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 // -*- C++ -*-
 //
 // This file is part of YODA -- Yet more Objects for Data Analysis
 // Copyright (C) 2008-2025 The YODA collaboration (see AUTHORS for details)
 //
 #ifndef YODA_BinnedDbn_h
 #define YODA_BinnedDbn_h
 
 #include "YODA/AnalysisObject.h"
 #include "YODA/Fillable.h"
 #include "YODA/FillableStorage.h"
 #include "YODA/Dbn.h"
 #include "YODA/BinnedEstimate.h"
 #include "YODA/Scatter.h"
 
 #ifdef HAVE_HDF5
 #include "YODA/Utils/H5Utils.h"
 #endif
 
 #include <memory>
 #include <utility>
 #include <iostream>
 #include <iomanip>
 
 namespace YODA {
 
 
   /// All histograms can be instantiated through this alias.
   /*
   ///               BinnedStorage                : Introduces binning backend.
   ///                     |
   ///              FillableStorage               : Introduces FillAdapterT
   ///                     |
   ///                 DbnStorage                 : Hooks up with AnalysisObject
   ///                     /\
   ///                    /  \
   ///    BinnedDbn<1>___/    \___ BinnedDbn<2>   : Introduces dimension specific
   ///          \                     /           : utility aliases
   ///           \_______     _______/            : (xMin(), yMax(), etc.)
   ///                   \   /
   ///                    \ /
   ///                     |
   ///         BinnedHisto/BinnedProfile          : Convenience alias
   */
   /// Since objects with continuous axes are by far the most commonly used type
   /// in practice, we define convenient short-hand aliases HistoND/ProfileND for
   /// with only continuous axes, along with the familar types Histo1D, Profile2D, etc.
 
 
   template <size_t DbnN, typename... AxisT>
   class DbnStorage;
 
   /// @brief User-facing BinnedDbn class in arbitrary dimension
   template <size_t DbnN, typename... AxisT>
   class BinnedDbn : public DbnStorage<DbnN, AxisT...> {
   public:
     using HistoT = BinnedDbn<DbnN, AxisT...>;
     using BaseT = DbnStorage<DbnN, AxisT...>;
     using FillType = typename BaseT::FillType;
     using BinType = typename BaseT::BinT;
     using Ptr = std::shared_ptr<HistoT>;
 
     /// @brief Inherit constructors.
     using BaseT::BaseT;
 
     BinnedDbn() = default;
     BinnedDbn(const HistoT&) = default;
     BinnedDbn(HistoT&&) = default;
     BinnedDbn& operator =(const HistoT&) = default;
     BinnedDbn& operator =(HistoT&&) = default;
     using AnalysisObject::operator =;
 
     /// @brief Copy constructor (needed for clone functions).
     ///
     /// @note Compiler won't generate this constructor automatically.
     BinnedDbn(const BaseT& other) : BaseT(other) {}
     //
     BinnedDbn(const HistoT& other, const std::string& path) : BaseT(other, path) {}
 
     /// @brief Move constructor
     BinnedDbn(BaseT&& other) : BaseT(std::move(other)) {}
     //
     BinnedDbn(HistoT&& other, const std::string& path) : BaseT(std::move(other), path) {}
 
     /// @brief Make a copy on the stack
     HistoT clone() const noexcept {
       return HistoT(*this);
     }
 
     /// @brief Make a copy on the heap
     HistoT* newclone() const noexcept {
       return new HistoT(*this);
     }
 
   };
 
 
   /// @name Define dimension-specific short-hands
   /// @{
 
   template <typename... AxisTypes>
   using BinnedHisto = BinnedDbn<sizeof...(AxisTypes), AxisTypes...>;
 
   template <typename... AxisTypes>
   using BinnedProfile = BinnedDbn<sizeof...(AxisTypes)+1, AxisTypes...>;
 
   /// @}
 
 
   /// @brief Histogram convenience class based on FillableStorage.
   ///
   /// @note We use this abstraction layer to implement the bulk once and only once.
   /// The user-facing BinnedDbn type(s) will inherit all their methods from this
   /// base class along with a few axis-specifc mixins.
   ///
   /// @note Alias generates index sequence later used to create
   /// a parameter pack consisting of axis types to instantiate
   /// the Binning template.
   template <size_t DbnN, typename... AxisT>
   class DbnStorage : public FillableStorage<DbnN, Dbn<DbnN>, AxisT...>,
                      public AnalysisObject, public Fillable {
   public:
 
     using BaseT = FillableStorage<DbnN, Dbn<DbnN>, AxisT...>;
     using BinningT = typename BaseT::BinningT;
     using BinT = typename BaseT::BinT;
     using BinType = typename BaseT::BinT;
     using FillType = typename BaseT::FillType;
     using AnalysisObject::operator =;
 
     /// @name Constructors
     /// @{
 
     /// @brief Nullary constructor for unique pointers etc.
     ///
     /// @note The setting of optional path/title is not possible here in order
     /// to avoid overload ambiguity for brace-initialised constructors.
     DbnStorage() : BaseT(), AnalysisObject(mkTypeString<DbnN, AxisT...>(), "") { }
 
     /// @brief Constructor giving explicit bin edges as rvalue reference.
     ///
     /// Discrete axes have as many edges as bins.
     /// Continuous axes have number of edges = number of bins + 1,
     /// the last one being the upper bound of the last bin.
     DbnStorage(std::vector<AxisT>&&... binsEdges,
                const std::string& path = "", const std::string& title = "")
          : BaseT(Axis<AxisT>(std::move(binsEdges))...),
            AnalysisObject(mkTypeString<DbnN, AxisT...>(), path, title) { }
 
     /// @brief Constructor giving explicit bin edges as lvalue const reference.
     ///
     /// Discrete axes have as many edges as bins.
     /// Continuous axes have bins.size()+1 edges, the last one
     /// being the upper bound of the last bin.
     DbnStorage(const std::vector<AxisT>&... binsEdges,
                const std::string& path = "", const std::string& title = "")
          : BaseT(Axis<AxisT>(binsEdges)...),
            AnalysisObject(mkTypeString<DbnN, AxisT...>(), path, title) { }
 
     /// @brief Constructor giving explicit bin edges as initializer list
     ///
     /// Discrete axes have as many edges as bins.
     /// Continuous axes have number of edges = number of bins + 1,
     /// the last one being the upper bound of the last bin.
     DbnStorage(std::initializer_list<AxisT>&&... binsEdges,
                const std::string& path = "", const std::string& title = "")
          : BaseT(Axis<AxisT>(std::move(binsEdges))...),
            AnalysisObject(mkTypeString<DbnN, AxisT...>(), path, title) { }
 
     /// @brief Constructor giving range and number of bins.
     ///
     /// @note This constructor is only supported for objects with purely continous axes.
     /// It is also the only place where the index sequence sequence is actually needed.
     template <typename EdgeT = double, typename = enable_if_all_CAxisT<EdgeT, AxisT...>>
     DbnStorage(const std::vector<size_t>& nBins, const std::vector<std::pair<EdgeT, EdgeT>>& limitsLowUp,
                const std::string& path = "", const std::string& title = "")
          : BaseT( _mkBinning(nBins, limitsLowUp, std::make_index_sequence<sizeof...(AxisT)>{}) ),
            AnalysisObject(mkTypeString<DbnN, AxisT...>(), path, title) { }
 
     /// @brief Constructor given a sequence of axes
     DbnStorage(const Axis<AxisT>&... axes, const std::string& path = "", const std::string& title = "")
          : BaseT(axes...), AnalysisObject(mkTypeString<DbnN, AxisT...>(), path, title) { }
 
     /// @brief Constructor given a sequence of rvalue axes
     DbnStorage(Axis<AxisT>&&... axes, const std::string& path = "", const std::string& title = "")
          : BaseT(std::move(axes)...), AnalysisObject(mkTypeString<DbnN, AxisT...>(), path, title) { }
 
     /// @brief Constructor given a BinningT (needed for type reductions)
     DbnStorage(const BinningT& binning, const std::string& path = "", const std::string& title = "")
          : BaseT(binning), AnalysisObject(mkTypeString<DbnN, AxisT...>(), path, title) { }
 
     /// @brief Constructor given an rvalue BinningT
     DbnStorage(BinningT&& binning, const std::string& path = "", const std::string& title = "")
          : BaseT(std::move(binning)), AnalysisObject(mkTypeString<DbnN, AxisT...>(), path, title) { }
 
     /// @brief Constructor given a scatter
     template <typename EdgeT = double, typename = enable_if_all_CAxisT<EdgeT, AxisT...>>
     DbnStorage(const ScatterND<sizeof...(AxisT)+1>& s, const std::string& path = "", const std::string& title = "")
          : BaseT(_mkBinning(s, std::make_index_sequence<sizeof...(AxisT)>{})),
            AnalysisObject(mkTypeString<DbnN, AxisT...>(), path, title) { }
 
     /// @brief Copy constructor
     ///
     /// @todo Also allow title setting from the constructor?
     DbnStorage(const DbnStorage& other, const std::string& path = "") : BaseT(other),
          AnalysisObject(mkTypeString<DbnN, AxisT...>(), path!=""? path : other.path(), other, other.title()) { }
 
     /// @brief Move constructor
     ///
     /// @todo Also allow title setting from the constructor?
     DbnStorage(DbnStorage&& other, const std::string& path = "") : BaseT(std::move(other)),
          AnalysisObject(mkTypeString<DbnN, AxisT...>(), path!=""? path : other.path(), other, other.title()) {  }
 
     /// @brief Make a copy on the stack
     DbnStorage clone() const noexcept {
       return DbnStorage(*this);
     }
 
     /// @brief Make a copy on the heap
     DbnStorage* newclone() const noexcept {
       return new DbnStorage(*this);
     }
 
     /// @}
 
 
     /// @name Transformations
     /// @{
 
     /// @brief Triggers fill adapter on the bin corresponding to coords.
     ///
     /// @note Accepts coordinates only as rvalue tuple. The tuple members
     /// are then moved (bringing tuple member to unspecified state) later in adapters.
     virtual int fill(FillType&& coords, const double weight = 1.0, const double fraction = 1.0) {
       return BaseT::fill(std::move(coords), std::make_index_sequence<sizeof...(AxisT)>{}, weight, fraction);
     }
 
     /// @brief Rescale as if all fill weights had been different by factor @a scalefactor.
     void scaleW(const double scalefactor) noexcept {
       setAnnotation("ScaledBy", annotation<double>("ScaledBy", 1.0) * scalefactor);
       for (auto& bin : BaseT::_bins) {
         bin.scaleW(scalefactor);
       }
     }
 
     /// @brief Rescale as if all fill weights had been different by factor @a scalefactor along dimension @a i.
     void scale(const size_t i, const double scalefactor) noexcept {
       setAnnotation("ScaledBy", annotation<double>("ScaledBy", 1.0) * scalefactor);
       for (auto& bin : BaseT::_bins) {
         bin.scale(i, scalefactor);
       }
     }
 
 
     /// @brief Normalize the (visible) histo "volume" to the @a normto value.
     ///
     /// If @a includeoverflows is true, the original normalisation is computed with
     /// the overflow bins included, so that the resulting visible normalisation can
     /// be less than @a normto. This is probably what you want.
     void normalize(const double normto=1.0, const bool includeOverflows=true) {
       const double oldintegral = integral(includeOverflows);
       if (oldintegral == 0) throw WeightError("Attempted to normalize a histogram with null area");
       scaleW(normto / oldintegral);
     }
 
 
     /// @brief Merge every group of @a n bins, from start to end inclusive
     ///
     /// If the number of bins is not a multiple of @a n, the last @a m < @a n
     /// bins on the RHS will also be merged, as the closest possible approach to
     /// factor @n rebinning everywhere.
     ///
     /// @note Only visible bins are being rebinned. Underflow (index = 0) and
     /// overflow (index = numBins() + 1) are not included.
     ///
     /// @note Only supported for continuous axes
     template <size_t axisN, typename = std::enable_if_t<BinningT::template is_CAxis<axisN>::value>>
     void rebinBy(unsigned int n, size_t begin=1, size_t end=UINT_MAX) {
       if (n < 1)  throw UserError("Rebinning requested in groups of 0!");
       if (!begin) throw UserError("Visible bins start with index 1!");
       if (end > BaseT::numBinsAt(axisN)+1)  end = BaseT::numBinsAt(axisN) + 1;
       for (size_t m = begin; m < end; ++m) {
         if (m > BaseT::numBinsAt(axisN)+1) break; // nothing to be done
         const size_t myend = (m+n-1 < BaseT::numBinsAt(axisN)+1) ? m+n-1 : BaseT::numBinsAt(axisN);
         if (myend > m) {
           BaseT::template mergeBins<axisN>({m, myend});
           end -= myend-m; //< reduce upper index by the number of removed bins
         }
       }
     }
 
     /// @brief Overloaded alias for rebinBy
     ///
     /// @note Only supported for continuous axes
     template <size_t axisN, typename = std::enable_if_t<BinningT::template is_CAxis<axisN>::value>>
     void rebin(unsigned int n, size_t begin=1, size_t end=UINT_MAX) {
       rebinBy<axisN>(n, begin, end);
     }
 
     /// @brief Rebin to the given list of bin edges
     ///
     /// @note Only supported for continuous axes
     template <size_t axisN, typename = std::enable_if_t<BinningT::template is_CAxis<axisN>::value>>
     void rebinTo(const std::vector<typename BinningT::template getAxisT<axisN>::EdgeT>& newedges) {
       if (newedges.size() < 2)
         throw UserError("Requested rebinning to an edge list which defines no bins");
       using thisAxisT = typename BinningT::template getAxisT<axisN>;
       using thisEdgeT = typename thisAxisT::EdgeT;
       // get list of shared edges
       thisAxisT& oldAxis = BaseT::_binning.template axis<axisN>();
       const thisAxisT newAxis(newedges);
       const std::vector<thisEdgeT> eshared = oldAxis.sharedEdges(newAxis);
       if (eshared.size() != newAxis.edges().size())
         throw BinningError("Requested rebinning to incompatible edges");
       // loop over new lower bin edges (= first bin index of merge range)
       for (size_t begin = 0; begin < eshared.size() - 1; ++begin) {
         // find index of upper edge along old axis
         // (subtracting 1 gives index of last bin to be merged)
         size_t end = oldAxis.index(eshared[begin+1]) - 1;
         // if the current edge is the last visible edge before the overflow
         // merge the remaining bins into the overflow
         if (begin == newAxis.numBins(true)-1)  end = oldAxis.numBins(true)-1;
         // merge this range
         if (end > begin)  BaseT::template mergeBins<axisN>({begin, end});
         if (eshared.size() == oldAxis.edges().size())  break; // we're done
       }
     }
 
     /// @brief Overloaded alias for rebinTo
     ///
     /// @note Only supported for continuous axes
     template <size_t axisN, typename = std::enable_if_t<BinningT::template is_CAxis<axisN>::value>>
     void rebin(const std::vector<typename BinningT::template getAxisT<axisN>::EdgeT>& newedges) {
       rebinTo<axisN>(newedges);
     }
 
     /// Copy assignment
     DbnStorage& operator = (const DbnStorage& dbn) noexcept {
       if (this != &dbn) {
         AnalysisObject::operator = (dbn);
         BaseT::operator = (dbn);
       }
       return *this;
     }
 
     /// Move assignment
     DbnStorage& operator = (DbnStorage&& dbn) noexcept {
       if (this != &dbn) {
         AnalysisObject::operator = (dbn);
         BaseT::operator = (std::move(dbn));
       }
       return *this;
     }
 
 
     /// @brief Add two DbnStorages
     ///
     /// @note Adding DbnStorages will unset any ScaledBy
     /// attribute from previous calls to scale or normalize.
     ///
     /// @todo What happens if two storages disagree on masked bins?
     DbnStorage& operator += (const DbnStorage& dbn) {
       if (*this != dbn)
         throw BinningError("Arithmetic operation requires compatible binning!");
       if (AO::hasAnnotation("ScaledBy")) AO::rmAnnotation("ScaledBy");
       for (size_t i = 0; i < BaseT::numBins(true, true); ++i) {
         BaseT::bin(i) += dbn.bin(i);
       }
       BaseT::maskBins(dbn.maskedBins(), true);
       return *this;
     }
     //
     DbnStorage& operator += (DbnStorage&& dbn) {
       if (*this != dbn)
         throw BinningError("Arithmetic operation requires compatible binning!");
       if (AO::hasAnnotation("ScaledBy")) AO::rmAnnotation("ScaledBy");
       for (size_t i = 0; i < BaseT::numBins(true, true); ++i) {
         BaseT::bin(i) += std::move(dbn.bin(i));
       }
       BaseT::maskBins(dbn.maskedBins(), true);
       return *this;
     }
 
 
     /// @brief Subtract one DbnStorages from another one
     ///
     /// @note Subtracting DbnStorages will unset any ScaledBy
     /// attribute from previous calls to scale or normalize.
     DbnStorage& operator -= (const DbnStorage& dbn) {
       if (*this != dbn)
         throw BinningError("Arithmetic operation requires compatible binning!");
       if (AO::hasAnnotation("ScaledBy")) AO::rmAnnotation("ScaledBy");
       for (size_t i = 0; i < BaseT::numBins(true, true); ++i) {
         BaseT::bin(i) -= dbn.bin(i);
       }
       BaseT::maskBins(dbn.maskedBins(), true);
       return *this;
     }
     //
     DbnStorage& operator -= (DbnStorage&& dbn) {
       if (*this != dbn)
         throw BinningError("Arithmetic operation requires compatible binning!");
       if (AO::hasAnnotation("ScaledBy")) AO::rmAnnotation("ScaledBy");
       for (size_t i = 0; i < BaseT::numBins(true, true); ++i) {
         BaseT::bin(i) -= std::move(dbn.bin(i));
       }
       BaseT::maskBins(dbn.maskedBins(), true);
       return *this;
     }
 
     /// @}
 
     /// @name Reset methods
     /// @{
 
     /// @brief Reset the histogram.
     ///
     /// Keep the binning but set all bin contents and related quantities to zero
     void reset() noexcept { BaseT::reset(); }
 
     /// @}
 
 
     /// @name Binning info.
     /// @{
 
     size_t fillDim() const noexcept { return BaseT::fillDim(); }
 
     /// @brief Total dimension of the object (number of axes + filled value)
     size_t dim() const noexcept { return sizeof...(AxisT) + 1; }
 
     /// @brief Returns the axis configuration
     std::string _config() const noexcept { return mkAxisConfig<AxisT...>(); }
 
     /// @}
 
 
     /// @name Whole histo data
     /// @{
 
     /// @brief Get the total volume of the histogram.
     double integral(const bool includeOverflows=true) const noexcept {
       return sumW(includeOverflows);
     }
 
     /// @brief Get the total volume error of the histogram.
     double integralError(const bool includeOverflows=true) const noexcept {
       return sqrt(sumW2(includeOverflows));
     }
 
     /// @brief Get the total volume of the histogram.
     double integralTo(const size_t binIndex) const noexcept {
       return integralRange(0, binIndex);
     }
 
     /// @brief Calculates the integrated volume of the histogram between
     /// global bins @a binindex1 and @a binIndex2.
     double integralRange(const size_t binIndex1, size_t binIndex2) const {
       assert(binIndex2 >= binIndex1);
       if (binIndex1 >= BaseT::numBins(true)) throw RangeError("binindex1 is out of range");
       if (binIndex2 >= BaseT::numBins(true)) throw RangeError("binindex2 is out of range");
       double sumw = 0;
       for (size_t idx = binIndex1; idx <= binIndex2; ++idx) {
         if (BaseT::bin(idx).isMasked())  continue;
         sumw += BaseT::bin(idx).sumW();
       }
       return sumw;
     }
 
     /// @brief Calculates the integrated volume error of the histogram between
     /// global bins @a binindex1 and @a binIndex2.
     double integralRangeError(const size_t binIndex1, size_t binIndex2) const {
       assert(binIndex2 >= binIndex1);
       if (binIndex1 >= BaseT::numBins(true)) throw RangeError("binindex1 is out of range");
       if (binIndex2 >= BaseT::numBins(true)) throw RangeError("binindex2 is out of range");
       double sumw2 = 0;
       for (size_t idx = binIndex1; idx <= binIndex2; ++idx) {
         if (BaseT::bin(idx).isMasked())  continue;
         sumw2 += BaseT::bin(idx).sumW2();
       }
       return sumw2;
     }
 
     /// @brief Get the number of fills (fractional fills are possible).
     double numEntries(const bool includeOverflows=true) const noexcept {
       double n = 0;
       for (const auto& b : BaseT::bins(includeOverflows)) {
         n += b.numEntries();
       }
       return n;
     }
 
     /// @brief Get the effective number of fills.
     double effNumEntries(const bool includeOverflows=true) const noexcept {
       double n = 0;
       for (const auto& b : BaseT::bins(includeOverflows)) {
         n += b.effNumEntries();
       }
       return n;
     }
 
     /// @brief Calculates sum of weights in histo.
     double sumW(const bool includeOverflows=true) const noexcept {
       double sumw = 0;
       for (const auto& b : BaseT::bins(includeOverflows)) {
         sumw += b.sumW();
       }
       return sumw;
     }
 
     /// @brief Calculates sum of squared weights in histo.
     double sumW2(const bool includeOverflows=true) const noexcept {
       double sumw2 = 0;
       for (const auto& b : BaseT::bins(includeOverflows)) {
         sumw2 += b.sumW2();
       }
       return sumw2;
     }
 
     /// @brief Calculates first moment along axis @a dim in histo.
     double sumWA(const size_t dim, const bool includeOverflows=true) const {
       if (dim >= DbnN)  throw RangeError("Invalid axis int, must be in range 0..dim-1");
       double sumwa = 0;
       for (const auto& b : BaseT::bins(includeOverflows)) {
         sumwa += b.sumW(dim+1);
       }
       return sumwa;
     }
 
     /// @brief Calculates second moment along axis @a dim in histo.
     double sumWA2(const size_t dim, const bool includeOverflows=true) const {
       if (dim >= DbnN)  throw RangeError("Invalid axis int, must be in range 0..dim-1");
       double sumwa2 = 0;
       for (const auto& b : BaseT::bins(includeOverflows)) {
         sumwa2 += b.sumW2(dim+1);
       }
       return sumwa2;
     }
 
     /// @brief Calculates cross-term along axes @a A1 and @a A2 in histo.
     template<size_t dim = DbnN, typename = std::enable_if_t<(dim >= 2)>>
     double crossTerm(const size_t A1, const size_t A2, const bool includeOverflows=true) const {
       if (A1 >= DbnN || A2 >= DbnN)  throw RangeError("Invalid axis int, must be in range 0..dim-1");
       if (A1 >= A2)  throw RangeError("Indices need to be different for cross term");
       double sumw = 0;
       for (const auto& b : BaseT::bins(includeOverflows)) {
         sumw += b.crossTerm(A1, A2);
       }
       return sumw;
     }
 
     /// @brief List of mean values at axis @a axisN.
     std::vector<double> means(size_t axisN, const bool includeOverflows=true) const noexcept {
       std::vector<double> rtn;
       rtn.reserve( BaseT::numBins(includeOverflows) );
       for (const auto& b : BaseT::bins(includeOverflows)) {
         rtn.push_back(b.mean(axisN+1));
       }
       return rtn;
     }
 
     /// @brief Calculates the mean value at axis @a axisN.
     double mean(size_t axisN, const bool includeOverflows=true) const noexcept {
       Dbn<DbnN> dbn;
       for (const auto& b : BaseT::bins(includeOverflows)) {
         dbn += b;
       }
       return dbn.mean(axisN+1);
     }
 
     /// @brief Calculates the variance at axis @a axisN.
     double variance(size_t axisN, const bool includeOverflows=true) const noexcept {
       Dbn<DbnN> dbn;
       for (const auto& b : BaseT::bins(includeOverflows)) {
         dbn += b;
       }
       return dbn.variance(axisN+1);
     }
 
     /// @brief Calculates the standard deviation at axis @a axisN.
     double stdDev(size_t axisN, const bool includeOverflows=true) const noexcept {
       return std::sqrt(variance(axisN, includeOverflows));
     }
 
     /// @brief Calculates the standard error at axis @a axisN.
     double stdErr(size_t axisN, const bool includeOverflows=true) const noexcept {
       Dbn<DbnN> dbn;
       for (const auto& b : BaseT::bins(includeOverflows)) {
         dbn += b;
       }
       return dbn.stdErr(axisN+1);
     }
 
     /// @brief Calculates the RMS at axis @a axisN.
     double rms(size_t axisN, const bool includeOverflows=true) const noexcept {
       Dbn<DbnN> dbn;
       for (const auto& b : BaseT::bins(includeOverflows)) {
         dbn += b;
       }
       return dbn.RMS(axisN+1);
     }
 
     /// @brief Calculates the total volume element covered by the binning.
     double dVol(const bool includeOverflows=true) const noexcept {
       double vol = 0.0;
       for (const auto& b : BaseT::bins(includeOverflows)) {
         vol += b.dVol();
       }
       return vol;
     }
 
     /// @brief Get the total density of the histogram.
     double density(const bool includeOverflows=true) const noexcept {
       const double vol = dVol(includeOverflows);
       if (vol)  return integral(includeOverflows) / vol;
       return std::numeric_limits<double>::quiet_NaN();
     }
 
     /// @brief Get the total density error of the histogram.
     double densityError(const bool includeOverflows=true) const noexcept {
       const double vol = dVol(includeOverflows);
       if (vol)  return integralError(includeOverflows) / vol;
       return std::numeric_limits<double>::quiet_NaN();
     }
 
     /// @brief Returns the sum of the bin densities
     double densitySum(const bool includeOverflows=true) const noexcept {
       double rho = 0.0;
       for (const auto& b : BaseT::bins(includeOverflows)) {
         rho += b.sumW() / b.dVol();
       }
       return rho;
     }
 
     /// @brief Returns the largest density in any of the bins
     double maxDensity(const bool includeOverflows=true) const noexcept {
       std::vector<double> vals;
       for (auto& b : BaseT::bins(includeOverflows)) {
         vals.emplace_back(b.sumW() / b.dVol());
       }
       return *max_element(vals.begin(), vals.end());
     }
 
     /// @}
 
     /// @name I/O
     /// @{
 
   private:
 
     /// @brief Render information about this AO (private implementation)
     template<size_t... Is>
     void _renderYODA_aux(std::ostream& os, const int width, std::index_sequence<Is...>) const noexcept {
 
       // YODA1-style metadata
       if ( effNumEntries(true) > 0 ) {
         os << "# Mean: ";
         if (DbnN > 1) {  os << "("; }
         (( os <<  std::string(Is? ", " : "") << mean(Is, true)), ...);
         if (DbnN > 1) {  os << ")"; }
         os << "\n# Integral: " << integral(true) << "\n";
       }
 
       // render bin edges
       BaseT::_binning._renderYODA(os);
 
       // column header: content types
       os << std::setw(width) << std::left << "# sumW" << "\t";
       os << std::setw(width) << std::left << "sumW2" << "\t";
       (( os << std::setw(width) << std::left << ("sumW(A"  + std::to_string(Is+1) + ")") << "\t"
             << std::setw(width) << std::left << ("sumW2(A" + std::to_string(Is+1) + ")") << "\t"), ...);
       if constexpr (DbnN >= 2) {
         for (size_t i = 0; i < (DbnN-1); ++i) {
           for (size_t j = i+1; j < DbnN; ++j) {
             const std::string scross = "sumW(A" + std::to_string(i+1) + ",A" + std::to_string(j+1) + ")";
             os << std::setw(width) << std::left << scross << "\t";
           }
         }
       }
       os << "numEntries\n";
       // now write one row per bin
       for (const auto& b : BaseT::bins(true, true)) {
         os << std::setw(width) << std::left << b.sumW() << "\t"; // renders sumW
         os << std::setw(width) << std::left << b.sumW2() << "\t"; // renders sumW2
         ((os << std::setw(width) << std::left << b.sumW( Is+1) << "\t"
              << std::setw(width) << std::left << b.sumW2(Is+1) << "\t"), ...); // renders first moments
         if constexpr (DbnN >= 2) {
           for (size_t i = 0; i < (DbnN-1); ++i) {
             for (size_t j = i+1; j < DbnN; ++j) {
               os << std::setw(width) << std::left << b.crossTerm(i,j) << "\t";
             }
           }
         }
         os << std::setw(width) << std::left << b.numEntries() << "\n"; // renders raw event count
       }
     }
 
   public:
 
     /// @brief Render information about this AO (public API)
     void _renderYODA(std::ostream& os, const int width = 13) const noexcept {
       _renderYODA_aux(os, width, std::make_index_sequence<DbnN>{});
     }
 
     /// @brief Render scatter-like information about this AO
     void _renderFLAT(std::ostream& os, const int width = 13) const noexcept {
       const ScatterND<sizeof...(AxisT)+1> tmp = mkScatter();
       tmp._renderYODA(os, width);
     }
 
     #ifdef HAVE_HDF5
     /// @brief Extract axes edges of this AO into map of @a edges
     void _extractEdges(std::map<std::string, EdgeHandlerBasePtr>& edges,
                        const std::vector<std::string>&) const noexcept {
 
       using lenT = EdgeHandler<size_t>;
       using lenPtr = EdgeHandlerPtr<size_t>;
       const std::string lengthID("sizeinfo");
       lenPtr nedges = std::static_pointer_cast<lenT>(edges.find(lengthID)->second);
 
       auto extractEdges = [&edges, &binning = BaseT::_binning, &nedges](auto I) {
 
         using thisEdgeT = typename BinningT::template getEdgeT<I>;
         using thisHandlerT = EdgeHandler<thisEdgeT>;
         using thisHandlerPtr = EdgeHandlerPtr<thisEdgeT>;
 
         const std::string edgeID = std::string("edges_") + TypeID<thisEdgeT>::name();
         std::vector<thisEdgeT> tmp = binning.template edges<I>();
         nedges->extend({ tmp.size() });
 
         auto itr = edges.find(edgeID);
         if (itr != edges.cend()) {
           thisHandlerPtr edgeset = std::static_pointer_cast<thisHandlerT>(itr->second);
           edgeset->extend(std::move(tmp));
         }
         else {
           edges[edgeID] = std::make_shared<thisHandlerT>(std::move(tmp));
         }
       };
       MetaUtils::staticFor<sizeof...(AxisT)>(extractEdges);
 
       std::vector<size_t> masks = BaseT::_binning.maskedBins();
       nedges->extend({ masks.size() });
       nedges->extend(std::move(masks));
 
     };
     #endif
 
     /// @}
 
     /// @name MPI (de-)serialisation
     /// @{
 
     size_t lengthContent(bool = false) const noexcept {
       return BaseT::numBins(true, true) * Dbn<DbnN>::DataSize::value;
     }
 
     std::vector<double> serializeContent(bool = false) const noexcept {
       std::vector<double> rtn;
       const size_t nBins = BaseT::numBins(true, true);
       rtn.reserve(nBins * Dbn<DbnN>::DataSize::value);
       for (size_t i = 0; i < nBins; ++i) {
         std::vector<double> bdata = BaseT::bin(i)._serializeContent();
         rtn.insert(std::end(rtn),
                    std::make_move_iterator(std::begin(bdata)),
                    std::make_move_iterator(std::end(bdata)));
       }
       return rtn;
     }
 
     void deserializeContent(const std::vector<double>& data) {
 
       constexpr size_t dbnSize = Dbn<DbnN>::DataSize::value;
       const size_t nBins = BaseT::numBins(true, true);
       if (data.size() != nBins * dbnSize)
         throw UserError("Length of serialized data should be "
                         + std::to_string(nBins * dbnSize)+"!");
 
       const auto itr = data.cbegin();
       for (size_t i = 0; i < nBins; ++i) {
         auto first = itr + i*dbnSize;
         auto last = first + dbnSize;
         BaseT::bin(i)._deserializeContent(std::vector<double>{first, last});
       }
 
     }
 
     /// @}
 
     /// @name Type reductions
     /// @{
 
     /// @brief Produce a BinnedEstimate from a DbnStorage
     ///
     /// The binning remains unchanged.
     ///
     /// @note The @a overflowsWidth argument will be applied
     /// to all bins outside the visible bin range.
     BinnedEstimate<AxisT...> mkEstimate(const std::string& path = "",
                                         const std::string& source = "",
                        [[maybe_unused]] const bool divbyvol = true,
                                         const double overflowsWidth = -1.0) const {
 
       /// @todo Should we check BaseT::nanCount() and report?
       BinnedEstimate<AxisT...> rtn(BaseT::_binning);
       for (const std::string& a : annotations()) {
         if (a != "Type")  rtn.setAnnotation(a, annotation(a));
       }
       rtn.setAnnotation("Path", path);
 
       if (BaseT::nanCount()) {
         const double nanc = BaseT::nanCount();
         const double nanw = BaseT::nanSumW();
         const double frac = nanc / (nanc + numEntries());
         const double wtot = nanw + effNumEntries();
         rtn.setAnnotation("NanFraction", frac);
         if (wtot)  rtn.setAnnotation("WeightedNanFraction", nanw/wtot);
       }
 
       for (const auto& b : BaseT::bins(true, true)) {
         if (overflowsWidth <= 0. && !b.isVisible())  continue;
         if constexpr(DbnN > sizeof...(AxisT)) {
           rtn.bin(b.index()).setVal(b.mean(DbnN));
           if (b.numEntries()) { // only set uncertainty for filled Dbns
             rtn.bin(b.index()).setErr(b.stdErr(DbnN), source);
           }
         }
         else {
           const double scale = divbyvol? (b.isVisible()? b.dVol() : overflowsWidth) : 1.0;
           rtn.bin(b.index()).setVal(b.sumW() / scale);
           if (b.numEntries()) { // only set uncertainty for filled Dbns
             rtn.bin(b.index()).setErr(b.errW() / scale, source);
           }
         }
       }
 
       return rtn;
     }
 
     /// @brief Produce a BinnedEstimate for each bin along axis @a axisN
     /// and return as a vector.
     ///
     /// The binning dimension is reduced by one unit.
     ///
     /// @note The @a overflowsWidth argument will be applied
     /// to all bins outside the visible bin range.
     template<size_t axisN, typename = std::enable_if_t< (axisN < sizeof...(AxisT)) >>
     auto mkEstimates(const std::string& path = "", const std::string source = "",
                      const bool divbyvol = true, const bool includeOverflows = false,
                      const double overflowsWidth = -1.0) {
 
       BinnedEstimate<AxisT...> est = mkEstimate(path, source, divbyvol, overflowsWidth);
       return est.template mkEstimates<axisN>(path, includeOverflows);
     }
 
 
     /// @brief Produce a ScatterND from a DbnStorage
     ///
     /// @note The @a overflowsWidth argument will be applied
     /// to all bins outside the visible bin range.
     auto mkScatter(const std::string& path="", const bool divbyvol = true,
                                                const bool usefocus = false,
                                                const bool includeOverflows = false,
                                                const bool includeMaskedBins = false,
                                                const double overflowsWidth = -1.0) const {
       const BinnedEstimate<AxisT...> est = mkEstimate("", "", divbyvol, overflowsWidth);
       ScatterND<sizeof...(AxisT)+1> rtn = est.mkScatter(path, "", includeOverflows, includeMaskedBins);
       if (usefocus) {
         size_t idx = 0;
         for (const auto& b : BaseT::bins(includeOverflows, includeMaskedBins)) {
           auto shiftIfContinuous = [&rtn, &b, &idx](auto I) {
             using isContinuous = typename BinningT::template is_CAxis<I>;
             if constexpr (isContinuous::value) {
               const double oldMax = rtn.point(idx).max(I);
               const double oldMin = rtn.point(idx).min(I);
               const double newVal = b.mean(I+1);
               rtn.point(idx).set(I, newVal, newVal - oldMin, oldMax - newVal);
             }
           };
           MetaUtils::staticFor<BinningT::Dimension::value>(shiftIfContinuous);
           ++idx;
         }
       }
       return rtn;
     }
 
     /// @brief Produce a BinnedHisto from BinnedProfile.
     ///
     /// The binning remains unchanged, but the fill
     /// dimension is reduced by one unit.
     template<size_t N = DbnN, typename = std::enable_if_t< (N == sizeof...(AxisT)+1) >>
     BinnedHisto<AxisT...> mkHisto(const std::string& path="") const {
 
       BinnedHisto<AxisT...> rtn(BaseT::_binning);
       rtn.setNanLog(BaseT::nanCount(), BaseT::nanSumW(), BaseT::nanSumW2());
       for (const std::string& a : annotations()) {
         if (a != "Type")  rtn.setAnnotation(a, annotation(a));
       }
       rtn.setAnnotation("Path", path);
 
       for (const auto& b : BaseT::bins(true)) {
         rtn.bin(b.index()) += b.template reduce<N-1>();
       }
 
       return rtn;
     }
 
     /// @brief Produce a BinnedProfile from a DbnStorage
     ///
     /// Case 1: BinnedHisto(N+1)D -> BinnedProfileND
     /// The fill dimension remains the same, but the
     /// binning is reduced by one dimension.
     ///
     /// Case 2: BinnedProfile(N+1)D -> BinnedProfileND
     /// Both fill and binning dimmensions are reduced
     /// by one unit.
     ///
     /// @todo use a parameter pack and allow marginalising over multiple axes?
     template<size_t axisN, typename = std::enable_if_t< (axisN < sizeof...(AxisT)) >>
     auto mkMarginalProfile(const std::string& path="") const {
 
       auto rtn = BaseT::template _mkBinnedT<BinnedProfile>(BaseT::_binning.template _getAxesExcept<axisN>());
       rtn.setNanLog(BaseT::nanCount(), BaseT::nanSumW(), BaseT::nanSumW2());
       for (const std::string& a : annotations()) {
         if (a != "Type")  rtn.setAnnotation(a, annotation(a));
       }
       rtn.setAnnotation("Path", path);
 
       auto collapseStorageBins =
         [&oldBinning = BaseT::_binning, &oldBins = BaseT::_bins, &rtn](auto I, auto dbnRed) {
 
         auto collapse = [&oldBins, &rtn](const auto& binsIndicesToMerge, auto axis) {
           assert(rtn.numBins(true) == binsIndicesToMerge.size());
 
           // for any given pivot, add the content
           // from the old slice to the new slice
           for (size_t i = 0; i < rtn.numBins(true); ++i) {
             auto& pivotBin = rtn.bin(i);
             auto& binToAppend = oldBins[binsIndicesToMerge[i]];
             pivotBin += binToAppend.template reduce<axis>();
           }
         };
 
         // get bin slice for any given bin along the axis that is to be
         // collapsed, then copy the values into the new binning
         ssize_t nBinRowsToBeMerged = oldBinning.numBinsAt(I);
         while (nBinRowsToBeMerged--) {
           /// @note Binning iteratively shrinks, so the next bin slice
           /// to merge will always be the next.
           collapse(oldBinning.sliceIndices(I, nBinRowsToBeMerged), dbnRed);
         }
       };
       /// If the calling object is a histogram, we can just copy the Dbn<N>,
       /// otherwise we need to collapse an axis first in order to produce a Dbn<N-1>.
       /// @note Dbn axes are 0-indexed, so asking to reduce DbnN doesn't reduce anything.
       auto dbnRed = std::integral_constant<size_t, (sizeof...(AxisT) == DbnN)? DbnN : axisN>();
       (void)collapseStorageBins(std::integral_constant<std::size_t, axisN>(), dbnRed);
 
       return rtn;
     }
 
     /// @brief Produce a BinnedHisto from a DbnStorage
     ///
     /// Case 1: BinnedProfile(N+1)D -> BinnedHistoND
     /// The binning dimension is reduced by one unit,
     /// and the fill dimension is reduced by two units.
     ///
     /// Case 2: BinnedHisto(N+1)D -> BinnedHisto
     /// Both fill and binning dimension are reduced
     /// by one unit.
     ///
     /// @todo use a parameter pack and allow marginalising over multiple axes?
     template<size_t axisN, typename = std::enable_if_t< (axisN < sizeof...(AxisT)) >>
     auto mkMarginalHisto(const std::string& path="") const {
 
       if constexpr (DbnN != sizeof...(AxisT)) {
         // Case 1: BP(N+1) -> BH(N+1) -> BHN
         return mkHisto().template mkMarginalHisto<axisN>(path);
       }
       else {
         // Case 2: BH(N+1) -> BHN
 
         auto rtn = BaseT::template _mkBinnedT<BinnedHisto>(BaseT::_binning.template _getAxesExcept<axisN>());
         rtn.setNanLog(BaseT::nanCount(), BaseT::nanSumW(), BaseT::nanSumW2());
         for (const std::string& a : annotations()) {
           if (a != "Type")  rtn.setAnnotation(a, annotation(a));
         }
         rtn.setAnnotation("Path", path);
 
         auto collapseStorageBins =
           [&oldBinning = BaseT::_binning, &oldBins = BaseT::_bins, &rtn](auto I, auto dbnRed) {
 
           auto collapse = [&oldBins, &rtn](const auto& binsIndicesToMerge, auto axis) {
             assert(rtn.numBins(true) == binsIndicesToMerge.size());
 
             // for any given pivot, add the content
             // from the old slice to the new slice
             for (size_t i = 0; i < rtn.numBins(true); ++i) {
               auto& pivotBin = rtn.bin(i);
               auto& binToAppend = oldBins[binsIndicesToMerge[i]];
               pivotBin += binToAppend.template reduce<axis>();
             }
           };
 
           // get bin slice for any given bin along the axis that is to be
           // collapsed, then copy the values into the new binning
           ssize_t nBinRowsToBeMerged = oldBinning.numBinsAt(I);
           while (nBinRowsToBeMerged--) {
             /// @note Binning iteratively shrinks, so the next bin slice
             /// to merge will always be the next.
             collapse(oldBinning.sliceIndices(I, nBinRowsToBeMerged), dbnRed);
           }
         };
         // collapse Dbn along axisN
         auto dbnRed = std::integral_constant<size_t, axisN>();
         (void)collapseStorageBins(std::integral_constant<std::size_t, axisN>(), dbnRed);
 
         return rtn;
       }
     }
 
 
     /// @brief Split into vector of BinnedProfile along axis @a axisN
     ///
     /// The binning dimension of the returned objects are reduced by one unit.
     /// @note Requires at least two binning dimensions.
     template<size_t axisN, typename = std::enable_if_t< (axisN < sizeof...(AxisT) &&
                                                          sizeof...(AxisT)>=2 &&
                                                          DbnN > sizeof...(AxisT)) >>
     auto mkProfiles(const std::string& path="", const bool includeOverflows=false) const {
 
       // Need to provide a prescription for how to add the two bin contents
       auto how2add = [](auto& pivot, const BinType& toCopy) { pivot = toCopy.template reduce<axisN>(); };
       auto rtn = BaseT::template mkBinnedSlices<axisN, BinnedProfile>(how2add, includeOverflows);
       for (const std::string& a : annotations()) {
         if (a == "Type")  continue;
         for (size_t i = 0; i < rtn.size(); ++i) {
           rtn[i].setAnnotation(a, annotation(a));
         }
       }
       for (size_t i = 0; i < rtn.size(); ++i) {
         rtn[i].setAnnotation("Path", path);
       }
       return rtn;
     }
 
 
     /// @brief Split into vector of BinnedHisto along axis @a axisN
     ///
     /// The binning dimension of the returned ojects are reduced by one unit.
     /// @note Requires at least two binning dimensions.
     template<size_t axisN, typename = std::enable_if_t< (axisN < sizeof...(AxisT) && sizeof...(AxisT)>=2) >>
     auto mkHistos(const std::string& path="", const bool includeOverflows=false) const {
 
       if constexpr (DbnN != sizeof...(AxisT)) {
         // Case 1: BP(N+1) -> BH(N+1) -> BHN
         return mkHisto().template mkHistos<axisN>(path, includeOverflows);
       }
       else {
         // Case 2: BH(N+1) -> BHN
 
         // Need to provide a prescription for how to add the two bin contents
         auto how2add = [](auto& pivot, const BinType& toCopy) { pivot = toCopy.template reduce<axisN>(); };
         auto rtn = BaseT::template mkBinnedSlices<axisN,BinnedHisto>(how2add, includeOverflows);
         for (const std::string& a : annotations()) {
           if (a == "Type")  continue;
           for (size_t i = 0; i < rtn.size(); ++i) {
             rtn[i].setAnnotation(a, annotation(a));
           }
         }
         for (size_t i = 0; i < rtn.size(); ++i) {
           rtn[i].setAnnotation("Path", path);
         }
         return rtn;
       }
     }
 
 
     /// @brief Convert the BinnedDbn to a BinnedEstimate representing
     /// the effective number of entries in each bin
     ///
     /// @note The @a overflowsWidth argument will be applied
     /// to all bins outside the visible bin range.
     BinnedEstimate<AxisT...> mkBinnedEffNumEntries(const std::string& path="",
                                                    const std::string& source = "",
                                                    const bool includeOverflows = true,
                                                    const bool divbyvol = true,
                                                    const double overflowsWidth = -1.0) {
 
       BinnedEstimate<AxisT...> rtn = mkEstimate(path);
 
       for (const auto& b : BaseT::bins(includeOverflows)) {
         double scale = 1.0;
         if (divbyvol) {
           scale = (overflowsWidth > 0. && !b.isVisible())? overflowsWidth : b.dVol();
         }
         const double effN = b.effNumEntries() / scale;
         const double err = effN * b.relErrW() / scale;
         rtn.bin(b.index()).set(effN, {-err, err}, source);
       }
 
       return rtn;
     }
 
 
     /// @brief Return an inert version of the analysis object (e.g. scatter, estimate)
     AnalysisObject* mkInert(const std::string& path = "",
                             const std::string& source = "") const noexcept {
       return mkEstimate(path, source).newclone();
     }
 
     /// @}
 
     private:
 
     /// @brief Helper function to create a BinningT from
     /// a given set @a nBins within a range @a limitsLowUp
     template<size_t... Is>
     BinningT _mkBinning(const std::vector<size_t>& nBins,
                         const std::vector<std::pair<double, double>>& limitsLowUp,
                         std::index_sequence<Is...>) const {
       return BinningT({((void)Is, Axis<AxisT>(nBins[Is], limitsLowUp[Is].first, limitsLowUp[Is].second))...});
     }
 
     /// @brief Helper function to create a BinningT from a scatter @a s
     template<size_t... Is>
     BinningT _mkBinning(const ScatterND<sizeof...(AxisT)+1>& s, std::index_sequence<Is...>) const {
       return BinningT(Axis<AxisT>(s.edges(Is))...);
     }
 
   };
 
 
 
   /// @name Combining BinnedDbn objects: global operators
   /// @{
 
   /// @brief Add two BinnedDbn objects
   template<size_t DbnN, typename... AxisT>
   inline BinnedDbn<DbnN, AxisT...>
   operator + (BinnedDbn<DbnN, AxisT...> first, BinnedDbn<DbnN, AxisT...>&& second) {
     first += std::move(second);
     return first;
   }
   //
   template <size_t DbnN, typename... AxisT>
   inline BinnedDbn<DbnN, AxisT...>
   operator + (BinnedDbn<DbnN, AxisT...> first, const BinnedDbn<DbnN, AxisT...>& second) {
     first += second;
     return first;
   }
 
 
   /// @brief Subtract one BinnedDbn object from another
   template <size_t DbnN, typename... AxisT>
   inline BinnedDbn<DbnN, AxisT...>
   operator - (BinnedDbn<DbnN, AxisT...> first, BinnedDbn<DbnN, AxisT...>&& second) {
     first -= std::move(second);
     return first;
   }
   //
   template <size_t DbnN, typename... AxisT>
   inline BinnedDbn<DbnN, AxisT...>
   operator - (BinnedDbn<DbnN, AxisT...> first, const BinnedDbn<DbnN, AxisT...>& second) {
     first -= second;
     return first;
   }
 
 
   /// @brief Divide two BinnedDbn objects
   template <size_t DbnN, typename... AxisT>
   inline BinnedEstimate<AxisT...>
   divide(const BinnedDbn<DbnN, AxisT...>& numer, const BinnedDbn<DbnN, AxisT...>& denom) {
 
     if (numer != denom) {
       throw BinningError("Arithmetic operation requires compatible binning!");
     }
 
     BinnedEstimate<AxisT...> rtn = numer.mkEstimate();
     if (numer.path() == denom.path())  rtn.setPath(numer.path());
     if (rtn.hasAnnotation("ScaledBy")) rtn.rmAnnotation("ScaledBy");
 
     for (const auto& b_num : numer.bins(true, true)) {
       const size_t idx = b_num.index();
       const auto& b_den = denom.bin(idx);
       double v, e;
       if (isZero(b_den.effNumEntries())) {
         v = std::numeric_limits<double>::quiet_NaN();
         e = std::numeric_limits<double>::quiet_NaN();
       }
       else {
         if constexpr(DbnN > sizeof...(AxisT)) {
           v = b_num.mean(DbnN) / b_den.mean(DbnN);
           const double e_num = isZero(b_num.effNumEntries())? 0 : b_num.relStdErr(DbnN);
           const double e_den = isZero(b_den.effNumEntries())? 0 : b_den.relStdErr(DbnN);
           e = fabs(v) * sqrt(sqr(e_num) + sqr(e_den));
         }
         else {
           v = b_num.sumW() / b_den.sumW();
           const double e_num = isZero(b_num.effNumEntries())? 0 : b_num.relErrW();
           const double e_den = isZero(b_den.effNumEntries())? 0 : b_den.relErrW();
           e = fabs(v) * sqrt(sqr(e_num) + sqr(e_den));
         }
       }
       rtn.bin(idx).set(v, {-e, e}); ///< @todo put "stats" as source?
     }
     rtn.maskBins(denom.maskedBins(), true);
 
     return rtn;
   }
   //
   template <size_t DbnN, typename... AxisT>
   inline BinnedEstimate<AxisT...>
   operator / (const BinnedDbn<DbnN, AxisT...>& numer, const BinnedDbn<DbnN, AxisT...>& denom) {
     return divide(numer, denom);
   }
   //
   template <size_t DbnN, typename... AxisT>
   inline BinnedEstimate<AxisT...>
   operator / (const BinnedDbn<DbnN, AxisT...>& numer, BinnedDbn<DbnN, AxisT...>&& denom) {
     return divide(numer, std::move(denom));
   }
   //
   template <size_t DbnN, typename... AxisT>
   inline BinnedEstimate<AxisT...>
   operator / (BinnedDbn<DbnN, AxisT...>&& numer, const BinnedDbn<DbnN, AxisT...>& denom) {
     return divide(std::move(numer), denom);
   }
   //
   template <size_t DbnN, typename... AxisT>
   inline BinnedEstimate<AxisT...>
   operator / (BinnedDbn<DbnN, AxisT...>&& numer, BinnedDbn<DbnN, AxisT...>&& denom) {
     return divide(std::move(numer), std::move(denom));
   }
 
 
   /// @brief Calculate a binned efficiency ratio of two BinnedDbn objects
   ///
   /// @note An efficiency is not the same thing as a standard division of two
   /// BinnedDbn objects: the errors are treated as correlated via binomial statistics.
   template <size_t DbnN, typename... AxisT>
   inline BinnedEstimate<AxisT...>
   efficiency(const BinnedDbn<DbnN, AxisT...>& accepted, const BinnedDbn<DbnN, AxisT...>& total) {
 
     if (accepted != total) {
       throw BinningError("Arithmetic operation requires compatible binning!");
     }
 
     BinnedEstimate<AxisT...> rtn = divide(accepted, total);
 
     for (const auto& b_acc : accepted.bins(true, true)) {
       const auto& b_tot = total.bin(b_acc.index());
       auto& b_rtn = rtn.bin(b_acc.index());
 
       // Check that the numerator is consistent with being a subset of the denominator
       /// @note Neither effNumEntries nor sumW are guaranteed to satisfy num <= den for general weights!
       if (b_acc.numEntries() > b_tot.numEntries())
         throw UserError("Attempt to calculate an efficiency when the numerator is not a subset of the denominator: "
                         + Utils::toStr(b_acc.numEntries()) + " entries / " + Utils::toStr(b_tot.numEntries()) + " entries");
 
       // If no entries on the denominator, set eff = err = 0 and move to the next bin
       double eff = std::numeric_limits<double>::quiet_NaN();
       double err = std::numeric_limits<double>::quiet_NaN();
       if (!isZero(b_tot.effNumEntries())) {
         eff = b_rtn.val();
         err = sqrt(fabs( add((1.0-2.0*eff)*b_acc.sumW2(), sqr(eff)*b_tot.sumW2()) / sqr(b_tot.sumW()) ));
       }
       b_rtn.setErr({-err, err}); ///< @todo put "stats" as source?
     }
     return rtn;
   }
 
 
   /// @brief Calculate the asymmetry (a-b)/(a+b) of two BinnedDbn objects
   template <size_t DbnN, typename... AxisT>
   inline BinnedEstimate<AxisT...>
   asymm(const BinnedDbn<DbnN, AxisT...>& a, const BinnedDbn<DbnN, AxisT...>& b) {
     return (a-b) / (a+b);
   }
 
 
   /// @brief Convert a BinnedDbn to a BinnedEstimate representing the integral of the histogram
   ///
   /// @note The integral histo errors are calculated as sqrt(binvalue), as if they
   /// are uncorrelated. This is not in general true for integral histograms, so if you
   /// need accurate errors you should explicitly monitor bin-to-bin correlations.
   ///
   /// The includeunderflow param chooses whether the underflow bin is included
   /// in the integral numbers as an offset.
   template <size_t DbnN, typename... AxisT>
   inline BinnedEstimate<AxisT...>
   mkIntegral(const BinnedDbn<DbnN, AxisT...>& histo, const bool includeOverflows = true) {
 
     BinnedEstimate<AxisT...> rtn = histo.mkEstimate();
 
     double sumW = 0.0, sumW2 = 0.0;
     for (const auto& b : histo.bins(includeOverflows)) {
       sumW  += b.sumW();
       sumW2 += b.sumW2();
       const double e = sqrt(sumW2);
       rtn.bin(b.index()).set(sumW, {-e, e});
     }
 
     return rtn;
   }
 
 
   /// @brief Convert a BinnedDbn to a BinnedEstimate where each bin is a fraction of the total
   ///
   /// @note This sounds weird: let's explain a bit more! Sometimes we want to
   /// take a histo h, make an integral histogram H from it, and then divide H by
   /// the total integral of h, such that every bin in H represents the
   /// cumulative efficiency of that bin as a fraction of the total. I.e. an
   /// integral histo, scaled by 1/total_integral and with binomial errors.
   ///
   /// The includeunderflow param behaves as for toIntegral, and applies to both
   /// the initial integration and the integral used for the scaling. The
   /// includeoverflow param applies only to obtaining the scaling factor.
   template <size_t DbnN, typename... AxisT>
   inline BinnedEstimate<AxisT...>
   mkIntegralEff(const BinnedDbn<DbnN, AxisT...>& histo, const bool includeOverflows = true) {
 
     BinnedEstimate<AxisT...> rtn = mkIntegral(histo, includeOverflows);
     const double integral = histo.integral(includeOverflows);
 
     // If the integral is empty, the (integrated) efficiency values may as well all be zero, so return here
     /// @todo Or throw a LowStatsError exception if h.effNumEntries() == 0?
     /// @todo Provide optional alt behaviours
     /// @todo Need to check that bins are all positive? Integral could be zero due to large +ve/-ve in different bins :O
     if (!integral) return rtn;
 
     const double integral_err = histo.integralError(includeOverflows);
     for (const auto& b : rtn.bins(includeOverflows)) {
       const double eff = b.val() / integral;
       const double err = sqrt(std::abs( ((1-2*eff)*sqr(b.relTotalErrAvg()) + sqr(eff)*sqr(integral_err)) / sqr(integral) ));
       b.set(eff, {-err,err});
     }
 
     return rtn;
   }
 
 
   /// @brief Calculate the addition of a BinnedDbn with a BinnedEstimate
   template <size_t DbnN, typename... AxisT>
   inline BinnedEstimate<AxisT...>
   add(const BinnedDbn<DbnN, AxisT...>& dbn, const BinnedEstimate<AxisT...>& est) {
     return dbn.mkEstimate() + est;
   }
   //
   template <size_t DbnN, typename... AxisT>
   inline BinnedEstimate<AxisT...>
   operator + (const BinnedDbn<DbnN, AxisT...>& dbn, const BinnedEstimate<AxisT...>& est) {
     return add(dbn, est);
   }
   //
   template <size_t DbnN, typename... AxisT>
   inline BinnedEstimate<AxisT...>
   operator + (BinnedDbn<DbnN, AxisT...>&& dbn, const BinnedEstimate<AxisT...>& est) {
     return add(std::move(dbn), est);
   }
   //
   template <size_t DbnN, typename... AxisT>
   inline BinnedEstimate<AxisT...>
   operator + (const BinnedDbn<DbnN, AxisT...>& dbn, BinnedEstimate<AxisT...>&& est) {
     return add(dbn, std::move(est));
   }
   //
   template <size_t DbnN, typename... AxisT>
   inline BinnedEstimate<AxisT...>
   operator + (BinnedDbn<DbnN, AxisT...>&& dbn, BinnedEstimate<AxisT...>&& est) {
     return add(std::move(dbn), std::move(est));
   }
 
 
   /// @brief Calculate the subtraction of a BinnedEstimate from a BinnedDbn
   template <size_t DbnN, typename... AxisT>
   inline BinnedEstimate<AxisT...>
   subtract(const BinnedDbn<DbnN, AxisT...>& dbn, const BinnedEstimate<AxisT...>& est) {
     return dbn.mkEstimate() - est;
   }
   //
   template <size_t DbnN, typename... AxisT>
   inline BinnedEstimate<AxisT...>
   operator - (const BinnedDbn<DbnN, AxisT...>& dbn, const BinnedEstimate<AxisT...>& est) {
     return subtract(dbn, est);
   }
   //
   template <size_t DbnN, typename... AxisT>
   inline BinnedEstimate<AxisT...>
   operator - (BinnedDbn<DbnN, AxisT...>&& dbn, const BinnedEstimate<AxisT...>& est) {
     return subtract(std::move(dbn), est);
   }
   //
   template <size_t DbnN, typename... AxisT>
   inline BinnedEstimate<AxisT...>
   operator - (const BinnedDbn<DbnN, AxisT...>& dbn, BinnedEstimate<AxisT...>&& est) {
     return subtract(dbn, std::move(est));
   }
   //
   template <size_t DbnN, typename... AxisT>
   inline BinnedEstimate<AxisT...>
   operator - (BinnedDbn<DbnN, AxisT...>&& dbn, BinnedEstimate<AxisT...>&& est) {
     return subtract(std::move(dbn), std::move(est));
   }
 
 
   /// @brief Calculate the division of a BinnedDbn and a BinnedEstimate
   template <size_t DbnN, typename... AxisT>
   inline BinnedEstimate<AxisT...>
   divide(const BinnedDbn<DbnN, AxisT...>& dbn, const BinnedEstimate<AxisT...>& est) {
     return dbn.mkEstimate() / est;
   }
   //
   template <size_t DbnN, typename... AxisT>
   inline BinnedEstimate<AxisT...>
   operator / (const BinnedDbn<DbnN, AxisT...>& dbn, const BinnedEstimate<AxisT...>& est) {
     return divide(dbn, est);
   }
   //
   template <size_t DbnN, typename... AxisT>
   inline BinnedEstimate<AxisT...>
   operator / (BinnedDbn<DbnN, AxisT...>&& dbn, const BinnedEstimate<AxisT...>& est) {
     return divide(std::move(dbn), est);
   }
   //
   template <size_t DbnN, typename... AxisT>
   inline BinnedEstimate<AxisT...>
   operator / (const BinnedDbn<DbnN, AxisT...>& dbn, BinnedEstimate<AxisT...>&& est) {
     return divide(dbn, std::move(est));
   }
   //
   template <size_t DbnN, typename... AxisT>
   inline BinnedEstimate<AxisT...>
   operator / (BinnedDbn<DbnN, AxisT...>&& dbn, BinnedEstimate<AxisT...>&& est) {
     return divide(std::move(dbn), std::move(est));
   }
 
 
   /// @brief Zip profile objects of the same type into a combined scatter object
   ///
   /// The resulting object has as many points as profile bins and whose central
   /// values are given by the means along the unbinned profile axes with means
   /// of first profile corresponding to x-coordinate, means of second profile
   /// corresponding to y-coordinate etc.
   ///
   /// @note The BinnedDbn objects must be profiles and have the same axis config.
   template<size_t DbnN, typename... AxisT, typename... Args,
            typename = std::enable_if_t<(DbnN == sizeof...(AxisT)+1 &&
                                        (std::is_same_v<BinnedDbn<DbnN, AxisT...>, Args> && ...))>>
   ScatterND<sizeof...(Args)+1> zipProfiles(const BinnedDbn<DbnN, AxisT...>& p1, Args&&... others,
                                            const std::string& path = "") {
 
     // Check profiles have the same binning
     if ( !((p1 == others) && ...) )
       throw BinningError("Requested zipping of profiles with incompatible binning!");
 
     // Construct resulting Scatter whose coordinates
     // are given by the unbinned means
     constexpr size_t N = sizeof...(Args)+1;
     ScatterND<N> rtn;
     rtn.setAnnotation("Path", path);
     for (const auto& b1 : p1.bins()) {
       typename ScatterND<N>::NdVal vals = { b1.mean(DbnN), others.bin(b1.binIndex()).mean(DbnN) ... };
       typename ScatterND<N>::NdVal errs = { b1.stdErr(DbnN), others.bin(b1.binIndex()).stdErr(DbnN) ... };
       rtn.addPoint(vals, errs);
     }
     return rtn;
   }
 
   /// @}
 
 }
 
 #endif

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