root/modules/core/include/opencv2/core/matx.hpp

INCLUDED FROM

DEFINITIONS

1. conjugate
2. conjugate
3. all
4. zeros
5. ones
6. eye
7. dot
8. ddot
9. diag
10. reshape
11. get_minor
12. row
13. col
14. mul
15. div
16. solve
17. determinant
18. trace
19. norm
20. norm
21. idx
22. all
23. mul
24. conj
25. conj
26. conj
27. conj
28. cross
29. cross
30. cross
31. normalize

/*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"

namespace cv
{

//! @addtogroup core_basic
//! @{

////////////////////////////// Small Matrix ///////////////////////////

//! @cond IGNORED
struct CV_EXPORTS Matx_AddOp {};
struct CV_EXPORTS Matx_SubOp {};
struct CV_EXPORTS Matx_ScaleOp {};
struct CV_EXPORTS Matx_MulOp {};
struct CV_EXPORTS Matx_DivOp {};
struct CV_EXPORTS Matx_MatMulOp {};
struct CV_EXPORTS 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
    Matx33f m(1, 2, 3,
              4, 5, 6,
              7, 8, 9);
    cout << sum(Mat(m*m.t())) << endl;
 @endcode
 */
template<typename _Tp, int m, int n> class Matx
{
public:
    enum { depth    = DataType<_Tp>::depth,
           rows     = m,
           cols     = n,
           channels = rows*cols,
           type     = CV_MAKETYPE(depth, channels),
           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();

    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, _Tp v14, _Tp v15); //!< 1x16, 4x4 or 16x1 matrix
    explicit Matx(const _Tp* vals); //!< initialize from a plain array

    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,
           depth        = DataType<channel_type>::depth,
           channels     = m * n,
           fmt          = DataType<channel_type>::fmt + ((channels - 1) << 8),
           type         = CV_MAKETYPE(depth, channels)
         };
};

/** @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 { depth    = Matx<_Tp, cn, 1>::depth,
           channels = cn,
           type     = CV_MAKETYPE(depth, channels)
         };

    //! 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
    explicit Vec(const _Tp* values);

    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,
           depth        = DataType<channel_type>::depth,
           channels     = cn,
           fmt          = DataType<channel_type>::fmt + ((channels - 1) << 8),
           type         = CV_MAKETYPE(depth, channels)
         };
};

/** @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 1./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 elaments.");
    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 elaments.");
    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 elaments.");
    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 elaments.");
    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 elaments.");
    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 elaments.");
    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 elaments.");
    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 elaments.");
    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 elaments.");
    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 elaments.");
    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;
}

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 elaments.");
    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;
}

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<_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)
{
    return normType == NORM_INF ? (double)normInf<_Tp, typename DataType<_Tp>::work_type>(M.val, m*n) :
        normType == NORM_L1 ? (double)normL1<_Tp, typename DataType<_Tp>::work_type>(M.val, m*n) :
        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(const _Tp* values)
    : Matx<_Tp, cn, 1>(values) {}

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>(val[1]*v.val[2] - val[2]*v.val[1],
                     val[2]*v.val[0] - val[0]*v.val[2],
                     val[0]*v.val[1] - val[1]*v.val[0]);
}

template<> inline
Vec<double, 3> Vec<double, 3>::cross(const Vec<double, 3>& v) const
{
    return Vec<double,3>(val[1]*v.val[2] - val[2]*v.val[1],
                     val[2]*v.val[0] - val[0]*v.val[2],
                     val[0]*v.val[1] - 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.);
}



//////////////////////////////// matx 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__