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     43 
     44 #ifndef __OPENCV_CORE_MATX_HPP__
     45 #define __OPENCV_CORE_MATX_HPP__
     46 
     47 #ifndef __cplusplus
     48 #  error matx.hpp header must be compiled as C++
     49 #endif
     50 
     51 #include "opencv2/core/cvdef.h"
     52 #include "opencv2/core/base.hpp"
     53 #include "opencv2/core/traits.hpp"
     54 
     55 namespace cv
     56 {
     57 
     58 //! @addtogroup core_basic
     59 //! @{
     60 
     61 ////////////////////////////// Small Matrix ///////////////////////////
     62 
     63 //! @cond IGNORED
     64 struct CV_EXPORTS Matx_AddOp {};
     65 struct CV_EXPORTS Matx_SubOp {};
     66 struct CV_EXPORTS Matx_ScaleOp {};
     67 struct CV_EXPORTS Matx_MulOp {};
     68 struct CV_EXPORTS Matx_DivOp {};
     69 struct CV_EXPORTS Matx_MatMulOp {};
     70 struct CV_EXPORTS Matx_TOp {};
     71 //! @endcond
     72 
     73 /** @brief Template class for small matrices whose type and size are known at compilation time
     74 
     75 If you need a more flexible type, use Mat . The elements of the matrix M are accessible using the
     76 M(i,j) notation. Most of the common matrix operations (see also @ref MatrixExpressions ) are
     77 available. To do an operation on Matx that is not implemented, you can easily convert the matrix to
     78 Mat and backwards:
     79 @code
     80     Matx33f m(1, 2, 3,
     81               4, 5, 6,
     82               7, 8, 9);
     83     cout << sum(Mat(m*m.t())) << endl;
     84  @endcode
     85  */
     86 template<typename _Tp, int m, int n> class Matx
     87 {
     88 public:
     89     enum { depth    = DataType<_Tp>::depth,
     90            rows     = m,
     91            cols     = n,
     92            channels = rows*cols,
     93            type     = CV_MAKETYPE(depth, channels),
     94            shortdim = (m < n ? m : n)
     95          };
     96 
     97     typedef _Tp                           value_type;
     98     typedef Matx<_Tp, m, n>               mat_type;
     99     typedef Matx<_Tp, shortdim, 1> diag_type;
    100 
    101     //! default constructor
    102     Matx();
    103 
    104     Matx(_Tp v0); //!< 1x1 matrix
    105     Matx(_Tp v0, _Tp v1); //!< 1x2 or 2x1 matrix
    106     Matx(_Tp v0, _Tp v1, _Tp v2); //!< 1x3 or 3x1 matrix
    107     Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3); //!< 1x4, 2x2 or 4x1 matrix
    108     Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4); //!< 1x5 or 5x1 matrix
    109     Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5); //!< 1x6, 2x3, 3x2 or 6x1 matrix
    110     Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6); //!< 1x7 or 7x1 matrix
    111     Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7); //!< 1x8, 2x4, 4x2 or 8x1 matrix
    112     Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7, _Tp v8); //!< 1x9, 3x3 or 9x1 matrix
    113     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
    114     Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3,
    115          _Tp v4, _Tp v5, _Tp v6, _Tp v7,
    116          _Tp v8, _Tp v9, _Tp v10, _Tp v11); //!< 1x12, 2x6, 3x4, 4x3, 6x2 or 12x1 matrix
    117     Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3,
    118          _Tp v4, _Tp v5, _Tp v6, _Tp v7,
    119          _Tp v8, _Tp v9, _Tp v10, _Tp v11,
    120          _Tp v12, _Tp v13, _Tp v14, _Tp v15); //!< 1x16, 4x4 or 16x1 matrix
    121     explicit Matx(const _Tp* vals); //!< initialize from a plain array
    122 
    123     static Matx all(_Tp alpha);
    124     static Matx zeros();
    125     static Matx ones();
    126     static Matx eye();
    127     static Matx diag(const diag_type& d);
    128     static Matx randu(_Tp a, _Tp b);
    129     static Matx randn(_Tp a, _Tp b);
    130 
    131     //! dot product computed with the default precision
    132     _Tp dot(const Matx<_Tp, m, n>& v) const;
    133 
    134     //! dot product computed in double-precision arithmetics
    135     double ddot(const Matx<_Tp, m, n>& v) const;
    136 
    137     //! conversion to another data type
    138     template<typename T2> operator Matx<T2, m, n>() const;
    139 
    140     //! change the matrix shape
    141     template<int m1, int n1> Matx<_Tp, m1, n1> reshape() const;
    142 
    143     //! extract part of the matrix
    144     template<int m1, int n1> Matx<_Tp, m1, n1> get_minor(int i, int j) const;
    145 
    146     //! extract the matrix row
    147     Matx<_Tp, 1, n> row(int i) const;
    148 
    149     //! extract the matrix column
    150     Matx<_Tp, m, 1> col(int i) const;
    151 
    152     //! extract the matrix diagonal
    153     diag_type diag() const;
    154 
    155     //! transpose the matrix
    156     Matx<_Tp, n, m> t() const;
    157 
    158     //! invert the matrix
    159     Matx<_Tp, n, m> inv(int method=DECOMP_LU, bool *p_is_ok = NULL) const;
    160 
    161     //! solve linear system
    162     template<int l> Matx<_Tp, n, l> solve(const Matx<_Tp, m, l>& rhs, int flags=DECOMP_LU) const;
    163     Vec<_Tp, n> solve(const Vec<_Tp, m>& rhs, int method) const;
    164 
    165     //! multiply two matrices element-wise
    166     Matx<_Tp, m, n> mul(const Matx<_Tp, m, n>& a) const;
    167 
    168     //! divide two matrices element-wise
    169     Matx<_Tp, m, n> div(const Matx<_Tp, m, n>& a) const;
    170 
    171     //! element access
    172     const _Tp& operator ()(int i, int j) const;
    173     _Tp& operator ()(int i, int j);
    174 
    175     //! 1D element access
    176     const _Tp& operator ()(int i) const;
    177     _Tp& operator ()(int i);
    178 
    179     Matx(const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b, Matx_AddOp);
    180     Matx(const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b, Matx_SubOp);
    181     template<typename _T2> Matx(const Matx<_Tp, m, n>& a, _T2 alpha, Matx_ScaleOp);
    182     Matx(const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b, Matx_MulOp);
    183     Matx(const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b, Matx_DivOp);
    184     template<int l> Matx(const Matx<_Tp, m, l>& a, const Matx<_Tp, l, n>& b, Matx_MatMulOp);
    185     Matx(const Matx<_Tp, n, m>& a, Matx_TOp);
    186 
    187     _Tp val[m*n]; //< matrix elements
    188 };
    189 
    190 typedef Matx<float, 1, 2> Matx12f;
    191 typedef Matx<double, 1, 2> Matx12d;
    192 typedef Matx<float, 1, 3> Matx13f;
    193 typedef Matx<double, 1, 3> Matx13d;
    194 typedef Matx<float, 1, 4> Matx14f;
    195 typedef Matx<double, 1, 4> Matx14d;
    196 typedef Matx<float, 1, 6> Matx16f;
    197 typedef Matx<double, 1, 6> Matx16d;
    198 
    199 typedef Matx<float, 2, 1> Matx21f;
    200 typedef Matx<double, 2, 1> Matx21d;
    201 typedef Matx<float, 3, 1> Matx31f;
    202 typedef Matx<double, 3, 1> Matx31d;
    203 typedef Matx<float, 4, 1> Matx41f;
    204 typedef Matx<double, 4, 1> Matx41d;
    205 typedef Matx<float, 6, 1> Matx61f;
    206 typedef Matx<double, 6, 1> Matx61d;
    207 
    208 typedef Matx<float, 2, 2> Matx22f;
    209 typedef Matx<double, 2, 2> Matx22d;
    210 typedef Matx<float, 2, 3> Matx23f;
    211 typedef Matx<double, 2, 3> Matx23d;
    212 typedef Matx<float, 3, 2> Matx32f;
    213 typedef Matx<double, 3, 2> Matx32d;
    214 
    215 typedef Matx<float, 3, 3> Matx33f;
    216 typedef Matx<double, 3, 3> Matx33d;
    217 
    218 typedef Matx<float, 3, 4> Matx34f;
    219 typedef Matx<double, 3, 4> Matx34d;
    220 typedef Matx<float, 4, 3> Matx43f;
    221 typedef Matx<double, 4, 3> Matx43d;
    222 
    223 typedef Matx<float, 4, 4> Matx44f;
    224 typedef Matx<double, 4, 4> Matx44d;
    225 typedef Matx<float, 6, 6> Matx66f;
    226 typedef Matx<double, 6, 6> Matx66d;
    227 
    228 /*!
    229   traits
    230 */
    231 template<typename _Tp, int m, int n> class DataType< Matx<_Tp, m, n> >
    232 {
    233 public:
    234     typedef Matx<_Tp, m, n>                               value_type;
    235     typedef Matx<typename DataType<_Tp>::work_type, m, n> work_type;
    236     typedef _Tp                                           channel_type;
    237     typedef value_type                                    vec_type;
    238 
    239     enum { generic_type = 0,
    240            depth        = DataType<channel_type>::depth,
    241            channels     = m * n,
    242            fmt          = DataType<channel_type>::fmt + ((channels - 1) << 8),
    243            type         = CV_MAKETYPE(depth, channels)
    244          };
    245 };
    246 
    247 /** @brief  Comma-separated Matrix Initializer
    248 */
    249 template<typename _Tp, int m, int n> class MatxCommaInitializer
    250 {
    251 public:
    252     MatxCommaInitializer(Matx<_Tp, m, n>* _mtx);
    253     template<typename T2> MatxCommaInitializer<_Tp, m, n>& operator , (T2 val);
    254     Matx<_Tp, m, n> operator *() const;
    255 
    256     Matx<_Tp, m, n>* dst;
    257     int idx;
    258 };
    259 
    260 /*
    261  Utility methods
    262 */
    263 template<typename _Tp, int m> static double determinant(const Matx<_Tp, m, m>& a);
    264 template<typename _Tp, int m, int n> static double trace(const Matx<_Tp, m, n>& a);
    265 template<typename _Tp, int m, int n> static double norm(const Matx<_Tp, m, n>& M);
    266 template<typename _Tp, int m, int n> static double norm(const Matx<_Tp, m, n>& M, int normType);
    267 
    268 
    269 
    270 /////////////////////// Vec (used as element of multi-channel images /////////////////////
    271 
    272 /** @brief Template class for short numerical vectors, a partial case of Matx
    273 
    274 This template class represents short numerical vectors (of 1, 2, 3, 4 ... elements) on which you
    275 can perform basic arithmetical operations, access individual elements using [] operator etc. The
    276 vectors are allocated on stack, as opposite to std::valarray, std::vector, cv::Mat etc., which
    277 elements are dynamically allocated in the heap.
    278 
    279 The template takes 2 parameters:
    280 @tparam _Tp element type
    281 @tparam cn the number of elements
    282 
    283 In addition to the universal notation like Vec<float, 3>, you can use shorter aliases
    284 for the most popular specialized variants of Vec, e.g. Vec3f ~ Vec<float, 3>.
    285 
    286 It is possible to convert Vec\<T,2\> to/from Point_, Vec\<T,3\> to/from Point3_ , and Vec\<T,4\>
    287 to CvScalar or Scalar_. Use operator[] to access the elements of Vec.
    288 
    289 All the expected vector operations are also implemented:
    290 -   v1 = v2 + v3
    291 -   v1 = v2 - v3
    292 -   v1 = v2 \* scale
    293 -   v1 = scale \* v2
    294 -   v1 = -v2
    295 -   v1 += v2 and other augmenting operations
    296 -   v1 == v2, v1 != v2
    297 -   norm(v1) (euclidean norm)
    298 The Vec class is commonly used to describe pixel types of multi-channel arrays. See Mat for details.
    299 */
    300 template<typename _Tp, int cn> class Vec : public Matx<_Tp, cn, 1>
    301 {
    302 public:
    303     typedef _Tp value_type;
    304     enum { depth    = Matx<_Tp, cn, 1>::depth,
    305            channels = cn,
    306            type     = CV_MAKETYPE(depth, channels)
    307          };
    308 
    309     //! default constructor
    310     Vec();
    311 
    312     Vec(_Tp v0); //!< 1-element vector constructor
    313     Vec(_Tp v0, _Tp v1); //!< 2-element vector constructor
    314     Vec(_Tp v0, _Tp v1, _Tp v2); //!< 3-element vector constructor
    315     Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3); //!< 4-element vector constructor
    316     Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4); //!< 5-element vector constructor
    317     Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5); //!< 6-element vector constructor
    318     Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6); //!< 7-element vector constructor
    319     Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7); //!< 8-element vector constructor
    320     Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7, _Tp v8); //!< 9-element vector constructor
    321     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
    322     explicit Vec(const _Tp* values);
    323 
    324     Vec(const Vec<_Tp, cn>& v);
    325 
    326     static Vec all(_Tp alpha);
    327 
    328     //! per-element multiplication
    329     Vec mul(const Vec<_Tp, cn>& v) const;
    330 
    331     //! conjugation (makes sense for complex numbers and quaternions)
    332     Vec conj() const;
    333 
    334     /*!
    335       cross product of the two 3D vectors.
    336 
    337       For other dimensionalities the exception is raised
    338     */
    339     Vec cross(const Vec& v) const;
    340     //! conversion to another data type
    341     template<typename T2> operator Vec<T2, cn>() const;
    342 
    343     /*! element access */
    344     const _Tp& operator [](int i) const;
    345     _Tp& operator[](int i);
    346     const _Tp& operator ()(int i) const;
    347     _Tp& operator ()(int i);
    348 
    349     Vec(const Matx<_Tp, cn, 1>& a, const Matx<_Tp, cn, 1>& b, Matx_AddOp);
    350     Vec(const Matx<_Tp, cn, 1>& a, const Matx<_Tp, cn, 1>& b, Matx_SubOp);
    351     template<typename _T2> Vec(const Matx<_Tp, cn, 1>& a, _T2 alpha, Matx_ScaleOp);
    352 };
    353 
    354 /** @name Shorter aliases for the most popular specializations of Vec<T,n>
    355   @{
    356 */
    357 typedef Vec<uchar, 2> Vec2b;
    358 typedef Vec<uchar, 3> Vec3b;
    359 typedef Vec<uchar, 4> Vec4b;
    360 
    361 typedef Vec<short, 2> Vec2s;
    362 typedef Vec<short, 3> Vec3s;
    363 typedef Vec<short, 4> Vec4s;
    364 
    365 typedef Vec<ushort, 2> Vec2w;
    366 typedef Vec<ushort, 3> Vec3w;
    367 typedef Vec<ushort, 4> Vec4w;
    368 
    369 typedef Vec<int, 2> Vec2i;
    370 typedef Vec<int, 3> Vec3i;
    371 typedef Vec<int, 4> Vec4i;
    372 typedef Vec<int, 6> Vec6i;
    373 typedef Vec<int, 8> Vec8i;
    374 
    375 typedef Vec<float, 2> Vec2f;
    376 typedef Vec<float, 3> Vec3f;
    377 typedef Vec<float, 4> Vec4f;
    378 typedef Vec<float, 6> Vec6f;
    379 
    380 typedef Vec<double, 2> Vec2d;
    381 typedef Vec<double, 3> Vec3d;
    382 typedef Vec<double, 4> Vec4d;
    383 typedef Vec<double, 6> Vec6d;
    384 /** @} */
    385 
    386 /*!
    387   traits
    388 */
    389 template<typename _Tp, int cn> class DataType< Vec<_Tp, cn> >
    390 {
    391 public:
    392     typedef Vec<_Tp, cn>                               value_type;
    393     typedef Vec<typename DataType<_Tp>::work_type, cn> work_type;
    394     typedef _Tp                                        channel_type;
    395     typedef value_type                                 vec_type;
    396 
    397     enum { generic_type = 0,
    398            depth        = DataType<channel_type>::depth,
    399            channels     = cn,
    400            fmt          = DataType<channel_type>::fmt + ((channels - 1) << 8),
    401            type         = CV_MAKETYPE(depth, channels)
    402          };
    403 };
    404 
    405 /** @brief  Comma-separated Vec Initializer
    406 */
    407 template<typename _Tp, int m> class VecCommaInitializer : public MatxCommaInitializer<_Tp, m, 1>
    408 {
    409 public:
    410     VecCommaInitializer(Vec<_Tp, m>* _vec);
    411     template<typename T2> VecCommaInitializer<_Tp, m>& operator , (T2 val);
    412     Vec<_Tp, m> operator *() const;
    413 };
    414 
    415 template<typename _Tp, int cn> static Vec<_Tp, cn> normalize(const Vec<_Tp, cn>& v);
    416 
    417 //! @} core_basic
    418 
    419 //! @cond IGNORED
    420 
    421 ///////////////////////////////////// helper classes /////////////////////////////////////
    422 namespace internal
    423 {
    424 
    425 template<typename _Tp, int m> struct Matx_DetOp
    426 {
    427     double operator ()(const Matx<_Tp, m, m>& a) const
    428     {
    429         Matx<_Tp, m, m> temp = a;
    430         double p = LU(temp.val, m*sizeof(_Tp), m, 0, 0, 0);
    431         if( p == 0 )
    432             return p;
    433         for( int i = 0; i < m; i++ )
    434             p *= temp(i, i);
    435         return 1./p;
    436     }
    437 };
    438 
    439 template<typename _Tp> struct Matx_DetOp<_Tp, 1>
    440 {
    441     double operator ()(const Matx<_Tp, 1, 1>& a) const
    442     {
    443         return a(0,0);
    444     }
    445 };
    446 
    447 template<typename _Tp> struct Matx_DetOp<_Tp, 2>
    448 {
    449     double operator ()(const Matx<_Tp, 2, 2>& a) const
    450     {
    451         return a(0,0)*a(1,1) - a(0,1)*a(1,0);
    452     }
    453 };
    454 
    455 template<typename _Tp> struct Matx_DetOp<_Tp, 3>
    456 {
    457     double operator ()(const Matx<_Tp, 3, 3>& a) const
    458     {
    459         return a(0,0)*(a(1,1)*a(2,2) - a(2,1)*a(1,2)) -
    460             a(0,1)*(a(1,0)*a(2,2) - a(2,0)*a(1,2)) +
    461             a(0,2)*(a(1,0)*a(2,1) - a(2,0)*a(1,1));
    462     }
    463 };
    464 
    465 template<typename _Tp> Vec<_Tp, 2> inline conjugate(const Vec<_Tp, 2>& v)
    466 {
    467     return Vec<_Tp, 2>(v[0], -v[1]);
    468 }
    469 
    470 template<typename _Tp> Vec<_Tp, 4> inline conjugate(const Vec<_Tp, 4>& v)
    471 {
    472     return Vec<_Tp, 4>(v[0], -v[1], -v[2], -v[3]);
    473 }
    474 
    475 } // internal
    476 
    477 
    478 
    479 ////////////////////////////////// Matx Implementation ///////////////////////////////////
    480 
    481 template<typename _Tp, int m, int n> inline
    482 Matx<_Tp, m, n>::Matx()
    483 {
    484     for(int i = 0; i < channels; i++) val[i] = _Tp(0);
    485 }
    486 
    487 template<typename _Tp, int m, int n> inline
    488 Matx<_Tp, m, n>::Matx(_Tp v0)
    489 {
    490     val[0] = v0;
    491     for(int i = 1; i < channels; i++) val[i] = _Tp(0);
    492 }
    493 
    494 template<typename _Tp, int m, int n> inline
    495 Matx<_Tp, m, n>::Matx(_Tp v0, _Tp v1)
    496 {
    497     CV_StaticAssert(channels >= 2, "Matx should have at least 2 elaments.");
    498     val[0] = v0; val[1] = v1;
    499     for(int i = 2; i < channels; i++) val[i] = _Tp(0);
    500 }
    501 
    502 template<typename _Tp, int m, int n> inline
    503 Matx<_Tp, m, n>::Matx(_Tp v0, _Tp v1, _Tp v2)
    504 {
    505     CV_StaticAssert(channels >= 3, "Matx should have at least 3 elaments.");
    506     val[0] = v0; val[1] = v1; val[2] = v2;
    507     for(int i = 3; i < channels; i++) val[i] = _Tp(0);
    508 }
    509 
    510 template<typename _Tp, int m, int n> inline
    511 Matx<_Tp, m, n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3)
    512 {
    513     CV_StaticAssert(channels >= 4, "Matx should have at least 4 elaments.");
    514     val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3;
    515     for(int i = 4; i < channels; i++) val[i] = _Tp(0);
    516 }
    517 
    518 template<typename _Tp, int m, int n> inline
    519 Matx<_Tp, m, n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4)
    520 {
    521     CV_StaticAssert(channels >= 5, "Matx should have at least 5 elaments.");
    522     val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3; val[4] = v4;
    523     for(int i = 5; i < channels; i++) val[i] = _Tp(0);
    524 }
    525 
    526 template<typename _Tp, int m, int n> inline
    527 Matx<_Tp, m, n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5)
    528 {
    529     CV_StaticAssert(channels >= 6, "Matx should have at least 6 elaments.");
    530     val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3;
    531     val[4] = v4; val[5] = v5;
    532     for(int i = 6; i < channels; i++) val[i] = _Tp(0);
    533 }
    534 
    535 template<typename _Tp, int m, int n> inline
    536 Matx<_Tp, m, n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6)
    537 {
    538     CV_StaticAssert(channels >= 7, "Matx should have at least 7 elaments.");
    539     val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3;
    540     val[4] = v4; val[5] = v5; val[6] = v6;
    541     for(int i = 7; i < channels; i++) val[i] = _Tp(0);
    542 }
    543 
    544 template<typename _Tp, int m, int n> inline
    545 Matx<_Tp, m, n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7)
    546 {
    547     CV_StaticAssert(channels >= 8, "Matx should have at least 8 elaments.");
    548     val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3;
    549     val[4] = v4; val[5] = v5; val[6] = v6; val[7] = v7;
    550     for(int i = 8; i < channels; i++) val[i] = _Tp(0);
    551 }
    552 
    553 template<typename _Tp, int m, int n> inline
    554 Matx<_Tp, m, n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7, _Tp v8)
    555 {
    556     CV_StaticAssert(channels >= 9, "Matx should have at least 9 elaments.");
    557     val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3;
    558     val[4] = v4; val[5] = v5; val[6] = v6; val[7] = v7;
    559     val[8] = v8;
    560     for(int i = 9; i < channels; i++) val[i] = _Tp(0);
    561 }
    562 
    563 template<typename _Tp, int m, int n> inline
    564 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)
    565 {
    566     CV_StaticAssert(channels >= 10, "Matx should have at least 10 elaments.");
    567     val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3;
    568     val[4] = v4; val[5] = v5; val[6] = v6; val[7] = v7;
    569     val[8] = v8; val[9] = v9;
    570     for(int i = 10; i < channels; i++) val[i] = _Tp(0);
    571 }
    572 
    573 
    574 template<typename _Tp, int m, int n> inline
    575 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)
    576 {
    577     CV_StaticAssert(channels == 12, "Matx should have at least 12 elaments.");
    578     val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3;
    579     val[4] = v4; val[5] = v5; val[6] = v6; val[7] = v7;
    580     val[8] = v8; val[9] = v9; val[10] = v10; val[11] = v11;
    581 }
    582 
    583 template<typename _Tp, int m, int n> inline
    584 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)
    585 {
    586     CV_StaticAssert(channels == 16, "Matx should have at least 16 elaments.");
    587     val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3;
    588     val[4] = v4; val[5] = v5; val[6] = v6; val[7] = v7;
    589     val[8] = v8; val[9] = v9; val[10] = v10; val[11] = v11;
    590     val[12] = v12; val[13] = v13; val[14] = v14; val[15] = v15;
    591 }
    592 
    593 template<typename _Tp, int m, int n> inline
    594 Matx<_Tp, m, n>::Matx(const _Tp* values)
    595 {
    596     for( int i = 0; i < channels; i++ ) val[i] = values[i];
    597 }
    598 
    599 template<typename _Tp, int m, int n> inline
    600 Matx<_Tp, m, n> Matx<_Tp, m, n>::all(_Tp alpha)
    601 {
    602     Matx<_Tp, m, n> M;
    603     for( int i = 0; i < m*n; i++ ) M.val[i] = alpha;
    604     return M;
    605 }
    606 
    607 template<typename _Tp, int m, int n> inline
    608 Matx<_Tp,m,n> Matx<_Tp,m,n>::zeros()
    609 {
    610     return all(0);
    611 }
    612 
    613 template<typename _Tp, int m, int n> inline
    614 Matx<_Tp,m,n> Matx<_Tp,m,n>::ones()
    615 {
    616     return all(1);
    617 }
    618 
    619 template<typename _Tp, int m, int n> inline
    620 Matx<_Tp,m,n> Matx<_Tp,m,n>::eye()
    621 {
    622     Matx<_Tp,m,n> M;
    623     for(int i = 0; i < shortdim; i++)
    624         M(i,i) = 1;
    625     return M;
    626 }
    627 
    628 template<typename _Tp, int m, int n> inline
    629 _Tp Matx<_Tp, m, n>::dot(const Matx<_Tp, m, n>& M) const
    630 {
    631     _Tp s = 0;
    632     for( int i = 0; i < channels; i++ ) s += val[i]*M.val[i];
    633     return s;
    634 }
    635 
    636 template<typename _Tp, int m, int n> inline
    637 double Matx<_Tp, m, n>::ddot(const Matx<_Tp, m, n>& M) const
    638 {
    639     double s = 0;
    640     for( int i = 0; i < channels; i++ ) s += (double)val[i]*M.val[i];
    641     return s;
    642 }
    643 
    644 template<typename _Tp, int m, int n> inline
    645 Matx<_Tp,m,n> Matx<_Tp,m,n>::diag(const typename Matx<_Tp,m,n>::diag_type& d)
    646 {
    647     Matx<_Tp,m,n> M;
    648     for(int i = 0; i < shortdim; i++)
    649         M(i,i) = d(i, 0);
    650     return M;
    651 }
    652 
    653 template<typename _Tp, int m, int n> template<typename T2>
    654 inline Matx<_Tp, m, n>::operator Matx<T2, m, n>() const
    655 {
    656     Matx<T2, m, n> M;
    657     for( int i = 0; i < m*n; i++ ) M.val[i] = saturate_cast<T2>(val[i]);
    658     return M;
    659 }
    660 
    661 template<typename _Tp, int m, int n> template<int m1, int n1> inline
    662 Matx<_Tp, m1, n1> Matx<_Tp, m, n>::reshape() const
    663 {
    664     CV_StaticAssert(m1*n1 == m*n, "Input and destnarion matrices must have the same number of elements");
    665     return (const Matx<_Tp, m1, n1>&)*this;
    666 }
    667 
    668 template<typename _Tp, int m, int n>
    669 template<int m1, int n1> inline
    670 Matx<_Tp, m1, n1> Matx<_Tp, m, n>::get_minor(int i, int j) const
    671 {
    672     CV_DbgAssert(0 <= i && i+m1 <= m && 0 <= j && j+n1 <= n);
    673     Matx<_Tp, m1, n1> s;
    674     for( int di = 0; di < m1; di++ )
    675         for( int dj = 0; dj < n1; dj++ )
    676             s(di, dj) = (*this)(i+di, j+dj);
    677     return s;
    678 }
    679 
    680 template<typename _Tp, int m, int n> inline
    681 Matx<_Tp, 1, n> Matx<_Tp, m, n>::row(int i) const
    682 {
    683     CV_DbgAssert((unsigned)i < (unsigned)m);
    684     return Matx<_Tp, 1, n>(&val[i*n]);
    685 }
    686 
    687 template<typename _Tp, int m, int n> inline
    688 Matx<_Tp, m, 1> Matx<_Tp, m, n>::col(int j) const
    689 {
    690     CV_DbgAssert((unsigned)j < (unsigned)n);
    691     Matx<_Tp, m, 1> v;
    692     for( int i = 0; i < m; i++ )
    693         v.val[i] = val[i*n + j];
    694     return v;
    695 }
    696 
    697 template<typename _Tp, int m, int n> inline
    698 typename Matx<_Tp, m, n>::diag_type Matx<_Tp, m, n>::diag() const
    699 {
    700     diag_type d;
    701     for( int i = 0; i < shortdim; i++ )
    702         d.val[i] = val[i*n + i];
    703     return d;
    704 }
    705 
    706 template<typename _Tp, int m, int n> inline
    707 const _Tp& Matx<_Tp, m, n>::operator()(int i, int j) const
    708 {
    709     CV_DbgAssert( (unsigned)i < (unsigned)m && (unsigned)j < (unsigned)n );
    710     return this->val[i*n + j];
    711 }
    712 
    713 template<typename _Tp, int m, int n> inline
    714 _Tp& Matx<_Tp, m, n>::operator ()(int i, int j)
    715 {
    716     CV_DbgAssert( (unsigned)i < (unsigned)m && (unsigned)j < (unsigned)n );
    717     return val[i*n + j];
    718 }
    719 
    720 template<typename _Tp, int m, int n> inline
    721 const _Tp& Matx<_Tp, m, n>::operator ()(int i) const
    722 {
    723     CV_StaticAssert(m == 1 || n == 1, "Single index indexation requires matrix to be a column or a row");
    724     CV_DbgAssert( (unsigned)i < (unsigned)(m+n-1) );
    725     return val[i];
    726 }
    727 
    728 template<typename _Tp, int m, int n> inline
    729 _Tp& Matx<_Tp, m, n>::operator ()(int i)
    730 {
    731     CV_StaticAssert(m == 1 || n == 1, "Single index indexation requires matrix to be a column or a row");
    732     CV_DbgAssert( (unsigned)i < (unsigned)(m+n-1) );
    733     return val[i];
    734 }
    735 
    736 template<typename _Tp, int m, int n> inline
    737 Matx<_Tp,m,n>::Matx(const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b, Matx_AddOp)
    738 {
    739     for( int i = 0; i < channels; i++ )
    740         val[i] = saturate_cast<_Tp>(a.val[i] + b.val[i]);
    741 }
    742 
    743 template<typename _Tp, int m, int n> inline
    744 Matx<_Tp,m,n>::Matx(const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b, Matx_SubOp)
    745 {
    746     for( int i = 0; i < channels; i++ )
    747         val[i] = saturate_cast<_Tp>(a.val[i] - b.val[i]);
    748 }
    749 
    750 template<typename _Tp, int m, int n> template<typename _T2> inline
    751 Matx<_Tp,m,n>::Matx(const Matx<_Tp, m, n>& a, _T2 alpha, Matx_ScaleOp)
    752 {
    753     for( int i = 0; i < channels; i++ )
    754         val[i] = saturate_cast<_Tp>(a.val[i] * alpha);
    755 }
    756 
    757 template<typename _Tp, int m, int n> inline
    758 Matx<_Tp,m,n>::Matx(const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b, Matx_MulOp)
    759 {
    760     for( int i = 0; i < channels; i++ )
    761         val[i] = saturate_cast<_Tp>(a.val[i] * b.val[i]);
    762 }
    763 
    764 template<typename _Tp, int m, int n> inline
    765 Matx<_Tp,m,n>::Matx(const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b, Matx_DivOp)
    766 {
    767     for( int i = 0; i < channels; i++ )
    768         val[i] = saturate_cast<_Tp>(a.val[i] / b.val[i]);
    769 }
    770 
    771 template<typename _Tp, int m, int n> template<int l> inline
    772 Matx<_Tp,m,n>::Matx(const Matx<_Tp, m, l>& a, const Matx<_Tp, l, n>& b, Matx_MatMulOp)
    773 {
    774     for( int i = 0; i < m; i++ )
    775         for( int j = 0; j < n; j++ )
    776         {
    777             _Tp s = 0;
    778             for( int k = 0; k < l; k++ )
    779                 s += a(i, k) * b(k, j);
    780             val[i*n + j] = s;
    781         }
    782 }
    783 
    784 template<typename _Tp, int m, int n> inline
    785 Matx<_Tp,m,n>::Matx(const Matx<_Tp, n, m>& a, Matx_TOp)
    786 {
    787     for( int i = 0; i < m; i++ )
    788         for( int j = 0; j < n; j++ )
    789             val[i*n + j] = a(j, i);
    790 }
    791 
    792 template<typename _Tp, int m, int n> inline
    793 Matx<_Tp, m, n> Matx<_Tp, m, n>::mul(const Matx<_Tp, m, n>& a) const
    794 {
    795     return Matx<_Tp, m, n>(*this, a, Matx_MulOp());
    796 }
    797 
    798 template<typename _Tp, int m, int n> inline
    799 Matx<_Tp, m, n> Matx<_Tp, m, n>::div(const Matx<_Tp, m, n>& a) const
    800 {
    801     return Matx<_Tp, m, n>(*this, a, Matx_DivOp());
    802 }
    803 
    804 template<typename _Tp, int m, int n> inline
    805 Matx<_Tp, n, m> Matx<_Tp, m, n>::t() const
    806 {
    807     return Matx<_Tp, n, m>(*this, Matx_TOp());
    808 }
    809 
    810 template<typename _Tp, int m, int n> inline
    811 Vec<_Tp, n> Matx<_Tp, m, n>::solve(const Vec<_Tp, m>& rhs, int method) const
    812 {
    813     Matx<_Tp, n, 1> x = solve((const Matx<_Tp, m, 1>&)(rhs), method);
    814     return (Vec<_Tp, n>&)(x);
    815 }
    816 
    817 template<typename _Tp, int m> static inline
    818 double determinant(const Matx<_Tp, m, m>& a)
    819 {
    820     return cv::internal::Matx_DetOp<_Tp, m>()(a);
    821 }
    822 
    823 template<typename _Tp, int m, int n> static inline
    824 double trace(const Matx<_Tp, m, n>& a)
    825 {
    826     _Tp s = 0;
    827     for( int i = 0; i < std::min(m, n); i++ )
    828         s += a(i,i);
    829     return s;
    830 }
    831 
    832 template<typename _Tp, int m, int n> static inline
    833 double norm(const Matx<_Tp, m, n>& M)
    834 {
    835     return std::sqrt(normL2Sqr<_Tp, double>(M.val, m*n));
    836 }
    837 
    838 template<typename _Tp, int m, int n> static inline
    839 double norm(const Matx<_Tp, m, n>& M, int normType)
    840 {
    841     return normType == NORM_INF ? (double)normInf<_Tp, typename DataType<_Tp>::work_type>(M.val, m*n) :
    842         normType == NORM_L1 ? (double)normL1<_Tp, typename DataType<_Tp>::work_type>(M.val, m*n) :
    843         std::sqrt((double)normL2Sqr<_Tp, typename DataType<_Tp>::work_type>(M.val, m*n));
    844 }
    845 
    846 
    847 
    848 //////////////////////////////// matx comma initializer //////////////////////////////////
    849 
    850 template<typename _Tp, typename _T2, int m, int n> static inline
    851 MatxCommaInitializer<_Tp, m, n> operator << (const Matx<_Tp, m, n>& mtx, _T2 val)
    852 {
    853     MatxCommaInitializer<_Tp, m, n> commaInitializer((Matx<_Tp, m, n>*)&mtx);
    854     return (commaInitializer, val);
    855 }
    856 
    857 template<typename _Tp, int m, int n> inline
    858 MatxCommaInitializer<_Tp, m, n>::MatxCommaInitializer(Matx<_Tp, m, n>* _mtx)
    859     : dst(_mtx), idx(0)
    860 {}
    861 
    862 template<typename _Tp, int m, int n> template<typename _T2> inline
    863 MatxCommaInitializer<_Tp, m, n>& MatxCommaInitializer<_Tp, m, n>::operator , (_T2 value)
    864 {
    865     CV_DbgAssert( idx < m*n );
    866     dst->val[idx++] = saturate_cast<_Tp>(value);
    867     return *this;
    868 }
    869 
    870 template<typename _Tp, int m, int n> inline
    871 Matx<_Tp, m, n> MatxCommaInitializer<_Tp, m, n>::operator *() const
    872 {
    873     CV_DbgAssert( idx == n*m );
    874     return *dst;
    875 }
    876 
    877 
    878 
    879 /////////////////////////////////// Vec Implementation ///////////////////////////////////
    880 
    881 template<typename _Tp, int cn> inline
    882 Vec<_Tp, cn>::Vec() {}
    883 
    884 template<typename _Tp, int cn> inline
    885 Vec<_Tp, cn>::Vec(_Tp v0)
    886     : Matx<_Tp, cn, 1>(v0) {}
    887 
    888 template<typename _Tp, int cn> inline
    889 Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1)
    890     : Matx<_Tp, cn, 1>(v0, v1) {}
    891 
    892 template<typename _Tp, int cn> inline
    893 Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2)
    894     : Matx<_Tp, cn, 1>(v0, v1, v2) {}
    895 
    896 template<typename _Tp, int cn> inline
    897 Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3)
    898     : Matx<_Tp, cn, 1>(v0, v1, v2, v3) {}
    899 
    900 template<typename _Tp, int cn> inline
    901 Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4)
    902     : Matx<_Tp, cn, 1>(v0, v1, v2, v3, v4) {}
    903 
    904 template<typename _Tp, int cn> inline
    905 Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5)
    906     : Matx<_Tp, cn, 1>(v0, v1, v2, v3, v4, v5) {}
    907 
    908 template<typename _Tp, int cn> inline
    909 Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6)
    910     : Matx<_Tp, cn, 1>(v0, v1, v2, v3, v4, v5, v6) {}
    911 
    912 template<typename _Tp, int cn> inline
    913 Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7)
    914     : Matx<_Tp, cn, 1>(v0, v1, v2, v3, v4, v5, v6, v7) {}
    915 
    916 template<typename _Tp, int cn> inline
    917 Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7, _Tp v8)
    918     : Matx<_Tp, cn, 1>(v0, v1, v2, v3, v4, v5, v6, v7, v8) {}
    919 
    920 template<typename _Tp, int cn> inline
    921 Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7, _Tp v8, _Tp v9)
    922     : Matx<_Tp, cn, 1>(v0, v1, v2, v3, v4, v5, v6, v7, v8, v9) {}
    923 
    924 template<typename _Tp, int cn> inline
    925 Vec<_Tp, cn>::Vec(const _Tp* values)
    926     : Matx<_Tp, cn, 1>(values) {}
    927 
    928 template<typename _Tp, int cn> inline
    929 Vec<_Tp, cn>::Vec(const Vec<_Tp, cn>& m)
    930     : Matx<_Tp, cn, 1>(m.val) {}
    931 
    932 template<typename _Tp, int cn> inline
    933 Vec<_Tp, cn>::Vec(const Matx<_Tp, cn, 1>& a, const Matx<_Tp, cn, 1>& b, Matx_AddOp op)
    934     : Matx<_Tp, cn, 1>(a, b, op) {}
    935 
    936 template<typename _Tp, int cn> inline
    937 Vec<_Tp, cn>::Vec(const Matx<_Tp, cn, 1>& a, const Matx<_Tp, cn, 1>& b, Matx_SubOp op)
    938     : Matx<_Tp, cn, 1>(a, b, op) {}
    939 
    940 template<typename _Tp, int cn> template<typename _T2> inline
    941 Vec<_Tp, cn>::Vec(const Matx<_Tp, cn, 1>& a, _T2 alpha, Matx_ScaleOp op)
    942     : Matx<_Tp, cn, 1>(a, alpha, op) {}
    943 
    944 template<typename _Tp, int cn> inline
    945 Vec<_Tp, cn> Vec<_Tp, cn>::all(_Tp alpha)
    946 {
    947     Vec v;
    948     for( int i = 0; i < cn; i++ ) v.val[i] = alpha;
    949     return v;
    950 }
    951 
    952 template<typename _Tp, int cn> inline
    953 Vec<_Tp, cn> Vec<_Tp, cn>::mul(const Vec<_Tp, cn>& v) const
    954 {
    955     Vec<_Tp, cn> w;
    956     for( int i = 0; i < cn; i++ ) w.val[i] = saturate_cast<_Tp>(this->val[i]*v.val[i]);
    957     return w;
    958 }
    959 
    960 template<> inline
    961 Vec<float, 2> Vec<float, 2>::conj() const
    962 {
    963     return cv::internal::conjugate(*this);
    964 }
    965 
    966 template<> inline
    967 Vec<double, 2> Vec<double, 2>::conj() const
    968 {
    969     return cv::internal::conjugate(*this);
    970 }
    971 
    972 template<> inline
    973 Vec<float, 4> Vec<float, 4>::conj() const
    974 {
    975     return cv::internal::conjugate(*this);
    976 }
    977 
    978 template<> inline
    979 Vec<double, 4> Vec<double, 4>::conj() const
    980 {
    981     return cv::internal::conjugate(*this);
    982 }
    983 
    984 template<typename _Tp, int cn> inline
    985 Vec<_Tp, cn> Vec<_Tp, cn>::cross(const Vec<_Tp, cn>&) const
    986 {
    987     CV_StaticAssert(cn == 3, "for arbitrary-size vector there is no cross-product defined");
    988     return Vec<_Tp, cn>();
    989 }
    990 
    991 template<> inline
    992 Vec<float, 3> Vec<float, 3>::cross(const Vec<float, 3>& v) const
    993 {
    994     return Vec<float,3>(val[1]*v.val[2] - val[2]*v.val[1],
    995                      val[2]*v.val[0] - val[0]*v.val[2],
    996                      val[0]*v.val[1] - val[1]*v.val[0]);
    997 }
    998 
    999 template<> inline
   1000 Vec<double, 3> Vec<double, 3>::cross(const Vec<double, 3>& v) const
   1001 {
   1002     return Vec<double,3>(val[1]*v.val[2] - val[2]*v.val[1],
   1003                      val[2]*v.val[0] - val[0]*v.val[2],
   1004                      val[0]*v.val[1] - val[1]*v.val[0]);
   1005 }
   1006 
   1007 template<typename _Tp, int cn> template<typename T2> inline
   1008 Vec<_Tp, cn>::operator Vec<T2, cn>() const
   1009 {
   1010     Vec<T2, cn> v;
   1011     for( int i = 0; i < cn; i++ ) v.val[i] = saturate_cast<T2>(this->val[i]);
   1012     return v;
   1013 }
   1014 
   1015 template<typename _Tp, int cn> inline
   1016 const _Tp& Vec<_Tp, cn>::operator [](int i) const
   1017 {
   1018     CV_DbgAssert( (unsigned)i < (unsigned)cn );
   1019     return this->val[i];
   1020 }
   1021 
   1022 template<typename _Tp, int cn> inline
   1023 _Tp& Vec<_Tp, cn>::operator [](int i)
   1024 {
   1025     CV_DbgAssert( (unsigned)i < (unsigned)cn );
   1026     return this->val[i];
   1027 }
   1028 
   1029 template<typename _Tp, int cn> inline
   1030 const _Tp& Vec<_Tp, cn>::operator ()(int i) const
   1031 {
   1032     CV_DbgAssert( (unsigned)i < (unsigned)cn );
   1033     return this->val[i];
   1034 }
   1035 
   1036 template<typename _Tp, int cn> inline
   1037 _Tp& Vec<_Tp, cn>::operator ()(int i)
   1038 {
   1039     CV_DbgAssert( (unsigned)i < (unsigned)cn );
   1040     return this->val[i];
   1041 }
   1042 
   1043 template<typename _Tp, int cn> inline
   1044 Vec<_Tp, cn> normalize(const Vec<_Tp, cn>& v)
   1045 {
   1046     double nv = norm(v);
   1047     return v * (nv ? 1./nv : 0.);
   1048 }
   1049 
   1050 
   1051 
   1052 //////////////////////////////// matx comma initializer //////////////////////////////////
   1053 
   1054 
   1055 template<typename _Tp, typename _T2, int cn> static inline
   1056 VecCommaInitializer<_Tp, cn> operator << (const Vec<_Tp, cn>& vec, _T2 val)
   1057 {
   1058     VecCommaInitializer<_Tp, cn> commaInitializer((Vec<_Tp, cn>*)&vec);
   1059     return (commaInitializer, val);
   1060 }
   1061 
   1062 template<typename _Tp, int cn> inline
   1063 VecCommaInitializer<_Tp, cn>::VecCommaInitializer(Vec<_Tp, cn>* _vec)
   1064     : MatxCommaInitializer<_Tp, cn, 1>(_vec)
   1065 {}
   1066 
   1067 template<typename _Tp, int cn> template<typename _T2> inline
   1068 VecCommaInitializer<_Tp, cn>& VecCommaInitializer<_Tp, cn>::operator , (_T2 value)
   1069 {
   1070     CV_DbgAssert( this->idx < cn );
   1071     this->dst->val[this->idx++] = saturate_cast<_Tp>(value);
   1072     return *this;
   1073 }
   1074 
   1075 template<typename _Tp, int cn> inline
   1076 Vec<_Tp, cn> VecCommaInitializer<_Tp, cn>::operator *() const
   1077 {
   1078     CV_DbgAssert( this->idx == cn );
   1079     return *this->dst;
   1080 }
   1081 
   1082 //! @endcond
   1083 
   1084 ///////////////////////////// Matx out-of-class operators ////////////////////////////////
   1085 
   1086 //! @relates cv::Matx
   1087 //! @{
   1088 
   1089 template<typename _Tp1, typename _Tp2, int m, int n> static inline
   1090 Matx<_Tp1, m, n>& operator += (Matx<_Tp1, m, n>& a, const Matx<_Tp2, m, n>& b)
   1091 {
   1092     for( int i = 0; i < m*n; i++ )
   1093         a.val[i] = saturate_cast<_Tp1>(a.val[i] + b.val[i]);
   1094     return a;
   1095 }
   1096 
   1097 template<typename _Tp1, typename _Tp2, int m, int n> static inline
   1098 Matx<_Tp1, m, n>& operator -= (Matx<_Tp1, m, n>& a, const Matx<_Tp2, m, n>& b)
   1099 {
   1100     for( int i = 0; i < m*n; i++ )
   1101         a.val[i] = saturate_cast<_Tp1>(a.val[i] - b.val[i]);
   1102     return a;
   1103 }
   1104 
   1105 template<typename _Tp, int m, int n> static inline
   1106 Matx<_Tp, m, n> operator + (const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b)
   1107 {
   1108     return Matx<_Tp, m, n>(a, b, Matx_AddOp());
   1109 }
   1110 
   1111 template<typename _Tp, int m, int n> static inline
   1112 Matx<_Tp, m, n> operator - (const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b)
   1113 {
   1114     return Matx<_Tp, m, n>(a, b, Matx_SubOp());
   1115 }
   1116 
   1117 template<typename _Tp, int m, int n> static inline
   1118 Matx<_Tp, m, n>& operator *= (Matx<_Tp, m, n>& a, int alpha)
   1119 {
   1120     for( int i = 0; i < m*n; i++ )
   1121         a.val[i] = saturate_cast<_Tp>(a.val[i] * alpha);
   1122     return a;
   1123 }
   1124 
   1125 template<typename _Tp, int m, int n> static inline
   1126 Matx<_Tp, m, n>& operator *= (Matx<_Tp, m, n>& a, float alpha)
   1127 {
   1128     for( int i = 0; i < m*n; i++ )
   1129         a.val[i] = saturate_cast<_Tp>(a.val[i] * alpha);
   1130     return a;
   1131 }
   1132 
   1133 template<typename _Tp, int m, int n> static inline
   1134 Matx<_Tp, m, n>& operator *= (Matx<_Tp, m, n>& a, double alpha)
   1135 {
   1136     for( int i = 0; i < m*n; i++ )
   1137         a.val[i] = saturate_cast<_Tp>(a.val[i] * alpha);
   1138     return a;
   1139 }
   1140 
   1141 template<typename _Tp, int m, int n> static inline
   1142 Matx<_Tp, m, n> operator * (const Matx<_Tp, m, n>& a, int alpha)
   1143 {
   1144     return Matx<_Tp, m, n>(a, alpha, Matx_ScaleOp());
   1145 }
   1146 
   1147 template<typename _Tp, int m, int n> static inline
   1148 Matx<_Tp, m, n> operator * (const Matx<_Tp, m, n>& a, float alpha)
   1149 {
   1150     return Matx<_Tp, m, n>(a, alpha, Matx_ScaleOp());
   1151 }
   1152 
   1153 template<typename _Tp, int m, int n> static inline
   1154 Matx<_Tp, m, n> operator * (const Matx<_Tp, m, n>& a, double alpha)
   1155 {
   1156     return Matx<_Tp, m, n>(a, alpha, Matx_ScaleOp());
   1157 }
   1158 
   1159 template<typename _Tp, int m, int n> static inline
   1160 Matx<_Tp, m, n> operator * (int alpha, const Matx<_Tp, m, n>& a)
   1161 {
   1162     return Matx<_Tp, m, n>(a, alpha, Matx_ScaleOp());
   1163 }
   1164 
   1165 template<typename _Tp, int m, int n> static inline
   1166 Matx<_Tp, m, n> operator * (float alpha, const Matx<_Tp, m, n>& a)
   1167 {
   1168     return Matx<_Tp, m, n>(a, alpha, Matx_ScaleOp());
   1169 }
   1170 
   1171 template<typename _Tp, int m, int n> static inline
   1172 Matx<_Tp, m, n> operator * (double alpha, const Matx<_Tp, m, n>& a)
   1173 {
   1174     return Matx<_Tp, m, n>(a, alpha, Matx_ScaleOp());
   1175 }
   1176 
   1177 template<typename _Tp, int m, int n> static inline
   1178 Matx<_Tp, m, n> operator - (const Matx<_Tp, m, n>& a)
   1179 {
   1180     return Matx<_Tp, m, n>(a, -1, Matx_ScaleOp());
   1181 }
   1182 
   1183 template<typename _Tp, int m, int n, int l> static inline
   1184 Matx<_Tp, m, n> operator * (const Matx<_Tp, m, l>& a, const Matx<_Tp, l, n>& b)
   1185 {
   1186     return Matx<_Tp, m, n>(a, b, Matx_MatMulOp());
   1187 }
   1188 
   1189 template<typename _Tp, int m, int n> static inline
   1190 Vec<_Tp, m> operator * (const Matx<_Tp, m, n>& a, const Vec<_Tp, n>& b)
   1191 {
   1192     Matx<_Tp, m, 1> c(a, b, Matx_MatMulOp());
   1193     return (const Vec<_Tp, m>&)(c);
   1194 }
   1195 
   1196 template<typename _Tp, int m, int n> static inline
   1197 bool operator == (const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b)
   1198 {
   1199     for( int i = 0; i < m*n; i++ )
   1200         if( a.val[i] != b.val[i] ) return false;
   1201     return true;
   1202 }
   1203 
   1204 template<typename _Tp, int m, int n> static inline
   1205 bool operator != (const Matx<_Tp, m, n>& a, const Matx<_Tp, m, n>& b)
   1206 {
   1207     return !(a == b);
   1208 }
   1209 
   1210 //! @}
   1211 
   1212 ////////////////////////////// Vec out-of-class operators ////////////////////////////////
   1213 
   1214 //! @relates cv::Vec
   1215 //! @{
   1216 
   1217 template<typename _Tp1, typename _Tp2, int cn> static inline
   1218 Vec<_Tp1, cn>& operator += (Vec<_Tp1, cn>& a, const Vec<_Tp2, cn>& b)
   1219 {
   1220     for( int i = 0; i < cn; i++ )
   1221         a.val[i] = saturate_cast<_Tp1>(a.val[i] + b.val[i]);
   1222     return a;
   1223 }
   1224 
   1225 template<typename _Tp1, typename _Tp2, int cn> static inline
   1226 Vec<_Tp1, cn>& operator -= (Vec<_Tp1, cn>& a, const Vec<_Tp2, cn>& b)
   1227 {
   1228     for( int i = 0; i < cn; i++ )
   1229         a.val[i] = saturate_cast<_Tp1>(a.val[i] - b.val[i]);
   1230     return a;
   1231 }
   1232 
   1233 template<typename _Tp, int cn> static inline
   1234 Vec<_Tp, cn> operator + (const Vec<_Tp, cn>& a, const Vec<_Tp, cn>& b)
   1235 {
   1236     return Vec<_Tp, cn>(a, b, Matx_AddOp());
   1237 }
   1238 
   1239 template<typename _Tp, int cn> static inline
   1240 Vec<_Tp, cn> operator - (const Vec<_Tp, cn>& a, const Vec<_Tp, cn>& b)
   1241 {
   1242     return Vec<_Tp, cn>(a, b, Matx_SubOp());
   1243 }
   1244 
   1245 template<typename _Tp, int cn> static inline
   1246 Vec<_Tp, cn>& operator *= (Vec<_Tp, cn>& a, int alpha)
   1247 {
   1248     for( int i = 0; i < cn; i++ )
   1249         a[i] = saturate_cast<_Tp>(a[i]*alpha);
   1250     return a;
   1251 }
   1252 
   1253 template<typename _Tp, int cn> static inline
   1254 Vec<_Tp, cn>& operator *= (Vec<_Tp, cn>& a, float alpha)
   1255 {
   1256     for( int i = 0; i < cn; i++ )
   1257         a[i] = saturate_cast<_Tp>(a[i]*alpha);
   1258     return a;
   1259 }
   1260 
   1261 template<typename _Tp, int cn> static inline
   1262 Vec<_Tp, cn>& operator *= (Vec<_Tp, cn>& a, double alpha)
   1263 {
   1264     for( int i = 0; i < cn; i++ )
   1265         a[i] = saturate_cast<_Tp>(a[i]*alpha);
   1266     return a;
   1267 }
   1268 
   1269 template<typename _Tp, int cn> static inline
   1270 Vec<_Tp, cn>& operator /= (Vec<_Tp, cn>& a, int alpha)
   1271 {
   1272     double ialpha = 1./alpha;
   1273     for( int i = 0; i < cn; i++ )
   1274         a[i] = saturate_cast<_Tp>(a[i]*ialpha);
   1275     return a;
   1276 }
   1277 
   1278 template<typename _Tp, int cn> static inline
   1279 Vec<_Tp, cn>& operator /= (Vec<_Tp, cn>& a, float alpha)
   1280 {
   1281     float ialpha = 1.f/alpha;
   1282     for( int i = 0; i < cn; i++ )
   1283         a[i] = saturate_cast<_Tp>(a[i]*ialpha);
   1284     return a;
   1285 }
   1286 
   1287 template<typename _Tp, int cn> static inline
   1288 Vec<_Tp, cn>& operator /= (Vec<_Tp, cn>& a, double alpha)
   1289 {
   1290     double ialpha = 1./alpha;
   1291     for( int i = 0; i < cn; i++ )
   1292         a[i] = saturate_cast<_Tp>(a[i]*ialpha);
   1293     return a;
   1294 }
   1295 
   1296 template<typename _Tp, int cn> static inline
   1297 Vec<_Tp, cn> operator * (const Vec<_Tp, cn>& a, int alpha)
   1298 {
   1299     return Vec<_Tp, cn>(a, alpha, Matx_ScaleOp());
   1300 }
   1301 
   1302 template<typename _Tp, int cn> static inline
   1303 Vec<_Tp, cn> operator * (int alpha, const Vec<_Tp, cn>& a)
   1304 {
   1305     return Vec<_Tp, cn>(a, alpha, Matx_ScaleOp());
   1306 }
   1307 
   1308 template<typename _Tp, int cn> static inline
   1309 Vec<_Tp, cn> operator * (const Vec<_Tp, cn>& a, float alpha)
   1310 {
   1311     return Vec<_Tp, cn>(a, alpha, Matx_ScaleOp());
   1312 }
   1313 
   1314 template<typename _Tp, int cn> static inline
   1315 Vec<_Tp, cn> operator * (float alpha, const Vec<_Tp, cn>& a)
   1316 {
   1317     return Vec<_Tp, cn>(a, alpha, Matx_ScaleOp());
   1318 }
   1319 
   1320 template<typename _Tp, int cn> static inline
   1321 Vec<_Tp, cn> operator * (const Vec<_Tp, cn>& a, double alpha)
   1322 {
   1323     return Vec<_Tp, cn>(a, alpha, Matx_ScaleOp());
   1324 }
   1325 
   1326 template<typename _Tp, int cn> static inline
   1327 Vec<_Tp, cn> operator * (double alpha, const Vec<_Tp, cn>& a)
   1328 {
   1329     return Vec<_Tp, cn>(a, alpha, Matx_ScaleOp());
   1330 }
   1331 
   1332 template<typename _Tp, int cn> static inline
   1333 Vec<_Tp, cn> operator / (const Vec<_Tp, cn>& a, int alpha)
   1334 {
   1335     return Vec<_Tp, cn>(a, 1./alpha, Matx_ScaleOp());
   1336 }
   1337 
   1338 template<typename _Tp, int cn> static inline
   1339 Vec<_Tp, cn> operator / (const Vec<_Tp, cn>& a, float alpha)
   1340 {
   1341     return Vec<_Tp, cn>(a, 1.f/alpha, Matx_ScaleOp());
   1342 }
   1343 
   1344 template<typename _Tp, int cn> static inline
   1345 Vec<_Tp, cn> operator / (const Vec<_Tp, cn>& a, double alpha)
   1346 {
   1347     return Vec<_Tp, cn>(a, 1./alpha, Matx_ScaleOp());
   1348 }
   1349 
   1350 template<typename _Tp, int cn> static inline
   1351 Vec<_Tp, cn> operator - (const Vec<_Tp, cn>& a)
   1352 {
   1353     Vec<_Tp,cn> t;
   1354     for( int i = 0; i < cn; i++ ) t.val[i] = saturate_cast<_Tp>(-a.val[i]);
   1355     return t;
   1356 }
   1357 
   1358 template<typename _Tp> inline Vec<_Tp, 4> operator * (const Vec<_Tp, 4>& v1, const Vec<_Tp, 4>& v2)
   1359 {
   1360     return Vec<_Tp, 4>(saturate_cast<_Tp>(v1[0]*v2[0] - v1[1]*v2[1] - v1[2]*v2[2] - v1[3]*v2[3]),
   1361                        saturate_cast<_Tp>(v1[0]*v2[1] + v1[1]*v2[0] + v1[2]*v2[3] - v1[3]*v2[2]),
   1362                        saturate_cast<_Tp>(v1[0]*v2[2] - v1[1]*v2[3] + v1[2]*v2[0] + v1[3]*v2[1]),
   1363                        saturate_cast<_Tp>(v1[0]*v2[3] + v1[1]*v2[2] - v1[2]*v2[1] + v1[3]*v2[0]));
   1364 }
   1365 
   1366 template<typename _Tp> inline Vec<_Tp, 4>& operator *= (Vec<_Tp, 4>& v1, const Vec<_Tp, 4>& v2)
   1367 {
   1368     v1 = v1 * v2;
   1369     return v1;
   1370 }
   1371 
   1372 //! @}
   1373 
   1374 } // cv
   1375 
   1376 #endif // __OPENCV_CORE_MATX_HPP__
   1377