ca-kernels.H

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/*
                          Aleph_w
 
  Data structures & Algorithms
  version 2.0.0b
  https://github.com/lrleon/Aleph-w
 
  This file is part of Aleph-w library
 
  Copyright (c) 2002-2026 Leandro Rabindranath Leon
 
  Permission is hereby granted, free of charge, to any person obtaining a copy
  of this software and associated documentation files (the "Software"), to deal
  in the Software without restriction, including without limitation the rights
  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  copies of the Software, and to permit persons to whom the Software is
  furnished to do so, subject to the following conditions:
 
  The above copyright notice and this permission notice shall be included in all
  copies or substantial portions of the Software.
 
  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  SOFTWARE.
*/
 
#ifndef CA_KERNELS_H
#define CA_KERNELS_H
 
#include <array>
#include <cstddef>
#include <initializer_list>
#include <memory>
#include <type_traits>
 
#include <ah-errors.H>
#include <al-domain.H>
#include <al-matrix.H>
 
#include <ca-traits.H>
 
namespace Aleph {
namespace CA {
 
template <typename T, std::size_t Rows, std::size_t Cols>
class Kernel2D
{
  static_assert(std::is_arithmetic_v<T>, "Kernel2D requires arithmetic weights");
  static_assert(Rows >= 3 and Cols >= 3, "Kernel2D requires at least 3x3 weights");
  static_assert(Rows % 2 == 1 and Cols % 2 == 1, "Kernel2D dimensions must be odd");
  static_assert(Rows == Cols, "Kernel2D currently expects square kernels");
 
public:
  using value_type = T;
 
  static constexpr std::size_t rows_v = Rows;
  static constexpr std::size_t cols_v = Cols;
  static constexpr std::size_t size_v = Rows * Cols;
  static constexpr std::size_t neighbour_count_v = size_v - 1;
  static constexpr std::size_t radius_v = Rows / 2;
 
private:
  std::array<T, size_v> weights_{};
 
  [[nodiscard]] static constexpr std::size_t index(const std::size_t row, const std::size_t col) noexcept
  {
    return row * Cols + col;
  }
 
public:
  constexpr Kernel2D() = default;
 
  constexpr explicit Kernel2D(const std::array<T, size_v> &weights) : weights_(weights) {}
 
  explicit Kernel2D(std::initializer_list<T> weights)
  {
    ah_length_error_if(weights.size() != size_v)
      << "Kernel2D: expected " << size_v << " weights, got " << weights.size();
    std::size_t i = 0;
    for (const auto &w : weights)
      weights_[i++] = w;
  }
 
  explicit Kernel2D(std::initializer_list<std::initializer_list<T>> rows)
  {
    ah_length_error_if(rows.size() != Rows)
      << "Kernel2D: expected " << Rows << " rows, got " << rows.size();
 
    std::size_t r = 0;
    for (const auto &row : rows)
      {
        ah_length_error_if(row.size() != Cols)
          << "Kernel2D: expected " << Cols << " columns, got " << row.size();
        std::size_t c = 0;
        for (const auto &w : row)
          weights_[index(r, c++)] = w;
        ++r;
      }
  }
 
  [[nodiscard]] T operator()(const std::size_t row, const std::size_t col) const
  {
    ah_out_of_range_error_if(row >= Rows or col >= Cols)
      << "Kernel2D::operator(): position (" << row << ", " << col << ") outside kernel";
    return weights_[index(row, col)];
  }
 
  [[nodiscard]] T weight_at_offset(const ca_index_t di, const ca_index_t dj) const
  {
    const ca_index_t r = di + static_cast<ca_index_t>(Rows / 2);
    const ca_index_t c = dj + static_cast<ca_index_t>(Cols / 2);
    ah_out_of_range_error_if(r < 0 or c < 0 or static_cast<std::size_t>(r) >= Rows
                             or static_cast<std::size_t>(c) >= Cols)
      << "Kernel2D::weight_at_offset: offset (" << di << ", " << dj << ") outside radius "
      << radius_v;
    return weights_[index(static_cast<std::size_t>(r), static_cast<std::size_t>(c))];
  }
 
  [[nodiscard]] T neighbour_weight(const std::size_t k) const
  {
    ah_out_of_range_error_if(k >= neighbour_count_v)
      << "Kernel2D::neighbour_weight: index " << k << " outside [0, " << neighbour_count_v << ")";
 
    std::size_t out = 0;
    for (std::size_t r = 0; r < Rows; ++r)
      for (std::size_t c = 0; c < Cols; ++c)
        {
          if (r == Rows / 2 and c == Cols / 2)
            continue;
          if (out == k)
            return weights_[index(r, c)];
          ++out;
        }
    return T{};
  }
 
  [[nodiscard]] constexpr T center() const noexcept
  {
    return weights_[index(Rows / 2, Cols / 2)];
  }
 
  [[nodiscard]] constexpr const std::array<T, size_v> &weights() const noexcept
  {
    return weights_;
  }
 
  [[nodiscard]] constexpr T sum() const noexcept
  {
    T acc{};
    for (const auto &w : weights_)
      acc += w;
    return acc;
  }
 
  template <typename State>
  [[nodiscard]] T apply(const State &center_value, Neighbor_View<State> neighbours) const
  {
    ah_length_error_if(neighbours.size() != neighbour_count_v)
      << "Kernel2D::apply: expected " << neighbour_count_v << " neighbours, got "
      << neighbours.size();
 
    T acc = static_cast<T>(center_value) * center();
    std::array<T, neighbour_count_v> neighbour_weights{};
    std::size_t out = 0;
    for (std::size_t r = 0; r < Rows; ++r)
      for (std::size_t c = 0; c < Cols; ++c)
        {
          if (r == Rows / 2 and c == Cols / 2)
            continue;
          neighbour_weights[out++] = weights_[index(r, c)];
        }
    for (std::size_t k = 0; k < neighbour_count_v; ++k)
      acc += static_cast<T>(neighbours[k]) * neighbour_weights[k];
    return acc;
  }
 
  [[nodiscard]] Matrix<int, int, T> to_matrix() const
  {
    auto rd = std::make_shared<IntRange>(static_cast<int>(Rows));
    auto cd = std::make_shared<IntRange>(static_cast<int>(Cols));
    Matrix<int, int, T> ret(rd, cd);
    for (std::size_t r = 0; r < Rows; ++r)
      for (std::size_t c = 0; c < Cols; ++c)
        ret.set_entry(static_cast<int>(r), static_cast<int>(c), weights_[index(r, c)]);
    return ret;
  }
};
 
template <typename T = double>
[[nodiscard]] constexpr Kernel2D<T, 3, 3> laplacian_5p_kernel() noexcept
{
  return Kernel2D<T, 3, 3>(std::array<T, 9>{T{0}, T{1}, T{0}, T{1}, T{-4}, T{1}, T{0}, T{1}, T{0}});
}
 
template <typename T = double>
[[nodiscard]] constexpr Kernel2D<T, 3, 3> laplacian_9p_kernel() noexcept
{
  return Kernel2D<T, 3, 3>(std::array<T, 9>{T{1} / T{6}, T{4} / T{6}, T{1} / T{6}, T{4} / T{6},
                                            T{-20} / T{6}, T{4} / T{6}, T{1} / T{6}, T{4} / T{6},
                                            T{1} / T{6}});
}
 
template <typename T = double>
[[nodiscard]] constexpr Kernel2D<T, 3, 3> mean_3x3_kernel() noexcept
{
  constexpr T w = T{1} / T{9};
  return Kernel2D<T, 3, 3>(std::array<T, 9>{w, w, w, w, w, w, w, w, w});
}
 
template <typename T = double>
[[nodiscard]] constexpr Kernel2D<T, 5, 5> mean_5x5_kernel() noexcept
{
  constexpr T w = T{1} / T{25};
  return Kernel2D<T, 5, 5>(
    std::array<T, 25>{w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w});
}
 
template <typename T = double>
[[nodiscard]] constexpr Kernel2D<T, 3, 3> sobel_x_kernel() noexcept
{
  return Kernel2D<T, 3, 3>(std::array<T, 9>{T{-1}, T{0}, T{1}, T{-2}, T{0}, T{2}, T{-1}, T{0}, T{1}});
}
 
template <typename T = double>
[[nodiscard]] constexpr Kernel2D<T, 3, 3> sobel_y_kernel() noexcept
{
  return Kernel2D<T, 3, 3>(std::array<T, 9>{T{-1}, T{-2}, T{-1}, T{0}, T{0}, T{0}, T{1}, T{2}, T{1}});
}
 
template <typename T = double>
[[nodiscard]] constexpr Kernel2D<T, 3, 3> gaussian_3x3_kernel() noexcept
{
  return Kernel2D<T, 3, 3>(std::array<T, 9>{T{1} / T{16}, T{2} / T{16}, T{1} / T{16}, T{2} / T{16},
                                            T{4} / T{16}, T{2} / T{16}, T{1} / T{16}, T{2} / T{16},
                                            T{1} / T{16}});
}
 
template <typename T = double>
[[nodiscard]] constexpr Kernel2D<T, 5, 5> gaussian_5x5_kernel() noexcept
{
  return Kernel2D<T, 5, 5>(std::array<T, 25>{
    T{1} / T{256}, T{4} / T{256},  T{6} / T{256},  T{4} / T{256},  T{1} / T{256},
    T{4} / T{256}, T{16} / T{256}, T{24} / T{256}, T{16} / T{256}, T{4} / T{256},
    T{6} / T{256}, T{24} / T{256}, T{36} / T{256}, T{24} / T{256}, T{6} / T{256},
    T{4} / T{256}, T{16} / T{256}, T{24} / T{256}, T{16} / T{256}, T{4} / T{256},
    T{1} / T{256}, T{4} / T{256},  T{6} / T{256},  T{4} / T{256},  T{1} / T{256}});
}
 
}  // namespace CA
}  // namespace Aleph
 
#endif  // CA_KERNELS_H