matx.inl.hpp

// This file is part of OpenCV project.
// It is subject to the license terms in the LICENSE file found in the top-level directory
// of this distribution and at http://opencv.org/license.html.
 
#ifndef OPENCV_CORE_MATX_INL_HPP
#define OPENCV_CORE_MATX_INL_HPP
 
#ifndef __cplusplus
#  error matx.inl.hpp header must be compiled as C++
#endif
 
#include "opencv2/core/matx.hpp"
 
namespace cv
{
 
//==============================================================================
// Helpers
 
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
 
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
 
 
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;
};
 
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;
}
 
 
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);
}
 
// WARNING: unreachable code using Ninja
#if defined _MSC_VER && _MSC_VER >= 1920
#pragma warning(push)
#pragma warning(disable: 4702)
#endif
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];
}
#if defined _MSC_VER && _MSC_VER >= 1920
#pragma warning(pop)
#endif
 
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 destination 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 base_row, int base_col) const
{
    CV_DbgAssert(0 <= base_row && base_row+m1 <= m && 0 <= base_col && base_col+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)(base_row+di, base_col+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 row_idx, int col_idx) const
{
    CV_DbgAssert( (unsigned)row_idx < (unsigned)m && (unsigned)col_idx < (unsigned)n );
    return this->val[row_idx*n + col_idx];
}
 
template<typename _Tp, int m, int n> inline
_Tp& Matx<_Tp, m, n>::operator ()(int row_idx, int col_idx)
{
    CV_DbgAssert( (unsigned)row_idx < (unsigned)m && (unsigned)col_idx < (unsigned)n );
    return val[row_idx*n + col_idx];
}
 
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));
    }
}
 
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 /= (Matx<_Tp, m, n>& a, float alpha)
{
    for( int i = 0; i < m*n; i++ )
        a.val[i] = 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] = 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, float alpha)
{
    return Matx<_Tp, m, n>(a, 1.f/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, 1./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
 
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
 
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, 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;
}
 
 
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>::ones()
{
    return Vec::all(1);
}
 
template<typename _Tp, int cn> inline
Vec<_Tp, cn> Vec<_Tp, cn>::zeros()
{
    return Vec::all(0);
}
 
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.);
}
 
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_INL_HPP