/*M///////////////////////////////////////////////////////////////////////////////////////
//
//  IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
//
//  By downloading, copying, installing or using the software you agree to this license.
//  If you do not agree to this license, do not download, install,
//  copy or use the software.
//
//
//                          License Agreement
//                For Open Source Computer Vision Library
//
// Copyright (C) 2000-2008, Intel Corporation, all rights reserved.
// Copyright (C) 2009, Willow Garage Inc., all rights reserved.
// Copyright (C) 2013, OpenCV Foundation, all rights reserved.
// Third party copyrights are property of their respective owners.
//
// Redistribution and use in source and binary forms, with or without modification,
// are permitted provided that the following conditions are met:
//
//   * Redistribution's of source code must retain the above copyright notice,
//     this list of conditions and the following disclaimer.
//
//   * Redistribution's in binary form must reproduce the above copyright notice,
//     this list of conditions and the following disclaimer in the documentation
//     and/or other materials provided with the distribution.
//
//   * The name of the copyright holders may not be used to endorse or promote products
//     derived from this software without specific prior written permission.
//
// This software is provided by the copyright holders and contributors "as is" and
// any express or implied warranties, including, but not limited to, the implied
// warranties of merchantability and fitness for a particular purpose are disclaimed.
// In no event shall the Intel Corporation or contributors be liable for any direct,
// indirect, incidental, special, exemplary, or consequential damages
// (including, but not limited to, procurement of substitute goods or services;
// loss of use, data, or profits; or business interruption) however caused
// and on any theory of liability, whether in contract, strict liability,
// or tort (including negligence or otherwise) arising in any way out of
// the use of this software, even if advised of the possibility of such damage.
//
//M*/

#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"

#ifdef CV_CXX11
#include <initializer_list>
#endif

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{.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 avaliable, std::initializer_list can be also used to initizlize Matx:
@code{.cpp}
    Matx31f m = { 1, 2, 3};
@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); //!< 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

#ifdef CV_CXX11
    Matx(std::initializer_list<_Tp>); //!< initialize from an initializer list
#endif

    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
    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);

#ifdef CV_CXX11
    Vec(std::initializer_list<_Tp>);
#endif

    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 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];
}

#ifdef CV_CXX11
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;
    }
}
#endif

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) {}

#ifdef CV_CXX11
template<typename _Tp, int cn> inline
Vec<_Tp, cn>::Vec(std::initializer_list<_Tp> list)
    : Matx<_Tp, cn, 1>(list) {}
#endif

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
