LinInterpolatedTableND.h

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#ifndef NPSTAT_LININTERPOLATEDTABLEND_HH_
#define NPSTAT_LININTERPOLATEDTABLEND_HH_

#include <climits>
#include <vector>
#include <utility>

#include "Alignment/Geners/interface/CPP11_auto_ptr.hh"

#include "JetMETCorrections/InterpolationTables/interface/ArrayND.h"
#include "JetMETCorrections/InterpolationTables/interface/UniformAxis.h"

namespace npstat {
  template <class Numeric, class Axis = UniformAxis>
  class LinInterpolatedTableND {
    template <typename Num2, typename Axis2>
    friend class LinInterpolatedTableND;

  public:
    typedef Numeric value_type;
    typedef Axis axis_type;

    LinInterpolatedTableND(const std::vector<Axis>& axes,
                           const std::vector<std::pair<bool, bool> >& extrapolationType,
                           const char* functionLabel = nullptr);

    LinInterpolatedTableND(const Axis& xAxis, bool leftX, bool rightX, const char* functionLabel = nullptr);

    LinInterpolatedTableND(const Axis& xAxis,
                           bool leftX,
                           bool rightX,
                           const Axis& yAxis,
                           bool leftY,
                           bool rightY,
                           const char* functionLabel = nullptr);

    LinInterpolatedTableND(const Axis& xAxis,
                           bool leftX,
                           bool rightX,
                           const Axis& yAxis,
                           bool leftY,
                           bool rightY,
                           const Axis& zAxis,
                           bool leftZ,
                           bool rightZ,
                           const char* functionLabel = nullptr);

    LinInterpolatedTableND(const Axis& xAxis,
                           bool leftX,
                           bool rightX,
                           const Axis& yAxis,
                           bool leftY,
                           bool rightY,
                           const Axis& zAxis,
                           bool leftZ,
                           bool rightZ,
                           const Axis& tAxis,
                           bool leftT,
                           bool rightT,
                           const char* functionLabel = nullptr);

    LinInterpolatedTableND(const Axis& xAxis,
                           bool leftX,
                           bool rightX,
                           const Axis& yAxis,
                           bool leftY,
                           bool rightY,
                           const Axis& zAxis,
                           bool leftZ,
                           bool rightZ,
                           const Axis& tAxis,
                           bool leftT,
                           bool rightT,
                           const Axis& vAxis,
                           bool leftV,
                           bool rightV,
                           const char* functionLabel = nullptr);

    template <class Num2>
    LinInterpolatedTableND(const LinInterpolatedTableND<Num2, Axis>&);

    Numeric operator()(const double* point, unsigned dim) const;


    Numeric operator()(const double& x0) const;
    Numeric operator()(const double& x0, const double& x1) const;
    Numeric operator()(const double& x0, const double& x1, const double& x2) const;
    Numeric operator()(const double& x0, const double& x1, const double& x2, const double& x3) const;
    Numeric operator()(const double& x0, const double& x1, const double& x2, const double& x3, const double& x4) const;


    inline unsigned dim() const { return dim_; }
    inline const std::vector<Axis>& axes() const { return axes_; }
    inline const Axis& axis(const unsigned i) const { return axes_.at(i); }
    inline unsigned long length() const { return data_.length(); }
    bool leftInterpolationLinear(unsigned i) const;
    bool rightInterpolationLinear(unsigned i) const;
    std::vector<std::pair<bool, bool> > interpolationType() const;
    inline const std::string& functionLabel() const { return functionLabel_; }


    inline const ArrayND<Numeric>& table() const { return data_; }
    inline ArrayND<Numeric>& table() { return data_; }

    void getCoords(unsigned long linearIndex, double* coords, unsigned coordsBufferSize) const;

    bool isUniformlyBinned() const;

    bool isWithinLimits(const double* point, unsigned dim) const;

    inline void setFunctionLabel(const char* newlabel) { functionLabel_ = newlabel ? newlabel : ""; }

    template <typename ConvertibleToUnsigned>
    CPP11_auto_ptr<LinInterpolatedTableND> invertWRTAxis(ConvertibleToUnsigned axisNumber,
                                                         const Axis& replacementAxis,
                                                         bool newAxisLeftLinear,
                                                         bool newAxisRightLinear,
                                                         const char* functionLabel = nullptr) const;

    template <class Functor1, class Functor2>
    CPP11_auto_ptr<LinInterpolatedTableND> invertRatioResponse(unsigned axisNumber,
                                                               const Axis& replacementAxis,
                                                               bool newAxisLeftLinear,
                                                               bool newAxisRightLinear,
                                                               Functor1 invg,
                                                               Functor2 invh,
                                                               const char* functionLabel = nullptr) const;

    bool operator==(const LinInterpolatedTableND&) const;

    inline bool operator!=(const LinInterpolatedTableND& r) const { return !(*this == r); }

    // Method related to "geners" I/O
    inline gs::ClassId classId() const { return gs::ClassId(*this); }
    bool write(std::ostream& of) const;

    static const char* classname();
    static inline unsigned version() { return 1; }
    static LinInterpolatedTableND* read(const gs::ClassId& id, std::istream& in);

  private:
    LinInterpolatedTableND() = delete;

    LinInterpolatedTableND(const ArrayND<Numeric>& data,
                           const std::vector<Axis>& axes,
                           const char* leftInterpolation,
                           const char* rightInterpolation,
                           const std::string& label);

    bool allConstInterpolated() const;

    ArrayND<Numeric> data_;
    std::vector<Axis> axes_;
    std::string functionLabel_;
    char leftInterpolationLinear_[CHAR_BIT * sizeof(unsigned long)];
    char rightInterpolationLinear_[CHAR_BIT * sizeof(unsigned long)];
    unsigned dim_;
    bool allConstInterpolated_;

    template <class Functor1>
    static double solveForRatioArg(double xmin, double xmax, double rmin, double rmax, double fval, Functor1 invg);

    template <class Functor1>
    static void invert1DResponse(const ArrayND<Numeric>& fromSlice,
                                 const Axis& fromAxis,
                                 const Axis& toAxis,
                                 bool newLeftLinear,
                                 bool newRightLinear,
                                 Functor1 invg,
                                 const double* rawx,
                                 const double* rawf,
                                 double* workspace,
                                 ArrayND<Numeric>* toSlice);
  };
}  // namespace npstat

#include <cmath>
#include <cfloat>
#include <cassert>
#include <algorithm>
#include <functional>

#include "Alignment/Geners/interface/binaryIO.hh"

#include "JetMETCorrections/InterpolationTables/interface/ArrayNDScanner.h"
#include "JetMETCorrections/InterpolationTables/interface/isMonotonous.h"

namespace npstat {
  namespace Private {
    template <class Axis>
    ArrayShape makeTableShape(const std::vector<Axis>& axes) {
      const unsigned n = axes.size();
      ArrayShape result;
      result.reserve(n);
      for (unsigned i = 0; i < n; ++i)
        result.push_back(axes[i].nCoords());
      return result;
    }

    template <class Axis>
    ArrayShape makeTableShape(const Axis& xAxis) {
      ArrayShape result;
      result.reserve(1U);
      result.push_back(xAxis.nCoords());
      return result;
    }

    template <class Axis>
    ArrayShape makeTableShape(const Axis& xAxis, const Axis& yAxis) {
      ArrayShape result;
      result.reserve(2U);
      result.push_back(xAxis.nCoords());
      result.push_back(yAxis.nCoords());
      return result;
    }

    template <class Axis>
    ArrayShape makeTableShape(const Axis& xAxis, const Axis& yAxis, const Axis& zAxis) {
      ArrayShape result;
      result.reserve(3U);
      result.push_back(xAxis.nCoords());
      result.push_back(yAxis.nCoords());
      result.push_back(zAxis.nCoords());
      return result;
    }

    template <class Axis>
    ArrayShape makeTableShape(const Axis& xAxis, const Axis& yAxis, const Axis& zAxis, const Axis& tAxis) {
      ArrayShape result;
      result.reserve(4U);
      result.push_back(xAxis.nCoords());
      result.push_back(yAxis.nCoords());
      result.push_back(zAxis.nCoords());
      result.push_back(tAxis.nCoords());
      return result;
    }

    template <class Axis>
    ArrayShape makeTableShape(
        const Axis& xAxis, const Axis& yAxis, const Axis& zAxis, const Axis& tAxis, const Axis& vAxis) {
      ArrayShape result;
      result.reserve(5U);
      result.push_back(xAxis.nCoords());
      result.push_back(yAxis.nCoords());
      result.push_back(zAxis.nCoords());
      result.push_back(tAxis.nCoords());
      result.push_back(vAxis.nCoords());
      return result;
    }

    inline double lind_interpolateSimple(
        const double x0, const double x1, const double y0, const double y1, const double x) {
      return y0 + (y1 - y0) * ((x - x0) / (x1 - x0));
    }

    template <typename Numeric, class Axis>
    void lind_invert1DSlice(const ArrayND<Numeric>& fromSlice,
                            const Axis& fromAxis,
                            const Axis& toAxis,
                            const bool leftLinear,
                            const bool rightLinear,
                            ArrayND<Numeric>* toSlice) {
      assert(toSlice);
      assert(fromSlice.rank() == 1U);
      assert(toSlice->rank() == 1U);

      const Numeric* fromData = fromSlice.data();
      const unsigned fromLen = fromSlice.length();
      assert(fromLen > 1U);
      assert(fromLen == fromAxis.nCoords());
      const Numeric* fromDataEnd = fromData + fromLen;
      if (!isStrictlyMonotonous(fromData, fromDataEnd))
        throw npstat::NpstatInvalidArgument(
            "In npstat::Private::lind_invert1DSlice: "
            "slice data is not monotonous and can not be inverted");

      const Numeric yfirst = fromData[0];
      const Numeric ylast = fromData[fromLen - 1U];
      const bool increasing = yfirst < ylast;

      Numeric* toD = const_cast<Numeric*>(toSlice->data());
      const unsigned nAxisPoints = toAxis.nCoords();
      assert(toSlice->length() == nAxisPoints);

      for (unsigned ipt = 0; ipt < nAxisPoints; ++ipt) {
        const Numeric y = static_cast<Numeric>(toAxis.coordinate(ipt));
        if (increasing) {
          if (y <= yfirst) {
            if (leftLinear)
              toD[ipt] = Private::lind_interpolateSimple(
                  yfirst, fromData[1], fromAxis.coordinate(0), fromAxis.coordinate(1), y);
            else
              toD[ipt] = fromAxis.coordinate(0);
          } else if (y >= ylast) {
            if (rightLinear)
              toD[ipt] = Private::lind_interpolateSimple(ylast,
                                                         fromData[fromLen - 2U],
                                                         fromAxis.coordinate(fromLen - 1U),
                                                         fromAxis.coordinate(fromLen - 2U),
                                                         y);
            else
              toD[ipt] = fromAxis.coordinate(fromLen - 1U);
          } else {
            const unsigned i = std::lower_bound(fromData, fromDataEnd, y) - fromData;
            toD[ipt] = Private::lind_interpolateSimple(
                fromData[i - 1U], fromData[i], fromAxis.coordinate(i - 1U), fromAxis.coordinate(i), y);
          }
        } else {
          // The role of left and right are exchanged
          // with respect to first and last point
          if (y <= ylast) {
            if (leftLinear)
              toD[ipt] = Private::lind_interpolateSimple(ylast,
                                                         fromData[fromLen - 2U],
                                                         fromAxis.coordinate(fromLen - 1U),
                                                         fromAxis.coordinate(fromLen - 2U),
                                                         y);
            else
              toD[ipt] = fromAxis.coordinate(fromLen - 1U);
          } else if (y >= yfirst) {
            if (rightLinear)
              toD[ipt] = Private::lind_interpolateSimple(
                  yfirst, fromData[1], fromAxis.coordinate(0), fromAxis.coordinate(1), y);
            else
              toD[ipt] = fromAxis.coordinate(0);
          } else {
            const unsigned i = std::lower_bound(fromData, fromDataEnd, y, std::greater<Numeric>()) - fromData;
            toD[ipt] = Private::lind_interpolateSimple(
                fromData[i - 1U], fromData[i], fromAxis.coordinate(i - 1U), fromAxis.coordinate(i), y);
          }
        }
      }
    }
  }  // namespace Private

  template <class Numeric, class Axis>
  bool LinInterpolatedTableND<Numeric, Axis>::allConstInterpolated() const {
    for (unsigned i = 0; i < dim_; ++i)
      if (leftInterpolationLinear_[i] || rightInterpolationLinear_[i])
        return false;
    return true;
  }

  template <class Numeric, class Axis>
  bool LinInterpolatedTableND<Numeric, Axis>::operator==(const LinInterpolatedTableND& r) const {
    if (dim_ != r.dim_)
      return false;
    for (unsigned i = 0; i < dim_; ++i) {
      if (leftInterpolationLinear_[i] != r.leftInterpolationLinear_[i])
        return false;
      if (rightInterpolationLinear_[i] != r.rightInterpolationLinear_[i])
        return false;
    }
    return data_ == r.data_ && axes_ == r.axes_ && functionLabel_ == r.functionLabel_;
  }

  template <typename Numeric, class Axis>
  const char* LinInterpolatedTableND<Numeric, Axis>::classname() {
    static const std::string myClass(gs::template_class_name<Numeric, Axis>("npstat::LinInterpolatedTableND"));
    return myClass.c_str();
  }

  template <typename Numeric, class Axis>
  bool LinInterpolatedTableND<Numeric, Axis>::write(std::ostream& of) const {
    const bool status = data_.classId().write(of) && data_.write(of) && gs::write_obj_vector(of, axes_);
    if (status) {
      gs::write_pod_array(of, leftInterpolationLinear_, dim_);
      gs::write_pod_array(of, rightInterpolationLinear_, dim_);
      gs::write_pod(of, functionLabel_);
    }
    return status && !of.fail();
  }

  template <typename Numeric, class Axis>
  LinInterpolatedTableND<Numeric, Axis>* LinInterpolatedTableND<Numeric, Axis>::read(const gs::ClassId& id,
                                                                                     std::istream& in) {
    static const gs::ClassId current(gs::ClassId::makeId<LinInterpolatedTableND<Numeric, Axis> >());
    current.ensureSameId(id);

    gs::ClassId ida(in, 1);
    ArrayND<Numeric> data;
    ArrayND<Numeric>::restore(ida, in, &data);
    std::vector<Axis> axes;
    gs::read_heap_obj_vector_as_placed(in, &axes);
    const unsigned dim = axes.size();
    if (dim > CHAR_BIT * sizeof(unsigned long) || data.rank() != dim)
      throw gs::IOInvalidData(
          "In npstat::LinInterpolatedTableND::read: "
          "read back invalid dimensionality");
    char leftInterpolation[CHAR_BIT * sizeof(unsigned long)];
    gs::read_pod_array(in, leftInterpolation, dim);
    char rightInterpolation[CHAR_BIT * sizeof(unsigned long)];
    gs::read_pod_array(in, rightInterpolation, dim);
    std::string label;
    gs::read_pod(in, &label);
    if (in.fail())
      throw gs::IOReadFailure("In npstat::LinInterpolatedTableND::read: input stream failure");
    return new LinInterpolatedTableND(data, axes, leftInterpolation, rightInterpolation, label);
  }

  template <typename Numeric, class Axis>
  bool LinInterpolatedTableND<Numeric, Axis>::leftInterpolationLinear(const unsigned i) const {
    if (i >= dim_)
      throw npstat::NpstatOutOfRange(
          "In npstat::LinInterpolatedTableND::leftInterpolationLinear: "
          "index out of range");
    return leftInterpolationLinear_[i];
  }

  template <typename Numeric, class Axis>
  bool LinInterpolatedTableND<Numeric, Axis>::rightInterpolationLinear(const unsigned i) const {
    if (i >= dim_)
      throw npstat::NpstatOutOfRange(
          "In npstat::LinInterpolatedTableND::rightInterpolationLinear: "
          "index out of range");
    return rightInterpolationLinear_[i];
  }

  template <typename Numeric, class Axis>
  bool LinInterpolatedTableND<Numeric, Axis>::isUniformlyBinned() const {
    for (unsigned i = 0; i < dim_; ++i)
      if (!axes_[i].isUniform())
        return false;
    return true;
  }

  template <typename Numeric, class Axis>
  std::vector<std::pair<bool, bool> > LinInterpolatedTableND<Numeric, Axis>::interpolationType() const {
    std::vector<std::pair<bool, bool> > vec;
    vec.reserve(dim_);
    for (unsigned i = 0; i < dim_; ++i)
      vec.push_back(std::pair<bool, bool>(leftInterpolationLinear_[i], rightInterpolationLinear_[i]));
    return vec;
  }

  template <typename Numeric, class Axis>
  LinInterpolatedTableND<Numeric, Axis>::LinInterpolatedTableND(
      const std::vector<Axis>& axes, const std::vector<std::pair<bool, bool> >& interpolationType, const char* label)
      : data_(Private::makeTableShape(axes)), axes_(axes), functionLabel_(label ? label : ""), dim_(axes.size()) {
    if (dim_ == 0 || dim_ >= CHAR_BIT * sizeof(unsigned long))
      throw npstat::NpstatInvalidArgument(
          "In npstat::LinInterpolatedTableND constructor: requested "
          "table dimensionality is not supported");
    if (dim_ != interpolationType.size())
      throw npstat::NpstatInvalidArgument(
          "In npstat::LinInterpolatedTableND constructor: "
          "incompatible number of interpolation specifications");
    for (unsigned i = 0; i < dim_; ++i) {
      const std::pair<bool, bool>& pair(interpolationType[i]);
      leftInterpolationLinear_[i] = pair.first;
      rightInterpolationLinear_[i] = pair.second;
    }

    allConstInterpolated_ = allConstInterpolated();
  }

  template <typename Numeric, class Axis>
  template <class Num2>
  LinInterpolatedTableND<Numeric, Axis>::LinInterpolatedTableND(const LinInterpolatedTableND<Num2, Axis>& r)
      : data_(r.data_),
        axes_(r.axes_),
        functionLabel_(r.functionLabel_),
        dim_(r.dim_),
        allConstInterpolated_(r.allConstInterpolated_) {
    for (unsigned i = 0; i < dim_; ++i) {
      leftInterpolationLinear_[i] = r.leftInterpolationLinear_[i];
      rightInterpolationLinear_[i] = r.rightInterpolationLinear_[i];
    }
  }

  template <typename Numeric, class Axis>
  LinInterpolatedTableND<Numeric, Axis>::LinInterpolatedTableND(const ArrayND<Numeric>& data,
                                                                const std::vector<Axis>& axes,
                                                                const char* leftInterpolation,
                                                                const char* rightInterpolation,
                                                                const std::string& label)
      : data_(data), axes_(axes), functionLabel_(label), dim_(data.rank()) {
    for (unsigned i = 0; i < dim_; ++i) {
      leftInterpolationLinear_[i] = leftInterpolation[i];
      rightInterpolationLinear_[i] = rightInterpolation[i];
    }
    allConstInterpolated_ = allConstInterpolated();
  }

  template <typename Numeric, class Axis>
  LinInterpolatedTableND<Numeric, Axis>::LinInterpolatedTableND(const Axis& xAxis,
                                                                bool leftX,
                                                                bool rightX,
                                                                const Axis& yAxis,
                                                                bool leftY,
                                                                bool rightY,
                                                                const Axis& zAxis,
                                                                bool leftZ,
                                                                bool rightZ,
                                                                const Axis& tAxis,
                                                                bool leftT,
                                                                bool rightT,
                                                                const Axis& vAxis,
                                                                bool leftV,
                                                                bool rightV,
                                                                const char* label)
      : data_(Private::makeTableShape(xAxis, yAxis, zAxis, tAxis, vAxis)),
        functionLabel_(label ? label : ""),
        dim_(5U) {
    axes_.reserve(dim_);
    axes_.push_back(xAxis);
    axes_.push_back(yAxis);
    axes_.push_back(zAxis);
    axes_.push_back(tAxis);
    axes_.push_back(vAxis);

    unsigned i = 0;
    leftInterpolationLinear_[i] = leftX;
    rightInterpolationLinear_[i++] = rightX;
    leftInterpolationLinear_[i] = leftY;
    rightInterpolationLinear_[i++] = rightY;
    leftInterpolationLinear_[i] = leftZ;
    rightInterpolationLinear_[i++] = rightZ;
    leftInterpolationLinear_[i] = leftT;
    rightInterpolationLinear_[i++] = rightT;
    leftInterpolationLinear_[i] = leftV;
    rightInterpolationLinear_[i++] = rightV;
    assert(i == dim_);

    allConstInterpolated_ = allConstInterpolated();
  }

  template <typename Numeric, class Axis>
  LinInterpolatedTableND<Numeric, Axis>::LinInterpolatedTableND(const Axis& xAxis,
                                                                bool leftX,
                                                                bool rightX,
                                                                const Axis& yAxis,
                                                                bool leftY,
                                                                bool rightY,
                                                                const Axis& zAxis,
                                                                bool leftZ,
                                                                bool rightZ,
                                                                const Axis& tAxis,
                                                                bool leftT,
                                                                bool rightT,
                                                                const char* label)
      : data_(Private::makeTableShape(xAxis, yAxis, zAxis, tAxis)), functionLabel_(label ? label : ""), dim_(4U) {
    axes_.reserve(dim_);
    axes_.push_back(xAxis);
    axes_.push_back(yAxis);
    axes_.push_back(zAxis);
    axes_.push_back(tAxis);

    unsigned i = 0;
    leftInterpolationLinear_[i] = leftX;
    rightInterpolationLinear_[i++] = rightX;
    leftInterpolationLinear_[i] = leftY;
    rightInterpolationLinear_[i++] = rightY;
    leftInterpolationLinear_[i] = leftZ;
    rightInterpolationLinear_[i++] = rightZ;
    leftInterpolationLinear_[i] = leftT;
    rightInterpolationLinear_[i++] = rightT;
    assert(i == dim_);

    allConstInterpolated_ = allConstInterpolated();
  }

  template <typename Numeric, class Axis>
  LinInterpolatedTableND<Numeric, Axis>::LinInterpolatedTableND(const Axis& xAxis,
                                                                bool leftX,
                                                                bool rightX,
                                                                const Axis& yAxis,
                                                                bool leftY,
                                                                bool rightY,
                                                                const Axis& zAxis,
                                                                bool leftZ,
                                                                bool rightZ,
                                                                const char* label)
      : data_(Private::makeTableShape(xAxis, yAxis, zAxis)), functionLabel_(label ? label : ""), dim_(3U) {
    axes_.reserve(dim_);
    axes_.push_back(xAxis);
    axes_.push_back(yAxis);
    axes_.push_back(zAxis);

    unsigned i = 0;
    leftInterpolationLinear_[i] = leftX;
    rightInterpolationLinear_[i++] = rightX;
    leftInterpolationLinear_[i] = leftY;
    rightInterpolationLinear_[i++] = rightY;
    leftInterpolationLinear_[i] = leftZ;
    rightInterpolationLinear_[i++] = rightZ;
    assert(i == dim_);

    allConstInterpolated_ = allConstInterpolated();
  }

  template <typename Numeric, class Axis>
  LinInterpolatedTableND<Numeric, Axis>::LinInterpolatedTableND(
      const Axis& xAxis, bool leftX, bool rightX, const Axis& yAxis, bool leftY, bool rightY, const char* label)
      : data_(Private::makeTableShape(xAxis, yAxis)), functionLabel_(label ? label : ""), dim_(2U) {
    axes_.reserve(dim_);
    axes_.push_back(xAxis);
    axes_.push_back(yAxis);

    unsigned i = 0;
    leftInterpolationLinear_[i] = leftX;
    rightInterpolationLinear_[i++] = rightX;
    leftInterpolationLinear_[i] = leftY;
    rightInterpolationLinear_[i++] = rightY;
    assert(i == dim_);

    allConstInterpolated_ = allConstInterpolated();
  }

  template <typename Numeric, class Axis>
  LinInterpolatedTableND<Numeric, Axis>::LinInterpolatedTableND(const Axis& xAxis,
                                                                bool leftX,
                                                                bool rightX,
                                                                const char* label)
      : data_(Private::makeTableShape(xAxis)), functionLabel_(label ? label : ""), dim_(1U) {
    axes_.reserve(dim_);
    axes_.push_back(xAxis);

    leftInterpolationLinear_[0] = leftX;
    rightInterpolationLinear_[0] = rightX;

    allConstInterpolated_ = allConstInterpolated();
  }

  template <typename Numeric, class Axis>
  template <typename ConvertibleToUnsigned>
  CPP11_auto_ptr<LinInterpolatedTableND<Numeric, Axis> > LinInterpolatedTableND<Numeric, Axis>::invertWRTAxis(
      const ConvertibleToUnsigned axisNumC,
      const Axis& replacementAxis,
      const bool leftLinear,
      const bool rightLinear,
      const char* functionLabel) const {
    const unsigned axisNumber = static_cast<unsigned>(axisNumC);

    if (axisNumber >= dim_)
      throw npstat::NpstatOutOfRange(
          "In npstat::LinInterpolatedTableND::invertAxis: "
          "axis number is out of range");

    // Generate the new set of axes
    std::vector<Axis> newAxes(axes_);
    newAxes[axisNumber] = replacementAxis;

    std::vector<std::pair<bool, bool> > iType(interpolationType());
    iType[axisNumber] = std::pair<bool, bool>(leftLinear, rightLinear);

    // Create the new table
    CPP11_auto_ptr<LinInterpolatedTableND> pTable(new LinInterpolatedTableND(newAxes, iType, functionLabel));

    if (dim_ > 1U) {
      // Prepare array slices
      unsigned sliceIndex[CHAR_BIT * sizeof(unsigned long)];
      unsigned fixedIndices[CHAR_BIT * sizeof(unsigned long)];
      unsigned count = 0;
      for (unsigned i = 0; i < dim_; ++i)
        if (i != axisNumber) {
          sliceIndex[count] = data_.span(i);
          fixedIndices[count++] = i;
        }
      ArrayND<Numeric> parentSlice(data_, fixedIndices, count);
      ArrayND<Numeric> dauSlice(pTable->data_, fixedIndices, count);

      // Cycle over the slices
      for (ArrayNDScanner scan(sliceIndex, count); scan.isValid(); ++scan) {
        scan.getIndex(sliceIndex, count);
        data_.exportSlice(&parentSlice, fixedIndices, sliceIndex, count);
        Private::lind_invert1DSlice(
            parentSlice, axes_[axisNumber], replacementAxis, leftLinear, rightLinear, &dauSlice);
        pTable->data_.importSlice(dauSlice, fixedIndices, sliceIndex, count);
      }
    } else
      Private::lind_invert1DSlice(data_, axes_[0], replacementAxis, leftLinear, rightLinear, &pTable->data_);
    return pTable;
  }

  template <typename Numeric, class Axis>
  template <class Functor1, class Functor2>
  CPP11_auto_ptr<LinInterpolatedTableND<Numeric, Axis> > LinInterpolatedTableND<Numeric, Axis>::invertRatioResponse(
      const unsigned axisNumber,
      const Axis& replacementAxis,
      const bool leftLinear,
      const bool rightLinear,
      Functor1 invg,
      Functor2 invh,
      const char* functionLabel) const {
    if (axisNumber >= dim_)
      throw npstat::NpstatOutOfRange(
          "In npstat::LinInterpolatedTableND::invertRatioResponse: "
          "axis number is out of range");

    // Generate the new set of axes
    std::vector<Axis> newAxes(axes_);
    newAxes[axisNumber] = replacementAxis;

    std::vector<std::pair<bool, bool> > iType(interpolationType());
    iType[axisNumber] = std::pair<bool, bool>(leftLinear, rightLinear);

    // Transform the original axis to the raw x values
    const Axis& oldAxis(axes_[axisNumber]);
    std::vector<double> rawx;
    const unsigned nCoords = oldAxis.nCoords();
    rawx.reserve(nCoords);
    for (unsigned i = 0; i < nCoords; ++i) {
      const double x = invg(oldAxis.coordinate(i));
      if (x < 0.0)
        throw npstat::NpstatInvalidArgument(
            "In npstat::LinInterpolatedTableND::invertRatioResponse: "
            "invalid original axis definition (negative transformed "
            "coordinate)");
      rawx.push_back(x);
    }

    // Transform the new axis to the raw f(x) values
    std::vector<double> rawf;
    const unsigned nFuncs = replacementAxis.nCoords();
    rawf.reserve(nFuncs);
    for (unsigned i = 0; i < nFuncs; ++i) {
      const double f = invh(replacementAxis.coordinate(i));
      if (f < 0.0)
        throw npstat::NpstatInvalidArgument(
            "In npstat::LinInterpolatedTableND::invertRatioResponse: "
            "invalid new axis definition (negative transformed "
            "coordinate)");
      rawf.push_back(f);
    }

    // Workspace needed for the inversion code
    std::vector<double> workspace(nCoords);

    // Create the new table
    CPP11_auto_ptr<LinInterpolatedTableND> pTable(new LinInterpolatedTableND(newAxes, iType, functionLabel));

    if (dim_ > 1U) {
      // Prepare array slices
      unsigned sliceIndex[CHAR_BIT * sizeof(unsigned long)];
      unsigned fixedIndices[CHAR_BIT * sizeof(unsigned long)];
      unsigned count = 0;
      for (unsigned i = 0; i < dim_; ++i)
        if (i != axisNumber) {
          sliceIndex[count] = data_.span(i);
          fixedIndices[count++] = i;
        }
      ArrayND<Numeric> parentSlice(data_, fixedIndices, count);
      ArrayND<Numeric> dauSlice(pTable->data_, fixedIndices, count);

      // Cycle over the slices
      for (ArrayNDScanner scan(sliceIndex, count); scan.isValid(); ++scan) {
        scan.getIndex(sliceIndex, count);
        data_.exportSlice(&parentSlice, fixedIndices, sliceIndex, count);
        invert1DResponse(parentSlice,
                         oldAxis,
                         replacementAxis,
                         leftLinear,
                         rightLinear,
                         invg,
                         &rawx[0],
                         &rawf[0],
                         &workspace[0],
                         &dauSlice);
        pTable->data_.importSlice(dauSlice, fixedIndices, sliceIndex, count);
      }
    } else
      invert1DResponse(data_,
                       oldAxis,
                       replacementAxis,
                       leftLinear,
                       rightLinear,
                       invg,
                       &rawx[0],
                       &rawf[0],
                       &workspace[0],
                       &pTable->data_);
    return pTable;
  }

  template <typename Numeric, class Axis>
  void LinInterpolatedTableND<Numeric, Axis>::getCoords(const unsigned long linearIndex,
                                                        double* coords,
                                                        const unsigned coordsBufferSize) const {
    if (coordsBufferSize < dim_)
      throw npstat::NpstatInvalidArgument(
          "In LinInterpolatedTableND::getCoords: "
          "insufficient buffer size");
    assert(coords);
    unsigned index[CHAR_BIT * sizeof(unsigned long)];
    data_.convertLinearIndex(linearIndex, index, dim_);
    for (unsigned i = 0; i < dim_; ++i)
      coords[i] = axes_[i].coordinate(index[i]);
  }

  template <typename Numeric, class Axis>
  bool LinInterpolatedTableND<Numeric, Axis>::isWithinLimits(const double* point, const unsigned len) const {
    if (len != dim_)
      throw npstat::NpstatInvalidArgument(
          "In npstat::LinInterpolatedTableND::isWithinLimits: "
          "incompatible point dimensionality");
    assert(point);

    for (unsigned i = 0; i < dim_; ++i)
      if (point[i] < axes_[i].min() || point[i] > axes_[i].max())
        return false;
    return true;
  }

  template <typename Numeric, class Axis>
  Numeric LinInterpolatedTableND<Numeric, Axis>::operator()(const double* point, const unsigned len) const {
    typedef typename ProperDblFromCmpl<Numeric>::type proper_double;

    if (len != dim_)
      throw npstat::NpstatInvalidArgument(
          "In npstat::LinInterpolatedTableND::operator(): "
          "incompatible point dimensionality");
    assert(point);

    bool interpolateArray = true;
    if (!allConstInterpolated_)
      for (unsigned i = 0; i < dim_; ++i)
        if ((leftInterpolationLinear_[i] && point[i] < axes_[i].min()) ||
            (rightInterpolationLinear_[i] && point[i] > axes_[i].max())) {
          interpolateArray = false;
          break;
        }

    if (interpolateArray) {
      // Translate coordinates into the array system and
      // simply use the ArrayND interpolation facilities
      double buf[CHAR_BIT * sizeof(unsigned long)];
      for (unsigned i = 0; i < dim_; ++i) {
        const std::pair<unsigned, double>& pair = axes_[i].getInterval(point[i]);
        buf[i] = pair.first + 1U - pair.second;
      }
      return data_.interpolate1(buf, dim_);
    } else {
      unsigned ix[CHAR_BIT * sizeof(unsigned long)];
      double weight[CHAR_BIT * sizeof(unsigned long)];
      for (unsigned i = 0; i < dim_; ++i) {
        const bool linear = (leftInterpolationLinear_[i] && point[i] < axes_[i].min()) ||
                            (rightInterpolationLinear_[i] && point[i] > axes_[i].max());
        const std::pair<unsigned, double>& pair =
            linear ? axes_[i].linearInterval(point[i]) : axes_[i].getInterval(point[i]);
        ix[i] = pair.first;
        weight[i] = pair.second;
      }

      Numeric sum = Numeric();
      const unsigned long maxcycle = 1UL << dim_;
      const unsigned long* strides = data_.strides();
      const Numeric* dat = data_.data();
      for (unsigned long icycle = 0UL; icycle < maxcycle; ++icycle) {
        double w = 1.0;
        unsigned long icell = 0UL;
        for (unsigned i = 0; i < dim_; ++i) {
          if (icycle & (1UL << i)) {
            w *= (1.0 - weight[i]);
            icell += strides[i] * (ix[i] + 1U);
          } else {
            w *= weight[i];
            icell += strides[i] * ix[i];
          }
        }
        sum += dat[icell] * static_cast<proper_double>(w);
      }
      return sum;
    }
  }

  template <typename Numeric, class Axis>
  Numeric LinInterpolatedTableND<Numeric, Axis>::operator()(const double& x0) const {
    const unsigned nArgs = 1U;
    if (dim_ != nArgs)
      throw npstat::NpstatInvalidArgument(
          "In npstat::LinInterpolatedTableND::operator(): number of "
          "arguments, 1, is incompatible with the interpolator dimensionality");
    double tmp[nArgs];
    tmp[0] = x0;
    return operator()(tmp, nArgs);
  }

  template <typename Numeric, class Axis>
  Numeric LinInterpolatedTableND<Numeric, Axis>::operator()(const double& x0, const double& x1) const {
    const unsigned nArgs = 2U;
    if (dim_ != nArgs)
      throw npstat::NpstatInvalidArgument(
          "In npstat::LinInterpolatedTableND::operator(): number of "
          "arguments, 2, is incompatible with the interpolator dimensionality");
    double tmp[nArgs];
    tmp[0] = x0;
    tmp[1] = x1;
    return operator()(tmp, nArgs);
  }

  template <typename Numeric, class Axis>
  Numeric LinInterpolatedTableND<Numeric, Axis>::operator()(const double& x0,
                                                            const double& x1,
                                                            const double& x2) const {
    const unsigned nArgs = 3U;
    if (dim_ != nArgs)
      throw npstat::NpstatInvalidArgument(
          "In npstat::LinInterpolatedTableND::operator(): number of "
          "arguments, 3, is incompatible with the interpolator dimensionality");
    double tmp[nArgs];
    tmp[0] = x0;
    tmp[1] = x1;
    tmp[2] = x2;
    return operator()(tmp, nArgs);
  }

  template <typename Numeric, class Axis>
  Numeric LinInterpolatedTableND<Numeric, Axis>::operator()(const double& x0,
                                                            const double& x1,
                                                            const double& x2,
                                                            const double& x3) const {
    const unsigned nArgs = 4U;
    if (dim_ != nArgs)
      throw npstat::NpstatInvalidArgument(
          "In npstat::LinInterpolatedTableND::operator(): number of "
          "arguments, 4, is incompatible with the interpolator dimensionality");
    double tmp[nArgs];
    tmp[0] = x0;
    tmp[1] = x1;
    tmp[2] = x2;
    tmp[3] = x3;
    return operator()(tmp, nArgs);
  }

  template <typename Numeric, class Axis>
  Numeric LinInterpolatedTableND<Numeric, Axis>::operator()(
      const double& x0, const double& x1, const double& x2, const double& x3, const double& x4) const {
    const unsigned nArgs = 5U;
    if (dim_ != nArgs)
      throw npstat::NpstatInvalidArgument(
          "In npstat::LinInterpolatedTableND::operator(): number of "
          "arguments, 5, is incompatible with the interpolator dimensionality");
    double tmp[nArgs];
    tmp[0] = x0;
    tmp[1] = x1;
    tmp[2] = x2;
    tmp[3] = x3;
    tmp[4] = x4;
    return operator()(tmp, nArgs);
  }

  template <typename Numeric, class Axis>
  template <class Functor1>
  double LinInterpolatedTableND<Numeric, Axis>::solveForRatioArg(
      const double xmin, const double xmax, const double rmin, const double rmax, const double fval, Functor1 invg) {
    // Find two values of x so that f(x0) <= fval <= f(x1)
    double x0 = xmin;
    double x1 = xmax;
    double fmin = invg(xmin) * rmin;
    double fmax = invg(xmax) * rmax;
    const double step = xmax - xmin;
    assert(fmin < fmax);
    assert(step > 0.0);

    unsigned stepcount = 0;
    const unsigned maxSteps = 1000U;
    for (double stepfactor = 1.0; (fval < fmin || fval > fmax) && stepcount < maxSteps; stepfactor *= 2.0, ++stepcount)
      if (fval < fmin) {
        x1 = x0;
        fmax = fmin;
        x0 -= stepfactor * step;
        fmin = invg(x0) * Private::lind_interpolateSimple(xmin, xmax, rmin, rmax, x0);
      } else {
        x0 = x1;
        fmin = fmax;
        x1 += stepfactor * step;
        fmax = invg(x1) * Private::lind_interpolateSimple(xmin, xmax, rmin, rmax, x1);
      }
    if (stepcount == maxSteps)
      throw npstat::NpstatRuntimeError(
          "In LinInterpolatedTableND::solveForRatioArg: "
          "faled to bracket the root");

    assert(x1 >= x0);
    while ((x1 - x0) / (std::abs(x1) + std::abs(x0) + DBL_EPSILON) > 4.0 * DBL_EPSILON) {
      const double xhalf = (x1 + x0) / 2.0;
      const double fhalf = invg(xhalf) * Private::lind_interpolateSimple(xmin, xmax, rmin, rmax, xhalf);
      if (fval < fhalf) {
        x1 = xhalf;
        fmax = fhalf;
      } else {
        x0 = xhalf;
        fmin = fhalf;
      }
    }
    return (x1 + x0) / 2.0;
  }

  template <typename Numeric, class Axis>
  template <class Functor1>
  void LinInterpolatedTableND<Numeric, Axis>::invert1DResponse(const ArrayND<Numeric>& fromSlice,
                                                               const Axis& fromAxis,
                                                               const Axis& toAxis,
                                                               const bool newLeftLinear,
                                                               const bool newRightLinear,
                                                               Functor1 invg,
                                                               const double* rawx,
                                                               const double* rawf,
                                                               double* workspace,
                                                               ArrayND<Numeric>* toSlice) {
    assert(toSlice);
    assert(fromSlice.rank() == 1U);
    assert(toSlice->rank() == 1U);

    const Numeric zero = Numeric();
    const Numeric* fromData = fromSlice.data();
    const unsigned fromLen = fromSlice.length();
    assert(fromLen > 1U);
    assert(fromLen == fromAxis.nCoords());
    Numeric* toD = const_cast<Numeric*>(toSlice->data());
    const unsigned nAxisPoints = toAxis.nCoords();
    assert(toSlice->length() == nAxisPoints);

    for (unsigned i = 0; i < fromLen; ++i) {
      if (fromData[i] <= zero)
        throw npstat::NpstatDomainError(
            "In LinInterpolatedTableND::invert1DResponse: "
            "non-positive response found. This ratio "
            "response table is not invertible.");
      workspace[i] = rawx[i] * fromData[i];
    }

    const double yfirst = workspace[0];
    const double ylast = workspace[fromLen - 1U];

    bool adjustZero = false;
    unsigned nBelow = 0;
    for (unsigned ipt = 0; ipt < nAxisPoints; ++ipt) {
      const double y = rawf[ipt];
      unsigned i0 = 0;
      bool solve = false;
      if (y == 0.0) {
        assert(ipt == 0U);
        if (newLeftLinear)
          adjustZero = true;
      } else if (y <= yfirst) {
        ++nBelow;
        solve = newLeftLinear;
      } else if (y >= ylast) {
        solve = newRightLinear;
        i0 = solve ? fromLen - 2 : fromLen - 1;
      } else {
        solve = true;
        i0 = static_cast<unsigned>(std::lower_bound(workspace, workspace + fromLen, y) - workspace) - 1U;
      }
      if (solve) {
        const double x = solveForRatioArg(
            fromAxis.coordinate(i0), fromAxis.coordinate(i0 + 1), fromData[i0], fromData[i0 + 1], y, invg);
        toD[ipt] = invg(x) / y;
      } else
        toD[ipt] = 1.0 / fromData[i0];
    }
    if (adjustZero && nBelow)
      toD[0] = toD[1];
  }
}  // namespace npstat

#endif  // NPSTAT_LININTERPOLATEDTABLEND_HH_