THistImpl.hxx

Go to the documentation of this file.

/// \file ROOT/THistImpl.h
/// \ingroup Hist ROOT7
/// \author Axel Naumann <axel@cern.ch>
/// \date 2015-03-23
/// \warning This is part of the ROOT 7 prototype! It will change without notice. It might trigger earthquakes. Feedback
/// is welcome!

/*************************************************************************
 * Copyright (C) 1995-2015, Rene Brun and Fons Rademakers.               *
 * All rights reserved.                                                  *
 *                                                                       *
 * For the licensing terms see $ROOTSYS/LICENSE.                         *
 * For the list of contributors see $ROOTSYS/README/CREDITS.             *
 *************************************************************************/

#ifndef ROOT7_THistImpl
#define ROOT7_THistImpl

#include <cctype>
#include <functional>
#include "ROOT/RArrayView.hxx"
#include "ROOT/RTupleApply.hxx"

#include "ROOT/TAxis.hxx"
#include "ROOT/THistBinIter.hxx"
#include "ROOT/THistUtils.hxx"

class TRootIOCtor;

namespace ROOT {
namespace Experimental {

template <int DIMENSIONS, class PRECISION,
          template <int D_, class P_, template <class P__> class STORAGE> class... STAT>
class THist;

namespace Hist {
/// Iterator over n dimensional axes - an array of n axis iterators.
template <int NDIM>
using AxisIter_t = std::array<TAxisBase::const_iterator, NDIM>;
/// Range over n dimensional axes - a pair of arrays of n axis iterators.
template <int NDIM>
using AxisIterRange_t = std::array<AxisIter_t<NDIM>, 2>;

/// Kinds of under- and overflow handling.
enum class EOverflow {
   kNoOverflow = 0x0, ///< Exclude under- and overflows
   kUnderflow = 0x1,  ///< Include underflows
   kOverflow = 0x2,   ///< Include overflows
   kUnderOver = 0x3,  ///< Include both under- and overflows
};

inline bool operator&(EOverflow a, EOverflow b)
{
   return static_cast<int>(a) & static_cast<int>(b);
}
} // namespace Hist

namespace Detail {

/**
 \class THistImplPrecisionAgnosticBase
 Base class for THistImplBase that abstracts out the histogram's PRECISION.

 For operations such as painting a histogram, the PRECISION (type of the bin
 content) is not relevant; painting will cast the underlying bin type to double.
 To facilitate this, THistImplBase itself inherits from the
 THistImplPrecisionAgnosticBase interface.
 */
template <int DIMENSIONS>
class THistImplPrecisionAgnosticBase {
public:
   /// Type of the coordinate: a DIMENSIONS-dimensional array of doubles.
   using CoordArray_t = Hist::CoordArray_t<DIMENSIONS>;
   /// Range type.
   using AxisIterRange_t = Hist::AxisIterRange_t<DIMENSIONS>;

   THistImplPrecisionAgnosticBase() = default;
   THistImplPrecisionAgnosticBase(const THistImplPrecisionAgnosticBase &) = default;
   THistImplPrecisionAgnosticBase(THistImplPrecisionAgnosticBase &&) = default;
   THistImplPrecisionAgnosticBase(std::string_view title): fTitle(title) {}
   virtual ~THistImplPrecisionAgnosticBase() {}

   /// Number of dimensions of the coordinates
   static constexpr int GetNDim() { return DIMENSIONS; }
   /// Number of bins of this histogram, including all overflow and underflow
   /// bins. Simply the product of all axes' number of bins.
   virtual int GetNBins() const noexcept = 0;

   /// Get the histogram title.
   const std::string &GetTitle() const { return fTitle; }

   /// Given the coordinate `x`, determine the index of the bin.
   virtual int GetBinIndex(const CoordArray_t &x) const = 0;
   /// Given the coordinate `x`, determine the index of the bin, possibly growing
   /// axes for which `x` is out of range.
   virtual int GetBinIndexAndGrow(const CoordArray_t &x) = 0;

   /// Get the center in all dimensions of the bin with index `binidx`.
   virtual CoordArray_t GetBinCenter(int binidx) const = 0;
   /// Get the lower edge in all dimensions of the bin with index `binidx`.
   virtual CoordArray_t GetBinFrom(int binidx) const = 0;
   /// Get the upper edge in all dimensions of the bin with index `binidx`.
   virtual CoordArray_t GetBinTo(int binidx) const = 0;

   /// The bin's uncertainty. size() of the vector is a multiple of 2:
   /// several kinds of uncertainty, same number of entries for lower and upper.
   virtual double GetBinUncertainty(int binidx) const = 0;

   /// Whether this histogram's statistics provide storage for uncertainties, or
   /// whether uncertainties are determined as poisson uncertainty of the content.
   virtual bool HasBinUncertainty() const = 0;

   /// The bin content, cast to double.
   virtual double GetBinContentAsDouble(int binidx) const = 0;

   /// Get a TAxisView on axis with index iAxis.
   ///
   /// \param iAxis - index of the axis, must be 0 <= iAxis < DIMENSION
   virtual TAxisView GetAxis(int iAxis) const = 0;

   /// Get a AxisIterRange_t for the whole histogram, possibly restricting the
   /// range to non-overflow bins.
   ///
   /// \param withOverUnder - specifies for each dimension whether under and
   /// overflow should be included in the returned range.
   virtual AxisIterRange_t GetRange(const std::array<Hist::EOverflow, DIMENSIONS> &withOverUnder) const = 0;

private:
   std::string fTitle; ///< Histogram title.
};

/**
 \class THistImplBase
 Interface class for THistImpl.

 THistImpl is templated for a specific configuration of axes. To enable access
 through THist, THistImpl inherits from THistImplBase, exposing only dimension
 (`DIMENSION`) and bin type (`PRECISION`).
 */
template <class DATA>
class THistImplBase: public THistImplPrecisionAgnosticBase<DATA::GetNDim()> {
public:
   /// Type of the statistics (bin content, uncertainties etc).
   using Stat_t = DATA;
   /// Type of the coordinate: a DIMENSIONS-dimensional array of doubles.
   using CoordArray_t = Hist::CoordArray_t<DATA::GetNDim()>;
   /// Type of the bin content (and thus weights).
   using Weight_t = typename DATA::Weight_t;

   /// Type of the Fill(x, w) function
   using FillFunc_t = void (THistImplBase::*)(const CoordArray_t &x, Weight_t w);

private:
   /// The histogram's bin content, uncertainties etc.
   Stat_t fStatistics;

public:
   THistImplBase() = default;
   THistImplBase(size_t numBins): fStatistics(numBins) {}
   THistImplBase(std::string_view title, size_t numBins)
      : THistImplPrecisionAgnosticBase<DATA::GetNDim()>(title), fStatistics(numBins)
   {}
   THistImplBase(const THistImplBase &) = default;
   THistImplBase(THistImplBase &&) = default;

   /// Interface function to fill a vector or array of coordinates with
   /// corresponding weights.
   /// \note the size of `xN` and `weightN` must be the same!
   virtual void FillN(const std::array_view<CoordArray_t> xN, const std::array_view<Weight_t> weightN) = 0;

   /// Interface function to fill a vector or array of coordinates.
   virtual void FillN(const std::array_view<CoordArray_t> xN) = 0;

   /// Retrieve the pointer to the overridden Fill(x, w) function.
   virtual FillFunc_t GetFillFunc() const = 0;

   /// Apply a function (lambda) to all bins of the histogram. The function takes
   /// the bin reference.
   virtual void Apply(std::function<void(THistBinRef<const THistImplBase>)>) const = 0;

   /// Apply a function (lambda) to all bins of the histogram. The function takes
   /// the bin coordinate and content.
   virtual void ApplyXC(std::function<void(const CoordArray_t &, Weight_t)>) const = 0;

   /// Apply a function (lambda) to all bins of the histogram. The function takes
   /// the bin coordinate, content and uncertainty ("error") of the content.
   virtual void ApplyXCE(std::function<void(const CoordArray_t &, Weight_t, double)>) const = 0;

   /// Get the bin content (sum of weights) for the bin at coordinate x.
   virtual Weight_t GetBinContent(const CoordArray_t &x) const = 0;

   using THistImplPrecisionAgnosticBase<DATA::GetNDim()>::GetBinUncertainty;

   /// Get the bin uncertainty for the bin at coordinate x.
   virtual double GetBinUncertainty(const CoordArray_t &x) const = 0;

   /// Get the number of bins in this histogram, including possible under- and
   /// overflow bins.
   int GetNBins() const noexcept final { return fStatistics.size(); }

   /// Get the bin content (sum of weights) for bin index `binidx`.
   Weight_t GetBinContent(int binidx) const { return fStatistics[binidx]; }

   /// Get the bin content (sum of weights) for bin index `binidx` (non-const).
   Weight_t &GetBinContent(int binidx) { return fStatistics[binidx]; }

   /// Const access to statistics.
   const Stat_t &GetStat() const noexcept { return fStatistics; }

   /// Non-const access to statistics.
   Stat_t &GetStat() noexcept { return fStatistics; }

   /// Get the bin content (sum of weights) for bin index `binidx`, cast to
   /// double.
   double GetBinContentAsDouble(int binidx) const final { return (double)GetBinContent(binidx); }

   /// Add `w` to the bin at index `bin`.
   void AddBinContent(int binidx, Weight_t w) { fStatistics[binidx] += w; }
};
} // namespace Detail

namespace Internal {
/** \name Histogram traits
    Helper traits for histogram operations.
 */
///\{

/// \name Axis tuple operations
/// Template operations on axis tuple.
///@{
template <int IDX, class AXISTUPLE>
struct TGetBinCount;

template <class AXES>
struct TGetBinCount<0, AXES> {
   int operator()(const AXES &axes) const { return std::get<0>(axes).GetNBins(); }
};

template <int I, class AXES>
struct TGetBinCount {
   int operator()(const AXES &axes) const { return std::get<I>(axes).GetNBins() * TGetBinCount<I - 1, AXES>()(axes); }
};

template <class... AXISCONFIG>
int GetNBinsFromAxes(AXISCONFIG... axisArgs)
{
   using axesTuple = std::tuple<AXISCONFIG...>;
   return TGetBinCount<sizeof...(AXISCONFIG) - 1, axesTuple>()(axesTuple{axisArgs...});
}

template <int IDX, class HISTIMPL, class AXES, bool GROW>
struct TGetBinIndex;

// Break recursion
template <class HISTIMPL, class AXES, bool GROW>
struct TGetBinIndex<-1, HISTIMPL, AXES, GROW> {
   int operator()(HISTIMPL *, const AXES &, const typename HISTIMPL::CoordArray_t &,
                  TAxisBase::EFindStatus &status) const
   {
      status = TAxisBase::EFindStatus::kValid;
      return 0;
   }
};

template <int I, class HISTIMPL, class AXES, bool GROW>
struct TGetBinIndex {
   int operator()(HISTIMPL *hist, const AXES &axes, const typename HISTIMPL::CoordArray_t &x,
                  TAxisBase::EFindStatus &status) const
   {
      constexpr const int thisAxis = HISTIMPL::GetNDim() - I - 1;
      int bin = std::get<thisAxis>(axes).FindBin(x[thisAxis]);
      if (GROW && std::get<thisAxis>(axes).CanGrow() && (bin < 0 || bin > std::get<thisAxis>(axes).GetNBinsNoOver())) {
         hist->GrowAxis(I, x[thisAxis]);
         status = TAxisBase::EFindStatus::kCanGrow;

         // Abort bin calculation; we don't care. Let THist::GetBinIndex() retry!
         return bin;
      }
      return bin +
             TGetBinIndex<I - 1, HISTIMPL, AXES, GROW>()(hist, axes, x, status) * std::get<thisAxis>(axes).GetNBins();
   }
};

template <int I, class AXES>
struct TFillIterRange;

// Break recursion.
template <class AXES>
struct TFillIterRange<-1, AXES> {
   void operator()(Hist::AxisIterRange_t<std::tuple_size<AXES>::value> & /*range*/, const AXES & /*axes*/,
                   const std::array<Hist::EOverflow, std::tuple_size<AXES>::value> & /*over*/) const
   {}
};

/** Fill `range` with begin() and end() of all axes, including under/overflow
  as specified by `over`.
*/
template <int I, class AXES>
struct TFillIterRange {
   void operator()(Hist::AxisIterRange_t<std::tuple_size<AXES>::value> &range, const AXES &axes,
                   const std::array<Hist::EOverflow, std::tuple_size<AXES>::value> &over) const
   {
      if (over[I] & Hist::EOverflow::kUnderflow)
         range[0][I] = std::get<I>(axes).begin_with_underflow();
      else
         range[0][I] = std::get<I>(axes).begin();
      if (over[I] & Hist::EOverflow::kOverflow)
         range[1][I] = std::get<I>(axes).end_with_overflow();
      else
         range[1][I] = std::get<I>(axes).end();
      TFillIterRange<I - 1, AXES>()(range, axes, over);
   }
};

enum class EBinCoord {
   kBinFrom,   ///< Get the lower bin edge
   kBinCenter, ///< Get the bin center
   kBinTo      ///< Get the bin high edge
};

template <int I, class COORD, class AXES>
struct TFillBinCoord;

// Break recursion.
template <class COORD, class AXES>
struct TFillBinCoord<-1, COORD, AXES> {
   void operator()(COORD & /*coord*/, const AXES & /*axes*/, EBinCoord /*kind*/, int /*binidx*/) const {}
};

/** Fill `coord` with low bin edge or center or high bin edge of all axes.
 */
template <int I, class COORD, class AXES>
struct TFillBinCoord {
   void operator()(COORD &coord, const AXES &axes, EBinCoord kind, int binidx) const
   {
      int axisbin = binidx % std::get<I>(axes).GetNBins();
      size_t coordidx = std::tuple_size<AXES>::value - I - 1;
      switch (kind) {
      case EBinCoord::kBinFrom: coord[coordidx] = std::get<I>(axes).GetBinFrom(axisbin); break;
      case EBinCoord::kBinCenter: coord[coordidx] = std::get<I>(axes).GetBinCenter(axisbin); break;
      case EBinCoord::kBinTo: coord[coordidx] = std::get<I>(axes).GetBinTo(axisbin); break;
      }
      TFillBinCoord<I - 1, COORD, AXES>()(coord, axes, kind, binidx / std::get<I>(axes).GetNBins());
   }
};

template <class... AXISCONFIG>
static std::array<TAxisView, sizeof...(AXISCONFIG)> GetAxisView(const AXISCONFIG &... axes) noexcept
{
   std::array<TAxisView, sizeof...(AXISCONFIG)> axisViews = {{TAxisView(axes)...}};
   return axisViews;
}

///\}
} // namespace Internal

namespace Detail {

template <class DATA, class... AXISCONFIG>
class THistImpl final: public THistImplBase<DATA> {
   static_assert(sizeof...(AXISCONFIG) == DATA::GetNDim(), "Number of axes must equal histogram dimension");

   friend typename DATA::Hist_t;

public:
   using ImplBase_t = THistImplBase<DATA>;
   using CoordArray_t = typename ImplBase_t::CoordArray_t;
   using Weight_t = typename ImplBase_t::Weight_t;
   using typename ImplBase_t::FillFunc_t;
   template <int NDIM = DATA::GetNDim()>
   using AxisIterRange_t = typename Hist::AxisIterRange_t<NDIM>;

private:
   std::tuple<AXISCONFIG...> fAxes; ///< The histogram's axes

public:
   THistImpl(TRootIOCtor *);
   THistImpl(AXISCONFIG... axisArgs);
   THistImpl(std::string_view title, AXISCONFIG... axisArgs);

   /// Retrieve the fill function for this histogram implementation, to prevent
   /// the virtual function call for high-frequency fills.
   FillFunc_t GetFillFunc() const final { return (FillFunc_t)&THistImpl::Fill; }

   /// Apply a function (lambda) to all bins of the histogram. The function takes
   /// the bin reference.
   void Apply(std::function<void(THistBinRef<const ImplBase_t>)> op) const final
   {
      for (THistBinRef<const ImplBase_t> binref: *this)
         op(binref);
   }

   /// Apply a function (lambda) to all bins of the histogram. The function takes
   /// the bin coordinate and content.
   void ApplyXC(std::function<void(const CoordArray_t &, Weight_t)> op) const final
   {
      for (auto binref: *this)
         op(binref.GetCenter(), binref.GetContent());
   }

   /// Apply a function (lambda) to all bins of the histogram. The function takes
   /// the bin coordinate, content and uncertainty ("error") of the content.
   virtual void ApplyXCE(std::function<void(const CoordArray_t &, Weight_t, double)> op) const final
   {
      for (auto binref: *this)
         op(binref.GetCenter(), binref.GetContent(), binref.GetUncertainty());
   }

   /// Get the axes of this histogram.
   const std::tuple<AXISCONFIG...> &GetAxes() const { return fAxes; }

   /// Normalized axes access, converting the actual axis to TAxisConfig
   TAxisView GetAxis(int iAxis) const final { return std::apply(Internal::GetAxisView<AXISCONFIG...>, fAxes)[iAxis]; }

   /// Gets the bin index for coordinate `x`; returns -1 if there is no such bin,
   /// e.g. for axes without over / underflow but coordinate out of range.
   int GetBinIndex(const CoordArray_t &x) const final
   {
      TAxisBase::EFindStatus status = TAxisBase::EFindStatus::kValid;
      int ret =
         Internal::TGetBinIndex<DATA::GetNDim() - 1, THistImpl, decltype(fAxes), false>()(nullptr, fAxes, x, status);
      if (status != TAxisBase::EFindStatus::kValid)
         return -1;
      return ret;
   }

   /// Gets the bin index for coordinate `x`, growing the axes as needed and
   /// possible. Returns -1 if there is no such bin,
   /// e.g. for axes without over / underflow but coordinate out of range.
   int GetBinIndexAndGrow(const CoordArray_t &x) final
   {
      TAxisBase::EFindStatus status = TAxisBase::EFindStatus::kCanGrow;
      int ret = -1;
      while (status == TAxisBase::EFindStatus::kCanGrow) {
         ret = Internal::TGetBinIndex<DATA::GetNDim() - 1, THistImpl, decltype(fAxes), true>()(this, fAxes, x, status);
      }
      return ret;
   }

   /// Get the center coordinate of the bin.
   CoordArray_t GetBinCenter(int binidx) const final
   {
      using TFillBinCoord = Internal::TFillBinCoord<DATA::GetNDim() - 1, CoordArray_t, decltype(fAxes)>;
      CoordArray_t coord;
      TFillBinCoord()(coord, fAxes, Internal::EBinCoord::kBinCenter, binidx);
      return coord;
   }

   /// Get the coordinate of the low limit of the bin.
   CoordArray_t GetBinFrom(int binidx) const final
   {
      using TFillBinCoord = Internal::TFillBinCoord<DATA::GetNDim() - 1, CoordArray_t, decltype(fAxes)>;
      CoordArray_t coord;
      TFillBinCoord()(coord, fAxes, Internal::EBinCoord::kBinFrom, binidx);
      return coord;
   }

   /// Get the coordinate of the high limit of the bin.
   CoordArray_t GetBinTo(int binidx) const final
   {
      using TFillBinCoord = Internal::TFillBinCoord<DATA::GetNDim() - 1, CoordArray_t, decltype(fAxes)>;
      CoordArray_t coord;
      TFillBinCoord()(coord, fAxes, Internal::EBinCoord::kBinTo, binidx);
      return coord;
   }

   /// Fill an array of `weightN` to the bins specified by coordinates `xN`.
   /// For each element `i`, the weight `weightN[i]` will be added to the bin
   /// at the coordinate `xN[i]`
   /// \note `xN` and `weightN` must have the same size!
   void FillN(const std::array_view<CoordArray_t> xN, const std::array_view<Weight_t> weightN) final
   {
#ifndef NDEBUG
      if (xN.size() != weightN.size()) {
         R__ERROR_HERE("HIST") << "Not the same number of points and weights!";
         return;
      }
#endif

      for (size_t i = 0; i < xN.size(); ++i) {
         Fill(xN[i], weightN[i]);
      }
   }

   /// Fill an array of `weightN` to the bins specified by coordinates `xN`.
   /// For each element `i`, the weight `weightN[i]` will be added to the bin
   /// at the coordinate `xN[i]`
   void FillN(const std::array_view<CoordArray_t> xN) final
   {
      for (auto &&x: xN) {
         Fill(x);
      }
   }

   /// Add a single weight `w` to the bin at coordinate `x`.
   void Fill(const CoordArray_t &x, Weight_t w = 1.)
   {
      int bin = GetBinIndexAndGrow(x);
      this->GetStat().Fill(x, bin, w);
   }

   /// Get the content of the bin at position `x`.
   Weight_t GetBinContent(const CoordArray_t &x) const final
   {
      int bin = GetBinIndex(x);
      if (bin >= 0)
         return ImplBase_t::GetBinContent(bin);
      return 0.;
   }

   /// Return the uncertainties for the given bin.
   double GetBinUncertainty(int binidx) const final { return this->GetStat().GetBinUncertainty(binidx); }

   /// Get the bin uncertainty for the bin at coordinate x.
   double GetBinUncertainty(const CoordArray_t &x) const final
   {
      const int bin = GetBinIndex(x);
      return this->GetBinUncertainty(bin);
   }

   /// Whether this histogram's statistics provide storage for uncertainties, or
   /// whether uncertainties are determined as poisson uncertainty of the content.
   bool HasBinUncertainty() const final { return this->GetStat().HasBinUncertainty(); }

   /// Get the begin() and end() for each axis.
   ///
   ///\param[in] withOverUnder - Whether the begin and end should contain over-
   /// or underflow. Ignored if the axis does not support over- / underflow.
   AxisIterRange_t<DATA::GetNDim()>
   GetRange(const std::array<Hist::EOverflow, DATA::GetNDim()> &withOverUnder) const final
   {
      std::array<std::array<TAxisBase::const_iterator, DATA::GetNDim()>, 2> ret;
      Internal::TFillIterRange<DATA::GetNDim() - 1, decltype(fAxes)>()(ret, fAxes, withOverUnder);
      return ret;
   }

   /// Grow the axis number `iAxis` to fit the coordinate `x`.
   ///
   /// The histogram (conceptually) combines pairs of bins along this axis until
   /// `x` is within the range of the axis.
   /// The axis must support growing for this to work (e.g. a `TAxisGrow`).
   void GrowAxis(int /*iAxis*/, double /*x*/)
   {
      // TODO: Implement GrowAxis()
   }

   /// \{
   /// \name Iterator interface
   using const_iterator = THistBinIter<const ImplBase_t>;
   using iterator = THistBinIter<ImplBase_t>;
   iterator begin() noexcept { return iterator(*this); }
   const_iterator begin() const noexcept { return const_iterator(*this); }
   iterator end() noexcept { return iterator(*this, this->GetNBins()); }
   const_iterator end() const noexcept { return const_iterator(*this, this->GetNBins()); }
   /// \}
};

template <class DATA, class... AXISCONFIG>
THistImpl<DATA, AXISCONFIG...>::THistImpl(TRootIOCtor *)
{}

template <class DATA, class... AXISCONFIG>
THistImpl<DATA, AXISCONFIG...>::THistImpl(AXISCONFIG... axisArgs)
   : ImplBase_t(Internal::GetNBinsFromAxes(axisArgs...)), fAxes{axisArgs...}
{}

template <class DATA, class... AXISCONFIG>
THistImpl<DATA, AXISCONFIG...>::THistImpl(std::string_view title, AXISCONFIG... axisArgs)
   : ImplBase_t(title, Internal::GetNBinsFromAxes(axisArgs...)), fAxes{axisArgs...}
{}

#if 0
// In principle we can also have a runtime version of THistImpl, that does not
// contain a tuple of concrete axis types but a vector of `TAxisConfig`.
template <class DATA>
class THistImplRuntime: public THistImplBase<DATA> {
public:
  THistImplRuntime(std::array<TAxisConfig, DATA::GetNDim()>&& axisCfg);
};
#endif

} // namespace Detail

} // namespace Experimental
} // namespace ROOT

#endif