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 // This file is part of the ACTS project.
 //
 // Copyright (C) 2016 CERN for the benefit of the ACTS project
 //
 // This Source Code Form is subject to the terms of the Mozilla Public
 // License, v. 2.0. If a copy of the MPL was not distributed with this
 // file, You can obtain one at https://mozilla.org/MPL/2.0/.
 
 #pragma once
 
 #include "Acts/Utilities/AxisDefinitions.hpp"
 #include "Acts/Utilities/IAxis.hpp"
 
 #include <algorithm>
 #include <cmath>
 #include <vector>
 
 namespace Acts {
 
 // This object can be iterated to produce up to two sequences of integer
 // indices, corresponding to the half-open integer ranges [begin1, end1[ and
 // [begin2, end2[.
 //
 // The goal is to emulate the effect of enumerating a range of neighbor
 // indices on an axis (which may go out of bounds and wrap around since we
 // have AxisBoundaryType::Closed), inserting them into an std::vector, and
 // discarding duplicates, without paying the price of duplicate removal
 // and dynamic memory allocation in hot magnetic field interpolation code.
 //
 /// Iterable indices for neighborhood lookups with optional wrap-around.
 class NeighborHoodIndices {
  public:
   NeighborHoodIndices() = default;
 
   /// Constructor for continuous range
   /// @param begin Start index
   /// @param end End index (exclusive)
   NeighborHoodIndices(std::size_t begin, std::size_t end)
       : m_begin1(begin), m_end1(end), m_begin2(end), m_end2(end) {}
 
   /// Constructor for wrapped range (two segments)
   /// @param begin1 Start of first segment
   /// @param end1 End of first segment (exclusive)
   /// @param begin2 Start of second segment
   /// @param end2 End of second segment (exclusive)
   NeighborHoodIndices(std::size_t begin1, std::size_t end1, std::size_t begin2,
                       std::size_t end2)
       : m_begin1(begin1), m_end1(end1), m_begin2(begin2), m_end2(end2) {}
 
   /// Iterator over the neighborhood index sequence.
   class iterator {
    public:
     iterator() = default;
 
     /// Constructor for end iterator
     /// @param current End position
     explicit iterator(std::size_t current)
         : m_current(current), m_wrapped(true) {}
 
     /// Constructor for begin iterator
     /// @param begin1 Start of first segment
     /// @param end1 End of first segment
     /// @param begin2 Start of second segment
     iterator(std::size_t begin1, std::size_t end1, std::size_t begin2)
         : m_current(begin1),
           m_end1(end1),
           m_begin2(begin2),
           m_wrapped(begin1 == begin2) {}
 
     /// Dereference operator
     /// @return Current index
     std::size_t operator*() const { return m_current; }
 
     /// Pre-increment operator
     /// @return Reference to this iterator
     iterator& operator++() {
       ++m_current;
       if (m_current == m_end1) {
         m_current = m_begin2;
         m_wrapped = true;
       }
       return *this;
     }
 
     /// Equality comparison operator
     /// @param it Other iterator
     /// @return True if iterators are equal
     bool operator==(const iterator& it) const {
       return (m_current == it.m_current) && (m_wrapped == it.m_wrapped);
     }
 
    private:
     std::size_t m_current = 0, m_end1 = 0, m_begin2 = 0;
     bool m_wrapped = false;
   };
 
   /// Get begin iterator
   /// @return Iterator to first index
   iterator begin() const { return iterator(m_begin1, m_end1, m_begin2); }
 
   /// Get end iterator
   /// @return Iterator past last index
   iterator end() const { return iterator(m_end2); }
 
   /// Get total number of indices in the sequence
   /// @return Number of indices
   std::size_t size() const { return (m_end1 - m_begin1) + (m_end2 - m_begin2); }
 
   /// Collect all indices into a vector
   /// @return Vector containing all indices
   std::vector<std::size_t> collect() const {
     std::vector<std::size_t> result;
     result.reserve(this->size());
     for (std::size_t idx : *this) {
       result.push_back(idx);
     }
     return result;
   }
 
  private:
   std::size_t m_begin1 = 0, m_end1 = 0, m_begin2 = 0, m_end2 = 0;
 };
 
 /// @brief calculate bin indices for an equidistant binning
 ///
 /// This class provides some basic functionality for calculating bin indices
 /// for a given equidistant binning.
 template <AxisBoundaryType bdt>
 class Axis<AxisType::Equidistant, bdt> : public IAxis {
  public:
   /// Static type identifier for this equidistant axis specialization
   static constexpr AxisType type = AxisType::Equidistant;
 
   /// @brief default constructor
   ///
   /// @param [in] xmin lower boundary of axis range
   /// @param [in] xmax upper boundary of axis range
   /// @param [in] nBins number of bins to divide the axis range into
   ///
   /// Divide the range \f$[\text{xmin},\text{xmax})\f$ into \f$\text{nBins}\f$
   /// equidistant bins.
   Axis(double xmin, double xmax, std::size_t nBins)
       : m_min(xmin),
         m_max(xmax),
         m_width((xmax - xmin) / nBins),
         m_bins(nBins) {}
 
   /// Constructor with a tag for the boundary type
   ///
   /// @param [in] typeTag boundary type tag
   /// @param [in] xmin lower boundary of axis range
   /// @param [in] xmax upper boundary of axis range
   /// @param [in] nBins number of bins to divide the axis range into
   ///
   /// Divide the range \f$[\text{xmin},\text{xmax})\f$ into \f$\text{nBins}\f$
   /// equidistant bins.
   Axis(AxisBoundaryTypeTag<bdt> typeTag, double xmin, double xmax,
        std::size_t nBins)
       : Axis(xmin, xmax, nBins) {
     static_cast<void>(typeTag);
   }
 
   /// @brief returns whether the axis is equidistant
   ///
   /// @return bool is equidistant
   bool isEquidistant() const final { return true; }
 
   /// @brief returns whether the axis is variable
   ///
   /// @return bool is variable
   bool isVariable() const final { return false; }
 
   /// @brief returns the type of the axis
   /// @return @c AxisType of this axis
   AxisType getType() const final { return type; }
 
   /// @brief returns the boundary type set in the template param
   ///
   /// @return @c AxisBoundaryType of this axis
   AxisBoundaryType getBoundaryType() const final { return bdt; }
 
   /// @brief Get #size bins which neighbor the one given
   ///
   /// Generic overload with symmetric size
   ///
   /// @param [in] idx requested bin index
   /// @param [in] size how many neighboring bins (up/down)
   /// @return Set of neighboring bin indices (global)
   NeighborHoodIndices neighborHoodIndices(std::size_t idx,
                                           std::size_t size = 1) const {
     return neighborHoodIndices(idx,
                                std::make_pair(-static_cast<int>(size), size));
   }
 
   /// @brief Get #size bins which neighbor the one given
   ///
   /// This is the version for Open
   ///
   /// @param [in] idx requested bin index
   /// @param [in] sizes how many neighboring bins (up/down)
   /// @return Set of neighboring bin indices (global)
   /// @note Open varies given bin and allows 0 and NBins+1 (underflow,
   /// overflow)
   ///       as neighbors
   NeighborHoodIndices neighborHoodIndices(std::size_t idx,
                                           std::pair<int, int> sizes = {-1,
                                                                        1}) const
     requires(bdt == AxisBoundaryType::Open)
   {
     constexpr int min = 0;
     const int max = getNBins() + 1;
     const int itmin = std::clamp(static_cast<int>(idx + sizes.first), min, max);
     const int itmax =
         std::clamp(static_cast<int>(idx + sizes.second), min, max);
     return NeighborHoodIndices(itmin, itmax + 1);
   }
 
   /// @brief Get #size bins which neighbor the one given
   ///
   /// This is the version for Bound
   ///
   /// @param [in] idx requested bin index
   /// @param [in] sizes how many neighboring bins (up/down)
   /// @return Set of neighboring bin indices (global)
   /// @note Bound varies given bin and allows 1 and NBins (regular bins)
   ///       as neighbors
   NeighborHoodIndices neighborHoodIndices(std::size_t idx,
                                           std::pair<int, int> sizes = {-1,
                                                                        1}) const
     requires(bdt == AxisBoundaryType::Bound)
   {
     if (idx <= 0 || idx >= (getNBins() + 1)) {
       return NeighborHoodIndices();
     }
     constexpr int min = 1;
     const int max = getNBins();
     const int itmin = std::clamp(static_cast<int>(idx) + sizes.first, min, max);
     const int itmax =
         std::clamp(static_cast<int>(idx) + sizes.second, min, max);
     return NeighborHoodIndices(itmin, itmax + 1);
   }
 
   /// @brief Get #size bins which neighbor the one given
   ///
   /// This is the version for Closed (i.e. Wrapping)
   ///
   /// @param [in] idx requested bin index
   /// @param [in] sizes how many neighboring bins (up/down)
   /// @return Set of neighboring bin indices (global)
   /// @note Closed varies given bin and allows bins on the opposite
   ///       side of the axis as neighbors. (excludes underflow / overflow)
   NeighborHoodIndices neighborHoodIndices(std::size_t idx,
                                           std::pair<int, int> sizes = {-1,
                                                                        1}) const
     requires(bdt == AxisBoundaryType::Closed)
   {
     // Handle invalid indices
     if (idx <= 0 || idx >= (getNBins() + 1)) {
       return NeighborHoodIndices();
     }
 
     // Handle corner case where user requests more neighbours than the number
     // of bins on the axis. All bins are returned in this case.
 
     const int max = getNBins();
     sizes.first = std::clamp(sizes.first, -max, max);
     sizes.second = std::clamp(sizes.second, -max, max);
     if (std::abs(sizes.first - sizes.second) >= max) {
       sizes.first = 1 - idx;
       sizes.second = max - idx;
     }
 
     // If the entire index range is not covered, we must wrap the range of
     // targeted neighbor indices into the range of valid bin indices. This may
     // split the range of neighbor indices in two parts:
     //
     // Before wraparound - [        XXXXX]XXX
     // After wraparound  - [ XXXX   XXXX ]
     //
     const int itmin = idx + sizes.first;
     const int itmax = idx + sizes.second;
     const std::size_t itfirst = wrapBin(itmin);
     const std::size_t itlast = wrapBin(itmax);
     if (itfirst <= itlast) {
       return NeighborHoodIndices(itfirst, itlast + 1);
     } else {
       return NeighborHoodIndices(itfirst, max + 1, 1, itlast + 1);
     }
   }
 
   /// @brief Converts bin index into a valid one for this axis.
   ///
   /// @note Open: bin index is clamped to [0, nBins+1]
   ///
   /// @param [in] bin The bin to wrap
   /// @return valid bin index
   std::size_t wrapBin(int bin) const
     requires(bdt == AxisBoundaryType::Open)
   {
     return std::max(std::min(bin, static_cast<int>(getNBins()) + 1), 0);
   }
 
   /// @brief Converts bin index into a valid one for this axis.
   ///
   /// @note Bound: bin index is clamped to [1, nBins]
   ///
   /// @param [in] bin The bin to wrap
   /// @return valid bin index
   std::size_t wrapBin(int bin) const
     requires(bdt == AxisBoundaryType::Bound)
   {
     return std::max(std::min(bin, static_cast<int>(getNBins())), 1);
   }
 
   /// @brief Converts bin index into a valid one for this axis.
   ///
   /// @note Closed: bin index wraps around to other side
   ///
   /// @param [in] bin The bin to wrap
   /// @return valid bin index
   std::size_t wrapBin(int bin) const
     requires(bdt == AxisBoundaryType::Closed)
   {
     const int w = getNBins();
     return 1 + (w + ((bin - 1) % w)) % w;
     // return int(bin<1)*w - int(bin>w)*w + bin;
   }
 
   /// @brief get corresponding bin index for given coordinate
   ///
   /// @param  [in] x input coordinate
   /// @return index of bin containing the given value
   ///
   /// @note Bin intervals are defined with closed lower bounds and open upper
   ///       bounds, that is \f$l <= x < u\f$ if the value @c x lies within a
   ///       bin with lower bound @c l and upper bound @c u.
   /// @note Bin indices start at @c 1. The underflow bin has the index @c 0
   ///       while the index <tt>nBins + 1</tt> indicates the overflow bin .
   std::size_t getBin(double x) const final {
     return wrapBin(
         static_cast<int>(std::floor((x - getMin()) / getBinWidth()) + 1));
   }
 
   /// @brief get bin width
   ///
   /// @return constant width for all bins
   double getBinWidth(std::size_t /*bin*/ = 0) const { return m_width; }
 
   /// @brief get lower bound of bin
   ///
   /// @param  [in] bin index of bin
   /// @return lower bin boundary
   ///
   /// @pre @c bin must be a valid bin index (excluding the underflow bin),
   ///      i.e. \f$1 \le \text{bin} \le \text{nBins} + 1\f$
   ///
   /// @note Bin intervals have a closed lower bound, i.e. the lower boundary
   ///       belongs to the bin with the given bin index.
   double getBinLowerBound(std::size_t bin) const {
     return getMin() + (bin - 1) * getBinWidth();
   }
 
   /// @brief get upper bound of bin
   ///
   /// @param  [in] bin index of bin
   /// @return upper bin boundary
   ///
   /// @pre @c bin must be a valid bin index (excluding the overflow bin),
   ///      i.e. \f$0 \le \text{bin} \le \text{nBins}\f$
   ///
   /// @note Bin intervals have an open upper bound, i.e. the upper boundary
   ///       does @b not belong to the bin with the given bin index.
   double getBinUpperBound(std::size_t bin) const {
     return getMin() + bin * getBinWidth();
   }
 
   /// @brief get bin center
   ///
   /// @param  [in] bin index of bin
   /// @return bin center position
   ///
   /// @pre @c bin must be a valid bin index (excluding under-/overflow bins),
   ///      i.e. \f$1 \le \text{bin} \le \text{nBins}\f$
   double getBinCenter(std::size_t bin) const {
     return getMin() + (bin - 0.5) * getBinWidth();
   }
 
   /// @brief get maximum of binning range
   ///
   /// @return maximum of binning range
   double getMax() const final { return m_max; }
 
   /// @brief get minimum of binning range
   ///
   /// @return minimum of binning range
   double getMin() const final { return m_min; }
 
   /// @brief get total number of bins
   ///
   /// @return total number of bins (excluding under-/overflow bins)
   std::size_t getNBins() const final { return m_bins; }
 
   /// @brief check whether value is inside axis limits
   /// @param x The value to check
   ///
   /// @return @c true if \f$\text{xmin} \le x < \text{xmax}\f$, otherwise
   ///         @c false
   ///
   /// @post If @c true is returned, the bin containing the given value is a
   ///       valid bin, i.e. it is neither the underflow nor the overflow bin.
   bool isInside(double x) const { return (m_min <= x) && (x < m_max); }
 
   /// @brief Return a vector of bin edges
   /// @return Vector which contains the bin edges
   std::vector<double> getBinEdges() const final {
     std::vector<double> binEdges;
     for (std::size_t i = 1; i <= m_bins; i++) {
       binEdges.push_back(getBinLowerBound(i));
     }
     binEdges.push_back(getBinUpperBound(m_bins));
     return binEdges;
   }
 
   friend std::ostream& operator<<(std::ostream& os, const Axis& axis) {
     os << "Axis<Equidistant, " << bdt << ">(";
     os << axis.m_min << ", ";
     os << axis.m_max << ", ";
     os << axis.m_bins << ")";
     return os;
   }
 
  protected:
   void toStream(std::ostream& os) const final { os << *this; }
 
  private:
   /// minimum of binning range
   double m_min{};
   /// maximum of binning range
   double m_max{};
   /// constant bin width
   double m_width{};
   /// number of bins (excluding under-/overflow bins)
   std::size_t m_bins{};
 };
 
 /// @brief calculate bin indices for a variable binning
 ///
 /// This class provides some basic functionality for calculating bin indices
 /// for a given binning with variable bin sizes.
 template <AxisBoundaryType bdt>
 class Axis<AxisType::Variable, bdt> : public IAxis {
  public:
   /// Static type identifier for this variable-width axis specialization
   static constexpr AxisType type = AxisType::Variable;
 
   /// @param [in] binEdges vector of bin edges
   /// @pre @c binEdges must be strictly sorted in ascending order.
   /// @pre @c binEdges must contain at least two entries.
   ///
   /// Create a binning structure with @c nBins variable-sized bins from the
   /// given bin boundaries. @c nBins is given by the number of bin edges
   /// reduced by one.
   explicit Axis(std::vector<double> binEdges)
       : m_binEdges(std::move(binEdges)) {}
 
   /// @param [in] typeTag boundary type tag
   /// @param [in] binEdges vector of bin edges
   /// @pre @c binEdges must be strictly sorted in ascending order.
   /// @pre @c binEdges must contain at least two entries.
   ///
   /// Create a binning structure with @c nBins variable-sized bins from the
   /// given bin boundaries. @c nBins is given by the number of bin edges
   /// reduced by one.
   Axis(AxisBoundaryTypeTag<bdt> typeTag, std::vector<double> binEdges)
       : Axis(std::move(binEdges)) {
     static_cast<void>(typeTag);
   }
 
   /// @brief returns whether the axis is equidistante
   ///
   /// @return bool is equidistant
   bool isEquidistant() const final { return false; }
 
   /// @brief returns whether the axis is variable
   ///
   /// @return bool is variable
   bool isVariable() const final { return true; }
 
   /// @brief returns the type of the axis
   /// @return @c AxisType of this axis
   AxisType getType() const final { return type; }
 
   /// @brief returns the boundary type set in the template param
   ///
   /// @return @c AxisBoundaryType of this axis
   AxisBoundaryType getBoundaryType() const final { return bdt; }
 
   /// @brief Get #size bins which neighbor the one given
   ///
   /// Generic overload with symmetric size
   ///
   /// @param [in] idx requested bin index
   /// @param [in] size how many neighboring bins
   /// @return Set of neighboring bin indices (global)
   NeighborHoodIndices neighborHoodIndices(std::size_t idx,
                                           std::size_t size = 1) const {
     return neighborHoodIndices(idx,
                                std::make_pair(-static_cast<int>(size), size));
   }
 
   /// @brief Get #size bins which neighbor the one given
   ///
   /// This is the version for Open
   ///
   /// @param [in] idx requested bin index
   /// @param [in] sizes how many neighboring bins (up/down)
   /// @return Set of neighboring bin indices (global)
   /// @note Open varies given bin and allows 0 and NBins+1 (underflow,
   /// overflow)
   ///       as neighbors
   NeighborHoodIndices neighborHoodIndices(std::size_t idx,
                                           std::pair<int, int> sizes = {-1,
                                                                        1}) const
     requires(bdt == AxisBoundaryType::Open)
   {
     constexpr int min = 0;
     const int max = getNBins() + 1;
     const int itmin = std::max(min, static_cast<int>(idx) + sizes.first);
     const int itmax = std::min(max, static_cast<int>(idx) + sizes.second);
     return NeighborHoodIndices(itmin, itmax + 1);
   }
 
   /// @brief Get #size bins which neighbor the one given
   ///
   /// This is the version for Bound
   ///
   /// @param [in] idx requested bin index
   /// @param [in] sizes how many neighboring bins (up/down)
   /// @return Set of neighboring bin indices (global)
   /// @note Bound varies given bin and allows 1 and NBins (regular bins)
   ///       as neighbors
   NeighborHoodIndices neighborHoodIndices(std::size_t idx,
                                           std::pair<int, int> sizes = {-1,
                                                                        1}) const
     requires(bdt == AxisBoundaryType::Bound)
   {
     if (idx <= 0 || idx >= (getNBins() + 1)) {
       return NeighborHoodIndices();
     }
     constexpr int min = 1;
     const int max = getNBins();
     const int itmin = std::max(min, static_cast<int>(idx) + sizes.first);
     const int itmax = std::min(max, static_cast<int>(idx) + sizes.second);
     return NeighborHoodIndices(itmin, itmax + 1);
   }
 
   /// @brief Get #size bins which neighbor the one given
   ///
   /// This is the version for Closed
   ///
   /// @param [in] idx requested bin index
   /// @param [in] sizes how many neighboring bins (up/down)
   /// @return Set of neighboring bin indices (global)
   /// @note Closed varies given bin and allows bins on the opposite
   ///       side of the axis as neighbors. (excludes underflow / overflow)
   NeighborHoodIndices neighborHoodIndices(std::size_t idx,
                                           std::pair<int, int> sizes = {-1,
                                                                        1}) const
     requires(bdt == AxisBoundaryType::Closed)
   {
     // Handle invalid indices
     if (idx <= 0 || idx >= (getNBins() + 1)) {
       return NeighborHoodIndices();
     }
 
     // Handle corner case where user requests more neighbours than the number
     // of bins on the axis. All bins are returned in this case
 
     const int max = getNBins();
     sizes.first = std::clamp(sizes.first, -max, max);
     sizes.second = std::clamp(sizes.second, -max, max);
     if (std::abs(sizes.first - sizes.second) >= max) {
       sizes.first = 1 - idx;
       sizes.second = max - idx;
     }
 
     // If the entire index range is not covered, we must wrap the range of
     // targeted neighbor indices into the range of valid bin indices. This may
     // split the range of neighbor indices in two parts:
     //
     // Before wraparound - [        XXXXX]XXX
     // After wraparound  - [ XXXX   XXXX ]
     //
     const int itmin = idx + sizes.first;
     const int itmax = idx + sizes.second;
     const std::size_t itfirst = wrapBin(itmin);
     const std::size_t itlast = wrapBin(itmax);
     if (itfirst <= itlast) {
       return NeighborHoodIndices(itfirst, itlast + 1);
     } else {
       return NeighborHoodIndices(itfirst, max + 1, 1, itlast + 1);
     }
   }
 
   /// @brief Converts bin index into a valid one for this axis.
   ///
   /// @note Open: bin index is clamped to [0, nBins+1]
   ///
   /// @param [in] bin The bin to wrap
   /// @return valid bin index
   std::size_t wrapBin(int bin) const
     requires(bdt == AxisBoundaryType::Open)
   {
     return std::max(std::min(bin, static_cast<int>(getNBins()) + 1), 0);
   }
 
   /// @brief Converts bin index into a valid one for this axis.
   ///
   /// @note Bound: bin index is clamped to [1, nBins]
   ///
   /// @param [in] bin The bin to wrap
   /// @return valid bin index
   std::size_t wrapBin(int bin) const
     requires(bdt == AxisBoundaryType::Bound)
   {
     return std::max(std::min(bin, static_cast<int>(getNBins())), 1);
   }
 
   /// @brief Converts bin index into a valid one for this axis.
   ///
   /// @note Closed: bin index wraps around to other side
   ///
   /// @param [in] bin The bin to wrap
   /// @return valid bin index
   std::size_t wrapBin(int bin) const
     requires(bdt == AxisBoundaryType::Closed)
   {
     const int w = getNBins();
     return 1 + (w + ((bin - 1) % w)) % w;
     // return int(bin<1)*w - int(bin>w)*w + bin;
   }
 
   /// @brief get corresponding bin index for given coordinate
   ///
   /// @param  [in] x input coordinate
   /// @return index of bin containing the given value
   ///
   /// @note Bin intervals are defined with closed lower bounds and open upper
   ///       bounds, that is \f$l <= x < u\f$ if the value @c x lies within a
   ///       bin with lower bound @c l and upper bound @c u.
   /// @note Bin indices start at @c 1. The underflow bin has the index @c 0
   ///       while the index <tt>nBins + 1</tt> indicates the overflow bin .
   std::size_t getBin(double x) const final {
     const auto it =
         std::upper_bound(std::begin(m_binEdges), std::end(m_binEdges), x);
     return wrapBin(std::distance(std::begin(m_binEdges), it));
   }
 
   /// @brief get bin width
   ///
   /// @param  [in] bin index of bin
   /// @return width of given bin
   ///
   /// @pre @c bin must be a valid bin index (excluding under-/overflow bins),
   ///      i.e. \f$1 \le \text{bin} \le \text{nBins}\f$
   double getBinWidth(std::size_t bin) const {
     return m_binEdges.at(bin) - m_binEdges.at(bin - 1);
   }
 
   /// @brief get lower bound of bin
   ///
   /// @param  [in] bin index of bin
   /// @return lower bin boundary
   ///
   /// @pre @c bin must be a valid bin index (excluding the underflow bin),
   ///      i.e. \f$1 \le \text{bin} \le \text{nBins} + 1\f$
   ///
   /// @note Bin intervals have a closed lower bound, i.e. the lower boundary
   ///       belongs to the bin with the given bin index.
   double getBinLowerBound(std::size_t bin) const {
     return m_binEdges.at(bin - 1);
   }
 
   /// @brief get upper bound of bin
   ///
   /// @param  [in] bin index of bin
   /// @return upper bin boundary
   ///
   /// @pre @c bin must be a valid bin index (excluding the overflow bin),
   ///      i.e. \f$0 \le \text{bin} \le \text{nBins}\f$
   ///
   /// @note Bin intervals have an open upper bound, i.e. the upper boundary
   ///       does @b not belong to the bin with the given bin index.
   double getBinUpperBound(std::size_t bin) const { return m_binEdges.at(bin); }
 
   /// @brief get bin center
   ///
   /// @param  [in] bin index of bin
   /// @return bin center position
   ///
   /// @pre @c bin must be a valid bin index (excluding under-/overflow bins),
   ///      i.e. \f$1 \le \text{bin} \le \text{nBins}\f$
   double getBinCenter(std::size_t bin) const {
     return 0.5 * (getBinLowerBound(bin) + getBinUpperBound(bin));
   }
 
   /// @brief get maximum of binning range
   ///
   /// @return maximum of binning range
   double getMax() const final { return m_binEdges.back(); }
 
   /// @brief get minimum of binning range
   ///
   /// @return minimum of binning range
   double getMin() const final { return m_binEdges.front(); }
 
   /// @brief get total number of bins
   ///
   /// @return total number of bins (excluding under-/overflow bins)
   std::size_t getNBins() const final { return m_binEdges.size() - 1; }
 
   /// @brief check whether value is inside axis limits
   /// @param x The value to check
   ///
   /// @return @c true if \f$\text{xmin} \le x < \text{xmax}\f$, otherwise
   ///         @c false
   ///
   /// @post If @c true is returned, the bin containing the given value is a
   ///       valid bin, i.e. it is neither the underflow nor the overflow bin.
   bool isInside(double x) const {
     return (m_binEdges.front() <= x) && (x < m_binEdges.back());
   }
 
   /// @brief Return a vector of bin edges
   /// @return Vector which contains the bin edges
   std::vector<double> getBinEdges() const final { return m_binEdges; }
 
   friend std::ostream& operator<<(std::ostream& os, const Axis& axis) {
     os << "Axis<Variable, " << bdt << ">(";
     os << axis.m_binEdges.front();
     for (std::size_t i = 1; i < axis.m_binEdges.size(); i++) {
       os << ", " << axis.m_binEdges[i];
     }
     os << ")";
     return os;
   }
 
  protected:
   void toStream(std::ostream& os) const final { os << *this; }
 
  private:
   /// vector of bin edges (sorted in ascending order)
   std::vector<double> m_binEdges;
 };
 }  // namespace Acts

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