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  /*! \internal \file
   * \brief
   * Implements Gaussian function evaluations on lattices and related functionality
   *
   * \author Christian Blau <blau@kth.se>
   *
   * \ingroup module_math
   */
  #include "gmxpre.h"
  
  #include "gausstransform.h"
  
  #include <cmath>
  
  #include <algorithm>
  #include <array>
  
  #include "gromacs/math/functions.h"
  #include "gromacs/math/multidimarray.h"
  #include "gromacs/math/units.h"
  #include "gromacs/math/utilities.h"
  #include "gromacs/utility/basedefinitions.h"
  
  namespace gmx
  {
  
  /********************************************************************
   * GaussianOn1DLattice::Impl
   */
  
  class GaussianOn1DLattice::Impl
  {
  public:
      Impl(int numGridPointsForSpreadingHalfWidth, real sigma);
      ~Impl()                 = default;
      Impl(const Impl& other) = default;
      Impl& operator=(const Impl& other) = default;
  
      /*! \brief evaluate Gaussian function at all lattice points
       * \param[in] amplitude the amplitude of the Gaussian
       * \param[in] dx distance from the center
       */
      void spread(double amplitude, real dx);
      //! Largest distance in number of gridpoints from 0
      int numGridPointsForSpreadingHalfWidth_;
      /*! \brief Avoid overflow for E2^offset and underflow for E3(i).
       *
       * Occurs when sigma is much smaller than numGridPointsForSpreadingHalfWidth_.
       *
       * E2^offset smaller than maximum float requires
       * \f$exp(dx / (2*square(sigma))^numGridPointsForSpreadingHalfWidth_ \leq max_float \f$
       * The maximum expected distance of the Gaussian center to the next lattice point is dx = 0.5,
       * thus the maximum spread distance here is \f$4 * sigma^2 * \log(\mathrm{maxfloat})\f$ .
       *
       * E3(i) larger than minmium float requires
       * exp(i^2 / 2*(sigma)^2) > min_float
       * Thus the maximum spread distance here is \f$\sigma \sqrt(-2\log(\mathrm{minfloat}))\f$
       */
      int maxEvaluatedSpreadDistance_;
      //! Width of the Gaussian function
      double sigma_;
      //! The result of the spreading calculation
      std::vector<float> spreadingResult_;
      //! Pre-calculated exp(-gridIndex^2/2 * (sigma^2)) named as in Greengard2004
      std::vector<float> e3_;
      /*! \brief Equal to std::floor(std::log(std::numeric_limits<float>::max())).
       * Above expression is not constexpr and a const variable would implicitly delete default copy
       * assignment. Therefore resorting to setting number manually.
       */
      static constexpr double c_logMaxFloat = 88.72284;
      static constexpr double c_logMinFloat = -87.33654;
  };
  
  GaussianOn1DLattice::Impl::Impl(int numGridPointsForSpreadingHalfWidth, real sigma) :
      numGridPointsForSpreadingHalfWidth_(numGridPointsForSpreadingHalfWidth),
      sigma_(sigma),
      spreadingResult_(2 * numGridPointsForSpreadingHalfWidth + 1)
  {
      maxEvaluatedSpreadDistance_ =
              std::min(numGridPointsForSpreadingHalfWidth_,
                       static_cast<int>(std::floor(4 * square(sigma) * c_logMaxFloat)) - 1);
      maxEvaluatedSpreadDistance_ =
              std::min(maxEvaluatedSpreadDistance_,
                       static_cast<int>(std::floor(sigma * sqrt(-2.0 * c_logMinFloat))) - 1);
  
      std::generate_n(
              std::back_inserter(e3_), maxEvaluatedSpreadDistance_ + 1, [sigma, latticeIndex = 0]() mutable {
                  return std::exp(-0.5 * square(latticeIndex++ / sigma));
              });
  
      std::fill(std::begin(spreadingResult_), std::end(spreadingResult_), 0.);
  };
  
  void GaussianOn1DLattice::Impl::spread(double amplitude, real dx)
  {
      /* The spreading routine implements the fast gaussian gridding as in
       *
       * Leslie Greengard and June-Yub Lee,
       * "Accelerating the Nonuniform Fast Fourier Transform"
       * SIAM REV 2004 Vol. 46, No. 3, pp. 443-454 DOI. 10.1137/S003614450343200X
       *
       * Following the naming conventions for e1, e2 and e3, nu = 1, m = numGridPointsForSpreadingHalfWidth_.
       *
       * Speed up is achieved by factorization of the exponential that is evaluted
       * at regular lattice points i, where the distance from the
       * Gaussian center is \f$x-i\f$:
       *
       * \f[
       *      a * \exp(-(x^2-2*i*x+ i^2)/(2*\sigma^2)) =
       *      a * \exp(-x^2/2*\sigma^2) * \exp(x/\sigma^2)^i * \exp(i/2*sigma^2) =
       *      e_1(x) * e_2(x)^i * e_3(i)
       * \f]
       *
       * Requiring only two exp evaluations per spreading operation.
       *
       */
      const double e1 = amplitude * exp(-0.5 * dx * dx / square(sigma_)) / (sqrt(2 * M_PI) * sigma_);
      spreadingResult_[numGridPointsForSpreadingHalfWidth_] = e1;
  
      const double e2 = exp(dx / square(sigma_));
  
      double e2pow = e2; //< powers of e2, e2^offset
  
      // Move outwards from mid-point, using e2pow value for both points simultaneously
      //      o    o    o<----O---->o    o    o
      for (int offset = 1; offset < maxEvaluatedSpreadDistance_; offset++)
      {
          const double e1_3                                              = e1 * e3_[offset];
          spreadingResult_[numGridPointsForSpreadingHalfWidth_ + offset] = e1_3 * e2pow;
          spreadingResult_[numGridPointsForSpreadingHalfWidth_ - offset] = e1_3 / e2pow;
          e2pow *= e2;
      }
      // separate statement for gridpoints at the end of the range avoids
      // overflow for large sigma and saves one e2 multiplication operation
      spreadingResult_[numGridPointsForSpreadingHalfWidth_ - maxEvaluatedSpreadDistance_] =
              (e1 / e2pow) * e3_[maxEvaluatedSpreadDistance_];
      spreadingResult_[numGridPointsForSpreadingHalfWidth_ + maxEvaluatedSpreadDistance_] =
              (e1 * e2pow) * e3_[maxEvaluatedSpreadDistance_];
  }
  
  /********************************************************************
   * GaussianOn1DLattice
   */
  
  GaussianOn1DLattice::GaussianOn1DLattice(int numGridPointsForSpreadingHalfWidth_, real sigma) :
      impl_(new Impl(numGridPointsForSpreadingHalfWidth_, sigma))
  {
  }
  
  GaussianOn1DLattice::~GaussianOn1DLattice() {}
  
  void GaussianOn1DLattice::spread(double amplitude, real dx)
  {
      impl_->spread(amplitude, dx);
  }
  
  ArrayRef<const float> GaussianOn1DLattice::view()
  {
      return impl_->spreadingResult_;
  }
  
  GaussianOn1DLattice::GaussianOn1DLattice(const GaussianOn1DLattice& other) :
      impl_(new Impl(*other.impl_))
  {
  }
  
  GaussianOn1DLattice& GaussianOn1DLattice::operator=(const GaussianOn1DLattice& other)
  {
      *impl_ = *other.impl_;
      return *this;
  }
  
  GaussianOn1DLattice::GaussianOn1DLattice(GaussianOn1DLattice&&) noexcept = default;
  
  GaussianOn1DLattice& GaussianOn1DLattice::operator=(GaussianOn1DLattice&&) noexcept = default;
  
  namespace
  {
  
  //! rounds real-valued coordinate to the closest integer values
  IVec closestIntegerPoint(const RVec& coordinate)
  {
      return { roundToInt(coordinate[XX]), roundToInt(coordinate[YY]), roundToInt(coordinate[ZZ]) };
  }
  
  /*! \brief Substracts a range from a three-dimensional integer coordinate and ensures
   * the resulting coordinate is within a lattice.
   * \param[in] index point in lattice
   * \param[in] range to be shifted
   * \returns Shifted index or zero if shifted index is smaller than zero.
   */
  IVec rangeBeginWithinLattice(const IVec& index, const IVec& range)
  {
      return elementWiseMax({ 0, 0, 0 }, index - range);
  }
  
  /*! \brief Adds a range from a three-dimensional integer coordinate and ensures
   * the resulting coordinate is within a lattice.
   * \param[in] index point in lattice
   * \param[in] extents extent of the lattice
   * \param[in] range to be shifted
   * \returns Shifted index or the lattice extent if shifted index is larger than the extent
   */
  IVec rangeEndWithinLattice(const IVec& index, const dynamicExtents3D& extents, const IVec& range)
  {
      IVec extentAsIvec(static_cast<int>(extents.extent(ZZ)),
                        static_cast<int>(extents.extent(YY)),
                        static_cast<int>(extents.extent(XX)));
      return elementWiseMin(extentAsIvec, index + range);
  }
  
  
  } // namespace
  
  /********************************************************************
   * OuterProductEvaluator
   */
  
  mdspan<const float, dynamic_extent, dynamic_extent>
  OuterProductEvaluator::operator()(ArrayRef<const float> x, ArrayRef<const float> y)
  {
      data_.resize(ssize(x), ssize(y));
      for (gmx::index xIndex = 0; xIndex < ssize(x); ++xIndex)
      {
          const auto xValue = x[xIndex];
          std::transform(std::begin(y), std::end(y), begin(data_.asView()[xIndex]), [xValue](float yValue) {
              return xValue * yValue;
          });
      }
      return data_.asConstView();
  }
  
  /********************************************************************
   * IntegerBox
   */
  
  IntegerBox::IntegerBox(const IVec& begin, const IVec& end) : begin_{ begin }, end_{ end } {}
  
  const IVec& IntegerBox::begin() const
  {
      return begin_;
  }
  const IVec& IntegerBox::end() const
  {
      return end_;
  }
  
  bool IntegerBox::empty() const
  {
      return !((begin_[XX] < end_[XX]) && (begin_[YY] < end_[YY]) && (begin_[ZZ] < end_[ZZ]));
  }
  
  IntegerBox spreadRangeWithinLattice(const IVec& center, dynamicExtents3D extent, IVec range)
  {
      const IVec begin = rangeBeginWithinLattice(center, range);
      const IVec end   = rangeEndWithinLattice(center, extent, range);
      return { begin, end };
  }
  /********************************************************************
   * GaussianSpreadKernel
   */
  
  IVec GaussianSpreadKernelParameters::Shape::latticeSpreadRange() const
  {
      DVec range(std::ceil(sigma_[XX] * spreadWidthMultiplesOfSigma_),
                 std::ceil(sigma_[YY] * spreadWidthMultiplesOfSigma_),
                 std::ceil(sigma_[ZZ] * spreadWidthMultiplesOfSigma_));
      return range.toIVec();
  }
  
  /********************************************************************
   * GaussTransform3D::Impl
   */
  
  /*! \internal \brief
   * Private implementation class for GaussTransform3D.
   */
  class GaussTransform3D::Impl
  {
  public:
      //! Construct from extent and spreading width and range
      Impl(const dynamicExtents3D& extent, const GaussianSpreadKernelParameters::Shape& kernelShapeParameters);
      ~Impl() = default;
      //! Copy constructor
      Impl(const Impl& other) = default;
      //! Copy assignment
      Impl& operator=(const Impl& other) = default;
      //! Add another gaussian
      void add(const GaussianSpreadKernelParameters::PositionAndAmplitude& localParamters);
      //! The width of the Gaussian in lattice spacing units
      BasicVector<double> sigma_;
      //! The spread range in lattice points
      IVec spreadRange_;
      //! The result of the Gauss transform
      MultiDimArray<std::vector<float>, dynamicExtents3D> data_;
      //! The outer product of a Gaussian along the z and y dimension
      OuterProductEvaluator outerProductZY_;
      //! The three one-dimensional Gaussians, whose outer product is added to the Gauss transform
      std::array<GaussianOn1DLattice, DIM> gauss1d_;
  };
  
  GaussTransform3D::Impl::Impl(const dynamicExtents3D&                      extent,
                               const GaussianSpreadKernelParameters::Shape& kernelShapeParameters) :
      sigma_{ kernelShapeParameters.sigma_ },
      spreadRange_{ kernelShapeParameters.latticeSpreadRange() },
      data_{ extent },
      gauss1d_({ GaussianOn1DLattice(spreadRange_[XX], sigma_[XX]),
                 GaussianOn1DLattice(spreadRange_[YY], sigma_[YY]),
                 GaussianOn1DLattice(spreadRange_[ZZ], sigma_[ZZ]) })
  {
  }
  
  void GaussTransform3D::Impl::add(const GaussianSpreadKernelParameters::PositionAndAmplitude& localParameters)
  {
      const IVec closestLatticePoint = closestIntegerPoint(localParameters.coordinate_);
      const auto spreadRange =
              spreadRangeWithinLattice(closestLatticePoint, data_.asView().extents(), spreadRange_);
  
      // do nothing if the added Gaussian will never reach the lattice
      if (spreadRange.empty())
      {
          return;
      }
  
      for (int dimension = XX; dimension <= ZZ; ++dimension)
      {
          // multiply with amplitude so that Gauss3D = (amplitude * Gauss_x) * Gauss_y * Gauss_z
          const float gauss1DAmplitude = dimension > XX ? 1.0 : localParameters.amplitude_;
          gauss1d_[dimension].spread(
                  gauss1DAmplitude, localParameters.coordinate_[dimension] - closestLatticePoint[dimension]);
      }
  
      const auto spreadZY         = outerProductZY_(gauss1d_[ZZ].view(), gauss1d_[YY].view());
      const auto spreadX          = gauss1d_[XX].view();
      const IVec spreadGridOffset = spreadRange_ - closestLatticePoint;
  
      // \todo optimize these loops if performance critical
      // The looping strategy uses that the last, x-dimension is contiguous in the memory layout
      for (int zLatticeIndex = spreadRange.begin()[ZZ]; zLatticeIndex < spreadRange.end()[ZZ]; ++zLatticeIndex)
      {
          const auto zSlice = data_.asView()[zLatticeIndex];
  
          for (int yLatticeIndex = spreadRange.begin()[YY]; yLatticeIndex < spreadRange.end()[YY]; ++yLatticeIndex)
          {
              const auto  ySlice      = zSlice[yLatticeIndex];
              const float zyPrefactor = spreadZY(zLatticeIndex + spreadGridOffset[ZZ],
                                                 yLatticeIndex + spreadGridOffset[YY]);
  
              for (int xLatticeIndex = spreadRange.begin()[XX]; xLatticeIndex < spreadRange.end()[XX];
                   ++xLatticeIndex)
              {
                  const float xPrefactor = spreadX[xLatticeIndex + spreadGridOffset[XX]];
                  ySlice[xLatticeIndex] += zyPrefactor * xPrefactor;
              }
          }
      }
  }
  
  /********************************************************************
   * GaussTransform3D
   */
  
  GaussTransform3D::GaussTransform3D(const dynamicExtents3D&                      extent,
                                     const GaussianSpreadKernelParameters::Shape& kernelShapeParameters) :
      impl_(new Impl(extent, kernelShapeParameters))
  {
  }
  
  void GaussTransform3D::add(const GaussianSpreadKernelParameters::PositionAndAmplitude& localParameters)
  {
      impl_->add(localParameters);
  }
  
  void GaussTransform3D::setZero()
  {
      std::fill(begin(impl_->data_), end(impl_->data_), 0.);
  }
  
  basic_mdspan<float, dynamicExtents3D> GaussTransform3D::view()
  {
      return impl_->data_.asView();
  }
  
  basic_mdspan<const float, dynamicExtents3D> GaussTransform3D::constView() const
  {
      return impl_->data_.asConstView();
  }
  
  GaussTransform3D::~GaussTransform3D() {}
  
  GaussTransform3D::GaussTransform3D(const GaussTransform3D& other) : impl_(new Impl(*other.impl_)) {}
  
  GaussTransform3D& GaussTransform3D::operator=(const GaussTransform3D& other)
  {
      *impl_ = *other.impl_;
      return *this;
  }
  
  GaussTransform3D::GaussTransform3D(GaussTransform3D&&) noexcept = default;
  
  GaussTransform3D& GaussTransform3D::operator=(GaussTransform3D&&) noexcept = default;
  
  } // namespace gmx
  