text: /*M///////////////////////////////////////////////////////////////////////////////////////
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  #ifndef OPENCV_CORE_MATX_HPP
  #define OPENCV_CORE_MATX_HPP
  
  #ifndef __cplusplus
  #  error matx.hpp header must be compiled as C++
  #endif
  
  #include "opencv2/core/cvdef.h"
  #include "opencv2/core/base.hpp"
  #include "opencv2/core/traits.hpp"
  #include "opencv2/core/saturate.hpp"
  
  #include <initializer_list>
  
  namespace cv
  {
  
  //! @addtogroup core_basic
  //! @{
  
  ////////////////////////////// Small Matrix ///////////////////////////
  
  //! @cond IGNORED
  // FIXIT Remove this (especially CV_EXPORTS modifier)
  struct CV_EXPORTS Matx_AddOp { Matx_AddOp() {} Matx_AddOp(const Matx_AddOp&) {} };
  struct CV_EXPORTS Matx_SubOp { Matx_SubOp() {} Matx_SubOp(const Matx_SubOp&) {} };
  struct CV_EXPORTS Matx_ScaleOp { Matx_ScaleOp() {} Matx_ScaleOp(const Matx_ScaleOp&) {} };
  struct CV_EXPORTS Matx_MulOp { Matx_MulOp() {} Matx_MulOp(const Matx_MulOp&) {} };
  struct CV_EXPORTS Matx_DivOp { Matx_DivOp() {} Matx_DivOp(const Matx_DivOp&) {} };
  struct CV_EXPORTS Matx_MatMulOp { Matx_MatMulOp() {} Matx_MatMulOp(const Matx_MatMulOp&) {} };
  struct CV_EXPORTS Matx_TOp { Matx_TOp() {} Matx_TOp(const Matx_TOp&) {} };
  //! @endcond
  
  /** @brief Template class for small matrices whose type and size are known at compilation time
  
  If you need a more flexible type, use Mat . The elements of the matrix M are accessible using the
  M(i,j) notation. Most of the common matrix operations (see also @ref MatrixExpressions ) are
  available. To do an operation on Matx that is not implemented, you can easily convert the matrix to
  Mat and backwards:
  @code{.cpp}
      Matx33f m(1, 2, 3,
                4, 5, 6,
                7, 8, 9);
      cout << sum(Mat(m*m.t())) << endl;
  @endcode
  Except of the plain constructor which takes a list of elements, Matx can be initialized from a C-array:
  @code{.cpp}
      float values[] = { 1, 2, 3};
      Matx31f m(values);
  @endcode
  In case if C++11 features are available, std::initializer_list can be also used to initialize Matx:
  @code{.cpp}
      Matx31f m = { 1, 2, 3};
  @endcode
   */
  template<typename _Tp, int m, int n> class Matx
  {
  public:
      enum {
             rows     = m,
             cols     = n,
             channels = rows*cols,
  #ifdef OPENCV_TRAITS_ENABLE_DEPRECATED
             depth    = traits::Type<_Tp>::value,
             type     = CV_MAKETYPE(depth, channels),
  #endif
             shortdim = (m < n ? m : n)
           };
  
      typedef _Tp                           value_type;
      typedef Matx<_Tp, m, n>               mat_type;
      typedef Matx<_Tp, shortdim, 1> diag_type;
  
      //! default constructor
      Matx();
  
      explicit Matx(_Tp v0); //!< 1x1 matrix
      Matx(_Tp v0, _Tp v1); //!< 1x2 or 2x1 matrix
      Matx(_Tp v0, _Tp v1, _Tp v2); //!< 1x3 or 3x1 matrix
      Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3); //!< 1x4, 2x2 or 4x1 matrix
      Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4); //!< 1x5 or 5x1 matrix
      Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5); //!< 1x6, 2x3, 3x2 or 6x1 matrix
      Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6); //!< 1x7 or 7x1 matrix
      Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7); //!< 1x8, 2x4, 4x2 or 8x1 matrix
      Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7, _Tp v8); //!< 1x9, 3x3 or 9x1 matrix
      Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7, _Tp v8, _Tp v9); //!< 1x10, 2x5 or 5x2 or 10x1 matrix
      Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3,
           _Tp v4, _Tp v5, _Tp v6, _Tp v7,
           _Tp v8, _Tp v9, _Tp v10, _Tp v11); //!< 1x12, 2x6, 3x4, 4x3, 6x2 or 12x1 matrix
      Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3,
           _Tp v4, _Tp v5, _Tp v6, _Tp v7,
           _Tp v8, _Tp v9, _Tp v10, _Tp v11,
           _Tp v12, _Tp v13); //!< 1x14, 2x7, 7x2 or 14x1 matrix
      Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3,
           _Tp v4, _Tp v5, _Tp v6, _Tp v7,
           _Tp v8, _Tp v9, _Tp v10, _Tp v11,
           _Tp v12, _Tp v13, _Tp v14, _Tp v15); //!< 1x16, 4x4 or 16x1 matrix
      explicit Matx(const _Tp* vals); //!< initialize from a plain array
  
      Matx(std::initializer_list<_Tp>); //!< initialize from an initializer list
  
      static Matx all(_Tp alpha);
      static Matx zeros();
      static Matx ones();
      static Matx eye();
      static Matx diag(const diag_type& d);
      static Matx randu(_Tp a, _Tp b);
      static Matx randn(_Tp a, _Tp b);
  
      //! dot product computed with the default precision
      _Tp dot(const Matx<_Tp, m, n>& v) const;
  
      //! dot product computed in double-precision arithmetics
      double ddot(const Matx<_Tp, m, n>& v) const;
  
      //! conversion to another data type
      template<typename T2> operator Matx<T2, m, n>() const;
  
      //! change the matrix shape
      template<int m1, int n1> Matx<_Tp, m1, n1> reshape() const;
  
      //! extract part of the matrix
      template<int m1, int n1> Matx<_Tp, m1, n1> get_minor(int i, int j) const;
  
      //! extract the matrix row
      Matx<_Tp, 1, n> row(int i) const;
  
      //! extract the matrix column
      Matx<_Tp, m, 1> col(int i) const;
  
      //! extract the matrix diagonal
      diag_type diag() const;
  
      //! transpose the matrix
      Matx<_Tp, n, m> t() const;
  
      //! invert the matrix
      Matx<_Tp, n, m> inv(int method=DECOMP_LU, bool *p_is_ok = NULL) const;
  
      //! solve linear system
      template<int l> Matx<_Tp, n, l> solve(const Matx<_Tp, m, l>& rhs, int flags=DECOMP_LU) const;
      Vec<_Tp, n> solve(const Vec<_Tp, m>& rhs, int method) const;
  
      //! multiply two matrices element-wise
      Matx<_Tp, m, n> mul(const Matx<_Tp, m, n>& a) const;
  
      //! divide two matrices element-wise
      Matx<_Tp, m, n> div(const Matx<_Tp, m, n>& a) const;
  
      //! element access
      const _Tp& operator ()(int i, int j) const;
      _Tp& operator ()(int i, int j);
  
      //! 1D element access
      const _Tp& operator ()(int i) const;
      _Tp& operator ()(int i);
  
      Matx(const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b, Matx_AddOp);
      Matx(const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b, Matx_SubOp);
      template<typename _T2> Matx(const Matx<_Tp, m, n>& a, _T2 alpha, Matx_ScaleOp);
      Matx(const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b, Matx_MulOp);
      Matx(const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b, Matx_DivOp);
      template<int l> Matx(const Matx<_Tp, m, l>& a, const Matx<_Tp, l, n>& b, Matx_MatMulOp);
      Matx(const Matx<_Tp, n, m>& a, Matx_TOp);
  
      _Tp val[m*n]; //< matrix elements
  };
  
  typedef Matx<float, 1, 2> Matx12f;
  typedef Matx<double, 1, 2> Matx12d;
  typedef Matx<float, 1, 3> Matx13f;
  typedef Matx<double, 1, 3> Matx13d;
  typedef Matx<float, 1, 4> Matx14f;
  typedef Matx<double, 1, 4> Matx14d;
  typedef Matx<float, 1, 6> Matx16f;
  typedef Matx<double, 1, 6> Matx16d;
  
  typedef Matx<float, 2, 1> Matx21f;
  typedef Matx<double, 2, 1> Matx21d;
  typedef Matx<float, 3, 1> Matx31f;
  typedef Matx<double, 3, 1> Matx31d;
  typedef Matx<float, 4, 1> Matx41f;
  typedef Matx<double, 4, 1> Matx41d;
  typedef Matx<float, 6, 1> Matx61f;
  typedef Matx<double, 6, 1> Matx61d;
  
  typedef Matx<float, 2, 2> Matx22f;
  typedef Matx<double, 2, 2> Matx22d;
  typedef Matx<float, 2, 3> Matx23f;
  typedef Matx<double, 2, 3> Matx23d;
  typedef Matx<float, 3, 2> Matx32f;
  typedef Matx<double, 3, 2> Matx32d;
  
  typedef Matx<float, 3, 3> Matx33f;
  typedef Matx<double, 3, 3> Matx33d;
  
  typedef Matx<float, 3, 4> Matx34f;
  typedef Matx<double, 3, 4> Matx34d;
  typedef Matx<float, 4, 3> Matx43f;
  typedef Matx<double, 4, 3> Matx43d;
  
  typedef Matx<float, 4, 4> Matx44f;
  typedef Matx<double, 4, 4> Matx44d;
  typedef Matx<float, 6, 6> Matx66f;
  typedef Matx<double, 6, 6> Matx66d;
  
  /*!
    traits
  */
  template<typename _Tp, int m, int n> class DataType< Matx<_Tp, m, n> >
  {
  public:
      typedef Matx<_Tp, m, n>                               value_type;
      typedef Matx<typename DataType<_Tp>::work_type, m, n> work_type;
      typedef _Tp                                           channel_type;
      typedef value_type                                    vec_type;
  
      enum { generic_type = 0,
             channels     = m * n,
             fmt          = traits::SafeFmt<channel_type>::fmt + ((channels - 1) << 8)
  #ifdef OPENCV_TRAITS_ENABLE_DEPRECATED
             ,depth        = DataType<channel_type>::depth
             ,type         = CV_MAKETYPE(depth, channels)
  #endif
           };
  };
  
  namespace traits {
  template<typename _Tp, int m, int n>
  struct Depth< Matx<_Tp, m, n> > { enum { value = Depth<_Tp>::value }; };
  template<typename _Tp, int m, int n>
  struct Type< Matx<_Tp, m, n> > { enum { value = CV_MAKETYPE(Depth<_Tp>::value, n*m) }; };
  } // namespace
  
  
  /** @brief  Comma-separated Matrix Initializer
  */
  template<typename _Tp, int m, int n> class MatxCommaInitializer
  {
  public:
      MatxCommaInitializer(Matx<_Tp, m, n>* _mtx);
      template<typename T2> MatxCommaInitializer<_Tp, m, n>& operator , (T2 val);
      Matx<_Tp, m, n> operator *() const;
  
      Matx<_Tp, m, n>* dst;
      int idx;
  };
  
  /*
   Utility methods
  */
  template<typename _Tp, int m> static double determinant(const Matx<_Tp, m, m>& a);
  template<typename _Tp, int m, int n> static double trace(const Matx<_Tp, m, n>& a);
  template<typename _Tp, int m, int n> static double norm(const Matx<_Tp, m, n>& M);
  template<typename _Tp, int m, int n> static double norm(const Matx<_Tp, m, n>& M, int normType);
  
  
  
  /////////////////////// Vec (used as element of multi-channel images /////////////////////
  
  /** @brief Template class for short numerical vectors, a partial case of Matx
  
  This template class represents short numerical vectors (of 1, 2, 3, 4 ... elements) on which you
  can perform basic arithmetical operations, access individual elements using [] operator etc. The
  vectors are allocated on stack, as opposite to std::valarray, std::vector, cv::Mat etc., which
  elements are dynamically allocated in the heap.
  
  The template takes 2 parameters:
  @tparam _Tp element type
  @tparam cn the number of elements
  
  In addition to the universal notation like Vec<float, 3>, you can use shorter aliases
  for the most popular specialized variants of Vec, e.g. Vec3f ~ Vec<float, 3>.
  
  It is possible to convert Vec\<T,2\> to/from Point_, Vec\<T,3\> to/from Point3_ , and Vec\<T,4\>
  to CvScalar or Scalar_. Use operator[] to access the elements of Vec.
  
  All the expected vector operations are also implemented:
  -   v1 = v2 + v3
  -   v1 = v2 - v3
  -   v1 = v2 \* scale
  -   v1 = scale \* v2
  -   v1 = -v2
  -   v1 += v2 and other augmenting operations
  -   v1 == v2, v1 != v2
  -   norm(v1) (euclidean norm)
  The Vec class is commonly used to describe pixel types of multi-channel arrays. See Mat for details.
  */
  template<typename _Tp, int cn> class Vec : public Matx<_Tp, cn, 1>
  {
  public:
      typedef _Tp value_type;
      enum {
             channels = cn,
  #ifdef OPENCV_TRAITS_ENABLE_DEPRECATED
             depth    = Matx<_Tp, cn, 1>::depth,
             type     = CV_MAKETYPE(depth, channels),
  #endif
             _dummy_enum_finalizer = 0
           };
  
      //! default constructor
      Vec();
  
      Vec(_Tp v0); //!< 1-element vector constructor
      Vec(_Tp v0, _Tp v1); //!< 2-element vector constructor
      Vec(_Tp v0, _Tp v1, _Tp v2); //!< 3-element vector constructor
      Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3); //!< 4-element vector constructor
      Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4); //!< 5-element vector constructor
      Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5); //!< 6-element vector constructor
      Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6); //!< 7-element vector constructor
      Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7); //!< 8-element vector constructor
      Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7, _Tp v8); //!< 9-element vector constructor
      Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7, _Tp v8, _Tp v9); //!< 10-element vector constructor
      Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7, _Tp v8, _Tp v9, _Tp v10, _Tp v11, _Tp v12, _Tp v13); //!< 14-element vector constructor
      explicit Vec(const _Tp* values);
  
      Vec(std::initializer_list<_Tp>);
  
      Vec(const Vec<_Tp, cn>& v);
  
      static Vec all(_Tp alpha);
  
      //! per-element multiplication
      Vec mul(const Vec<_Tp, cn>& v) const;
  
      //! conjugation (makes sense for complex numbers and quaternions)
      Vec conj() const;
  
      /*!
        cross product of the two 3D vectors.
  
        For other dimensionalities the exception is raised
      */
      Vec cross(const Vec& v) const;
      //! conversion to another data type
      template<typename T2> operator Vec<T2, cn>() const;
  
      /*! element access */
      const _Tp& operator [](int i) const;
      _Tp& operator[](int i);
      const _Tp& operator ()(int i) const;
      _Tp& operator ()(int i);
  
      Vec(const Matx<_Tp, cn, 1>& a, const Matx<_Tp, cn, 1>& b, Matx_AddOp);
      Vec(const Matx<_Tp, cn, 1>& a, const Matx<_Tp, cn, 1>& b, Matx_SubOp);
      template<typename _T2> Vec(const Matx<_Tp, cn, 1>& a, _T2 alpha, Matx_ScaleOp);
  };
  
  /** @name Shorter aliases for the most popular specializations of Vec<T,n>
    @{
  */
  typedef Vec<uchar, 2> Vec2b;
  typedef Vec<uchar, 3> Vec3b;
  typedef Vec<uchar, 4> Vec4b;
  
  typedef Vec<short, 2> Vec2s;
  typedef Vec<short, 3> Vec3s;
  typedef Vec<short, 4> Vec4s;
  
  typedef Vec<ushort, 2> Vec2w;
  typedef Vec<ushort, 3> Vec3w;
  typedef Vec<ushort, 4> Vec4w;
  
  typedef Vec<int, 2> Vec2i;
  typedef Vec<int, 3> Vec3i;
  typedef Vec<int, 4> Vec4i;
  typedef Vec<int, 6> Vec6i;
  typedef Vec<int, 8> Vec8i;
  
  typedef Vec<float, 2> Vec2f;
  typedef Vec<float, 3> Vec3f;
  typedef Vec<float, 4> Vec4f;
  typedef Vec<float, 6> Vec6f;
  
  typedef Vec<double, 2> Vec2d;
  typedef Vec<double, 3> Vec3d;
  typedef Vec<double, 4> Vec4d;
  typedef Vec<double, 6> Vec6d;
  /** @} */
  
  /*!
    traits
  */
  template<typename _Tp, int cn> class DataType< Vec<_Tp, cn> >
  {
  public:
      typedef Vec<_Tp, cn>                               value_type;
      typedef Vec<typename DataType<_Tp>::work_type, cn> work_type;
      typedef _Tp                                        channel_type;
      typedef value_type                                 vec_type;
  
      enum { generic_type = 0,
             channels     = cn,
             fmt          = DataType<channel_type>::fmt + ((channels - 1) << 8),
  #ifdef OPENCV_TRAITS_ENABLE_DEPRECATED
             depth        = DataType<channel_type>::depth,
             type         = CV_MAKETYPE(depth, channels),
  #endif
             _dummy_enum_finalizer = 0
           };
  };
  
  namespace traits {
  template<typename _Tp, int cn>
  struct Depth< Vec<_Tp, cn> > { enum { value = Depth<_Tp>::value }; };
  template<typename _Tp, int cn>
  struct Type< Vec<_Tp, cn> > { enum { value = CV_MAKETYPE(Depth<_Tp>::value, cn) }; };
  } // namespace
  
  
  /** @brief  Comma-separated Vec Initializer
  */
  template<typename _Tp, int m> class VecCommaInitializer : public MatxCommaInitializer<_Tp, m, 1>
  {
  public:
      VecCommaInitializer(Vec<_Tp, m>* _vec);
      template<typename T2> VecCommaInitializer<_Tp, m>& operator , (T2 val);
      Vec<_Tp, m> operator *() const;
  };
  
  template<typename _Tp, int cn> static Vec<_Tp, cn> normalize(const Vec<_Tp, cn>& v);
  
  //! @} core_basic
  
  //! @cond IGNORED
  
  ///////////////////////////////////// helper classes /////////////////////////////////////
  namespace internal
  {
  
  template<typename _Tp, int m> struct Matx_DetOp
  {
      double operator ()(const Matx<_Tp, m, m>& a) const
      {
          Matx<_Tp, m, m> temp = a;
          double p = LU(temp.val, m*sizeof(_Tp), m, 0, 0, 0);
          if( p == 0 )
              return p;
          for( int i = 0; i < m; i++ )
              p *= temp(i, i);
          return p;
      }
  };
  
  template<typename _Tp> struct Matx_DetOp<_Tp, 1>
  {
      double operator ()(const Matx<_Tp, 1, 1>& a) const
      {
          return a(0,0);
      }
  };
  
  template<typename _Tp> struct Matx_DetOp<_Tp, 2>
  {
      double operator ()(const Matx<_Tp, 2, 2>& a) const
      {
          return a(0,0)*a(1,1) - a(0,1)*a(1,0);
      }
  };
  
  template<typename _Tp> struct Matx_DetOp<_Tp, 3>
  {
      double operator ()(const Matx<_Tp, 3, 3>& a) const
      {
          return a(0,0)*(a(1,1)*a(2,2) - a(2,1)*a(1,2)) -
              a(0,1)*(a(1,0)*a(2,2) - a(2,0)*a(1,2)) +
              a(0,2)*(a(1,0)*a(2,1) - a(2,0)*a(1,1));
      }
  };
  
  template<typename _Tp> Vec<_Tp, 2> inline conjugate(const Vec<_Tp, 2>& v)
  {
      return Vec<_Tp, 2>(v[0], -v[1]);
  }
  
  template<typename _Tp> Vec<_Tp, 4> inline conjugate(const Vec<_Tp, 4>& v)
  {
      return Vec<_Tp, 4>(v[0], -v[1], -v[2], -v[3]);
  }
  
  } // internal
  
  
  
  ////////////////////////////////// Matx Implementation ///////////////////////////////////
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp, m, n>::Matx()
  {
      for(int i = 0; i < channels; i++) val[i] = _Tp(0);
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp, m, n>::Matx(_Tp v0)
  {
      val[0] = v0;
      for(int i = 1; i < channels; i++) val[i] = _Tp(0);
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp, m, n>::Matx(_Tp v0, _Tp v1)
  {
      CV_StaticAssert(channels >= 2, "Matx should have at least 2 elements.");
      val[0] = v0; val[1] = v1;
      for(int i = 2; i < channels; i++) val[i] = _Tp(0);
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp, m, n>::Matx(_Tp v0, _Tp v1, _Tp v2)
  {
      CV_StaticAssert(channels >= 3, "Matx should have at least 3 elements.");
      val[0] = v0; val[1] = v1; val[2] = v2;
      for(int i = 3; i < channels; i++) val[i] = _Tp(0);
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp, m, n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3)
  {
      CV_StaticAssert(channels >= 4, "Matx should have at least 4 elements.");
      val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3;
      for(int i = 4; i < channels; i++) val[i] = _Tp(0);
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp, m, n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4)
  {
      CV_StaticAssert(channels >= 5, "Matx should have at least 5 elements.");
      val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3; val[4] = v4;
      for(int i = 5; i < channels; i++) val[i] = _Tp(0);
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp, m, n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5)
  {
      CV_StaticAssert(channels >= 6, "Matx should have at least 6 elements.");
      val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3;
      val[4] = v4; val[5] = v5;
      for(int i = 6; i < channels; i++) val[i] = _Tp(0);
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp, m, n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6)
  {
      CV_StaticAssert(channels >= 7, "Matx should have at least 7 elements.");
      val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3;
      val[4] = v4; val[5] = v5; val[6] = v6;
      for(int i = 7; i < channels; i++) val[i] = _Tp(0);
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp, m, n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7)
  {
      CV_StaticAssert(channels >= 8, "Matx should have at least 8 elements.");
      val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3;
      val[4] = v4; val[5] = v5; val[6] = v6; val[7] = v7;
      for(int i = 8; i < channels; i++) val[i] = _Tp(0);
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp, m, n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7, _Tp v8)
  {
      CV_StaticAssert(channels >= 9, "Matx should have at least 9 elements.");
      val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3;
      val[4] = v4; val[5] = v5; val[6] = v6; val[7] = v7;
      val[8] = v8;
      for(int i = 9; i < channels; i++) val[i] = _Tp(0);
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp, m, n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7, _Tp v8, _Tp v9)
  {
      CV_StaticAssert(channels >= 10, "Matx should have at least 10 elements.");
      val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3;
      val[4] = v4; val[5] = v5; val[6] = v6; val[7] = v7;
      val[8] = v8; val[9] = v9;
      for(int i = 10; i < channels; i++) val[i] = _Tp(0);
  }
  
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp,m,n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7, _Tp v8, _Tp v9, _Tp v10, _Tp v11)
  {
      CV_StaticAssert(channels >= 12, "Matx should have at least 12 elements.");
      val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3;
      val[4] = v4; val[5] = v5; val[6] = v6; val[7] = v7;
      val[8] = v8; val[9] = v9; val[10] = v10; val[11] = v11;
      for(int i = 12; i < channels; i++) val[i] = _Tp(0);
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp,m,n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7, _Tp v8, _Tp v9, _Tp v10, _Tp v11, _Tp v12, _Tp v13)
  {
      CV_StaticAssert(channels >= 14, "Matx should have at least 14 elements.");
      val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3;
      val[4] = v4; val[5] = v5; val[6] = v6; val[7] = v7;
      val[8] = v8; val[9] = v9; val[10] = v10; val[11] = v11;
      val[12] = v12; val[13] = v13;
      for (int i = 14; i < channels; i++) val[i] = _Tp(0);
  }
  
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp,m,n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7, _Tp v8, _Tp v9, _Tp v10, _Tp v11, _Tp v12, _Tp v13, _Tp v14, _Tp v15)
  {
      CV_StaticAssert(channels >= 16, "Matx should have at least 16 elements.");
      val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3;
      val[4] = v4; val[5] = v5; val[6] = v6; val[7] = v7;
      val[8] = v8; val[9] = v9; val[10] = v10; val[11] = v11;
      val[12] = v12; val[13] = v13; val[14] = v14; val[15] = v15;
      for(int i = 16; i < channels; i++) val[i] = _Tp(0);
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp, m, n>::Matx(const _Tp* values)
  {
      for( int i = 0; i < channels; i++ ) val[i] = values[i];
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp, m, n>::Matx(std::initializer_list<_Tp> list)
  {
      CV_DbgAssert(list.size() == channels);
      int i = 0;
      for(const auto& elem : list)
      {
          val[i++] = elem;
      }
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp, m, n> Matx<_Tp, m, n>::all(_Tp alpha)
  {
      Matx<_Tp, m, n> M;
      for( int i = 0; i < m*n; i++ ) M.val[i] = alpha;
      return M;
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp,m,n> Matx<_Tp,m,n>::zeros()
  {
      return all(0);
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp,m,n> Matx<_Tp,m,n>::ones()
  {
      return all(1);
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp,m,n> Matx<_Tp,m,n>::eye()
  {
      Matx<_Tp,m,n> M;
      for(int i = 0; i < shortdim; i++)
          M(i,i) = 1;
      return M;
  }
  
  template<typename _Tp, int m, int n> inline
  _Tp Matx<_Tp, m, n>::dot(const Matx<_Tp, m, n>& M) const
  {
      _Tp s = 0;
      for( int i = 0; i < channels; i++ ) s += val[i]*M.val[i];
      return s;
  }
  
  template<typename _Tp, int m, int n> inline
  double Matx<_Tp, m, n>::ddot(const Matx<_Tp, m, n>& M) const
  {
      double s = 0;
      for( int i = 0; i < channels; i++ ) s += (double)val[i]*M.val[i];
      return s;
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp,m,n> Matx<_Tp,m,n>::diag(const typename Matx<_Tp,m,n>::diag_type& d)
  {
      Matx<_Tp,m,n> M;
      for(int i = 0; i < shortdim; i++)
          M(i,i) = d(i, 0);
      return M;
  }
  
  template<typename _Tp, int m, int n> template<typename T2>
  inline Matx<_Tp, m, n>::operator Matx<T2, m, n>() const
  {
      Matx<T2, m, n> M;
      for( int i = 0; i < m*n; i++ ) M.val[i] = saturate_cast<T2>(val[i]);
      return M;
  }
  
  template<typename _Tp, int m, int n> template<int m1, int n1> inline
  Matx<_Tp, m1, n1> Matx<_Tp, m, n>::reshape() const
  {
      CV_StaticAssert(m1*n1 == m*n, "Input and destnarion matrices must have the same number of elements");
      return (const Matx<_Tp, m1, n1>&)*this;
  }
  
  template<typename _Tp, int m, int n>
  template<int m1, int n1> inline
  Matx<_Tp, m1, n1> Matx<_Tp, m, n>::get_minor(int i, int j) const
  {
      CV_DbgAssert(0 <= i && i+m1 <= m && 0 <= j && j+n1 <= n);
      Matx<_Tp, m1, n1> s;
      for( int di = 0; di < m1; di++ )
          for( int dj = 0; dj < n1; dj++ )
              s(di, dj) = (*this)(i+di, j+dj);
      return s;
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp, 1, n> Matx<_Tp, m, n>::row(int i) const
  {
      CV_DbgAssert((unsigned)i < (unsigned)m);
      return Matx<_Tp, 1, n>(&val[i*n]);
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp, m, 1> Matx<_Tp, m, n>::col(int j) const
  {
      CV_DbgAssert((unsigned)j < (unsigned)n);
      Matx<_Tp, m, 1> v;
      for( int i = 0; i < m; i++ )
          v.val[i] = val[i*n + j];
      return v;
  }
  
  template<typename _Tp, int m, int n> inline
  typename Matx<_Tp, m, n>::diag_type Matx<_Tp, m, n>::diag() const
  {
      diag_type d;
      for( int i = 0; i < shortdim; i++ )
          d.val[i] = val[i*n + i];
      return d;
  }
  
  template<typename _Tp, int m, int n> inline
  const _Tp& Matx<_Tp, m, n>::operator()(int i, int j) const
  {
      CV_DbgAssert( (unsigned)i < (unsigned)m && (unsigned)j < (unsigned)n );
      return this->val[i*n + j];
  }
  
  template<typename _Tp, int m, int n> inline
  _Tp& Matx<_Tp, m, n>::operator ()(int i, int j)
  {
      CV_DbgAssert( (unsigned)i < (unsigned)m && (unsigned)j < (unsigned)n );
      return val[i*n + j];
  }
  
  template<typename _Tp, int m, int n> inline
  const _Tp& Matx<_Tp, m, n>::operator ()(int i) const
  {
      CV_StaticAssert(m == 1 || n == 1, "Single index indexation requires matrix to be a column or a row");
      CV_DbgAssert( (unsigned)i < (unsigned)(m+n-1) );
      return val[i];
  }
  
  template<typename _Tp, int m, int n> inline
  _Tp& Matx<_Tp, m, n>::operator ()(int i)
  {
      CV_StaticAssert(m == 1 || n == 1, "Single index indexation requires matrix to be a column or a row");
      CV_DbgAssert( (unsigned)i < (unsigned)(m+n-1) );
      return val[i];
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp,m,n>::Matx(const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b, Matx_AddOp)
  {
      for( int i = 0; i < channels; i++ )
          val[i] = saturate_cast<_Tp>(a.val[i] + b.val[i]);
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp,m,n>::Matx(const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b, Matx_SubOp)
  {
      for( int i = 0; i < channels; i++ )
          val[i] = saturate_cast<_Tp>(a.val[i] - b.val[i]);
  }
  
  template<typename _Tp, int m, int n> template<typename _T2> inline
  Matx<_Tp,m,n>::Matx(const Matx<_Tp, m, n>& a, _T2 alpha, Matx_ScaleOp)
  {
      for( int i = 0; i < channels; i++ )
          val[i] = saturate_cast<_Tp>(a.val[i] * alpha);
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp,m,n>::Matx(const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b, Matx_MulOp)
  {
      for( int i = 0; i < channels; i++ )
          val[i] = saturate_cast<_Tp>(a.val[i] * b.val[i]);
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp,m,n>::Matx(const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b, Matx_DivOp)
  {
      for( int i = 0; i < channels; i++ )
          val[i] = saturate_cast<_Tp>(a.val[i] / b.val[i]);
  }
  
  template<typename _Tp, int m, int n> template<int l> inline
  Matx<_Tp,m,n>::Matx(const Matx<_Tp, m, l>& a, const Matx<_Tp, l, n>& b, Matx_MatMulOp)
  {
      for( int i = 0; i < m; i++ )
          for( int j = 0; j < n; j++ )
          {
              _Tp s = 0;
              for( int k = 0; k < l; k++ )
                  s += a(i, k) * b(k, j);
              val[i*n + j] = s;
          }
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp,m,n>::Matx(const Matx<_Tp, n, m>& a, Matx_TOp)
  {
      for( int i = 0; i < m; i++ )
          for( int j = 0; j < n; j++ )
              val[i*n + j] = a(j, i);
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp, m, n> Matx<_Tp, m, n>::mul(const Matx<_Tp, m, n>& a) const
  {
      return Matx<_Tp, m, n>(*this, a, Matx_MulOp());
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp, m, n> Matx<_Tp, m, n>::div(const Matx<_Tp, m, n>& a) const
  {
      return Matx<_Tp, m, n>(*this, a, Matx_DivOp());
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp, n, m> Matx<_Tp, m, n>::t() const
  {
      return Matx<_Tp, n, m>(*this, Matx_TOp());
  }
  
  template<typename _Tp, int m, int n> inline
  Vec<_Tp, n> Matx<_Tp, m, n>::solve(const Vec<_Tp, m>& rhs, int method) const
  {
      Matx<_Tp, n, 1> x = solve((const Matx<_Tp, m, 1>&)(rhs), method);
      return (Vec<_Tp, n>&)(x);
  }
  
  template<typename _Tp, int m> static inline
  double determinant(const Matx<_Tp, m, m>& a)
  {
      return cv::internal::Matx_DetOp<_Tp, m>()(a);
  }
  
  template<typename _Tp, int m, int n> static inline
  double trace(const Matx<_Tp, m, n>& a)
  {
      _Tp s = 0;
      for( int i = 0; i < std::min(m, n); i++ )
          s += a(i,i);
      return s;
  }
  
  template<typename _Tp, int m, int n> static inline
  double norm(const Matx<_Tp, m, n>& M)
  {
      return std::sqrt(normL2Sqr<_Tp, double>(M.val, m*n));
  }
  
  template<typename _Tp, int m, int n> static inline
  double norm(const Matx<_Tp, m, n>& M, int normType)
  {
      switch(normType) {
      case NORM_INF:
          return (double)normInf<_Tp, typename DataType<_Tp>::work_type>(M.val, m*n);
      case NORM_L1:
          return (double)normL1<_Tp, typename DataType<_Tp>::work_type>(M.val, m*n);
      case NORM_L2SQR:
          return (double)normL2Sqr<_Tp, typename DataType<_Tp>::work_type>(M.val, m*n);
      default:
      case NORM_L2:
          return std::sqrt((double)normL2Sqr<_Tp, typename DataType<_Tp>::work_type>(M.val, m*n));
      }
  }
  
  
  
  //////////////////////////////// matx comma initializer //////////////////////////////////
  
  template<typename _Tp, typename _T2, int m, int n> static inline
  MatxCommaInitializer<_Tp, m, n> operator << (const Matx<_Tp, m, n>& mtx, _T2 val)
  {
      MatxCommaInitializer<_Tp, m, n> commaInitializer((Matx<_Tp, m, n>*)&mtx);
      return (commaInitializer, val);
  }
  
  template<typename _Tp, int m, int n> inline
  MatxCommaInitializer<_Tp, m, n>::MatxCommaInitializer(Matx<_Tp, m, n>* _mtx)
      : dst(_mtx), idx(0)
  {}
  
  template<typename _Tp, int m, int n> template<typename _T2> inline
  MatxCommaInitializer<_Tp, m, n>& MatxCommaInitializer<_Tp, m, n>::operator , (_T2 value)
  {
      CV_DbgAssert( idx < m*n );
      dst->val[idx++] = saturate_cast<_Tp>(value);
      return *this;
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp, m, n> MatxCommaInitializer<_Tp, m, n>::operator *() const
  {
      CV_DbgAssert( idx == n*m );
      return *dst;
  }
  
  
  
  /////////////////////////////////// Vec Implementation ///////////////////////////////////
  
  template<typename _Tp, int cn> inline
  Vec<_Tp, cn>::Vec() {}
  
  template<typename _Tp, int cn> inline
  Vec<_Tp, cn>::Vec(_Tp v0)
      : Matx<_Tp, cn, 1>(v0) {}
  
  template<typename _Tp, int cn> inline
  Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1)
      : Matx<_Tp, cn, 1>(v0, v1) {}
  
  template<typename _Tp, int cn> inline
  Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2)
      : Matx<_Tp, cn, 1>(v0, v1, v2) {}
  
  template<typename _Tp, int cn> inline
  Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3)
      : Matx<_Tp, cn, 1>(v0, v1, v2, v3) {}
  
  template<typename _Tp, int cn> inline
  Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4)
      : Matx<_Tp, cn, 1>(v0, v1, v2, v3, v4) {}
  
  template<typename _Tp, int cn> inline
  Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5)
      : Matx<_Tp, cn, 1>(v0, v1, v2, v3, v4, v5) {}
  
  template<typename _Tp, int cn> inline
  Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6)
      : Matx<_Tp, cn, 1>(v0, v1, v2, v3, v4, v5, v6) {}
  
  template<typename _Tp, int cn> inline
  Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7)
      : Matx<_Tp, cn, 1>(v0, v1, v2, v3, v4, v5, v6, v7) {}
  
  template<typename _Tp, int cn> inline
  Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7, _Tp v8)
      : Matx<_Tp, cn, 1>(v0, v1, v2, v3, v4, v5, v6, v7, v8) {}
  
  template<typename _Tp, int cn> inline
  Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7, _Tp v8, _Tp v9)
      : Matx<_Tp, cn, 1>(v0, v1, v2, v3, v4, v5, v6, v7, v8, v9) {}
  
  template<typename _Tp, int cn> inline
  Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7, _Tp v8, _Tp v9, _Tp v10, _Tp v11, _Tp v12, _Tp v13)
      : Matx<_Tp, cn, 1>(v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13) {}
  
  template<typename _Tp, int cn> inline
  Vec<_Tp, cn>::Vec(const _Tp* values)
      : Matx<_Tp, cn, 1>(values) {}
  
  template<typename _Tp, int cn> inline
  Vec<_Tp, cn>::Vec(std::initializer_list<_Tp> list)
      : Matx<_Tp, cn, 1>(list) {}
  
  template<typename _Tp, int cn> inline
  Vec<_Tp, cn>::Vec(const Vec<_Tp, cn>& m)
      : Matx<_Tp, cn, 1>(m.val) {}
  
  template<typename _Tp, int cn> inline
  Vec<_Tp, cn>::Vec(const Matx<_Tp, cn, 1>& a, const Matx<_Tp, cn, 1>& b, Matx_AddOp op)
      : Matx<_Tp, cn, 1>(a, b, op) {}
  
  template<typename _Tp, int cn> inline
  Vec<_Tp, cn>::Vec(const Matx<_Tp, cn, 1>& a, const Matx<_Tp, cn, 1>& b, Matx_SubOp op)
      : Matx<_Tp, cn, 1>(a, b, op) {}
  
  template<typename _Tp, int cn> template<typename _T2> inline
  Vec<_Tp, cn>::Vec(const Matx<_Tp, cn, 1>& a, _T2 alpha, Matx_ScaleOp op)
      : Matx<_Tp, cn, 1>(a, alpha, op) {}
  
  template<typename _Tp, int cn> inline
  Vec<_Tp, cn> Vec<_Tp, cn>::all(_Tp alpha)
  {
      Vec v;
      for( int i = 0; i < cn; i++ ) v.val[i] = alpha;
      return v;
  }
  
  template<typename _Tp, int cn> inline
  Vec<_Tp, cn> Vec<_Tp, cn>::mul(const Vec<_Tp, cn>& v) const
  {
      Vec<_Tp, cn> w;
      for( int i = 0; i < cn; i++ ) w.val[i] = saturate_cast<_Tp>(this->val[i]*v.val[i]);
      return w;
  }
  
  template<> inline
  Vec<float, 2> Vec<float, 2>::conj() const
  {
      return cv::internal::conjugate(*this);
  }
  
  template<> inline
  Vec<double, 2> Vec<double, 2>::conj() const
  {
      return cv::internal::conjugate(*this);
  }
  
  template<> inline
  Vec<float, 4> Vec<float, 4>::conj() const
  {
      return cv::internal::conjugate(*this);
  }
  
  template<> inline
  Vec<double, 4> Vec<double, 4>::conj() const
  {
      return cv::internal::conjugate(*this);
  }
  
  template<typename _Tp, int cn> inline
  Vec<_Tp, cn> Vec<_Tp, cn>::cross(const Vec<_Tp, cn>&) const
  {
      CV_StaticAssert(cn == 3, "for arbitrary-size vector there is no cross-product defined");
      return Vec<_Tp, cn>();
  }
  
  template<> inline
  Vec<float, 3> Vec<float, 3>::cross(const Vec<float, 3>& v) const
  {
      return Vec<float,3>(this->val[1]*v.val[2] - this->val[2]*v.val[1],
                       this->val[2]*v.val[0] - this->val[0]*v.val[2],
                       this->val[0]*v.val[1] - this->val[1]*v.val[0]);
  }
  
  template<> inline
  Vec<double, 3> Vec<double, 3>::cross(const Vec<double, 3>& v) const
  {
      return Vec<double,3>(this->val[1]*v.val[2] - this->val[2]*v.val[1],
                       this->val[2]*v.val[0] - this->val[0]*v.val[2],
                       this->val[0]*v.val[1] - this->val[1]*v.val[0]);
  }
  
  template<typename _Tp, int cn> template<typename T2> inline
  Vec<_Tp, cn>::operator Vec<T2, cn>() const
  {
      Vec<T2, cn> v;
      for( int i = 0; i < cn; i++ ) v.val[i] = saturate_cast<T2>(this->val[i]);
      return v;
  }
  
  template<typename _Tp, int cn> inline
  const _Tp& Vec<_Tp, cn>::operator [](int i) const
  {
      CV_DbgAssert( (unsigned)i < (unsigned)cn );
      return this->val[i];
  }
  
  template<typename _Tp, int cn> inline
  _Tp& Vec<_Tp, cn>::operator [](int i)
  {
      CV_DbgAssert( (unsigned)i < (unsigned)cn );
      return this->val[i];
  }
  
  template<typename _Tp, int cn> inline
  const _Tp& Vec<_Tp, cn>::operator ()(int i) const
  {
      CV_DbgAssert( (unsigned)i < (unsigned)cn );
      return this->val[i];
  }
  
  template<typename _Tp, int cn> inline
  _Tp& Vec<_Tp, cn>::operator ()(int i)
  {
      CV_DbgAssert( (unsigned)i < (unsigned)cn );
      return this->val[i];
  }
  
  template<typename _Tp, int cn> inline
  Vec<_Tp, cn> normalize(const Vec<_Tp, cn>& v)
  {
      double nv = norm(v);
      return v * (nv ? 1./nv : 0.);
  }
  
  
  
  //////////////////////////////// vec comma initializer //////////////////////////////////
  
  
  template<typename _Tp, typename _T2, int cn> static inline
  VecCommaInitializer<_Tp, cn> operator << (const Vec<_Tp, cn>& vec, _T2 val)
  {
      VecCommaInitializer<_Tp, cn> commaInitializer((Vec<_Tp, cn>*)&vec);
      return (commaInitializer, val);
  }
  
  template<typename _Tp, int cn> inline
  VecCommaInitializer<_Tp, cn>::VecCommaInitializer(Vec<_Tp, cn>* _vec)
      : MatxCommaInitializer<_Tp, cn, 1>(_vec)
  {}
  
  template<typename _Tp, int cn> template<typename _T2> inline
  VecCommaInitializer<_Tp, cn>& VecCommaInitializer<_Tp, cn>::operator , (_T2 value)
  {
      CV_DbgAssert( this->idx < cn );
      this->dst->val[this->idx++] = saturate_cast<_Tp>(value);
      return *this;
  }
  
  template<typename _Tp, int cn> inline
  Vec<_Tp, cn> VecCommaInitializer<_Tp, cn>::operator *() const
  {
      CV_DbgAssert( this->idx == cn );
      return *this->dst;
  }
  
  //! @endcond
  
  ///////////////////////////// Matx out-of-class operators ////////////////////////////////
  
  //! @relates cv::Matx
  //! @{
  
  template<typename _Tp1, typename _Tp2, int m, int n> static inline
  Matx<_Tp1, m, n>& operator += (Matx<_Tp1, m, n>& a, const Matx<_Tp2, m, n>& b)
  {
      for( int i = 0; i < m*n; i++ )
          a.val[i] = saturate_cast<_Tp1>(a.val[i] + b.val[i]);
      return a;
  }
  
  template<typename _Tp1, typename _Tp2, int m, int n> static inline
  Matx<_Tp1, m, n>& operator -= (Matx<_Tp1, m, n>& a, const Matx<_Tp2, m, n>& b)
  {
      for( int i = 0; i < m*n; i++ )
          a.val[i] = saturate_cast<_Tp1>(a.val[i] - b.val[i]);
      return a;
  }
  
  template<typename _Tp, int m, int n> static inline
  Matx<_Tp, m, n> operator + (const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b)
  {
      return Matx<_Tp, m, n>(a, b, Matx_AddOp());
  }
  
  template<typename _Tp, int m, int n> static inline
  Matx<_Tp, m, n> operator - (const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b)
  {
      return Matx<_Tp, m, n>(a, b, Matx_SubOp());
  }
  
  template<typename _Tp, int m, int n> static inline
  Matx<_Tp, m, n>& operator *= (Matx<_Tp, m, n>& a, int alpha)
  {
      for( int i = 0; i < m*n; i++ )
          a.val[i] = saturate_cast<_Tp>(a.val[i] * alpha);
      return a;
  }
  
  template<typename _Tp, int m, int n> static inline
  Matx<_Tp, m, n>& operator *= (Matx<_Tp, m, n>& a, float alpha)
  {
      for( int i = 0; i < m*n; i++ )
          a.val[i] = saturate_cast<_Tp>(a.val[i] * alpha);
      return a;
  }
  
  template<typename _Tp, int m, int n> static inline
  Matx<_Tp, m, n>& operator *= (Matx<_Tp, m, n>& a, double alpha)
  {
      for( int i = 0; i < m*n; i++ )
          a.val[i] = saturate_cast<_Tp>(a.val[i] * alpha);
      return a;
  }
  
  template<typename _Tp, int m, int n> static inline
  Matx<_Tp, m, n> operator * (const Matx<_Tp, m, n>& a, int alpha)
  {
      return Matx<_Tp, m, n>(a, alpha, Matx_ScaleOp());
  }
  
  template<typename _Tp, int m, int n> static inline
  Matx<_Tp, m, n> operator * (const Matx<_Tp, m, n>& a, float alpha)
  {
      return Matx<_Tp, m, n>(a, alpha, Matx_ScaleOp());
  }
  
  template<typename _Tp, int m, int n> static inline
  Matx<_Tp, m, n> operator * (const Matx<_Tp, m, n>& a, double alpha)
  {
      return Matx<_Tp, m, n>(a, alpha, Matx_ScaleOp());
  }
  
  template<typename _Tp, int m, int n> static inline
  Matx<_Tp, m, n> operator * (int alpha, const Matx<_Tp, m, n>& a)
  {
      return Matx<_Tp, m, n>(a, alpha, Matx_ScaleOp());
  }
  
  template<typename _Tp, int m, int n> static inline
  Matx<_Tp, m, n> operator * (float alpha, const Matx<_Tp, m, n>& a)
  {
      return Matx<_Tp, m, n>(a, alpha, Matx_ScaleOp());
  }
  
  template<typename _Tp, int m, int n> static inline
  Matx<_Tp, m, n> operator * (double alpha, const Matx<_Tp, m, n>& a)
  {
      return Matx<_Tp, m, n>(a, alpha, Matx_ScaleOp());
  }
  
  template<typename _Tp, int m, int n> static inline
  Matx<_Tp, m, n> operator - (const Matx<_Tp, m, n>& a)
  {
      return Matx<_Tp, m, n>(a, -1, Matx_ScaleOp());
  }
  
  template<typename _Tp, int m, int n, int l> static inline
  Matx<_Tp, m, n> operator * (const Matx<_Tp, m, l>& a, const Matx<_Tp, l, n>& b)
  {
      return Matx<_Tp, m, n>(a, b, Matx_MatMulOp());
  }
  
  template<typename _Tp, int m, int n> static inline
  Vec<_Tp, m> operator * (const Matx<_Tp, m, n>& a, const Vec<_Tp, n>& b)
  {
      Matx<_Tp, m, 1> c(a, b, Matx_MatMulOp());
      return (const Vec<_Tp, m>&)(c);
  }
  
  template<typename _Tp, int m, int n> static inline
  bool operator == (const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b)
  {
      for( int i = 0; i < m*n; i++ )
          if( a.val[i] != b.val[i] ) return false;
      return true;
  }
  
  template<typename _Tp, int m, int n> static inline
  bool operator != (const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b)
  {
      return !(a == b);
  }
  
  //! @}
  
  ////////////////////////////// Vec out-of-class operators ////////////////////////////////
  
  //! @relates cv::Vec
  //! @{
  
  template<typename _Tp1, typename _Tp2, int cn> static inline
  Vec<_Tp1, cn>& operator += (Vec<_Tp1, cn>& a, const Vec<_Tp2, cn>& b)
  {
      for( int i = 0; i < cn; i++ )
          a.val[i] = saturate_cast<_Tp1>(a.val[i] + b.val[i]);
      return a;
  }
  
  template<typename _Tp1, typename _Tp2, int cn> static inline
  Vec<_Tp1, cn>& operator -= (Vec<_Tp1, cn>& a, const Vec<_Tp2, cn>& b)
  {
      for( int i = 0; i < cn; i++ )
          a.val[i] = saturate_cast<_Tp1>(a.val[i] - b.val[i]);
      return a;
  }
  
  template<typename _Tp, int cn> static inline
  Vec<_Tp, cn> operator + (const Vec<_Tp, cn>& a, const Vec<_Tp, cn>& b)
  {
      return Vec<_Tp, cn>(a, b, Matx_AddOp());
  }
  
  template<typename _Tp, int cn> static inline
  Vec<_Tp, cn> operator - (const Vec<_Tp, cn>& a, const Vec<_Tp, cn>& b)
  {
      return Vec<_Tp, cn>(a, b, Matx_SubOp());
  }
  
  template<typename _Tp, int cn> static inline
  Vec<_Tp, cn>& operator *= (Vec<_Tp, cn>& a, int alpha)
  {
      for( int i = 0; i < cn; i++ )
          a[i] = saturate_cast<_Tp>(a[i]*alpha);
      return a;
  }
  
  template<typename _Tp, int cn> static inline
  Vec<_Tp, cn>& operator *= (Vec<_Tp, cn>& a, float alpha)
  {
      for( int i = 0; i < cn; i++ )
          a[i] = saturate_cast<_Tp>(a[i]*alpha);
      return a;
  }
  
  template<typename _Tp, int cn> static inline
  Vec<_Tp, cn>& operator *= (Vec<_Tp, cn>& a, double alpha)
  {
      for( int i = 0; i < cn; i++ )
          a[i] = saturate_cast<_Tp>(a[i]*alpha);
      return a;
  }
  
  template<typename _Tp, int cn> static inline
  Vec<_Tp, cn>& operator /= (Vec<_Tp, cn>& a, int alpha)
  {
      double ialpha = 1./alpha;
      for( int i = 0; i < cn; i++ )
          a[i] = saturate_cast<_Tp>(a[i]*ialpha);
      return a;
  }
  
  template<typename _Tp, int cn> static inline
  Vec<_Tp, cn>& operator /= (Vec<_Tp, cn>& a, float alpha)
  {
      float ialpha = 1.f/alpha;
      for( int i = 0; i < cn; i++ )
          a[i] = saturate_cast<_Tp>(a[i]*ialpha);
      return a;
  }
  
  template<typename _Tp, int cn> static inline
  Vec<_Tp, cn>& operator /= (Vec<_Tp, cn>& a, double alpha)
  {
      double ialpha = 1./alpha;
      for( int i = 0; i < cn; i++ )
          a[i] = saturate_cast<_Tp>(a[i]*ialpha);
      return a;
  }
  
  template<typename _Tp, int cn> static inline
  Vec<_Tp, cn> operator * (const Vec<_Tp, cn>& a, int alpha)
  {
      return Vec<_Tp, cn>(a, alpha, Matx_ScaleOp());
  }
  
  template<typename _Tp, int cn> static inline
  Vec<_Tp, cn> operator * (int alpha, const Vec<_Tp, cn>& a)
  {
      return Vec<_Tp, cn>(a, alpha, Matx_ScaleOp());
  }
  
  template<typename _Tp, int cn> static inline
  Vec<_Tp, cn> operator * (const Vec<_Tp, cn>& a, float alpha)
  {
      return Vec<_Tp, cn>(a, alpha, Matx_ScaleOp());
  }
  
  template<typename _Tp, int cn> static inline
  Vec<_Tp, cn> operator * (float alpha, const Vec<_Tp, cn>& a)
  {
      return Vec<_Tp, cn>(a, alpha, Matx_ScaleOp());
  }
  
  template<typename _Tp, int cn> static inline
  Vec<_Tp, cn> operator * (const Vec<_Tp, cn>& a, double alpha)
  {
      return Vec<_Tp, cn>(a, alpha, Matx_ScaleOp());
  }
  
  template<typename _Tp, int cn> static inline
  Vec<_Tp, cn> operator * (double alpha, const Vec<_Tp, cn>& a)
  {
      return Vec<_Tp, cn>(a, alpha, Matx_ScaleOp());
  }
  
  template<typename _Tp, int cn> static inline
  Vec<_Tp, cn> operator / (const Vec<_Tp, cn>& a, int alpha)
  {
      return Vec<_Tp, cn>(a, 1./alpha, Matx_ScaleOp());
  }
  
  template<typename _Tp, int cn> static inline
  Vec<_Tp, cn> operator / (const Vec<_Tp, cn>& a, float alpha)
  {
      return Vec<_Tp, cn>(a, 1.f/alpha, Matx_ScaleOp());
  }
  
  template<typename _Tp, int cn> static inline
  Vec<_Tp, cn> operator / (const Vec<_Tp, cn>& a, double alpha)
  {
      return Vec<_Tp, cn>(a, 1./alpha, Matx_ScaleOp());
  }
  
  template<typename _Tp, int cn> static inline
  Vec<_Tp, cn> operator - (const Vec<_Tp, cn>& a)
  {
      Vec<_Tp,cn> t;
      for( int i = 0; i < cn; i++ ) t.val[i] = saturate_cast<_Tp>(-a.val[i]);
      return t;
  }
  
  template<typename _Tp> inline Vec<_Tp, 4> operator * (const Vec<_Tp, 4>& v1, const Vec<_Tp, 4>& v2)
  {
      return Vec<_Tp, 4>(saturate_cast<_Tp>(v1[0]*v2[0] - v1[1]*v2[1] - v1[2]*v2[2] - v1[3]*v2[3]),
                         saturate_cast<_Tp>(v1[0]*v2[1] + v1[1]*v2[0] + v1[2]*v2[3] - v1[3]*v2[2]),
                         saturate_cast<_Tp>(v1[0]*v2[2] - v1[1]*v2[3] + v1[2]*v2[0] + v1[3]*v2[1]),
                         saturate_cast<_Tp>(v1[0]*v2[3] + v1[1]*v2[2] - v1[2]*v2[1] + v1[3]*v2[0]));
  }
  
  template<typename _Tp> inline Vec<_Tp, 4>& operator *= (Vec<_Tp, 4>& v1, const Vec<_Tp, 4>& v2)
  {
      v1 = v1 * v2;
      return v1;
  }
  
  //! @}
  
  } // cv
  
  #endif // OPENCV_CORE_MATX_HPP
  