Matrix.hpp

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// This code is based on Jet framework.
// Copyright (c) 2018 Doyub Kim
// CubbyFlow is voxel-based fluid simulation engine for computer games.
// Copyright (c) 2020 CubbyFlow Team
// Core Part: Chris Ohk, Junwoo Hwang, Jihong Sin, Seungwoo Yoo
// AI Part: Dongheon Cho, Minseo Kim
// We are making my contributions/submissions to this project solely in our
// personal capacity and are not conveying any rights to any intellectual
// property of any third parties.
 
#ifndef CUBBYFLOW_MATRIX_HPP
#define CUBBYFLOW_MATRIX_HPP
 
#include <Core/Matrix/MatrixDenseBase.hpp>
#include <Core/Matrix/MatrixExpression.hpp>
#include <Core/Utils/Macros.hpp>
#include <Core/Utils/NestedInitializerList.hpp>
#include <Core/Utils/TypeHelpers.hpp>
 
#include <array>
#include <cstdint>
#include <vector>
 
namespace CubbyFlow
{
template <typename T, size_t Rows, size_t Cols>
class Matrix final
    : public MatrixExpression<T, Rows, Cols, Matrix<T, Rows, Cols>>,
      public MatrixDenseBase<T, Rows, Cols, Matrix<T, Rows, Cols>>
{
 public:
    static_assert(IsMatrixSizeStatic<Rows, Cols>(),
                  "This class should be a static-sized matrix.");
 
    using Base = MatrixDenseBase<T, Rows, Cols, Matrix<T, Rows, Cols>>;
    using Base::CopyFrom;
    using Base::operator();
 
    using ValueType = T;
    using Reference = T&;
    using ConstReference = const T&;
    using Pointer = T*;
    using ConstPointer = const T*;
    using Iterator = Pointer;
    using ConstIterator = ConstPointer;
 
    constexpr Matrix() : m_elements{}
    {
        // Do nothing
    }
 
    Matrix(ConstReference value);
 
    template <typename... Args>
    constexpr Matrix(ConstReference first, Args... rest)
        : m_elements{ { first, static_cast<ValueType>(rest)... } }
    {
        // Do nothing
    }
 
    template <size_t R, size_t C, typename E>
    Matrix(const MatrixExpression<T, R, C, E>& expression);
 
    Matrix(const NestedInitializerListsT<T, 2>& lst);
 
    explicit Matrix(ConstPointer ptr);
 
    ~Matrix() = default;
 
    constexpr Matrix(const Matrix&) = default;
 
    constexpr Matrix(Matrix&&) noexcept = default;
 
    Matrix& operator=(const Matrix&) = default;
 
    Matrix& operator=(Matrix&&) noexcept = default;
 
    void Fill(const T& val);
 
    void Fill(const std::function<T(size_t i)>& func);
 
    void Fill(const std::function<T(size_t i, size_t j)>& func);
 
    void Swap(Matrix& other);
 
    [[nodiscard]] constexpr size_t GetRows() const;
 
    [[nodiscard]] constexpr size_t GetCols() const;
 
    Iterator begin();
 
    constexpr ConstIterator begin() const;
 
    Iterator end();
 
    constexpr ConstIterator end() const;
 
    Pointer data();
 
    constexpr ConstPointer data() const;
 
    Reference operator[](size_t i);
 
    ConstReference operator[](size_t i) const;
 
 private:
    std::array<T, Rows * Cols> m_elements;
};
 
template <typename T>
class Matrix<T, 1, 1> final : public MatrixExpression<T, 1, 1, Matrix<T, 1, 1>>,
                              public MatrixDenseBase<T, 1, 1, Matrix<T, 1, 1>>
{
 public:
    using Base = MatrixDenseBase<T, 1, 1, Matrix<T, 1, 1>>;
    using Base::operator();
 
    using ValueType = T;
    using Reference = T&;
    using ConstReference = const T&;
    using Pointer = T*;
    using ConstPointer = const T*;
    using Iterator = Pointer;
    using ConstIterator = ConstPointer;
 
    constexpr Matrix() : x(T{})
    {
        // Do nothing
    }
 
    constexpr Matrix(const T& _x) : x(_x)
    {
        // Do nothing
    }
 
    template <size_t R, size_t C, typename E>
    Matrix(const MatrixExpression<T, R, C, E>& expression);
 
    Matrix(const std::initializer_list<T>& lst);
 
    ~Matrix() = default;
 
    constexpr Matrix(const Matrix&) = default;
 
    constexpr Matrix(Matrix&&) noexcept = default;
 
    Matrix& operator=(const Matrix&) = default;
 
    Matrix& operator=(Matrix&&) noexcept = default;
 
    void Fill(const T& val);
 
    void Fill(const std::function<T(size_t i)>& func);
 
    void Fill(const std::function<T(size_t i, size_t j)>& func);
 
    void Swap(Matrix& other);
 
    [[nodiscard]] constexpr size_t GetRows() const;
 
    [[nodiscard]] constexpr size_t GetCols() const;
 
    [[nodiscard]] Iterator begin();
 
    [[nodiscard]] constexpr ConstIterator begin() const;
 
    [[nodiscard]] Iterator end();
 
    [[nodiscard]] constexpr ConstIterator end() const;
 
    [[nodiscard]] Pointer data();
 
    [[nodiscard]] constexpr ConstPointer data() const;
 
    Reference operator[](size_t i);
 
    ConstReference operator[](size_t i) const;
 
    constexpr static Matrix MakeUnitX();
 
    constexpr static Matrix MakeUnit(size_t i);
 
    ValueType x;
};
 
template <typename T>
class Matrix<T, 2, 1> final : public MatrixExpression<T, 2, 1, Matrix<T, 2, 1>>,
                              public MatrixDenseBase<T, 2, 1, Matrix<T, 2, 1>>
{
 public:
    using Base = MatrixDenseBase<T, 2, 1, Matrix<T, 2, 1>>;
    using Base::operator();
 
    using ValueType = T;
    using Reference = T&;
    using ConstReference = const T&;
    using Pointer = T*;
    using ConstPointer = const T*;
    using Iterator = Pointer;
    using ConstIterator = ConstPointer;
 
    constexpr Matrix() : x(T{}), y(T{})
    {
        // Do nothing
    }
 
    constexpr Matrix(const T& _x, const T& _y) : x(_x), y(_y)
    {
        // Do nothing
    }
 
    template <size_t R, size_t C, typename E>
    Matrix(const MatrixExpression<T, R, C, E>& expression);
 
    Matrix(const std::initializer_list<T>& lst);
 
    ~Matrix() = default;
 
    constexpr Matrix(const Matrix&) = default;
 
    constexpr Matrix(Matrix&&) noexcept = default;
 
    Matrix& operator=(const Matrix&) = default;
 
    Matrix& operator=(Matrix&&) noexcept = default;
 
    void Fill(const T& val);
 
    void Fill(const std::function<T(size_t i)>& func);
 
    void Fill(const std::function<T(size_t i, size_t j)>& func);
 
    void Swap(Matrix& other);
 
    [[nodiscard]] constexpr size_t GetRows() const;
 
    [[nodiscard]] constexpr size_t GetCols() const;
 
    [[nodiscard]] Iterator begin();
 
    [[nodiscard]] constexpr ConstIterator begin() const;
 
    [[nodiscard]] Iterator end();
 
    [[nodiscard]] constexpr ConstIterator end() const;
 
    [[nodiscard]] Pointer data();
 
    [[nodiscard]] constexpr ConstPointer data() const;
 
    Reference operator[](size_t i);
 
    ConstReference operator[](size_t i) const;
 
    constexpr static Matrix MakeUnitX();
 
    constexpr static Matrix MakeUnitY();
 
    constexpr static Matrix MakeUnit(size_t i);
 
    ValueType x;
    ValueType y;
};
 
template <typename T>
class Matrix<T, 3, 1> final : public MatrixExpression<T, 3, 1, Matrix<T, 3, 1>>,
                              public MatrixDenseBase<T, 3, 1, Matrix<T, 3, 1>>
{
 public:
    using Base = MatrixDenseBase<T, 3, 1, Matrix<T, 3, 1>>;
    using Base::operator();
 
    using ValueType = T;
    using Reference = T&;
    using ConstReference = const T&;
    using Pointer = T*;
    using ConstPointer = const T*;
    using Iterator = Pointer;
    using ConstIterator = ConstPointer;
 
    constexpr Matrix() : x(T{}), y(T{}), z(T{})
    {
        // Do nothing
    }
 
    constexpr Matrix(const Matrix<T, 2, 1>& _xy, const T& _z)
        : x(_xy.x), y(_xy.y), z(_z)
    {
        // Do nothing
    }
 
    constexpr Matrix(const T& _x, const T& _y, const T& _z)
        : x(_x), y(_y), z(_z)
    {
        // Do nothing
    }
 
    template <size_t R, size_t C, typename E>
    Matrix(const MatrixExpression<T, R, C, E>& expression);
 
    Matrix(const std::initializer_list<T>& lst);
 
    ~Matrix() = default;
 
    constexpr Matrix(const Matrix&) = default;
 
    constexpr Matrix(Matrix&&) noexcept = default;
 
    Matrix& operator=(const Matrix&) = default;
 
    Matrix& operator=(Matrix&&) noexcept = default;
 
    void Fill(const T& val);
 
    void Fill(const std::function<T(size_t i)>& func);
 
    void Fill(const std::function<T(size_t i, size_t j)>& func);
 
    void Swap(Matrix& other);
 
    [[nodiscard]] constexpr size_t GetRows() const;
 
    [[nodiscard]] constexpr size_t GetCols() const;
 
    [[nodiscard]] Iterator begin();
 
    [[nodiscard]] constexpr ConstIterator begin() const;
 
    [[nodiscard]] Iterator end();
 
    [[nodiscard]] constexpr ConstIterator end() const;
 
    [[nodiscard]] Pointer data();
 
    [[nodiscard]] constexpr ConstPointer data() const;
 
    Reference operator[](size_t i);
 
    ConstReference operator[](size_t i) const;
 
    constexpr static Matrix MakeUnitX();
 
    constexpr static Matrix MakeUnitY();
 
    constexpr static Matrix MakeUnitZ();
 
    constexpr static Matrix MakeUnit(size_t i);
 
    ValueType x;
    ValueType y;
    ValueType z;
};
 
template <typename T>
class Matrix<T, 4, 1> final : public MatrixExpression<T, 4, 1, Matrix<T, 4, 1>>,
                              public MatrixDenseBase<T, 4, 1, Matrix<T, 4, 1>>
{
 public:
    using Base = MatrixDenseBase<T, 4, 1, Matrix<T, 4, 1>>;
    using Base::operator();
 
    using ValueType = T;
    using Reference = T&;
    using ConstReference = const T&;
    using Pointer = T*;
    using ConstPointer = const T*;
    using Iterator = Pointer;
    using ConstIterator = ConstPointer;
 
    constexpr Matrix() : x(T{}), y(T{}), z(T{}), w(T{})
    {
        // Do nothing
    }
 
    constexpr Matrix(const T& _x, const T& _y, const T& _z, const T& _w)
        : x(_x), y(_y), z(_z), w(_w)
    {
        // Do nothing
    }
 
    template <size_t R, size_t C, typename E>
    Matrix(const MatrixExpression<T, R, C, E>& expression);
 
    Matrix(const std::initializer_list<T>& lst);
 
    ~Matrix() = default;
 
    constexpr Matrix(const Matrix&) = default;
 
    constexpr Matrix(Matrix&&) noexcept = default;
 
    Matrix& operator=(const Matrix&) = default;
 
    Matrix& operator=(Matrix&&) noexcept = default;
 
    void Fill(const T& val);
 
    void Fill(const std::function<T(size_t i)>& func);
 
    void Fill(const std::function<T(size_t i, size_t j)>& func);
 
    void Swap(Matrix& other);
 
    [[nodiscard]] constexpr size_t GetRows() const;
 
    [[nodiscard]] constexpr size_t GetCols() const;
 
    [[nodiscard]] Iterator begin();
 
    [[nodiscard]] constexpr ConstIterator begin() const;
 
    [[nodiscard]] Iterator end();
 
    [[nodiscard]] constexpr ConstIterator end() const;
 
    [[nodiscard]] Pointer data();
 
    [[nodiscard]] constexpr ConstPointer data() const;
 
    Reference operator[](size_t i);
 
    ConstReference operator[](size_t i) const;
 
    constexpr static Matrix MakeUnitX();
 
    constexpr static Matrix MakeUnitY();
 
    constexpr static Matrix MakeUnitZ();
 
    constexpr static Matrix MakeUnitW();
 
    constexpr static Matrix MakeUnit(size_t i);
 
    ValueType x;
    ValueType y;
    ValueType z;
    ValueType w;
};
 
template <typename T>
class Matrix<T, MATRIX_SIZE_DYNAMIC, MATRIX_SIZE_DYNAMIC> final
    : public MatrixExpression<
          T, MATRIX_SIZE_DYNAMIC, MATRIX_SIZE_DYNAMIC,
          Matrix<T, MATRIX_SIZE_DYNAMIC, MATRIX_SIZE_DYNAMIC>>,
      public MatrixDenseBase<
          T, MATRIX_SIZE_DYNAMIC, MATRIX_SIZE_DYNAMIC,
          Matrix<T, MATRIX_SIZE_DYNAMIC, MATRIX_SIZE_DYNAMIC>>
{
 public:
    using ValueType = T;
    using Reference = T&;
    using ConstReference = const T&;
    using Pointer = T*;
    using ConstPointer = const T*;
    using Iterator = Pointer;
    using ConstIterator = ConstPointer;
    using MatrixDenseBase<
        T, MATRIX_SIZE_DYNAMIC, MATRIX_SIZE_DYNAMIC,
        Matrix<T, MATRIX_SIZE_DYNAMIC, MATRIX_SIZE_DYNAMIC>>::CopyFrom;
 
    Matrix();
 
    Matrix(size_t rows, size_t cols, ConstReference value = ValueType{});
 
    template <size_t R, size_t C, typename E>
    Matrix(const MatrixExpression<T, R, C, E>& expression);
 
    Matrix(const NestedInitializerListsT<T, 2>& lst);
 
    explicit Matrix(size_t rows, size_t cols, ConstPointer ptr);
 
    ~Matrix() = default;
 
    Matrix(const Matrix& other);
 
    Matrix(Matrix&& other) noexcept;
 
    Matrix& operator=(const Matrix& other);
 
    Matrix& operator=(Matrix&& other) noexcept;
 
    void Fill(const T& val);
 
    void Fill(const std::function<T(size_t i)>& func);
 
    void Fill(const std::function<T(size_t i, size_t j)>& func);
 
    void Swap(Matrix& other);
 
    void Resize(size_t rows, size_t cols, ConstReference val = ValueType{});
 
    void Clear();
 
    [[nodiscard]] size_t GetRows() const;
 
    [[nodiscard]] size_t GetCols() const;
 
    [[nodiscard]] Iterator begin();
 
    [[nodiscard]] ConstIterator begin() const;
 
    [[nodiscard]] Iterator end();
 
    [[nodiscard]] ConstIterator end() const;
 
    [[nodiscard]] Pointer data();
 
    [[nodiscard]] ConstPointer data() const;
 
    Reference operator[](size_t i);
 
    ConstReference operator[](size_t i) const;
 
 private:
    std::vector<T> m_elements;
    size_t m_rows = 0;
    size_t m_cols = 0;
};
 
template <typename T>
class Matrix<T, MATRIX_SIZE_DYNAMIC, 1> final
    : public MatrixExpression<T, MATRIX_SIZE_DYNAMIC, 1,
                              Matrix<T, MATRIX_SIZE_DYNAMIC, 1>>,
      public MatrixDenseBase<T, MATRIX_SIZE_DYNAMIC, 1,
                             Matrix<T, MATRIX_SIZE_DYNAMIC, 1>>
{
 public:
    using ValueType = T;
    using Reference = T&;
    using ConstReference = const T&;
    using Pointer = T*;
    using ConstPointer = const T*;
    using Iterator = Pointer;
    using ConstIterator = ConstPointer;
    using MatrixDenseBase<T, MATRIX_SIZE_DYNAMIC, 1,
                          Matrix<T, MATRIX_SIZE_DYNAMIC, 1>>::CopyFrom;
 
    Matrix();
 
    explicit Matrix(size_t rows, ConstReference value = ValueType{});
 
    template <size_t R, size_t C, typename E>
    Matrix(const MatrixExpression<T, R, C, E>& expression);
 
    Matrix(const std::initializer_list<T>& lst);
 
    explicit Matrix(size_t rows, ConstPointer ptr);
 
    ~Matrix() = default;
 
    Matrix(const Matrix& other);
 
    Matrix(Matrix&& other) noexcept;
 
    Matrix& operator=(const Matrix& other);
 
    Matrix& operator=(Matrix&& other) noexcept;
 
    void Fill(const T& val);
 
    void Fill(const std::function<T(size_t i)>& func);
 
    void Fill(const std::function<T(size_t i, size_t j)>& func);
 
    void Swap(Matrix& other);
 
    void Resize(size_t rows, ConstReference val = ValueType{});
 
    void AddElement(ConstReference newElem);
 
    void AddElement(const Matrix& newElems);
 
    void Clear();
 
    [[nodiscard]] size_t GetRows() const;
 
    [[nodiscard]] constexpr size_t GetCols() const;
 
    [[nodiscard]] Iterator begin();
 
    [[nodiscard]] ConstIterator begin() const;
 
    [[nodiscard]] Iterator end();
 
    [[nodiscard]] ConstIterator end() const;
 
    [[nodiscard]] Pointer data();
 
    [[nodiscard]] ConstPointer data() const;
 
    Reference operator[](size_t i);
 
    ConstReference operator[](size_t i) const;
 
 private:
    std::vector<T> m_elements;
};
 
template <typename T>
using Matrix2x2 = Matrix<T, 2, 2>;
 
template <typename T>
using Matrix3x3 = Matrix<T, 3, 3>;
 
template <typename T>
using Matrix4x4 = Matrix<T, 4, 4>;
 
using Matrix2x2B = Matrix2x2<int8_t>;
using Matrix2x2UB = Matrix2x2<uint8_t>;
using Matrix2x2S = Matrix2x2<int16_t>;
using Matrix2x2US = Matrix2x2<uint16_t>;
using Matrix2x2I = Matrix2x2<int32_t>;
using Matrix2x2UI = Matrix2x2<uint32_t>;
using Matrix2x2L = Matrix2x2<int64_t>;
using Matrix2x2UL = Matrix2x2<uint64_t>;
using Matrix2x2F = Matrix2x2<float>;
using Matrix2x2D = Matrix2x2<double>;
using Matrix2x2Z = Matrix2x2<ssize_t>;
using Matrix2x2UZ = Matrix2x2<size_t>;
 
using Matrix3x3B = Matrix3x3<int8_t>;
using Matrix3x3UB = Matrix3x3<uint8_t>;
using Matrix3x3S = Matrix3x3<int16_t>;
using Matrix3x3US = Matrix3x3<uint16_t>;
using Matrix3x3I = Matrix3x3<int32_t>;
using Matrix3x3UI = Matrix3x3<uint32_t>;
using Matrix3x3L = Matrix3x3<int64_t>;
using Matrix3x3UL = Matrix3x3<uint64_t>;
using Matrix3x3F = Matrix3x3<float>;
using Matrix3x3D = Matrix3x3<double>;
using Matrix3x3Z = Matrix3x3<ssize_t>;
using Matrix3x3UZ = Matrix3x3<size_t>;
 
using Matrix4x4B = Matrix4x4<int8_t>;
using Matrix4x4UB = Matrix4x4<uint8_t>;
using Matrix4x4S = Matrix4x4<int16_t>;
using Matrix4x4US = Matrix4x4<uint16_t>;
using Matrix4x4I = Matrix4x4<int32_t>;
using Matrix4x4UI = Matrix4x4<uint32_t>;
using Matrix4x4L = Matrix4x4<int64_t>;
using Matrix4x4UL = Matrix4x4<uint64_t>;
using Matrix4x4F = Matrix4x4<float>;
using Matrix4x4D = Matrix4x4<double>;
using Matrix4x4Z = Matrix4x4<ssize_t>;
using Matrix4x4UZ = Matrix4x4<size_t>;
 
template <typename T, size_t Rows>
using Vector = Matrix<T, Rows, 1>;
 
template <typename T>
using Vector1 = Vector<T, 1>;
 
template <typename T>
using Vector2 = Vector<T, 2>;
 
template <typename T>
using Vector3 = Vector<T, 3>;
 
template <typename T>
using Vector4 = Vector<T, 4>;
 
using Vector1B = Vector1<int8_t>;
using Vector1UB = Vector1<uint8_t>;
using Vector1S = Vector1<int16_t>;
using Vector1US = Vector1<uint16_t>;
using Vector1I = Vector1<int32_t>;
using Vector1UI = Vector1<uint32_t>;
using Vector1L = Vector1<int64_t>;
using Vector1UL = Vector1<uint64_t>;
using Vector1F = Vector1<float>;
using Vector1D = Vector1<double>;
using Vector1Z = Vector1<ssize_t>;
using Vector1UZ = Vector1<size_t>;
 
using Vector2B = Vector2<int8_t>;
using Vector2UB = Vector2<uint8_t>;
using Vector2S = Vector2<int16_t>;
using Vector2US = Vector2<uint16_t>;
using Vector2I = Vector2<int32_t>;
using Vector2UI = Vector2<uint32_t>;
using Vector2L = Vector2<int64_t>;
using Vector2UL = Vector2<uint64_t>;
using Vector2F = Vector2<float>;
using Vector2D = Vector2<double>;
using Vector2Z = Vector2<ssize_t>;
using Vector2UZ = Vector2<size_t>;
 
using Vector3B = Vector3<int8_t>;
using Vector3UB = Vector3<uint8_t>;
using Vector3S = Vector3<int16_t>;
using Vector3US = Vector3<uint16_t>;
using Vector3I = Vector3<int32_t>;
using Vector3UI = Vector3<uint32_t>;
using Vector3L = Vector3<int64_t>;
using Vector3UL = Vector3<uint64_t>;
using Vector3F = Vector3<float>;
using Vector3D = Vector3<double>;
using Vector3Z = Vector3<ssize_t>;
using Vector3UZ = Vector3<size_t>;
 
using Vector4B = Vector4<int8_t>;
using Vector4UB = Vector4<uint8_t>;
using Vector4S = Vector4<int16_t>;
using Vector4US = Vector4<uint16_t>;
using Vector4I = Vector4<int32_t>;
using Vector4UI = Vector4<uint32_t>;
using Vector4L = Vector4<int64_t>;
using Vector4UL = Vector4<uint64_t>;
using Vector4F = Vector4<float>;
using Vector4D = Vector4<double>;
using Vector4Z = Vector4<ssize_t>;
using Vector4UZ = Vector4<size_t>;
 
template <typename T>
using MatrixMxN = Matrix<T, MATRIX_SIZE_DYNAMIC, MATRIX_SIZE_DYNAMIC>;
 
using MatrixMxNB = MatrixMxN<int8_t>;
using MatrixMxNUB = MatrixMxN<uint8_t>;
using MatrixMxNS = MatrixMxN<int16_t>;
using MatrixMxNUS = MatrixMxN<uint16_t>;
using MatrixMxNI = MatrixMxN<int32_t>;
using MatrixMxNUI = MatrixMxN<uint32_t>;
using MatrixMxNL = MatrixMxN<int64_t>;
using MatrixMxNUL = MatrixMxN<uint64_t>;
using MatrixMxNF = MatrixMxN<float>;
using MatrixMxND = MatrixMxN<double>;
using MatrixMxNZ = MatrixMxN<ssize_t>;
using MatrixMxNUZ = MatrixMxN<size_t>;
 
template <typename T>
using VectorN = Matrix<T, MATRIX_SIZE_DYNAMIC, 1>;
 
using VectorNB = VectorN<int8_t>;
using VectorNUB = VectorN<uint8_t>;
using VectorNS = VectorN<int16_t>;
using VectorNUS = VectorN<uint16_t>;
using VectorNI = VectorN<int32_t>;
using VectorNUI = VectorN<uint32_t>;
using VectorNL = VectorN<int64_t>;
using VectorNUL = VectorN<uint64_t>;
using VectorNF = VectorN<float>;
using VectorND = VectorN<double>;
using VectorNZ = VectorN<ssize_t>;
using VectorNUZ = VectorN<size_t>;
 
template <typename T, size_t Rows, size_t Cols>
struct GetScalarType<Matrix<T, Rows, Cols>>
{
    using value = T;
};
 
template <typename T, size_t R1, size_t C1, size_t R2, size_t C2, typename M2>
void operator+=(Matrix<T, R1, C1>& a, const MatrixExpression<T, R2, C2, M2>& b);
 
template <typename T, size_t Rows, size_t Cols>
void operator+=(Matrix<T, Rows, Cols>& a, const T& b);
 
template <typename T, size_t R1, size_t C1, size_t R2, size_t C2, typename M2>
void operator-=(Matrix<T, R1, C1>& a, const MatrixExpression<T, R2, C2, M2>& b);
 
template <typename T, size_t Rows, size_t Cols>
void operator-=(Matrix<T, Rows, Cols>& a, const T& b);
 
template <typename T, size_t R1, size_t C1, size_t R2, size_t C2, typename M2>
void operator*=(Matrix<T, R1, C1>& a, const MatrixExpression<T, R2, C2, M2>& b);
 
template <typename T, size_t R1, size_t C1, size_t R2, size_t C2, typename M2>
void ElemIMul(Matrix<T, R1, C1>& a, const MatrixExpression<T, R2, C2, M2>& b);
 
template <typename T, size_t Rows, size_t Cols>
void operator*=(Matrix<T, Rows, Cols>& a, const T& b);
 
template <typename T, size_t R1, size_t C1, size_t R2, size_t C2, typename M2>
void ElemIDiv(Matrix<T, R1, C1>& a, const MatrixExpression<T, R2, C2, M2>& b);
 
template <typename T, size_t Rows, size_t Cols>
void operator/=(Matrix<T, Rows, Cols>& a, const T& b);
 
template <typename T, size_t Rows, size_t Cols, typename M1, typename M2>
constexpr std::enable_if_t<IsMatrixSizeStatic<Rows, Cols>(), bool> operator==(
    const MatrixExpression<T, Rows, Cols, M1>& a,
    const MatrixExpression<T, Rows, Cols, M2>& b);
 
template <typename T, size_t R1, size_t C1, size_t R2, size_t C2, typename M1,
          typename M2>
bool operator==(const MatrixExpression<T, R1, C1, M1>& a,
                const MatrixExpression<T, R2, C2, M2>& b);
 
template <typename T, size_t R1, size_t C1, size_t R2, size_t C2, typename M1,
          typename M2>
bool operator!=(const MatrixExpression<T, R1, C1, M1>& a,
                const MatrixExpression<T, R2, C2, M2>& b);
 
template <typename T, size_t Rows, size_t Cols, typename M1,
          typename BinaryOperation>
constexpr std::enable_if_t<TraitIsMatrixSizeStatic<Rows, Cols>::value, T>
Accumulate(const MatrixExpression<T, Rows, Cols, M1>& a, const T& init,
           BinaryOperation op);
 
template <typename T, size_t Rows, size_t Cols, typename M1>
constexpr std::enable_if_t<TraitIsMatrixSizeStatic<Rows, Cols>::value, T>
Accumulate(const MatrixExpression<T, Rows, Cols, M1>& a, const T& init);
 
template <typename T, size_t Rows, size_t Cols, typename M1>
constexpr std::enable_if_t<TraitIsMatrixSizeStatic<Rows, Cols>::value, T>
Accumulate(const MatrixExpression<T, Rows, Cols, M1>& a);
 
template <typename T, size_t Rows, size_t Cols, typename M1,
          typename BinaryOperation>
constexpr std::enable_if_t<TraitIsMatrixSizeDynamic<Rows, Cols>::value, T>
Accumulate(const MatrixExpression<T, Rows, Cols, M1>& a, const T& init,
           BinaryOperation op);
 
template <typename T, size_t Rows, size_t Cols, typename M1>
constexpr std::enable_if_t<TraitIsMatrixSizeDynamic<Rows, Cols>::value, T>
Accumulate(const MatrixExpression<T, Rows, Cols, M1>& a, const T& init);
 
template <typename T, size_t Rows, size_t Cols, typename M1>
constexpr std::enable_if_t<TraitIsMatrixSizeDynamic<Rows, Cols>::value, T>
Accumulate(const MatrixExpression<T, Rows, Cols, M1>& a);
 
template <typename T, size_t Rows, size_t Cols, typename M1>
constexpr T Product(const MatrixExpression<T, Rows, Cols, M1>& a,
                    const T& init);
 
template <typename T, size_t Rows, size_t Cols, typename M1, typename M2,
          typename M3, typename M4>
std::enable_if_t<IsMatrixSizeStatic<Rows, Cols>(), Matrix<T, Rows, Cols>>
MonotonicCatmullRom(const MatrixExpression<T, Rows, Cols, M1>& f0,
                    const MatrixExpression<T, Rows, Cols, M2>& f1,
                    const MatrixExpression<T, Rows, Cols, M3>& f2,
                    const MatrixExpression<T, Rows, Cols, M4>& f3, T f);
}  // namespace CubbyFlow
 
#include <Core/Matrix/Matrix-Impl.hpp>
 
#endif