin_Sw2[ibin] = sw2a / swb2 + sw2b * swa * swa /(swb2*swb2);
        for(dim_t iaxis=0;iaxis<parent::m_dimension;iaxis++) {
          TC x = parent::m_axes[iaxis].bin_center(is[iaxis]);
          parent::m_bin_Sxw[ibin][iaxis] = x * sw;
          parent::m_bin_Sx2w[ibin][iaxis] = x * x * sw;
        }
      } else {
        parent::m_bin_entries[ibin] = 0;
        parent::m_bin_Sw[ibin] = 0;
        parent::m_bin_Sw2[ibin] = 0;
        for(dim_t iaxis=0;iaxis<parent::m_dimension;iaxis++) {
          parent::m_bin_Sxw[ibin][iaxis] = 0;
          parent::m_bin_Sx2w[ibin][iaxis] = 0;
        }
      }
    }
 
 //{for(dim_t iplane=0;iplane<nplane;iplane++) parent::m_in_range_plane_Sxyw[iplane] ??? a_histo.m_in_range_plane_Sxyw[iplane];}
 
    parent::update_fast_getters();
    return true;
  }
 
  bool base_multiply(TW a_factor) {
    if(a_factor<0) return false;
    TW factor2 = a_factor * a_factor;
    for(TO ibin=0;ibin<parent::m_bin_number;ibin++) {
      parent::m_bin_Sw[ibin] *= a_factor;
      parent::m_bin_Sw2[ibin] *= factor2;
      for(dim_t iaxis=0;iaxis<parent::m_dimension;iaxis++) {
        parent::m_bin_Sxw[ibin][iaxis] *= a_factor;
        parent::m_bin_Sx2w[ibin][iaxis] *= a_factor;
      }
    }
   {size_t nplane = parent::m_in_range_plane_Sxyw.size();
    for(size_t iplane=0;iplane<nplane;iplane++) parent::m_in_range_plane_Sxyw[iplane] *= a_factor;}
    parent::update_fast_getters();
    return true;
  }
 
  bool get_ith_axis_mean(dim_t a_axis,TC& a_value) const {
    a_value = 0;
    if(a_axis>=parent::m_dimension) return false;
    TW sw = 0;
    TC sxw = 0;
    for(TO ibin=0;ibin<parent::m_bin_number;ibin++) {
      if(!histo::is_out(parent::m_axes,ibin)) {
        sw += parent::m_bin_Sw[ibin];
        sxw += parent::m_bin_Sxw[ibin][a_axis];
      }
    }
    if(sw==0) return false;
    a_value = sxw/sw;
    return true;
  }
 
  bool get_ith_axis_rms(dim_t a_axis,TC& a_value) const {
    a_value = 0;
    if(a_axis>=parent::m_dimension) return false;
    TW sw = 0;
    TC sxw = 0;
    TC sx2w = 0;
    for(TO ibin=0;ibin<parent::m_bin_number;ibin++) {
      if(!histo::is_out(parent::m_axes,ibin)) {
        sw += parent::m_bin_Sw[ibin];
        sxw += parent::m_bin_Sxw[ibin][a_axis];
        sx2w += parent::m_bin_Sx2w[ibin][a_axis];
      }
    }
    if(sw==0) return false;
    TC mean = sxw/sw;
    a_value = ::sqrt(::fabs((sx2w / sw) - mean * mean));
    return true;
  }
 
  TN get_bin_entries(const std::vector<int>& aIs) const {
    if(parent::m_bin_number==0) return 0;
    TO offset;
    if(!histo::get_offset(parent::m_axes,aIs,offset)) return 0;
    return parent::m_bin_entries[offset];
  }
};
 
// predefined annotation keys :
inline const std::string& key_axis_x_title() {
  static const std::string s_v("axis_x.title");
  return s_v;
}
inline const std::string& key_axis_y_title() {
  static const std::string s_v("axis_y.title");
  return s_v;
}
inline const std::string& key_axis_z_title() {
  static const std::string s_v("axis_z.title");
  return s_v;
}
 
}}
 
#endif