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#ifndef OPENCV_CORE_MAT_HPP
#define OPENCV_CORE_MAT_HPP

#ifndef __cplusplus
#error mat.hpp header must be compiled as C++
#endif

#include "opencv2/core/matx.hpp"
#include "opencv2/core/types.hpp"

#include "opencv2/core/bufferpool.hpp"

#include <array>
#include <type_traits>

namespace cv {

//! @addtogroup core_basic
//! @{

enum AccessFlag {
  ACCESS_READ = 1 << 24,
  ACCESS_WRITE = 1 << 25,
  ACCESS_RW = 3 << 24,
  ACCESS_MASK = ACCESS_RW,
  ACCESS_FAST = 1 << 26
};
CV_ENUM_FLAGS(AccessFlag)
__CV_ENUM_FLAGS_BITWISE_AND(AccessFlag, int, AccessFlag)

CV__DEBUG_NS_BEGIN

class CV_EXPORTS _OutputArray;

//////////////////////// Input/Output Array Arguments
////////////////////////////////////

/** @brief This is the proxy class for passing read-only input arrays into
OpenCV functions.

It is defined as:
@code
    typedef const _InputArray& InputArray;
@endcode
where \ref cv::_InputArray is a class that can be constructed from \ref cv::Mat,
\ref cv::Mat_<T>,
\ref cv::Matx<T, m, n>, std::vector<T>, std::vector<std::vector<T>>,
std::vector<Mat>, std::vector<Mat_<T>>, \ref cv::UMat, std::vector<UMat> or
`double`. It can also be constructed from a matrix expression.

Since this is mostly implementation-level class, and its interface may change in
future versions, we do not describe it in details. There are a few key things,
though, that should be kept in mind:

-   When you see in the reference manual or in OpenCV source code a function
that takes InputArray, it means that you can actually pass `Mat`, `Matx`,
`vector<T>` etc. (see above the complete list).
-   Optional input arguments: If some of the input arrays may be empty, pass
cv::noArray() (or simply cv::Mat() as you probably did before).
-   The class is designed solely for passing parameters. That is, normally you
*should not* declare class members, local and global variables of this type.
-   If you want to design your own function or a class method that can operate
of arrays of multiple types, you can use InputArray (or OutputArray) for the
respective parameters. Inside a function you should use _InputArray::getMat()
method to construct a matrix header for the array (without copying data).
_InputArray::kind() can be used to distinguish Mat from `vector<>` etc., but
normally it is not needed.

Here is how you can use a function that takes InputArray :
@code
    std::vector<Point2f> vec;
    // points or a circle
    for( int i = 0; i < 30; i++ )
        vec.push_back(Point2f((float)(100 + 30*cos(i*CV_PI*2/5)),
                              (float)(100 - 30*sin(i*CV_PI*2/5))));
    cv::transform(vec, vec, cv::Matx23f(0.707, -0.707, 10, 0.707, 0.707, 20));
@endcode
That is, we form an STL vector containing points, and apply in-place affine
transformation to the vector using the 2x3 matrix created inline as `Matx<float,
2, 3>` instance.

Here is how such a function can be implemented (for simplicity, we implement a
very specific case of it, according to the assertion statement inside) :
@code
    void myAffineTransform(InputArray _src, OutputArray _dst, InputArray _m)
    {
        // get Mat headers for input arrays. This is O(1) operation,
        // unless _src and/or _m are matrix expressions.
        Mat src = _src.getMat(), m = _m.getMat();
        CV_Assert( src.type() == CV_32FC2 && m.type() == CV_32F && m.size() ==
Size(3, 2) );

        // [re]create the output array so that it has the proper size and type.
        // In case of Mat it calls Mat::create, in case of STL vector it calls
vector::resize. _dst.create(src.size(), src.type()); Mat dst = _dst.getMat();

        for( int i = 0; i < src.rows; i++ )
            for( int j = 0; j < src.cols; j++ )
            {
                Point2f pt = src.at<Point2f>(i, j);
                dst.at<Point2f>(i, j) = Point2f(m.at<float>(0, 0)*pt.x +
                                                m.at<float>(0, 1)*pt.y +
                                                m.at<float>(0, 2),
                                                m.at<float>(1, 0)*pt.x +
                                                m.at<float>(1, 1)*pt.y +
                                                m.at<float>(1, 2));
            }
    }
@endcode
There is another related type, InputArrayOfArrays, which is currently defined as
a synonym for InputArray:
@code
    typedef InputArray InputArrayOfArrays;
@endcode
It denotes function arguments that are either vectors of vectors or vectors of
matrices. A separate synonym is needed to generate Python/Java etc. wrappers
properly. At the function implementation level their use is similar, but
_InputArray::getMat(idx) should be used to get header for the idx-th component
of the outer vector and _InputArray::size().area() should be used to find the
number of components (vectors/matrices) of the outer vector.

In general, type support is limited to cv::Mat types. Other types are forbidden.
But in some cases we need to support passing of custom non-general Mat types,
like arrays of cv::KeyPoint, cv::DMatch, etc. This data is not intended to be
interpreted as an image data, or processed somehow like regular cv::Mat. To pass
such custom type use rawIn() / rawOut() / rawInOut() wrappers. Custom type is
wrapped as Mat-compatible `CV_8UC<N>` values (N = sizeof(T), N <= CV_CN_MAX).
 */
class CV_EXPORTS _InputArray {
public:
  enum KindFlag {
    KIND_SHIFT = 16,
    FIXED_TYPE = 0x8000 << KIND_SHIFT,
    FIXED_SIZE = 0x4000 << KIND_SHIFT,
    KIND_MASK = 31 << KIND_SHIFT,

    NONE = 0 << KIND_SHIFT,
    MAT = 1 << KIND_SHIFT,
    MATX = 2 << KIND_SHIFT,
    STD_VECTOR = 3 << KIND_SHIFT,
    STD_VECTOR_VECTOR = 4 << KIND_SHIFT,
    STD_VECTOR_MAT = 5 << KIND_SHIFT,
#if OPENCV_ABI_COMPATIBILITY < 500
    EXPR =
        6
        << KIND_SHIFT, //!< removed: https://github.com/opencv/opencv/pull/17046
#endif
    STD_BOOL_VECTOR = 12 << KIND_SHIFT,
#if OPENCV_ABI_COMPATIBILITY < 500
    STD_ARRAY =
        14 << KIND_SHIFT, //!< removed:
                          //!< https://github.com/opencv/opencv/issues/18897
#endif
    STD_ARRAY_MAT = 15 << KIND_SHIFT
  };

  _InputArray();
  _InputArray(int _flags, void *_obj);
  _InputArray(const Mat &m);
  _InputArray(const MatExpr &expr);
  _InputArray(const std::vector<Mat> &vec);
  template <typename _Tp> _InputArray(const Mat_<_Tp> &m);
  template <typename _Tp> _InputArray(const std::vector<_Tp> &vec);
  _InputArray(const std::vector<bool> &vec);
  template <typename _Tp> _InputArray(const std::vector<std::vector<_Tp>> &vec);
  _InputArray(const std::vector<std::vector<bool>> &) = delete; // not supported
  template <typename _Tp> _InputArray(const std::vector<Mat_<_Tp>> &vec);
  template <typename _Tp> _InputArray(const _Tp *vec, int n);
  template <typename _Tp, int m, int n>
  _InputArray(const Matx<_Tp, m, n> &matx);
  _InputArray(const double &val);

  template <typename _Tp, std::size_t _Nm>
  _InputArray(const std::array<_Tp, _Nm> &arr);
  template <std::size_t _Nm> _InputArray(const std::array<Mat, _Nm> &arr);

  template <typename _Tp> static _InputArray rawIn(const std::vector<_Tp> &vec);
  template <typename _Tp, std::size_t _Nm>
  static _InputArray rawIn(const std::array<_Tp, _Nm> &arr);

  Mat getMat(int idx = -1) const;
  Mat getMat_(int idx = -1) const;
  void getMatVector(std::vector<Mat> &mv) const;

  int getFlags() const;
  void *getObj() const;
  Size getSz() const;

  _InputArray::KindFlag kind() const;
  int dims(int i = -1) const;
  int cols(int i = -1) const;
  int rows(int i = -1) const;
  Size size(int i = -1) const;
  int sizend(int *sz, int i = -1) const;
  bool sameSize(const _InputArray &arr) const;
  size_t total(int i = -1) const;
  int type(int i = -1) const;
  int depth(int i = -1) const;
  int channels(int i = -1) const;
  bool isContinuous(int i = -1) const;
  bool isSubmatrix(int i = -1) const;
  bool empty() const;
  void copyTo(const _OutputArray &arr) const;
  void copyTo(const _OutputArray &arr, const _InputArray &mask) const;
  size_t offset(int i = -1) const;
  size_t step(int i = -1) const;
  bool isMat() const;
  bool isMatVector() const;
  bool isMatx() const;
  bool isVector() const;
  ~_InputArray();

protected:
  int flags;
  void *obj;
  Size sz;

  void init(int _flags, const void *_obj);
  void init(int _flags, const void *_obj, Size _sz);
};
CV_ENUM_FLAGS(_InputArray::KindFlag)
__CV_ENUM_FLAGS_BITWISE_AND(_InputArray::KindFlag, int, _InputArray::KindFlag)

/** @brief This type is very similar to InputArray except that it is used for
input/output and output function parameters.

Just like with InputArray, OpenCV users should not care about OutputArray, they
just pass `Mat`, `vector<T>` etc. to the functions. The same limitation as for
`InputArray`: *Do not explicitly create OutputArray instances* applies here too.

If you want to make your function polymorphic (i.e. accept different arrays as
output parameters), it is also not very difficult. Take the sample above as the
reference. Note that _OutputArray::create() needs to be called before
_OutputArray::getMat(). This way you guarantee that the output array is properly
allocated.

Optional output parameters. If you do not need certain output array to be
computed and returned to you, pass cv::noArray(), just like you would in the
case of optional input array. At the implementation level, use
_OutputArray::needed() to check if certain output array needs to be computed or
not.

There are several synonyms for OutputArray that are used to assist automatic
Python/Java/... wrapper generators:
@code
    typedef OutputArray OutputArrayOfArrays;
    typedef OutputArray InputOutputArray;
    typedef OutputArray InputOutputArrayOfArrays;
@endcode
 */
class CV_EXPORTS _OutputArray : public _InputArray {
public:
  enum DepthMask {
    DEPTH_MASK_8U = 1 << CV_8U,
    DEPTH_MASK_8S = 1 << CV_8S,
    DEPTH_MASK_16U = 1 << CV_16U,
    DEPTH_MASK_16S = 1 << CV_16S,
    DEPTH_MASK_32S = 1 << CV_32S,
    DEPTH_MASK_32F = 1 << CV_32F,
    DEPTH_MASK_64F = 1 << CV_64F,
    DEPTH_MASK_16F = 1 << CV_16F,
    DEPTH_MASK_ALL = (DEPTH_MASK_64F << 1) - 1,
    DEPTH_MASK_ALL_BUT_8S = DEPTH_MASK_ALL & ~DEPTH_MASK_8S,
    DEPTH_MASK_ALL_16F = (DEPTH_MASK_16F << 1) - 1,
    DEPTH_MASK_FLT = DEPTH_MASK_32F + DEPTH_MASK_64F
  };

  _OutputArray();
  _OutputArray(int _flags, void *_obj);
  _OutputArray(Mat &m);
  _OutputArray(std::vector<Mat> &vec);
  template <typename _Tp> _OutputArray(std::vector<_Tp> &vec);
  _OutputArray(std::vector<bool> &vec) = delete; // not supported
  template <typename _Tp> _OutputArray(std::vector<std::vector<_Tp>> &vec);
  _OutputArray(std::vector<std::vector<bool>> &) = delete; // not supported
  template <typename _Tp> _OutputArray(std::vector<Mat_<_Tp>> &vec);
  template <typename _Tp> _OutputArray(Mat_<_Tp> &m);
  template <typename _Tp> _OutputArray(_Tp *vec, int n);
  template <typename _Tp, int m, int n> _OutputArray(Matx<_Tp, m, n> &matx);

  _OutputArray(const Mat &m);
  _OutputArray(const std::vector<Mat> &vec);
  template <typename _Tp> _OutputArray(const std::vector<_Tp> &vec);
  template <typename _Tp>
  _OutputArray(const std::vector<std::vector<_Tp>> &vec);
  template <typename _Tp> _OutputArray(const std::vector<Mat_<_Tp>> &vec);
  template <typename _Tp> _OutputArray(const Mat_<_Tp> &m);
  template <typename _Tp> _OutputArray(const _Tp *vec, int n);
  template <typename _Tp, int m, int n>
  _OutputArray(const Matx<_Tp, m, n> &matx);

  template <typename _Tp, std::size_t _Nm>
  _OutputArray(std::array<_Tp, _Nm> &arr);
  template <typename _Tp, std::size_t _Nm>
  _OutputArray(const std::array<_Tp, _Nm> &arr);
  template <std::size_t _Nm> _OutputArray(std::array<Mat, _Nm> &arr);
  template <std::size_t _Nm> _OutputArray(const std::array<Mat, _Nm> &arr);

  template <typename _Tp> static _OutputArray rawOut(std::vector<_Tp> &vec);
  template <typename _Tp, std::size_t _Nm>
  static _OutputArray rawOut(std::array<_Tp, _Nm> &arr);

  bool fixedSize() const;
  bool fixedType() const;
  bool needed() const;
  Mat &getMatRef(int i = -1) const;
  void create(Size sz, int type, int i = -1, bool allowTransposed = false,
              _OutputArray::DepthMask fixedDepthMask =
                  static_cast<_OutputArray::DepthMask>(0)) const;
  void create(int rows, int cols, int type, int i = -1,
              bool allowTransposed = false,
              _OutputArray::DepthMask fixedDepthMask =
                  static_cast<_OutputArray::DepthMask>(0)) const;
  void create(int dims, const int *size, int type, int i = -1,
              bool allowTransposed = false,
              _OutputArray::DepthMask fixedDepthMask =
                  static_cast<_OutputArray::DepthMask>(0)) const;
  void createSameSize(const _InputArray &arr, int mtype) const;
  void release() const;
  void clear() const;
  void setTo(const _InputArray &value,
             const _InputArray &mask = _InputArray()) const;

  void assign(const Mat &m) const;

  void assign(const std::vector<Mat> &v) const;

  void move(Mat &m) const;
};

class CV_EXPORTS _InputOutputArray : public _OutputArray {
public:
  _InputOutputArray();
  _InputOutputArray(int _flags, void *_obj);
  _InputOutputArray(Mat &m);
  _InputOutputArray(std::vector<Mat> &vec);
  template <typename _Tp> _InputOutputArray(std::vector<_Tp> &vec);
  _InputOutputArray(std::vector<bool> &vec) = delete; // not supported
  template <typename _Tp> _InputOutputArray(std::vector<std::vector<_Tp>> &vec);
  template <typename _Tp> _InputOutputArray(std::vector<Mat_<_Tp>> &vec);
  template <typename _Tp> _InputOutputArray(Mat_<_Tp> &m);
  template <typename _Tp> _InputOutputArray(_Tp *vec, int n);
  template <typename _Tp, int m, int n>
  _InputOutputArray(Matx<_Tp, m, n> &matx);

  _InputOutputArray(const Mat &m);
  _InputOutputArray(const std::vector<Mat> &vec);
  template <typename _Tp> _InputOutputArray(const std::vector<_Tp> &vec);
  template <typename _Tp>
  _InputOutputArray(const std::vector<std::vector<_Tp>> &vec);
  template <typename _Tp> _InputOutputArray(const std::vector<Mat_<_Tp>> &vec);
  template <typename _Tp> _InputOutputArray(const Mat_<_Tp> &m);
  template <typename _Tp> _InputOutputArray(const _Tp *vec, int n);
  template <typename _Tp, int m, int n>
  _InputOutputArray(const Matx<_Tp, m, n> &matx);

  template <typename _Tp, std::size_t _Nm>
  _InputOutputArray(std::array<_Tp, _Nm> &arr);
  template <typename _Tp, std::size_t _Nm>
  _InputOutputArray(const std::array<_Tp, _Nm> &arr);
  template <std::size_t _Nm> _InputOutputArray(std::array<Mat, _Nm> &arr);
  template <std::size_t _Nm> _InputOutputArray(const std::array<Mat, _Nm> &arr);

  template <typename _Tp>
  static _InputOutputArray rawInOut(std::vector<_Tp> &vec);
  template <typename _Tp, std::size_t _Nm>
  _InputOutputArray rawInOut(std::array<_Tp, _Nm> &arr);
};

/** Helper to wrap custom types. @see InputArray */
template <typename _Tp> static inline _InputArray rawIn(_Tp &v);
/** Helper to wrap custom types. @see InputArray */
template <typename _Tp> static inline _OutputArray rawOut(_Tp &v);
/** Helper to wrap custom types. @see InputArray */
template <typename _Tp> static inline _InputOutputArray rawInOut(_Tp &v);

CV__DEBUG_NS_END

typedef const _InputArray &InputArray;
typedef InputArray InputArrayOfArrays;
typedef const _OutputArray &OutputArray;
typedef OutputArray OutputArrayOfArrays;
typedef const _InputOutputArray &InputOutputArray;
typedef InputOutputArray InputOutputArrayOfArrays;

/** @brief Returns an empty InputArray or OutputArray.

 This function is used to provide an "empty" or "null" array when certain
 functions take optional input or output arrays that you don't want to provide.

 Many OpenCV functions accept optional arguments as `cv::InputArray` or
 `cv::OutputArray`. When you don't want to pass any data for these optional
 parameters, you can use `cv::noArray()` to indicate that you are omitting them.

 @return An empty `cv::InputArray` or `cv::OutputArray` that can be used as a
 placeholder.

 @note This is often used when a function has optional arrays, and you do not
 want to provide a specific input or output array.

 @see cv::InputArray, cv::OutputArray
 */
CV_EXPORTS InputOutputArray noArray();

/////////////////////////////////// MatAllocator
/////////////////////////////////////////

/** @brief  Usage flags for allocator

 @warning  All flags except `USAGE_DEFAULT` are experimental.

 @warning  For the OpenCL allocator, `USAGE_ALLOCATE_SHARED_MEMORY` depends on
 OpenCV's optional, experimental integration with OpenCL SVM. To enable this
 integration, build OpenCV using the `WITH_OPENCL_SVM=ON` CMake option and, at
 runtime, call `cv::ocl::Context::getDefault().setUseSVM(true);` or similar
 code. Note that SVM is incompatible with OpenCL 1.x.
*/
enum UMatUsageFlags {
  USAGE_DEFAULT = 0,

  // buffer allocation policy is platform and usage specific
  USAGE_ALLOCATE_HOST_MEMORY = 1 << 0,
  USAGE_ALLOCATE_DEVICE_MEMORY = 1 << 1,
  USAGE_ALLOCATE_SHARED_MEMORY =
      1 << 2, // It is not equal to: USAGE_ALLOCATE_HOST_MEMORY |
              // USAGE_ALLOCATE_DEVICE_MEMORY

  __UMAT_USAGE_FLAGS_32BIT = 0x7fffffff // Binary compatibility hint
};

struct CV_EXPORTS UMatData;

/** @brief  Custom array allocator
 */
class CV_EXPORTS MatAllocator {
public:
  MatAllocator() {}
  virtual ~MatAllocator() {}

  // let's comment it off for now to detect and fix all the uses of allocator
  // virtual void allocate(int dims, const int* sizes, int type, int*& refcount,
  //                      uchar*& datastart, uchar*& data, size_t* step) = 0;
  // virtual void deallocate(int* refcount, uchar* datastart, uchar* data) = 0;
  virtual UMatData *allocate(int dims, const int *sizes, int type, void *data,
                             size_t *step, AccessFlag flags,
                             UMatUsageFlags usageFlags) const = 0;
  virtual bool allocate(UMatData *data, AccessFlag accessflags,
                        UMatUsageFlags usageFlags) const = 0;
  virtual void deallocate(UMatData *data) const = 0;
  virtual void map(UMatData *data, AccessFlag accessflags) const;
  virtual void unmap(UMatData *data) const;
  virtual void download(UMatData *data, void *dst, int dims, const size_t sz[],
                        const size_t srcofs[], const size_t srcstep[],
                        const size_t dststep[]) const;
  virtual void upload(UMatData *data, const void *src, int dims,
                      const size_t sz[], const size_t dstofs[],
                      const size_t dststep[], const size_t srcstep[]) const;
  virtual void copy(UMatData *srcdata, UMatData *dstdata, int dims,
                    const size_t sz[], const size_t srcofs[],
                    const size_t srcstep[], const size_t dstofs[],
                    const size_t dststep[], bool sync) const;

  // default implementation returns DummyBufferPoolController
  virtual BufferPoolController *
  getBufferPoolController(const char *id = NULL) const;
};

//////////////////////////////// MatCommaInitializer
/////////////////////////////////////

/** @brief  Comma-separated Matrix Initializer

 The class instances are usually not created explicitly.
 Instead, they are created on "matrix << firstValue" operator.

 The sample below initializes 2x2 rotation matrix:

 \code
 double angle = 30, a = cos(angle*CV_PI/180), b = sin(angle*CV_PI/180);
 Mat R = (Mat_<double>(2,2) << a, -b, b, a);
 \endcode
*/
template <typename _Tp> class MatCommaInitializer_ {
public:
  //! the constructor, created by "matrix << firstValue" operator, where matrix
  //! is cv::Mat
  MatCommaInitializer_(Mat_<_Tp> *_m);
  //! the operator that takes the next value and put it to the matrix
  template <typename T2> MatCommaInitializer_<_Tp> &operator,(T2 v);
  //! another form of conversion operator
  operator Mat_<_Tp>() const;

protected:
  MatIterator_<_Tp> it;
};

/////////////////////////////////////// Mat
//////////////////////////////////////////////

// note that umatdata might be allocated together
// with the matrix data, not as a separate object.
// therefore, it does not have constructor or destructor;
// it should be explicitly initialized using init().
struct CV_EXPORTS UMatData {
  enum MemoryFlag {
    COPY_ON_MAP = 1,
    HOST_COPY_OBSOLETE = 2,
    DEVICE_COPY_OBSOLETE = 4,
    TEMP_UMAT = 8,
    TEMP_COPIED_UMAT = 24,
    USER_ALLOCATED = 32,
    DEVICE_MEM_MAPPED = 64,
    ASYNC_CLEANUP = 128
  };
  UMatData(const MatAllocator *allocator);
  ~UMatData();

  // provide atomic access to the structure
  void lock();
  void unlock();

  bool hostCopyObsolete() const;
  bool deviceCopyObsolete() const;
  bool deviceMemMapped() const;
  bool copyOnMap() const;
  bool tempUMat() const;
  bool tempCopiedUMat() const;
  void markHostCopyObsolete(bool flag);
  void markDeviceCopyObsolete(bool flag);
  void markDeviceMemMapped(bool flag);

  const MatAllocator *prevAllocator;
  const MatAllocator *currAllocator;
  int urefcount;
  int refcount;
  uchar *data;
  uchar *origdata;
  size_t size;

  UMatData::MemoryFlag flags;
  void *handle;
  void *userdata;
  int allocatorFlags_;
  int mapcount;
  UMatData *originalUMatData;
  std::shared_ptr<void> allocatorContext;
};
CV_ENUM_FLAGS(UMatData::MemoryFlag)

struct CV_EXPORTS MatSize {
  explicit MatSize(int *_p) CV_NOEXCEPT;
  int dims() const CV_NOEXCEPT;
  Size operator()() const;
  const int &operator[](int i) const;
  int &operator[](int i);
  operator const int *() const CV_NOEXCEPT; // TODO OpenCV 4.0: drop this
  bool operator==(const MatSize &sz) const CV_NOEXCEPT;
  bool operator!=(const MatSize &sz) const CV_NOEXCEPT;

  int *p;
};

struct CV_EXPORTS MatStep {
  MatStep() CV_NOEXCEPT;
  explicit MatStep(size_t s) CV_NOEXCEPT;
  const size_t &operator[](int i) const CV_NOEXCEPT;
  size_t &operator[](int i) CV_NOEXCEPT;
  operator size_t() const;
  MatStep &operator=(size_t s);

  size_t *p;
  size_t buf[2];

protected:
  MatStep &operator=(const MatStep &);
};

/** @example samples/cpp/cout_mat.cpp
An example demonstrating the serial out capabilities of cv::Mat
*/

/** @brief n-dimensional dense array class \anchor CVMat_Details

The class Mat represents an n-dimensional dense numerical single-channel or
multi-channel array. It can be used to store real or complex-valued vectors and
matrices, grayscale or color images, voxel volumes, vector fields, point clouds,
tensors, histograms (though, very high-dimensional histograms may be better
stored in a SparseMat ). The data layout of the array `M` is defined by the
array `M.step[]`, so that the address of element \f$(i_0,...,i_{M.dims-1})\f$,
where \f$0\leq i_k<M.size[k]\f$, is computed as:
\f[addr(M_{i_0,...,i_{M.dims-1}}) = M.data + M.step[0]*i_0 + M.step[1]*i_1 + ...
+ M.step[M.dims-1]*i_{M.dims-1}\f] In case of a 2-dimensional array, the above
formula is reduced to:
\f[addr(M_{i,j}) = M.data + M.step[0]*i + M.step[1]*j\f]
Note that `M.step[i] >= M.step[i+1]` (in fact, `M.step[i] >=
M.step[i+1]*M.size[i+1]` ). This means that 2-dimensional matrices are stored
row-by-row, 3-dimensional matrices are stored plane-by-plane, and so on.
M.step[M.dims-1] is minimal and always equal to the element size M.elemSize() .

So, the data layout in Mat is compatible with the majority of dense array types
from the standard toolkits and SDKs, such as Numpy (ndarray), Win32 (independent
device bitmaps), and others, that is, with any array that uses *steps* (or
*strides*) to compute the position of a pixel. Due to this compatibility, it is
possible to make a Mat header for user-allocated data and process it in-place
using OpenCV functions.

There are many different ways to create a Mat object. The most popular options
are listed below:

- Use the create(nrows, ncols, type) method or the similar Mat(nrows, ncols,
type[, fillValue]) constructor. A new array of the specified size and type is
allocated. type has the same meaning as in the cvCreateMat method. For example,
CV_8UC1 means a 8-bit single-channel array, CV_32FC2 means a 2-channel (complex)
floating-point array, and so on.
@code
   // make a 7x7 complex matrix filled with 1+3j.
   Mat M(7,7,CV_32FC2,Scalar(1,3));
   // and now turn M to a 100x60 15-channel 8-bit matrix.
   // The old content will be deallocated
   M.create(100,60,CV_8UC(15));
@endcode
As noted in the introduction to this chapter, create() allocates only a new
array when the shape or type of the current array are different from the
specified ones.

- Create a multi-dimensional array:
@code
   // create a 100x100x100 8-bit array
   int sz[] = {100, 100, 100};
   Mat bigCube(3, sz, CV_8U, Scalar::all(0));
@endcode
It passes the number of dimensions =1 to the Mat constructor but the created
array will be 2-dimensional with the number of columns set to 1. So, Mat::dims
is always \>= 2 (can also be 0 when the array is empty).

- Use a copy constructor or assignment operator where there can be an array or
expression on the right side (see below). As noted in the introduction, the
array assignment is an O(1) operation because it only copies the header and
increases the reference counter. The Mat::clone() method can be used to get a
full (deep) copy of the array when you need it.

- Construct a header for a part of another array. It can be a single row, single
column, several rows, several columns, rectangular region in the array (called a
*minor* in algebra) or a diagonal. Such operations are also O(1) because the new
header references the same data. You can actually modify a part of the array
using this feature, for example:
@code
   // add the 5-th row, multiplied by 3 to the 3rd row
   M.row(3) = M.row(3) + M.row(5)*3;
   // now copy the 7-th column to the 1-st column
   // M.col(1) = M.col(7); // this will not work
   Mat M1 = M.col(1);
   M.col(7).copyTo(M1);
   // create a new 320x240 image
   Mat img(Size(320,240),CV_8UC3);
   // select a ROI
   Mat roi(img, Rect(10,10,100,100));
   // fill the ROI with (0,255,0) (which is green in RGB space);
   // the original 320x240 image will be modified
   roi = Scalar(0,255,0);
@endcode
Due to the additional datastart and dataend members, it is possible to compute a
relative sub-array position in the main *container* array using locateROI():
@code
   Mat A = Mat::eye(10, 10, CV_32S);
   // extracts A columns, 1 (inclusive) to 3 (exclusive).
   Mat B = A(Range::all(), Range(1, 3));
   // extracts B rows, 5 (inclusive) to 9 (exclusive).
   // that is, C \~ A(Range(5, 9), Range(1, 3))
   Mat C = B(Range(5, 9), Range::all());
   Size size; Point ofs;
   C.locateROI(size, ofs);
   // size will be (width=10,height=10) and the ofs will be (x=1, y=5)
@endcode
As in case of whole matrices, if you need a deep copy, use the `clone()` method
of the extracted sub-matrices.

- Make a header for user-allocated data. It can be useful to do the following:
   -# Process "foreign" data using OpenCV (for example, when you implement a
DirectShow\* filter or a processing module for gstreamer, and so on). For
example:
   @code
       Mat process_video_frame(const unsigned char* pixels,
                               int width, int height, int step)
       {
           // wrap input buffer
           Mat img(height, width, CV_8UC3, (unsigned char*)pixels, step);

           Mat result;
           GaussianBlur(img, result, Size(7, 7), 1.5, 1.5);

           return result;
       }
   @endcode
   -# Quickly initialize small matrices and/or get a super-fast element access.
   @code
       double m[3][3] = {{a, b, c}, {d, e, f}, {g, h, i}};
       Mat M = Mat(3, 3, CV_64F, m).inv();
   @endcode
   .

- Use MATLAB-style array initializers, zeros(), ones(), eye(), for example:
@code
   // create a double-precision identity matrix and add it to M.
   M += Mat::eye(M.rows, M.cols, CV_64F);
@endcode

- Use a comma-separated initializer:
@code
   // create a 3x3 double-precision identity matrix
   Mat M = (Mat_<double>(3,3) << 1, 0, 0, 0, 1, 0, 0, 0, 1);
@endcode
With this approach, you first call a constructor of the Mat class with the
proper parameters, and then you just put `<< operator` followed by
comma-separated values that can be constants, variables, expressions, and so on.
Also, note the extra parentheses required to avoid compilation errors.

Once the array is created, it is automatically managed via a reference-counting
mechanism. If the array header is built on top of user-allocated data, you
should handle the data by yourself. The array data is deallocated when no one
points to it. If you want to release the data pointed by a array header before
the array destructor is called, use Mat::release().

The next important thing to learn about the array class is element access. This
manual already described how to compute an address of each array element.
Normally, you are not required to use the formula directly in the code. If you
know the array element type (which can be retrieved using the method Mat::type()
), you can access the element \f$M_{ij}\f$ of a 2-dimensional array as:
@code
   M.at<double>(i,j) += 1.f;
@endcode
assuming that `M` is a double-precision floating-point array. There are several
variants of the method at for a different number of dimensions.

If you need to process a whole row of a 2D array, the most efficient way is to
get the pointer to the row first, and then just use the plain C operator [] :
@code
   // compute sum of positive matrix elements
   // (assuming that M is a double-precision matrix)
   double sum=0;
   for(int i = 0; i < M.rows; i++)
   {
       const double* Mi = M.ptr<double>(i);
       for(int j = 0; j < M.cols; j++)
           sum += std::max(Mi[j], 0.);
   }
@endcode
Some operations, like the one above, do not actually depend on the array shape.
They just process elements of an array one by one (or elements from multiple
arrays that have the same coordinates, for example, array addition). Such
operations are called *element-wise*. It makes sense to check whether all the
input/output arrays are continuous, namely, have no gaps at the end of each row.
If yes, process them as a long single row:
@code
   // compute the sum of positive matrix elements, optimized variant
   double sum=0;
   int cols = M.cols, rows = M.rows;
   if(M.isContinuous())
   {
       cols *= rows;
       rows = 1;
   }
   for(int i = 0; i < rows; i++)
   {
       const double* Mi = M.ptr<double>(i);
       for(int j = 0; j < cols; j++)
           sum += std::max(Mi[j], 0.);
   }
@endcode
In case of the continuous matrix, the outer loop body is executed just once. So,
the overhead is smaller, which is especially noticeable in case of small
matrices.

Finally, there are STL-style iterators that are smart enough to skip gaps
between successive rows:
@code
   // compute sum of positive matrix elements, iterator-based variant
   double sum=0;
   MatConstIterator_<double> it = M.begin<double>(), it_end = M.end<double>();
   for(; it != it_end; ++it)
       sum += std::max(*it, 0.);
@endcode
The matrix iterators are random-access iterators, so they can be passed to any
STL algorithm, including std::sort().

@note Matrix Expressions and arithmetic see MatExpr
*/
class CV_EXPORTS Mat {
public:
  /**
  These are various constructors that form a matrix. As noted in the
  AutomaticAllocation, often the default constructor is enough, and the proper
  matrix will be allocated by an OpenCV function. The constructed matrix can
  further be assigned to another matrix or matrix expression or can be allocated
  with Mat::create . In the former case, the old content is de-referenced.
   */
  Mat() CV_NOEXCEPT;

  /** @overload
  @param rows Number of rows in a 2D array.
  @param cols Number of columns in a 2D array.
  @param type Array type. Use CV_8UC1, ..., CV_64FC4 to create 1-4 channel
  matrices, or CV_8UC(n), ..., CV_64FC(n) to create multi-channel (up to
  CV_CN_MAX channels) matrices.
  */
  Mat(int rows, int cols, int type);

  /** @overload
  @param size 2D array size: Size(cols, rows) . In the Size() constructor, the
  number of rows and the number of columns go in the reverse order.
  @param type Array type. Use CV_8UC1, ..., CV_64FC4 to create 1-4 channel
  matrices, or CV_8UC(n), ..., CV_64FC(n) to create multi-channel (up to
  CV_CN_MAX channels) matrices.
    */
  Mat(Size size, int type);

  /** @overload
  @param rows Number of rows in a 2D array.
  @param cols Number of columns in a 2D array.
  @param type Array type. Use CV_8UC1, ..., CV_64FC4 to create 1-4 channel
  matrices, or CV_8UC(n), ..., CV_64FC(n) to create multi-channel (up to
  CV_CN_MAX channels) matrices.
  @param s An optional value to initialize each matrix element with. To set all
  the matrix elements to the particular value after the construction, use the
  assignment operator Mat::operator=(const Scalar& value) .
  */
  Mat(int rows, int cols, int type, const Scalar &s);

  /** @overload
  @param size 2D array size: Size(cols, rows) . In the Size() constructor, the
  number of rows and the number of columns go in the reverse order.
  @param type Array type. Use CV_8UC1, ..., CV_64FC4 to create 1-4 channel
  matrices, or CV_8UC(n), ..., CV_64FC(n) to create multi-channel (up to
  CV_CN_MAX channels) matrices.
  @param s An optional value to initialize each matrix element with. To set all
  the matrix elements to the particular value after the construction, use the
  assignment operator Mat::operator=(const Scalar& value) .
    */
  Mat(Size size, int type, const Scalar &s);

  /** @overload
  @param ndims Array dimensionality.
  @param sizes Array of integers specifying an n-dimensional array shape.
  @param type Array type. Use CV_8UC1, ..., CV_64FC4 to create 1-4 channel
  matrices, or CV_8UC(n), ..., CV_64FC(n) to create multi-channel (up to
  CV_CN_MAX channels) matrices.
  */
  Mat(int ndims, const int *sizes, int type);

  /** @overload
  @param sizes Array of integers specifying an n-dimensional array shape.
  @param type Array type. Use CV_8UC1, ..., CV_64FC4 to create 1-4 channel
  matrices, or CV_8UC(n), ..., CV_64FC(n) to create multi-channel (up to
  CV_CN_MAX channels) matrices.
  */
  Mat(const std::vector<int> &sizes, int type);

  /** @overload
  @param ndims Array dimensionality.
  @param sizes Array of integers specifying an n-dimensional array shape.
  @param type Array type. Use CV_8UC1, ..., CV_64FC4 to create 1-4 channel
  matrices, or CV_8UC(n), ..., CV_64FC(n) to create multi-channel (up to
  CV_CN_MAX channels) matrices.
  @param s An optional value to initialize each matrix element with. To set all
  the matrix elements to the particular value after the construction, use the
  assignment operator Mat::operator=(const Scalar& value) .
  */
  Mat(int ndims, const int *sizes, int type, const Scalar &s);

  /** @overload
  @param sizes Array of integers specifying an n-dimensional array shape.
  @param type Array type. Use CV_8UC1, ..., CV_64FC4 to create 1-4 channel
  matrices, or CV_8UC(n), ..., CV_64FC(n) to create multi-channel (up to
  CV_CN_MAX channels) matrices.
  @param s An optional value to initialize each matrix element with. To set all
  the matrix elements to the particular value after the construction, use the
  assignment operator Mat::operator=(const Scalar& value) .
  */
  Mat(const std::vector<int> &sizes, int type, const Scalar &s);

  /** @overload
  @param m Array that (as a whole or partly) is assigned to the constructed
  matrix. No data is copied by these constructors. Instead, the header pointing
  to m data or its sub-array is constructed and associated with it. The
  reference counter, if any, is incremented. So, when you modify the matrix
  formed using such a constructor, you also modify the corresponding elements of
  m . If you want to have an independent copy of the sub-array, use Mat::clone()
  .
  */
  Mat(const Mat &m);

  /** @overload
  @param rows Number of rows in a 2D array.
  @param cols Number of columns in a 2D array.
  @param type Array type. Use CV_8UC1, ..., CV_64FC4 to create 1-4 channel
  matrices, or CV_8UC(n), ..., CV_64FC(n) to create multi-channel (up to
  CV_CN_MAX channels) matrices.
  @param data Pointer to the user data. Matrix constructors that take data and
  step parameters do not allocate matrix data. Instead, they just initialize the
  matrix header that points to the specified data, which means that no data is
  copied. This operation is very efficient and can be used to process external
  data using OpenCV functions. The external data is not automatically
  deallocated, so you should take care of it.
  @param step Number of bytes each matrix row occupies. The value should include
  the padding bytes at the end of each row, if any. If the parameter is missing
  (set to AUTO_STEP ), no padding is assumed and the actual step is calculated
  as cols*elemSize(). See Mat::elemSize.
  */
  Mat(int rows, int cols, int type, void *data, size_t step = AUTO_STEP);

  /** @overload
  @param size 2D array size: Size(cols, rows) . In the Size() constructor, the
  number of rows and the number of columns go in the reverse order.
  @param type Array type. Use CV_8UC1, ..., CV_64FC4 to create 1-4 channel
  matrices, or CV_8UC(n), ..., CV_64FC(n) to create multi-channel (up to
  CV_CN_MAX channels) matrices.
  @param data Pointer to the user data. Matrix constructors that take data and
  step parameters do not allocate matrix data. Instead, they just initialize the
  matrix header that points to the specified data, which means that no data is
  copied. This operation is very efficient and can be used to process external
  data using OpenCV functions. The external data is not automatically
  deallocated, so you should take care of it.
  @param step Number of bytes each matrix row occupies. The value should include
  the padding bytes at the end of each row, if any. If the parameter is missing
  (set to AUTO_STEP ), no padding is assumed and the actual step is calculated
  as cols*elemSize(). See Mat::elemSize.
  */
  Mat(Size size, int type, void *data, size_t step = AUTO_STEP);

  /** @overload
  @param ndims Array dimensionality.
  @param sizes Array of integers specifying an n-dimensional array shape.
  @param type Array type. Use CV_8UC1, ..., CV_64FC4 to create 1-4 channel
  matrices, or CV_8UC(n), ..., CV_64FC(n) to create multi-channel (up to
  CV_CN_MAX channels) matrices.
  @param data Pointer to the user data. Matrix constructors that take data and
  step parameters do not allocate matrix data. Instead, they just initialize the
  matrix header that points to the specified data, which means that no data is
  copied. This operation is very efficient and can be used to process external
  data using OpenCV functions. The external data is not automatically
  deallocated, so you should take care of it.
  @param steps Array of ndims-1 steps in case of a multi-dimensional array (the
  last step is always set to the element size). If not specified, the matrix is
  assumed to be continuous.
  */
  Mat(int ndims, const int *sizes, int type, void *data,
      const size_t *steps = 0);

  /** @overload
  @param sizes Array of integers specifying an n-dimensional array shape.
  @param type Array type. Use CV_8UC1, ..., CV_64FC4 to create 1-4 channel
  matrices, or CV_8UC(n), ..., CV_64FC(n) to create multi-channel (up to
  CV_CN_MAX channels) matrices.
  @param data Pointer to the user data. Matrix constructors that take data and
  step parameters do not allocate matrix data. Instead, they just initialize the
  matrix header that points to the specified data, which means that no data is
  copied. This operation is very efficient and can be used to process external
  data using OpenCV functions. The external data is not automatically
  deallocated, so you should take care of it.
  @param steps Array of ndims-1 steps in case of a multi-dimensional array (the
  last step is always set to the element size). If not specified, the matrix is
  assumed to be continuous.
  */
  Mat(const std::vector<int> &sizes, int type, void *data,
      const size_t *steps = 0);

  /** @overload
  @param m Array that (as a whole or partly) is assigned to the constructed
  matrix. No data is copied by these constructors. Instead, the header pointing
  to m data or its sub-array is constructed and associated with it. The
  reference counter, if any, is incremented. So, when you modify the matrix
  formed using such a constructor, you also modify the corresponding elements of
  m . If you want to have an independent copy of the sub-array, use Mat::clone()
  .
  @param rowRange Range of the m rows to take. As usual, the range start is
  inclusive and the range end is exclusive. Use Range::all() to take all the
  rows.
  @param colRange Range of the m columns to take. Use Range::all() to take all
  the columns.
  */
  Mat(const Mat &m, const Range &rowRange,
      const Range &colRange = Range::all());

  /** @overload
  @param m Array that (as a whole or partly) is assigned to the constructed
  matrix. No data is copied by these constructors. Instead, the header pointing
  to m data or its sub-array is constructed and associated with it. The
  reference counter, if any, is incremented. So, when you modify the matrix
  formed using such a constructor, you also modify the corresponding elements of
  m . If you want to have an independent copy of the sub-array, use Mat::clone()
  .
  @param roi Region of interest.
  */
  Mat(const Mat &m, const Rect &roi);

  /** @overload
  @param m Array that (as a whole or partly) is assigned to the constructed
  matrix. No data is copied by these constructors. Instead, the header pointing
  to m data or its sub-array is constructed and associated with it. The
  reference counter, if any, is incremented. So, when you modify the matrix
  formed using such a constructor, you also modify the corresponding elements of
  m . If you want to have an independent copy of the sub-array, use Mat::clone()
  .
  @param ranges Array of selected ranges of m along each dimensionality.
  */
  Mat(const Mat &m, const Range *ranges);

  /** @overload
  @param m Array that (as a whole or partly) is assigned to the constructed
  matrix. No data is copied by these constructors. Instead, the header pointing
  to m data or its sub-array is constructed and associated with it. The
  reference counter, if any, is incremented. So, when you modify the matrix
  formed using such a constructor, you also modify the corresponding elements of
  m . If you want to have an independent copy of the sub-array, use Mat::clone()
  .
  @param ranges Array of selected ranges of m along each dimensionality.
  */
  Mat(const Mat &m, const std::vector<Range> &ranges);

  /** @overload
  @param vec STL vector whose elements form the matrix. The matrix has a single
  column and the number of rows equal to the number of vector elements. Type of
  the matrix matches the type of vector elements. The constructor can handle
  arbitrary types, for which there is a properly declared DataType . This means
  that the vector elements must be primitive numbers or uni-type numerical
  tuples of numbers. Mixed-type structures are not supported. The corresponding
  constructor is explicit. Since STL vectors are not automatically converted to
  Mat instances, you should write Mat(vec) explicitly. Unless you copy the data
  into the matrix ( copyData=true ), no new elements will be added to the vector
  because it can potentially yield vector data reallocation, and, thus, the
  matrix data pointer will be invalid.
  @param copyData Flag to specify whether the underlying data of the STL vector
  should be copied to (true) or shared with (false) the newly constructed
  matrix. When the data is copied, the allocated buffer is managed using Mat
  reference counting mechanism. While the data is shared, the reference counter
  is NULL, and you should not deallocate the data until the matrix is
  destructed.
  */
  template <typename _Tp>
  explicit Mat(const std::vector<_Tp> &vec, bool copyData = false);

  /** @overload
   */
  template <typename _Tp, typename = typename std::enable_if<
                              std::is_arithmetic<_Tp>::value>::type>
  explicit Mat(const std::initializer_list<_Tp> list);

  /** @overload
   */
  template <typename _Tp>
  explicit Mat(const std::initializer_list<int> sizes,
               const std::initializer_list<_Tp> list);

  /** @overload
   */
  template <typename _Tp, size_t _Nm>
  explicit Mat(const std::array<_Tp, _Nm> &arr, bool copyData = false);

  /** @overload
   */
  template <typename _Tp, int n>
  explicit Mat(const Vec<_Tp, n> &vec, bool copyData = true);

  /** @overload
   */
  template <typename _Tp, int m, int n>
  explicit Mat(const Matx<_Tp, m, n> &mtx, bool copyData = true);

  /** @overload
   */
  template <typename _Tp>
  explicit Mat(const Point_<_Tp> &pt, bool copyData = true);

  /** @overload
   */
  template <typename _Tp>
  explicit Mat(const Point3_<_Tp> &pt, bool copyData = true);

  /** @overload
   */
  template <typename _Tp>
  explicit Mat(const MatCommaInitializer_<_Tp> &commaInitializer);

  //! destructor - calls release()
  ~Mat();

  /** @brief assignment operators

  These are available assignment operators. Since they all are very different,
  make sure to read the operator parameters description.
  @param m Assigned, right-hand-side matrix. Matrix assignment is an O(1)
  operation. This means that no data is copied but the data is shared and the
  reference counter, if any, is incremented. Before assigning new data, the old
  data is de-referenced via Mat::release .
   */
  Mat &operator=(const Mat &m);

  /** @overload
  @param expr Assigned matrix expression object. As opposite to the first form
  of the assignment operation, the second form can reuse already allocated
  matrix if it has the right size and type to fit the matrix expression result.
  It is automatically handled by the real function that the matrix expressions
  is expanded to. For example, C=A+B is expanded to add(A, B, C), and add takes
  care of automatic C reallocation.
  */
  Mat &operator=(const MatExpr &expr);

  /** @brief Creates a matrix header for the specified matrix row.

  The method makes a new header for the specified matrix row and returns it.
  This is an O(1) operation, regardless of the matrix size. The underlying data
  of the new matrix is shared with the original matrix. Here is the example of
  one of the classical basic matrix processing operations, axpy, used by LU and
  many other algorithms:
  @code
      inline void matrix_axpy(Mat& A, int i, int j, double alpha)
      {
          A.row(i) += A.row(j)*alpha;
      }
  @endcode
  @note In the current implementation, the following code does not work as
  expected:
  @code
      Mat A;
      ...
      A.row(i) = A.row(j); // will not work
  @endcode
  This happens because A.row(i) forms a temporary header that is further
  assigned to another header. Remember that each of these operations is O(1),
  that is, no data is copied. Thus, the above assignment is not true if you may
  have expected the j-th row to be copied to the i-th row. To achieve that, you
  should either turn this simple assignment into an expression or use the
  Mat::copyTo method:
  @code
      Mat A;
      ...
      // works, but looks a bit obscure.
      A.row(i) = A.row(j) + 0;
      // this is a bit longer, but the recommended method.
      A.row(j).copyTo(A.row(i));
  @endcode
  @param y A 0-based row index.
   */
  Mat row(int y) const;

  /** @brief Creates a matrix header for the specified matrix column.

  The method makes a new header for the specified matrix column and returns it.
  This is an O(1) operation, regardless of the matrix size. The underlying data
  of the new matrix is shared with the original matrix. See also the Mat::row
  description.
  @param x A 0-based column index.
   */
  Mat col(int x) const;

  /** @brief Creates a matrix header for the specified row span.

  The method makes a new header for the specified row span of the matrix.
  Similarly to Mat::row and Mat::col , this is an O(1) operation.
  @param startrow An inclusive 0-based start index of the row span.
  @param endrow An exclusive 0-based ending index of the row span.
   */
  Mat rowRange(int startrow, int endrow) const;

  /** @overload
  @param r Range structure containing both the start and the end indices.
  */
  Mat rowRange(const Range &r) const;

  /** @brief Creates a matrix header for the specified column span.

  The method makes a new header for the specified column span of the matrix.
  Similarly to Mat::row and Mat::col , this is an O(1) operation.
  @param startcol An inclusive 0-based start index of the column span.
  @param endcol An exclusive 0-based ending index of the column span.
   */
  Mat colRange(int startcol, int endcol) const;

  /** @overload
  @param r Range structure containing both the start and the end indices.
  */
  Mat colRange(const Range &r) const;

  /** @brief Extracts a diagonal from a matrix

  The method makes a new header for the specified matrix diagonal. The new
  matrix is represented as a single-column matrix. Similarly to Mat::row and
  Mat::col, this is an O(1) operation.
  @param d index of the diagonal, with the following values:
  - `d=0` is the main diagonal.
  - `d<0` is a diagonal from the lower half. For example, d=-1 means the
  diagonal is set immediately below the main one.
  - `d>0` is a diagonal from the upper half. For example, d=1 means the diagonal
  is set immediately above the main one. For example:
  @code
      Mat m = (Mat_<int>(3,3) <<
                  1,2,3,
                  4,5,6,
                  7,8,9);
      Mat d0 = m.diag(0);
      Mat d1 = m.diag(1);
      Mat d_1 = m.diag(-1);
  @endcode
  The resulting matrices are
  @code
   d0 =
     [1;
      5;
      9]
   d1 =
     [2;
      6]
   d_1 =
     [4;
      8]
  @endcode
   */
  Mat diag(int d = 0) const;

  /** @brief creates a diagonal matrix

  The method creates a square diagonal matrix from specified main diagonal.
  @param d One-dimensional matrix that represents the main diagonal.
   */
  CV_NODISCARD_STD static Mat diag(const Mat &d);

  /** @brief Creates a full copy of the array and the underlying data.

  The method creates a full copy of the array. The original step[] is not taken
  into account. So, the array copy is a continuous array occupying
  total()*elemSize() bytes.
   */
  CV_NODISCARD_STD Mat clone() const;

  /** @brief Copies the matrix to another one.

  The method copies the matrix data to another matrix. Before copying the data,
  the method invokes :
  @code
      m.create(this->size(), this->type());
  @endcode
  so that the destination matrix is reallocated if needed. While m.copyTo(m);
  works flawlessly, the function does not handle the case of a partial overlap
  between the source and the destination matrices.

  When the operation mask is specified, if the Mat::create call shown above
  reallocates the matrix, the newly allocated matrix is initialized with all
  zeros before copying the data.
  @param m Destination matrix. If it does not have a proper size or type before
  the operation, it is reallocated.
   */
  void copyTo(OutputArray m) const;

  /** @overload
  @param m Destination matrix. If it does not have a proper size or type before
  the operation, it is reallocated.
  @param mask Operation mask of the same size as \*this. Its non-zero elements
  indicate which matrix elements need to be copied. The mask has to be of type
  CV_8U and can have 1 or multiple channels.
  */
  void copyTo(OutputArray m, InputArray mask) const;

  /** @brief Converts an array to another data type with optional scaling.

  The method converts source pixel values to the target data type.
  saturate_cast\<\> is applied at the end to avoid possible overflows:

  \f[m(x,y) = saturate \_ cast<rType>( \alpha (*this)(x,y) +  \beta )\f]
  @param m output matrix; if it does not have a proper size or type before the
  operation, it is reallocated.
  @param rtype desired output matrix type or, rather, the depth since the number
  of channels are the same as the input has; if rtype is negative, the output
  matrix will have the same type as the input.
  @param alpha optional scale factor.
  @param beta optional delta added to the scaled values.
   */
  void convertTo(OutputArray m, int rtype, double alpha = 1,
                 double beta = 0) const;

  /** @brief Provides a functional form of convertTo.

  This is an internally used method called by the @ref MatrixExpressions engine.
  @param m Destination array.
  @param type Desired destination array depth (or -1 if it should be the same as
  the source type).
   */
  void assignTo(Mat &m, int type = -1) const;

  /** @brief Sets all or some of the array elements to the specified value.
  @param s Assigned scalar converted to the actual array type.
  */
  Mat &operator=(const Scalar &s);

  /** @brief Sets all or some of the array elements to the specified value.

  This is an advanced variant of the Mat::operator=(const Scalar& s) operator.
  @param value Assigned scalar converted to the actual array type.
  @param mask Operation mask of the same size as \*this. Its non-zero elements
  indicate which matrix elements need to be copied. The mask has to be of type
  CV_8U and can have 1 or multiple channels
   */
  Mat &setTo(InputArray value, InputArray mask = noArray());

  /** @brief Changes the shape and/or the number of channels of a 2D matrix
  without copying the data.

  The method makes a new matrix header for \*this elements. The new matrix may
  have a different size and/or different number of channels. Any combination is
  possible if:
  -   No extra elements are included into the new matrix and no elements are
  excluded. Consequently, the product rows\*cols\*channels() must stay the same
  after the transformation.
  -   No data is copied. That is, this is an O(1) operation. Consequently, if
  you change the number of rows, or the operation changes the indices of
  elements row in some other way, the matrix must be continuous. See
  Mat::isContinuous .

  For example, if there is a set of 3D points stored as an STL vector, and you
  want to represent the points as a 3xN matrix, do the following:
  @code
      std::vector<Point3f> vec;
      ...
      Mat pointMat = Mat(vec). // convert vector to Mat, O(1) operation
                        reshape(1). // make Nx3 1-channel matrix out of Nx1
  3-channel.
                                    // Also, an O(1) operation
                           t(); // finally, transpose the Nx3 matrix.
                                // This involves copying all the elements
  @endcode
  3-channel 2x2 matrix reshaped to 1-channel 4x3 matrix, each column has values
  from one of original channels:
  @code
  Mat m(Size(2, 2), CV_8UC3, Scalar(1, 2, 3));
  vector<int> new_shape {4, 3};
  m = m.reshape(1, new_shape);
  @endcode
  or:
  @code
  Mat m(Size(2, 2), CV_8UC3, Scalar(1, 2, 3));
  const int new_shape[] = {4, 3};
  m = m.reshape(1, 2, new_shape);
  @endcode
  @param cn New number of channels. If the parameter is 0, the number of
  channels remains the same.
  @param rows New number of rows. If the parameter is 0, the number of rows
  remains the same.
   */
  Mat reshape(int cn, int rows = 0) const;

  /** @overload
   * @param cn New number of channels. If the parameter is 0, the number of
   * channels remains the same.
   * @param newndims New number of dimentions.
   * @param newsz Array with new matrix size by all dimentions. If some sizes
   * are zero, the original sizes in those dimensions are presumed.
   */
  Mat reshape(int cn, int newndims, const int *newsz) const;

  /** @overload
   * @param cn New number of channels. If the parameter is 0, the number of
   * channels remains the same.
   * @param newshape Vector with new matrix size by all dimentions. If some
   * sizes are zero, the original sizes in those dimensions are presumed.
   */
  Mat reshape(int cn, const std::vector<int> &newshape) const;

  /** @brief Transposes a matrix.

  The method performs matrix transposition by means of matrix expressions. It
  does not perform the actual transposition but returns a temporary matrix
  transposition object that can be further used as a part of more complex matrix
  expressions or can be assigned to a matrix:
  @code
      Mat A1 = A + Mat::eye(A.size(), A.type())*lambda;
      Mat C = A1.t()*A1; // compute (A + lambda*I)^t * (A + lamda*I)
  @endcode
   */
  MatExpr t() const;

  /** @brief Inverses a matrix.

  The method performs a matrix inversion by means of matrix expressions. This
  means that a temporary matrix inversion object is returned by the method and
  can be used further as a part of more complex matrix expressions or can be
  assigned to a matrix.
  @param method Matrix inversion method. One of cv::DecompTypes
   */
  MatExpr inv(int method = DECOMP_LU) const;

  /** @brief Performs an element-wise multiplication or division of the two
  matrices.

  The method returns a temporary object encoding per-element array
  multiplication, with optional scale. Note that this is not a matrix
  multiplication that corresponds to a simpler "\*" operator.

  Example:
  @code
      Mat C = A.mul(5/B); // equivalent to divide(A, B, C, 5)
  @endcode
  @param m Another array of the same type and the same size as \*this, or a
  matrix expression.
  @param scale Optional scale factor.
   */
  MatExpr mul(InputArray m, double scale = 1) const;

  /** @brief Computes a cross-product of two 3-element vectors.

  The method computes a cross-product of two 3-element vectors. The vectors must
  be 3-element floating-point vectors of the same shape and size. The result is
  another 3-element vector of the same shape and type as operands.
  @param m Another cross-product operand.
   */
  Mat cross(InputArray m) const;

  /** @brief Computes a dot-product of two vectors.

  The method computes a dot-product of two matrices. If the matrices are not
  single-column or single-row vectors, the top-to-bottom left-to-right scan
  ordering is used to treat them as 1D vectors. The vectors must have the same
  size and type. If the matrices have more than one channel, the dot products
  from all the channels are summed together.
  @param m another dot-product operand.
   */
  double dot(InputArray m) const;

  /** @brief Returns a zero array of the specified size and type.

  The method returns a Matlab-style zero array initializer. It can be used to
  quickly form a constant array as a function parameter, part of a matrix
  expression, or as a matrix initializer:
  @code
      Mat A;
      A = Mat::zeros(3, 3, CV_32F);
  @endcode
  In the example above, a new matrix is allocated only if A is not a 3x3
  floating-point matrix. Otherwise, the existing matrix A is filled with zeros.
  @param rows Number of rows.
  @param cols Number of columns.
  @param type Created matrix type.
   */
  CV_NODISCARD_STD static MatExpr zeros(int rows, int cols, int type);

  /** @overload
  @param size Alternative to the matrix size specification Size(cols, rows) .
  @param type Created matrix type.
  */
  CV_NODISCARD_STD static MatExpr zeros(Size size, int type);

  /** @overload
  @param ndims Array dimensionality.
  @param sz Array of integers specifying the array shape.
  @param type Created matrix type.
  */
  CV_NODISCARD_STD static MatExpr zeros(int ndims, const int *sz, int type);

  /** @brief Returns an array of all 1's of the specified size and type.

  The method returns a Matlab-style 1's array initializer, similarly to
  Mat::zeros. Note that using this method you can initialize an array with an
  arbitrary value, using the following Matlab idiom:
  @code
      Mat A = Mat::ones(100, 100, CV_8U)*3; // make 100x100 matrix filled
  with 3.
  @endcode
  The above operation does not form a 100x100 matrix of 1's and then multiply it
  by 3. Instead, it just remembers the scale factor (3 in this case) and use it
  when actually invoking the matrix initializer.
  @note In case of multi-channels type, only the first channel will be
  initialized with 1's, the others will be set to 0's.
  @param rows Number of rows.
  @param cols Number of columns.
  @param type Created matrix type.
   */
  CV_NODISCARD_STD static MatExpr ones(int rows, int cols, int type);

  /** @overload
  @param size Alternative to the matrix size specification Size(cols, rows) .
  @param type Created matrix type.
  */
  CV_NODISCARD_STD static MatExpr ones(Size size, int type);

  /** @overload
  @param ndims Array dimensionality.
  @param sz Array of integers specifying the array shape.
  @param type Created matrix type.
  */
  CV_NODISCARD_STD static MatExpr ones(int ndims, const int *sz, int type);

  /** @brief Returns an identity matrix of the specified size and type.

  The method returns a Matlab-style identity matrix initializer, similarly to
  Mat::zeros. Similarly to Mat::ones, you can use a scale operation to create a
  scaled identity matrix efficiently:
  @code
      // make a 4x4 diagonal matrix with 0.1's on the diagonal.
      Mat A = Mat::eye(4, 4, CV_32F)*0.1;
  @endcode
  @note In case of multi-channels type, identity matrix will be initialized only
  for the first channel, the others will be set to 0's
  @param rows Number of rows.
  @param cols Number of columns.
  @param type Created matrix type.
   */
  CV_NODISCARD_STD static MatExpr eye(int rows, int cols, int type);

  /** @overload
  @param size Alternative matrix size specification as Size(cols, rows) .
  @param type Created matrix type.
  */
  CV_NODISCARD_STD static MatExpr eye(Size size, int type);

  /** @brief Allocates new array data if needed.

  This is one of the key Mat methods. Most new-style OpenCV functions and
  methods that produce arrays call this method for each output array. The method
  uses the following algorithm:

  -# If the current array shape and the type match the new ones, return
  immediately. Otherwise, de-reference the previous data by calling
  Mat::release.
  -# Initialize the new header.
  -# Allocate the new data of total()\*elemSize() bytes.
  -# Allocate the new, associated with the data, reference counter and set it
  to 1.

  Such a scheme makes the memory management robust and efficient at the same
  time and helps avoid extra typing for you. This means that usually there is no
  need to explicitly allocate output arrays. That is, instead of writing:
  @code
      Mat color;
      ...
      Mat gray(color.rows, color.cols, color.depth());
      cvtColor(color, gray, COLOR_BGR2GRAY);
  @endcode
  you can simply write:
  @code
      Mat color;
      ...
      Mat gray;
      cvtColor(color, gray, COLOR_BGR2GRAY);
  @endcode
  because cvtColor, as well as the most of OpenCV functions, calls Mat::create()
  for the output array internally.
  @param rows New number of rows.
  @param cols New number of columns.
  @param type New matrix type.
   */
  void create(int rows, int cols, int type);

  /** @overload
  @param size Alternative new matrix size specification: Size(cols, rows)
  @param type New matrix type.
  */
  void create(Size size, int type);

  /** @overload
  @param ndims New array dimensionality.
  @param sizes Array of integers specifying a new array shape.
  @param type New matrix type.
  */
  void create(int ndims, const int *sizes, int type);

  /** @overload
  @param sizes Array of integers specifying a new array shape.
  @param type New matrix type.
  */
  void create(const std::vector<int> &sizes, int type);

  /** @brief Increments the reference counter.

  The method increments the reference counter associated with the matrix data.
  If the matrix header points to an external data set (see Mat::Mat ), the
  reference counter is NULL, and the method has no effect in this case.
  Normally, to avoid memory leaks, the method should not be called explicitly.
  It is called implicitly by the matrix assignment operator. The reference
  counter increment is an atomic operation on the platforms that support it.
  Thus, it is safe to operate on the same matrices asynchronously in different
  threads.
   */
  void addref();

  /** @brief Decrements the reference counter and deallocates the matrix if
  needed.

  The method decrements the reference counter associated with the matrix data.
  When the reference counter reaches 0, the matrix data is deallocated and the
  data and the reference counter pointers are set to NULL's. If the matrix
  header points to an external data set (see Mat::Mat ), the reference counter
  is NULL, and the method has no effect in this case.

  This method can be called manually to force the matrix data deallocation. But
  since this method is automatically called in the destructor, or by any other
  method that changes the data pointer, it is usually not needed. The reference
  counter decrement and check for 0 is an atomic operation on the platforms that
  support it. Thus, it is safe to operate on the same matrices asynchronously in
  different threads.
   */
  void release();

  //! internal use function, consider to use 'release' method instead;
  //! deallocates the matrix data
  void deallocate();
  //! internal use function; properly re-allocates _size, _step arrays
  void copySize(const Mat &m);

  /** @brief Reserves space for the certain number of rows.

  The method reserves space for sz rows. If the matrix already has enough space
  to store sz rows, nothing happens. If the matrix is reallocated, the first
  Mat::rows rows are preserved. The method emulates the corresponding method of
  the STL vector class.
  @param sz Number of rows.
   */
  void reserve(size_t sz);

  /** @brief Reserves space for the certain number of bytes.

  The method reserves space for sz bytes. If the matrix already has enough space
  to store sz bytes, nothing happens. If matrix has to be reallocated its
  previous content could be lost.
  @param sz Number of bytes.
  */
  void reserveBuffer(size_t sz);

  /** @brief Changes the number of matrix rows.

  The methods change the number of matrix rows. If the matrix is reallocated,
  the first min(Mat::rows, sz) rows are preserved. The methods emulate the
  corresponding methods of the STL vector class.
  @param sz New number of rows.
   */
  void resize(size_t sz);

  /** @overload
  @param sz New number of rows.
  @param s Value assigned to the newly added elements.
   */
  void resize(size_t sz, const Scalar &s);

  //! internal function
  void push_back_(const void *elem);

  /** @brief Adds elements to the bottom of the matrix.

  The methods add one or more elements to the bottom of the matrix. They emulate
  the corresponding method of the STL vector class. When elem is Mat , its type
  and the number of columns must be the same as in the container matrix.
  @param elem Added element(s).
   */
  template <typename _Tp> void push_back(const _Tp &elem);

  /** @overload
  @param elem Added element(s).
  */
  template <typename _Tp> void push_back(const Mat_<_Tp> &elem);

  /** @overload
  @param elem Added element(s).
  */
  template <typename _Tp> void push_back(const std::vector<_Tp> &elem);

  /** @overload
  @param m Added line(s).
  */
  void push_back(const Mat &m);

  /** @brief Removes elements from the bottom of the matrix.

  The method removes one or more rows from the bottom of the matrix.
  @param nelems Number of removed rows. If it is greater than the total number
  of rows, an exception is thrown.
   */
  void pop_back(size_t nelems = 1);

  /** @brief Locates the matrix header within a parent matrix.

  After you extracted a submatrix from a matrix using Mat::row, Mat::col,
  Mat::rowRange, Mat::colRange, and others, the resultant submatrix points just
  to the part of the original big matrix. However, each submatrix contains
  information (represented by datastart and dataend fields) that helps
  reconstruct the original matrix size and the position of the extracted
  submatrix within the original matrix. The method locateROI does exactly that.
  @param wholeSize Output parameter that contains the size of the whole matrix
  containing *this* as a part.
  @param ofs Output parameter that contains an offset of *this* inside the whole
  matrix.
   */
  void locateROI(Size &wholeSize, Point &ofs) const;

  /** @brief Adjusts a submatrix size and position within the parent matrix.

  The method is complimentary to Mat::locateROI . The typical use of these
  functions is to determine the submatrix position within the parent matrix and
  then shift the position somehow. Typically, it can be required for filtering
  operations when pixels outside of the ROI should be taken into account. When
  all the method parameters are positive, the ROI needs to grow in all
  directions by the specified amount, for example:
  @code
      A.adjustROI(2, 2, 2, 2);
  @endcode
  In this example, the matrix size is increased by 4 elements in each direction.
  The matrix is shifted by 2 elements to the left and 2 elements up, which
  brings in all the necessary pixels for the filtering with the 5x5 kernel.

  adjustROI forces the adjusted ROI to be inside of the parent matrix that is
  boundaries of the adjusted ROI are constrained by boundaries of the parent
  matrix. For example, if the submatrix A is located in the first row of a
  parent matrix and you called A.adjustROI(2, 2, 2, 2) then A will not be
  increased in the upward direction.

  The function is used internally by the OpenCV filtering functions, like
  filter2D , morphological operations, and so on.
  @param dtop Shift of the top submatrix boundary upwards.
  @param dbottom Shift of the bottom submatrix boundary downwards.
  @param dleft Shift of the left submatrix boundary to the left.
  @param dright Shift of the right submatrix boundary to the right.
  @sa copyMakeBorder
   */
  Mat &adjustROI(int dtop, int dbottom, int dleft, int dright);

  /** @brief Extracts a rectangular submatrix.

  The operators make a new header for the specified sub-array of \*this . They
  are the most generalized forms of Mat::row, Mat::col, Mat::rowRange, and
  Mat::colRange . For example, `A(Range(0, 10), Range::all())` is equivalent to
  `A.rowRange(0, 10)`. Similarly to all of the above, the operators are O(1)
  operations, that is, no matrix data is copied.
  @param rowRange Start and end row of the extracted submatrix. The upper
  boundary is not included. To select all the rows, use Range::all().
  @param colRange Start and end column of the extracted submatrix. The upper
  boundary is not included. To select all the columns, use Range::all().
   */
  Mat operator()(Range rowRange, Range colRange) const;

  /** @overload
  @param roi Extracted submatrix specified as a rectangle.
  */
  Mat operator()(const Rect &roi) const;

  /** @overload
  @param ranges Array of selected ranges along each array dimension.
  */
  Mat operator()(const Range *ranges) const;

  /** @overload
  @param ranges Array of selected ranges along each array dimension.
  */
  Mat operator()(const std::vector<Range> &ranges) const;

  template <typename _Tp> operator std::vector<_Tp>() const;
  template <typename _Tp, int n> operator Vec<_Tp, n>() const;
  template <typename _Tp, int m, int n> operator Matx<_Tp, m, n>() const;

  template <typename _Tp, std::size_t _Nm>
  operator std::array<_Tp, _Nm>() const;

  /** @brief Reports whether the matrix is continuous or not.

  The method returns true if the matrix elements are stored continuously without
  gaps at the end of each row. Otherwise, it returns false. Obviously, 1x1 or
  1xN matrices are always continuous. Matrices created with Mat::create are
  always continuous. But if you extract a part of the matrix using Mat::col,
  Mat::diag, and so on, or constructed a matrix header for externally allocated
  data, such matrices may no longer have this property.

  The continuity flag is stored as a bit in the Mat::flags field and is computed
  automatically when you construct a matrix header. Thus, the continuity check
  is a very fast operation, though theoretically it could be done as follows:
  @code
      // alternative implementation of Mat::isContinuous()
      bool myCheckMatContinuity(const Mat& m)
      {
          //return (m.flags & Mat::CONTINUOUS_FLAG) != 0;
          return m.rows == 1 || m.step == m.cols*m.elemSize();
      }
  @endcode
  The method is used in quite a few of OpenCV functions. The point is that
  element-wise operations (such as arithmetic and logical operations, math
  functions, alpha blending, color space transformations, and others) do not
  depend on the image geometry. Thus, if all the input and output arrays are
  continuous, the functions can process them as very long single-row vectors.
  The example below illustrates how an alpha-blending function can be
  implemented:
  @code
      template<typename T>
      void alphaBlendRGBA(const Mat& src1, const Mat& src2, Mat& dst)
      {
          const float alpha_scale = (float)std::numeric_limits<T>::max(),
                      inv_scale = 1.f/alpha_scale;

          CV_Assert( src1.type() == src2.type() &&
                     src1.type() == CV_MAKETYPE(traits::Depth<T>::value, 4) &&
                     src1.size() == src2.size());
          Size size = src1.size();
          dst.create(size, src1.type());

          // here is the idiom: check the arrays for continuity and,
          // if this is the case,
          // treat the arrays as 1D vectors
          if( src1.isContinuous() && src2.isContinuous() && dst.isContinuous() )
          {
              size.width *= size.height;
              size.height = 1;
          }
          size.width *= 4;

          for( int i = 0; i < size.height; i++ )
          {
              // when the arrays are continuous,
              // the outer loop is executed only once
              const T* ptr1 = src1.ptr<T>(i);
              const T* ptr2 = src2.ptr<T>(i);
              T* dptr = dst.ptr<T>(i);

              for( int j = 0; j < size.width; j += 4 )
              {
                  float alpha = ptr1[j+3]*inv_scale, beta = ptr2[j+3]*inv_scale;
                  dptr[j] = saturate_cast<T>(ptr1[j]*alpha + ptr2[j]*beta);
                  dptr[j+1] = saturate_cast<T>(ptr1[j+1]*alpha +
  ptr2[j+1]*beta); dptr[j+2] = saturate_cast<T>(ptr1[j+2]*alpha +
  ptr2[j+2]*beta); dptr[j+3] = saturate_cast<T>((1 -
  (1-alpha)*(1-beta))*alpha_scale);
              }
          }
      }
  @endcode
  This approach, while being very simple, can boost the performance of a simple
  element-operation by 10-20 percents, especially if the image is rather small
  and the operation is quite simple.

  Another OpenCV idiom in this function, a call of Mat::create for the
  destination array, that allocates the destination array unless it already has
  the proper size and type. And while the newly allocated arrays are always
  continuous, you still need to check the destination array because Mat::create
  does not always allocate a new matrix.
   */
  bool isContinuous() const;

  //! returns true if the matrix is a submatrix of another matrix
  bool isSubmatrix() const;

  /** @brief Returns the matrix element size in bytes.

  The method returns the matrix element size in bytes. For example, if the
  matrix type is CV_16SC3 , the method returns 3\*sizeof(short) or 6.
   */
  size_t elemSize() const;

  /** @brief Returns the size of each matrix element channel in bytes.

  The method returns the matrix element channel size in bytes, that is, it
  ignores the number of channels. For example, if the matrix type is CV_16SC3 ,
  the method returns sizeof(short) or 2.
   */
  size_t elemSize1() const;

  /** @brief Returns the type of a matrix element.

  The method returns a matrix element type. This is an identifier compatible
  with the CvMat type system, like CV_16SC3 or 16-bit signed 3-channel array,
  and so on.
   */
  int type() const;

  /** @brief Returns the depth of a matrix element.

  The method returns the identifier of the matrix element depth (the type of
  each individual channel). For example, for a 16-bit signed element array, the
  method returns CV_16S . A complete list of matrix types contains the following
  values:
  -   CV_8U - 8-bit unsigned integers ( 0..255 )
  -   CV_8S - 8-bit signed integers ( -128..127 )
  -   CV_16U - 16-bit unsigned integers ( 0..65535 )
  -   CV_16S - 16-bit signed integers ( -32768..32767 )
  -   CV_32S - 32-bit signed integers ( -2147483648..2147483647 )
  -   CV_32F - 32-bit floating-point numbers ( -FLT_MAX..FLT_MAX, INF, NAN )
  -   CV_64F - 64-bit floating-point numbers ( -DBL_MAX..DBL_MAX, INF, NAN )
   */
  int depth() const;

  /** @brief Returns the number of matrix channels.

  The method returns the number of matrix channels.
   */
  int channels() const;

  /** @brief Returns a normalized step.

  The method returns a matrix step divided by Mat::elemSize1() . It can be
  useful to quickly access an arbitrary matrix element.
   */
  size_t step1(int i = 0) const;

  /** @brief Returns true if the array has no elements.

  The method returns true if Mat::total() is 0 or if Mat::data is NULL. Because
  of pop_back() and resize() methods `M.total() == 0` does not imply that
  `M.data == NULL`.
   */
  bool empty() const;

  /** @brief Returns the total number of array elements.

  The method returns the number of array elements (a number of pixels if the
  array represents an image).
   */
  size_t total() const;

  /** @brief Returns the total number of array elements.

   The method returns the number of elements within a certain sub-array slice
   with startDim <= dim < endDim
   */
  size_t total(int startDim, int endDim = INT_MAX) const;

  /**
   * @param elemChannels Number of channels or number of columns the matrix
   * should have. For a 2-D matrix, when the matrix has only 1 column, then it
   * should have elemChannels channels; When the matrix has only 1 channel, then
   * it should have elemChannels columns. For a 3-D matrix, it should have only
   * one channel. Furthermore, if the number of planes is not one, then the
   * number of rows within every plane has to be 1; if the number of rows within
   *                     every plane is not 1, then the number of planes has to
   * be 1.
   * @param depth The depth the matrix should have. Set it to -1 when any depth
   * is fine.
   * @param requireContinuous Set it to true to require the matrix to be
   * continuous
   * @return -1 if the requirement is not satisfied.
   *         Otherwise, it returns the number of elements in the matrix. Note
   *         that an element may have multiple channels.
   *
   * The following code demonstrates its usage for a 2-d matrix:
   * @snippet snippets/core_mat_checkVector.cpp example-2d
   *
   * The following code demonstrates its usage for a 3-d matrix:
   * @snippet snippets/core_mat_checkVector.cpp example-3d
   */
  int checkVector(int elemChannels, int depth = -1,
                  bool requireContinuous = true) const;

  /** @brief Returns a pointer to the specified matrix row.

  The methods return `uchar*` or typed pointer to the specified matrix row. See
  the sample in Mat::isContinuous to know how to use these methods.
  @param i0 A 0-based row index.
   */
  uchar *ptr(int i0 = 0);
  /** @overload */
  const uchar *ptr(int i0 = 0) const;

  /** @overload
  @param row Index along the dimension 0
  @param col Index along the dimension 1
  */
  uchar *ptr(int row, int col);
  /** @overload
  @param row Index along the dimension 0
  @param col Index along the dimension 1
  */
  const uchar *ptr(int row, int col) const;

  /** @overload */
  uchar *ptr(int i0, int i1, int i2);
  /** @overload */
  const uchar *ptr(int i0, int i1, int i2) const;

  /** @overload */
  uchar *ptr(const int *idx);
  /** @overload */
  const uchar *ptr(const int *idx) const;
  /** @overload */
  template <int n> uchar *ptr(const Vec<int, n> &idx);
  /** @overload */
  template <int n> const uchar *ptr(const Vec<int, n> &idx) const;

  /** @overload */
  template <typename _Tp> _Tp *ptr(int i0 = 0);
  /** @overload */
  template <typename _Tp> const _Tp *ptr(int i0 = 0) const;
  /** @overload
  @param row Index along the dimension 0
  @param col Index along the dimension 1
  */
  template <typename _Tp> _Tp *ptr(int row, int col);
  /** @overload
  @param row Index along the dimension 0
  @param col Index along the dimension 1
  */
  template <typename _Tp> const _Tp *ptr(int row, int col) const;
  /** @overload */
  template <typename _Tp> _Tp *ptr(int i0, int i1, int i2);
  /** @overload */
  template <typename _Tp> const _Tp *ptr(int i0, int i1, int i2) const;
  /** @overload */
  template <typename _Tp> _Tp *ptr(const int *idx);
  /** @overload */
  template <typename _Tp> const _Tp *ptr(const int *idx) const;
  /** @overload */
  template <typename _Tp, int n> _Tp *ptr(const Vec<int, n> &idx);
  /** @overload */
  template <typename _Tp, int n> const _Tp *ptr(const Vec<int, n> &idx) const;

  /** @brief Returns a reference to the specified array element.

  The template methods return a reference to the specified array element. For
  the sake of higher performance, the index range checks are only performed in
  the Debug configuration.

  Note that the variants with a single index (i) can be used to access elements
  of single-row or single-column 2-dimensional arrays. That is, if, for example,
  A is a 1 x N floating-point matrix and B is an M x 1 integer matrix, you can
  simply write `A.at<float>(k+4)` and `B.at<int>(2*i+1)` instead of
  `A.at<float>(0,k+4)` and `B.at<int>(2*i+1,0)`, respectively.

  The example below initializes a Hilbert matrix:
  @code
      Mat H(100, 100, CV_64F);
      for(int i = 0; i < H.rows; i++)
          for(int j = 0; j < H.cols; j++)
              H.at<double>(i,j)=1./(i+j+1);
  @endcode

  Keep in mind that the size identifier used in the at operator cannot be chosen
  at random. It depends on the image from which you are trying to retrieve the
  data. The table below gives a better insight in this:
   - If matrix is of type `CV_8U` then use `Mat.at<uchar>(y,x)`.
   - If matrix is of type `CV_8S` then use `Mat.at<schar>(y,x)`.
   - If matrix is of type `CV_16U` then use `Mat.at<ushort>(y,x)`.
   - If matrix is of type `CV_16S` then use `Mat.at<short>(y,x)`.
   - If matrix is of type `CV_32S`  then use `Mat.at<int>(y,x)`.
   - If matrix is of type `CV_32F`  then use `Mat.at<float>(y,x)`.
   - If matrix is of type `CV_64F` then use `Mat.at<double>(y,x)`.

  @param i0 Index along the dimension 0
   */
  template <typename _Tp> _Tp &at(int i0 = 0);
  /** @overload
  @param i0 Index along the dimension 0
  */
  template <typename _Tp> const _Tp &at(int i0 = 0) const;
  /** @overload
  @param row Index along the dimension 0
  @param col Index along the dimension 1
  */
  template <typename _Tp> _Tp &at(int row, int col);
  /** @overload
  @param row Index along the dimension 0
  @param col Index along the dimension 1
  */
  template <typename _Tp> const _Tp &at(int row, int col) const;

  /** @overload
  @param i0 Index along the dimension 0
  @param i1 Index along the dimension 1
  @param i2 Index along the dimension 2
  */
  template <typename _Tp> _Tp &at(int i0, int i1, int i2);
  /** @overload
  @param i0 Index along the dimension 0
  @param i1 Index along the dimension 1
  @param i2 Index along the dimension 2
  */
  template <typename _Tp> const _Tp &at(int i0, int i1, int i2) const;

  /** @overload
  @param idx Array of Mat::dims indices.
  */
  template <typename _Tp> _Tp &at(const int *idx);
  /** @overload
  @param idx Array of Mat::dims indices.
  */
  template <typename _Tp> const _Tp &at(const int *idx) const;

  /** @overload */
  template <typename _Tp, int n> _Tp &at(const Vec<int, n> &idx);
  /** @overload */
  template <typename _Tp, int n> const _Tp &at(const Vec<int, n> &idx) const;

  /** @overload
  special versions for 2D arrays (especially convenient for referencing image
  pixels)
  @param pt Element position specified as Point(j,i) .
  */
  template <typename _Tp> _Tp &at(Point pt);
  /** @overload
  special versions for 2D arrays (especially convenient for referencing image
  pixels)
  @param pt Element position specified as Point(j,i) .
  */
  template <typename _Tp> const _Tp &at(Point pt) const;

  /** @brief Returns the matrix iterator and sets it to the first matrix
  element.

  The methods return the matrix read-only or read-write iterators. The use of
  matrix iterators is very similar to the use of bi-directional STL iterators.
  In the example below, the alpha blending function is rewritten using the
  matrix iterators:
  @code
      template<typename T>
      void alphaBlendRGBA(const Mat& src1, const Mat& src2, Mat& dst)
      {
          typedef Vec<T, 4> VT;

          const float alpha_scale = (float)std::numeric_limits<T>::max(),
                      inv_scale = 1.f/alpha_scale;

          CV_Assert( src1.type() == src2.type() &&
                     src1.type() == traits::Type<VT>::value &&
                     src1.size() == src2.size());
          Size size = src1.size();
          dst.create(size, src1.type());

          MatConstIterator_<VT> it1 = src1.begin<VT>(), it1_end =
  src1.end<VT>(); MatConstIterator_<VT> it2 = src2.begin<VT>(); MatIterator_<VT>
  dst_it = dst.begin<VT>();

          for( ; it1 != it1_end; ++it1, ++it2, ++dst_it )
          {
              VT pix1 = *it1, pix2 = *it2;
              float alpha = pix1[3]*inv_scale, beta = pix2[3]*inv_scale;
              *dst_it = VT(saturate_cast<T>(pix1[0]*alpha + pix2[0]*beta),
                           saturate_cast<T>(pix1[1]*alpha + pix2[1]*beta),
                           saturate_cast<T>(pix1[2]*alpha + pix2[2]*beta),
                           saturate_cast<T>((1 -
  (1-alpha)*(1-beta))*alpha_scale));
          }
      }
  @endcode
   */
  template <typename _Tp> MatIterator_<_Tp> begin();
  template <typename _Tp> MatConstIterator_<_Tp> begin() const;

  /** @brief Same as begin() but for inverse traversal
   */
  template <typename _Tp> std::reverse_iterator<MatIterator_<_Tp>> rbegin();
  template <typename _Tp>
  std::reverse_iterator<MatConstIterator_<_Tp>> rbegin() const;

  /** @brief Returns the matrix iterator and sets it to the after-last matrix
  element.

  The methods return the matrix read-only or read-write iterators, set to the
  point following the last matrix element.
   */
  template <typename _Tp> MatIterator_<_Tp> end();
  template <typename _Tp> MatConstIterator_<_Tp> end() const;

  /** @brief Same as end() but for inverse traversal
   */
  template <typename _Tp> std::reverse_iterator<MatIterator_<_Tp>> rend();
  template <typename _Tp>
  std::reverse_iterator<MatConstIterator_<_Tp>> rend() const;

  /** @brief Runs the given functor over all matrix elements in parallel.

  The operation passed as argument has to be a function pointer, a function
  object or a lambda(C++11).

  Example 1. All of the operations below put 0xFF the first channel of all
  matrix elements:
  @code
      Mat image(1920, 1080, CV_8UC3);
      typedef cv::Point3_<uint8_t> Pixel;

      // first. raw pointer access.
      for (int r = 0; r < image.rows; ++r) {
          Pixel* ptr = image.ptr<Pixel>(r, 0);
          const Pixel* ptr_end = ptr + image.cols;
          for (; ptr != ptr_end; ++ptr) {
              ptr->x = 255;
          }
      }

      // Using MatIterator. (Simple but there are a Iterator's overhead)
      for (Pixel &p : cv::Mat_<Pixel>(image)) {
          p.x = 255;
      }

      // Parallel execution with function object.
      struct Operator {
          void operator ()(Pixel &pixel, const int * position) {
              pixel.x = 255;
          }
      };
      image.forEach<Pixel>(Operator());

      // Parallel execution using C++11 lambda.
      image.forEach<Pixel>([](Pixel &p, const int * position) -> void {
          p.x = 255;
      });
  @endcode
  Example 2. Using the pixel's position:
  @code
      // Creating 3D matrix (255 x 255 x 255) typed uint8_t
      // and initialize all elements by the value which equals elements
  position.
      // i.e. pixels (x,y,z) = (1,2,3) is (b,g,r) = (1,2,3).

      int sizes[] = { 255, 255, 255 };
      typedef cv::Point3_<uint8_t> Pixel;

      Mat_<Pixel> image = Mat::zeros(3, sizes, CV_8UC3);

      image.forEach<Pixel>([](Pixel& pixel, const int position[]) -> void {
          pixel.x = position[0];
          pixel.y = position[1];
          pixel.z = position[2];
      });
  @endcode
   */
  template <typename _Tp, typename Functor>
  void forEach(const Functor &operation);
  /** @overload */
  template <typename _Tp, typename Functor>
  void forEach(const Functor &operation) const;

  Mat(Mat &&m) CV_NOEXCEPT;
  Mat &operator=(Mat &&m);

  enum {
    MAGIC_VAL = 0x42FF0000,
    AUTO_STEP = 0,
    CONTINUOUS_FLAG = CV_MAT_CONT_FLAG,
    SUBMATRIX_FLAG = CV_SUBMAT_FLAG
  };
  enum { MAGIC_MASK = 0xFFFF0000, TYPE_MASK = 0x00000FFF, DEPTH_MASK = 7 };

  /*! includes several bit-fields:
       - the magic signature
       - continuity flag
       - depth
       - number of channels
   */
  int flags;
  //! the matrix dimensionality, >= 2
  int dims;
  //! the number of rows and columns or (-1, -1) when the matrix has more than 2
  //! dimensions
  int rows, cols;
  //! pointer to the data
  uchar *data;

  //! helper fields used in locateROI and adjustROI
  const uchar *datastart;
  const uchar *dataend;
  const uchar *datalimit;

  //! custom allocator
  MatAllocator *allocator;
  //! and the standard allocator
  static MatAllocator *getStdAllocator();
  static MatAllocator *getDefaultAllocator();
  static void setDefaultAllocator(MatAllocator *allocator);

  //! internal use method: updates the continuity flag
  void updateContinuityFlag();

  //! interaction with UMat
  UMatData *u;

  MatSize size;
  MatStep step;

protected:
  template <typename _Tp, typename Functor>
  void forEach_impl(const Functor &operation);
};

///////////////////////////////// Mat_<_Tp> ////////////////////////////////////

/** @brief Template matrix class derived from Mat

@code{.cpp}
    template<typename _Tp> class Mat_ : public Mat
    {
    public:
        // ... some specific methods
        //         and
        // no new extra fields
    };
@endcode
The class `Mat_<_Tp>` is a *thin* template wrapper on top of the Mat class. It
does not have any extra data fields. Nor this class nor Mat has any virtual
methods. Thus, references or pointers to these two classes can be freely but
carefully converted one to another. For example:
@code{.cpp}
    // create a 100x100 8-bit matrix
    Mat M(100,100,CV_8U);
    // this will be compiled fine. no any data conversion will be done.
    Mat_<float>& M1 = (Mat_<float>&)M;
    // the program is likely to crash at the statement below
    M1(99,99) = 1.f;
@endcode
While Mat is sufficient in most cases, Mat_ can be more convenient if you use a
lot of element access operations and if you know matrix type at the compilation
time. Note that `Mat::at(int y,int x)` and `Mat_::operator()(int y,int x)` do
absolutely the same and run at the same speed, but the latter is certainly
shorter:
@code{.cpp}
    Mat_<double> M(20,20);
    for(int i = 0; i < M.rows; i++)
        for(int j = 0; j < M.cols; j++)
            M(i,j) = 1./(i+j+1);
    Mat E, V;
    eigen(M,E,V);
    cout << E.at<double>(0,0)/E.at<double>(M.rows-1,0);
@endcode
To use Mat_ for multi-channel images/matrices, pass Vec as a Mat_ parameter:
@code{.cpp}
    // allocate a 320x240 color image and fill it with green (in RGB space)
    Mat_<Vec3b> img(240, 320, Vec3b(0,255,0));
    // now draw a diagonal white line
    for(int i = 0; i < 100; i++)
        img(i,i)=Vec3b(255,255,255);
    // and now scramble the 2nd (red) channel of each pixel
    for(int i = 0; i < img.rows; i++)
        for(int j = 0; j < img.cols; j++)
            img(i,j)[2] ^= (uchar)(i ^ j);
@endcode
Mat_ is fully compatible with C++11 range-based for loop. For example such loop
can be used to safely apply look-up table:
@code{.cpp}
void applyTable(Mat_<uchar>& I, const uchar* const table)
{
    for(auto& pixel : I)
    {
        pixel = table[pixel];
    }
}
@endcode
 */
template <typename _Tp> class Mat_ : public Mat {
public:
  typedef _Tp value_type;
  typedef typename DataType<_Tp>::channel_type channel_type;
  typedef MatIterator_<_Tp> iterator;
  typedef MatConstIterator_<_Tp> const_iterator;

  //! default constructor
  Mat_() CV_NOEXCEPT;
  //! equivalent to Mat(_rows, _cols, DataType<_Tp>::type)
  Mat_(int _rows, int _cols);
  //! constructor that sets each matrix element to specified value
  Mat_(int _rows, int _cols, const _Tp &value);
  //! equivalent to Mat(_size, DataType<_Tp>::type)
  explicit Mat_(Size _size);
  //! constructor that sets each matrix element to specified value
  Mat_(Size _size, const _Tp &value);
  //! n-dim array constructor
  Mat_(int _ndims, const int *_sizes);
  //! n-dim array constructor that sets each matrix element to specified value
  Mat_(int _ndims, const int *_sizes, const _Tp &value);
  //! copy/conversion constructor. If m is of different type, it's converted
  Mat_(const Mat &m);
  //! copy constructor
  Mat_(const Mat_ &m);
  //! constructs a matrix on top of user-allocated data. step is in bytes(!!!),
  //! regardless of the type
  Mat_(int _rows, int _cols, _Tp *_data, size_t _step = AUTO_STEP);
  //! constructs n-dim matrix on top of user-allocated data. steps are in
  //! bytes(!!!), regardless of the type
  Mat_(int _ndims, const int *_sizes, _Tp *_data, const size_t *_steps = 0);
  //! selects a submatrix
  Mat_(const Mat_ &m, const Range &rowRange,
       const Range &colRange = Range::all());
  //! selects a submatrix
  Mat_(const Mat_ &m, const Rect &roi);
  //! selects a submatrix, n-dim version
  Mat_(const Mat_ &m, const Range *ranges);
  //! selects a submatrix, n-dim version
  Mat_(const Mat_ &m, const std::vector<Range> &ranges);
  //! from a matrix expression
  explicit Mat_(const MatExpr &e);
  //! makes a matrix out of Vec, std::vector, Point_ or Point3_. The matrix will
  //! have a single column
  explicit Mat_(const std::vector<_Tp> &vec, bool copyData = false);
  template <int n>
  explicit Mat_(const Vec<typename DataType<_Tp>::channel_type, n> &vec,
                bool copyData = true);
  template <int m, int n>
  explicit Mat_(const Matx<typename DataType<_Tp>::channel_type, m, n> &mtx,
                bool copyData = true);
  explicit Mat_(const Point_<typename DataType<_Tp>::channel_type> &pt,
                bool copyData = true);
  explicit Mat_(const Point3_<typename DataType<_Tp>::channel_type> &pt,
                bool copyData = true);
  explicit Mat_(const MatCommaInitializer_<_Tp> &commaInitializer);

  Mat_(std::initializer_list<_Tp> values);
  explicit Mat_(const std::initializer_list<int> sizes,
                const std::initializer_list<_Tp> values);

  template <std::size_t _Nm>
  explicit Mat_(const std::array<_Tp, _Nm> &arr, bool copyData = false);

  Mat_ &operator=(const Mat &m);
  Mat_ &operator=(const Mat_ &m);
  //! set all the elements to s.
  Mat_ &operator=(const _Tp &s);
  //! assign a matrix expression
  Mat_ &operator=(const MatExpr &e);

  //! iterators; they are smart enough to skip gaps in the end of rows
  iterator begin();
  iterator end();
  const_iterator begin() const;
  const_iterator end() const;

  // reverse iterators
  std::reverse_iterator<iterator> rbegin();
  std::reverse_iterator<iterator> rend();
  std::reverse_iterator<const_iterator> rbegin() const;
  std::reverse_iterator<const_iterator> rend() const;

  //! template methods for operation over all matrix elements.
  // the operations take care of skipping gaps in the end of rows (if any)
  template <typename Functor> void forEach(const Functor &operation);
  template <typename Functor> void forEach(const Functor &operation) const;

  //! equivalent to Mat::create(_rows, _cols, DataType<_Tp>::type)
  void create(int _rows, int _cols);
  //! equivalent to Mat::create(_size, DataType<_Tp>::type)
  void create(Size _size);
  //! equivalent to Mat::create(_ndims, _sizes, DatType<_Tp>::type)
  void create(int _ndims, const int *_sizes);
  //! equivalent to Mat::release()
  void release();
  //! cross-product
  Mat_ cross(const Mat_ &m) const;
  //! data type conversion
  template <typename T2> operator Mat_<T2>() const;
  //! overridden forms of Mat::row() etc.
  Mat_ row(int y) const;
  Mat_ col(int x) const;
  Mat_ diag(int d = 0) const;
  CV_NODISCARD_STD Mat_ clone() const;

  //! overridden forms of Mat::elemSize() etc.
  size_t elemSize() const;
  size_t elemSize1() const;
  int type() const;
  int depth() const;
  int channels() const;
  size_t step1(int i = 0) const;
  //! returns step()/sizeof(_Tp)
  size_t stepT(int i = 0) const;

  //! overridden forms of Mat::zeros() etc. Data type is omitted, of course
  CV_NODISCARD_STD static MatExpr zeros(int rows, int cols);
  CV_NODISCARD_STD static MatExpr zeros(Size size);
  CV_NODISCARD_STD static MatExpr zeros(int _ndims, const int *_sizes);
  CV_NODISCARD_STD static MatExpr ones(int rows, int cols);
  CV_NODISCARD_STD static MatExpr ones(Size size);
  CV_NODISCARD_STD static MatExpr ones(int _ndims, const int *_sizes);
  CV_NODISCARD_STD static MatExpr eye(int rows, int cols);
  CV_NODISCARD_STD static MatExpr eye(Size size);

  //! some more overridden methods
  Mat_ &adjustROI(int dtop, int dbottom, int dleft, int dright);
  Mat_ operator()(const Range &rowRange, const Range &colRange) const;
  Mat_ operator()(const Rect &roi) const;
  Mat_ operator()(const Range *ranges) const;
  Mat_ operator()(const std::vector<Range> &ranges) const;

  //! more convenient forms of row and element access operators
  _Tp *operator[](int y);
  const _Tp *operator[](int y) const;

  //! returns reference to the specified element
  _Tp &operator()(const int *idx);
  //! returns read-only reference to the specified element
  const _Tp &operator()(const int *idx) const;

  //! returns reference to the specified element
  template <int n> _Tp &operator()(const Vec<int, n> &idx);
  //! returns read-only reference to the specified element
  template <int n> const _Tp &operator()(const Vec<int, n> &idx) const;

  //! returns reference to the specified element (1D case)
  _Tp &operator()(int idx0);
  //! returns read-only reference to the specified element (1D case)
  const _Tp &operator()(int idx0) const;
  //! returns reference to the specified element (2D case)
  _Tp &operator()(int row, int col);
  //! returns read-only reference to the specified element (2D case)
  const _Tp &operator()(int row, int col) const;
  //! returns reference to the specified element (3D case)
  _Tp &operator()(int idx0, int idx1, int idx2);
  //! returns read-only reference to the specified element (3D case)
  const _Tp &operator()(int idx0, int idx1, int idx2) const;

  _Tp &operator()(Point pt);
  const _Tp &operator()(Point pt) const;

  //! conversion to vector.
  operator std::vector<_Tp>() const;

  //! conversion to array.
  template <std::size_t _Nm> operator std::array<_Tp, _Nm>() const;

  //! conversion to Vec
  template <int n>
  operator Vec<typename DataType<_Tp>::channel_type, n>() const;
  //! conversion to Matx
  template <int m, int n>
  operator Matx<typename DataType<_Tp>::channel_type, m, n>() const;

  Mat_(Mat_ &&m);
  Mat_ &operator=(Mat_ &&m);

  Mat_(Mat &&m);
  Mat_ &operator=(Mat &&m);

  Mat_(MatExpr &&e);
};

typedef Mat_<uchar> Mat1b;
typedef Mat_<Vec2b> Mat2b;
typedef Mat_<Vec3b> Mat3b;
typedef Mat_<Vec4b> Mat4b;

typedef Mat_<short> Mat1s;
typedef Mat_<Vec2s> Mat2s;
typedef Mat_<Vec3s> Mat3s;
typedef Mat_<Vec4s> Mat4s;

typedef Mat_<ushort> Mat1w;
typedef Mat_<Vec2w> Mat2w;
typedef Mat_<Vec3w> Mat3w;
typedef Mat_<Vec4w> Mat4w;

typedef Mat_<int> Mat1i;
typedef Mat_<Vec2i> Mat2i;
typedef Mat_<Vec3i> Mat3i;
typedef Mat_<Vec4i> Mat4i;

typedef Mat_<float> Mat1f;
typedef Mat_<Vec2f> Mat2f;
typedef Mat_<Vec3f> Mat3f;
typedef Mat_<Vec4f> Mat4f;

typedef Mat_<double> Mat1d;
typedef Mat_<Vec2d> Mat2d;
typedef Mat_<Vec3d> Mat3d;
typedef Mat_<Vec4d> Mat4d;

/////////////////////////// multi-dimensional sparse matrix
/////////////////////////////

/** @brief The class SparseMat represents multi-dimensional sparse numerical
arrays.

Such a sparse array can store elements of any type that Mat can store. *Sparse*
means that only non-zero elements are stored (though, as a result of operations
on a sparse matrix, some of its stored elements can actually become 0. It is up
to you to detect such elements and delete them using SparseMat::erase ). The
non-zero elements are stored in a hash table that grows when it is filled so
that the search time is O(1) in average (regardless of whether element is there
or not). Elements can be accessed using the following methods:
-   Query operations (SparseMat::ptr and the higher-level SparseMat::ref,
SparseMat::value and SparseMat::find), for example:
    @code
        const int dims = 5;
        int size[5] = {10, 10, 10, 10, 10};
        SparseMat sparse_mat(dims, size, CV_32F);
        for(int i = 0; i < 1000; i++)
        {
            int idx[dims];
            for(int k = 0; k < dims; k++)
                idx[k] = rand() % size[k];
            sparse_mat.ref<float>(idx) += 1.f;
        }
        cout << "nnz = " << sparse_mat.nzcount() << endl;
    @endcode
-   Sparse matrix iterators. They are similar to MatIterator but different from
NAryMatIterator. That is, the iteration loop is familiar to STL users:
    @code
        // prints elements of a sparse floating-point matrix
        // and the sum of elements.
        SparseMatConstIterator_<float>
            it = sparse_mat.begin<float>(),
            it_end = sparse_mat.end<float>();
        double s = 0;
        int dims = sparse_mat.dims();
        for(; it != it_end; ++it)
        {
            // print element indices and the element value
            const SparseMat::Node* n = it.node();
            printf("(");
            for(int i = 0; i < dims; i++)
                printf("%d%s", n->idx[i], i < dims-1 ? ", " : ")");
            printf(": %g\n", it.value<float>());
            s += *it;
        }
        printf("Element sum is %g\n", s);
    @endcode
    If you run this loop, you will notice that elements are not enumerated in a
logical order (lexicographical, and so on). They come in the same order as they
are stored in the hash table (semi-randomly). You may collect pointers to the
nodes and sort them to get the proper ordering. Note, however, that pointers to
the nodes may become invalid when you add more elements to the matrix. This may
happen due to possible buffer reallocation.
-   Combination of the above 2 methods when you need to process 2 or more sparse
matrices simultaneously. For example, this is how you can compute unnormalized
cross-correlation of the 2 floating-point sparse matrices:
    @code
        double cross_corr(const SparseMat& a, const SparseMat& b)
        {
            const SparseMat *_a = &a, *_b = &b;
            // if b contains less elements than a,
            // it is faster to iterate through b
            if(_a->nzcount() > _b->nzcount())
                std::swap(_a, _b);
            SparseMatConstIterator_<float> it = _a->begin<float>(),
                                           it_end = _a->end<float>();
            double ccorr = 0;
            for(; it != it_end; ++it)
            {
                // take the next element from the first matrix
                float avalue = *it;
                const Node* anode = it.node();
                // and try to find an element with the same index in the second
matrix.
                // since the hash value depends only on the element index,
                // reuse the hash value stored in the node
                float bvalue = _b->value<float>(anode->idx,&anode->hashval);
                ccorr += avalue*bvalue;
            }
            return ccorr;
        }
    @endcode
 */
class CV_EXPORTS SparseMat {
public:
  typedef SparseMatIterator iterator;
  typedef SparseMatConstIterator const_iterator;

  enum {
    MAGIC_VAL = 0x42FD0000,
    MAX_DIM = 32,
    HASH_SCALE = 0x5bd1e995,
    HASH_BIT = 0x80000000
  };

  //! the sparse matrix header
  struct CV_EXPORTS Hdr {
    Hdr(int _dims, const int *_sizes, int _type);
    void clear();
    int refcount;
    int dims;
    int valueOffset;
    size_t nodeSize;
    size_t nodeCount;
    size_t freeList;
    std::vector<uchar> pool;
    std::vector<size_t> hashtab;
    int size[MAX_DIM];
  };

  //! sparse matrix node - element of a hash table
  struct CV_EXPORTS Node {
    //! hash value
    size_t hashval;
    //! index of the next node in the same hash table entry
    size_t next;
    //! index of the matrix element
    int idx[MAX_DIM];
  };

  /** @brief Various SparseMat constructors.
   */
  SparseMat();

  /** @overload
  @param dims Array dimensionality.
  @param _sizes Sparce matrix size on all dementions.
  @param _type Sparse matrix data type.
  */
  SparseMat(int dims, const int *_sizes, int _type);

  /** @overload
  @param m Source matrix for copy constructor. If m is dense matrix (ocvMat)
  then it will be converted to sparse representation.
  */
  SparseMat(const SparseMat &m);

  /** @overload
  @param m Source matrix for copy constructor. If m is dense matrix (ocvMat)
  then it will be converted to sparse representation.
  */
  explicit SparseMat(const Mat &m);

  //! the destructor
  ~SparseMat();

  //! assignment operator. This is O(1) operation, i.e. no data is copied
  SparseMat &operator=(const SparseMat &m);
  //! equivalent to the corresponding constructor
  SparseMat &operator=(const Mat &m);

  //! creates full copy of the matrix
  CV_NODISCARD_STD SparseMat clone() const;

  //! copies all the data to the destination matrix. All the previous content of
  //! m is erased
  void copyTo(SparseMat &m) const;
  //! converts sparse matrix to dense matrix.
  void copyTo(Mat &m) const;
  //! multiplies all the matrix elements by the specified scale factor alpha and
  //! converts the results to the specified data type
  void convertTo(SparseMat &m, int rtype, double alpha = 1) const;
  //! converts sparse matrix to dense n-dim matrix with optional type conversion
  //! and scaling.
  /*!
      @param [out] m - output matrix; if it does not have a proper size or type
     before the operation, it is reallocated
      @param [in] rtype - desired output matrix type or, rather, the depth since
     the number of channels are the same as the input has; if rtype is negative,
     the output matrix will have the same type as the input.
      @param [in] alpha - optional scale factor
      @param [in] beta - optional delta added to the scaled values
  */
  void convertTo(Mat &m, int rtype, double alpha = 1, double beta = 0) const;

  // not used now
  void assignTo(SparseMat &m, int type = -1) const;

  //! reallocates sparse matrix.
  /*!
      If the matrix already had the proper size and type,
      it is simply cleared with clear(), otherwise,
      the old matrix is released (using release()) and the new one is allocated.
  */
  void create(int dims, const int *_sizes, int _type);
  //! sets all the sparse matrix elements to 0, which means clearing the hash
  //! table.
  void clear();
  //! manually increments the reference counter to the header.
  void addref();
  // decrements the header reference counter. When the counter reaches 0, the
  // header and all the underlying data are deallocated.
  void release();

  //! converts sparse matrix to the old-style representation; all the elements
  //! are copied.
  // operator CvSparseMat*() const;
  //! returns the size of each element in bytes (not including the overhead -
  //! the space occupied by SparseMat::Node elements)
  size_t elemSize() const;
  //! returns elemSize()/channels()
  size_t elemSize1() const;

  //! returns type of sparse matrix elements
  int type() const;
  //! returns the depth of sparse matrix elements
  int depth() const;
  //! returns the number of channels
  int channels() const;

  //! returns the array of sizes, or NULL if the matrix is not allocated
  const int *size() const;
  //! returns the size of i-th matrix dimension (or 0)
  int size(int i) const;
  //! returns the matrix dimensionality
  int dims() const;
  //! returns the number of non-zero elements (=the number of hash table nodes)
  size_t nzcount() const;

  //! computes the element hash value (1D case)
  size_t hash(int i0) const;
  //! computes the element hash value (2D case)
  size_t hash(int i0, int i1) const;
  //! computes the element hash value (3D case)
  size_t hash(int i0, int i1, int i2) const;
  //! computes the element hash value (nD case)
  size_t hash(const int *idx) const;

  //!@{
  /*!
   specialized variants for 1D, 2D, 3D cases and the generic_type one for n-D
   case. return pointer to the matrix element.
    - if the element is there (it's non-zero), the pointer to it is returned
    - if it's not there and createMissing=false, NULL pointer is returned
    - if it's not there and createMissing=true, then the new element
      is created and initialized with 0. Pointer to it is returned
    - if the optional hashval pointer is not NULL, the element hash value is
      not computed, but *hashval is taken instead.
  */
  //! returns pointer to the specified element (1D case)
  uchar *ptr(int i0, bool createMissing, size_t *hashval = 0);
  //! returns pointer to the specified element (2D case)
  uchar *ptr(int i0, int i1, bool createMissing, size_t *hashval = 0);
  //! returns pointer to the specified element (3D case)
  uchar *ptr(int i0, int i1, int i2, bool createMissing, size_t *hashval = 0);
  //! returns pointer to the specified element (nD case)
  uchar *ptr(const int *idx, bool createMissing, size_t *hashval = 0);
  //!@}

  //!@{
  /*!
   return read-write reference to the specified sparse matrix element.

   `ref<_Tp>(i0,...[,hashval])` is equivalent to
   `*(_Tp*)ptr(i0,...,true[,hashval])`. The methods always return a valid
   reference. If the element did not exist, it is created and initialized with
   0.
  */
  //! returns reference to the specified element (1D case)
  template <typename _Tp> _Tp &ref(int i0, size_t *hashval = 0);
  //! returns reference to the specified element (2D case)
  template <typename _Tp> _Tp &ref(int i0, int i1, size_t *hashval = 0);
  //! returns reference to the specified element (3D case)
  template <typename _Tp> _Tp &ref(int i0, int i1, int i2, size_t *hashval = 0);
  //! returns reference to the specified element (nD case)
  template <typename _Tp> _Tp &ref(const int *idx, size_t *hashval = 0);
  //!@}

  //!@{
  /*!
   return value of the specified sparse matrix element.

   `value<_Tp>(i0,...[,hashval])` is equivalent to
   @code
   { const _Tp* p = find<_Tp>(i0,...[,hashval]); return p ? *p : _Tp(); }
   @endcode

   That is, if the element did not exist, the methods return 0.
   */
  //! returns value of the specified element (1D case)
  template <typename _Tp> _Tp value(int i0, size_t *hashval = 0) const;
  //! returns value of the specified element (2D case)
  template <typename _Tp> _Tp value(int i0, int i1, size_t *hashval = 0) const;
  //! returns value of the specified element (3D case)
  template <typename _Tp>
  _Tp value(int i0, int i1, int i2, size_t *hashval = 0) const;
  //! returns value of the specified element (nD case)
  template <typename _Tp> _Tp value(const int *idx, size_t *hashval = 0) const;
  //!@}

  //!@{
  /*!
   Return pointer to the specified sparse matrix element if it exists

   `find<_Tp>(i0,...[,hashval])` is equivalent to `(_const
   Tp*)ptr(i0,...false[,hashval])`.

   If the specified element does not exist, the methods return NULL.
  */
  //! returns pointer to the specified element (1D case)
  template <typename _Tp> const _Tp *find(int i0, size_t *hashval = 0) const;
  //! returns pointer to the specified element (2D case)
  template <typename _Tp>
  const _Tp *find(int i0, int i1, size_t *hashval = 0) const;
  //! returns pointer to the specified element (3D case)
  template <typename _Tp>
  const _Tp *find(int i0, int i1, int i2, size_t *hashval = 0) const;
  //! returns pointer to the specified element (nD case)
  template <typename _Tp>
  const _Tp *find(const int *idx, size_t *hashval = 0) const;
  //!@}

  //! erases the specified element (2D case)
  void erase(int i0, int i1, size_t *hashval = 0);
  //! erases the specified element (3D case)
  void erase(int i0, int i1, int i2, size_t *hashval = 0);
  //! erases the specified element (nD case)
  void erase(const int *idx, size_t *hashval = 0);

  //!@{
  /*!
     return the sparse matrix iterator pointing to the first sparse matrix
     element
  */
  //! returns the sparse matrix iterator at the matrix beginning
  SparseMatIterator begin();
  //! returns the sparse matrix iterator at the matrix beginning
  template <typename _Tp> SparseMatIterator_<_Tp> begin();
  //! returns the read-only sparse matrix iterator at the matrix beginning
  SparseMatConstIterator begin() const;
  //! returns the read-only sparse matrix iterator at the matrix beginning
  template <typename _Tp> SparseMatConstIterator_<_Tp> begin() const;
  //!@}
  /*!
     return the sparse matrix iterator pointing to the element following the
     last sparse matrix element
  */
  //! returns the sparse matrix iterator at the matrix end
  SparseMatIterator end();
  //! returns the read-only sparse matrix iterator at the matrix end
  SparseMatConstIterator end() const;
  //! returns the typed sparse matrix iterator at the matrix end
  template <typename _Tp> SparseMatIterator_<_Tp> end();
  //! returns the typed read-only sparse matrix iterator at the matrix end
  template <typename _Tp> SparseMatConstIterator_<_Tp> end() const;

  //! returns the value stored in the sparse martix node
  template <typename _Tp> _Tp &value(Node *n);
  //! returns the value stored in the sparse martix node
  template <typename _Tp> const _Tp &value(const Node *n) const;

  ////////////// some internal-use methods ///////////////
  Node *node(size_t nidx);
  const Node *node(size_t nidx) const;

  uchar *newNode(const int *idx, size_t hashval);
  void removeNode(size_t hidx, size_t nidx, size_t previdx);
  void resizeHashTab(size_t newsize);

  int flags;
  Hdr *hdr;
};

///////////////////////////////// SparseMat_<_Tp>
///////////////////////////////////////

/** @brief Template sparse n-dimensional array class derived from SparseMat

SparseMat_ is a thin wrapper on top of SparseMat created in the same way as Mat_
. It simplifies notation of some operations:
@code
    int sz[] = {10, 20, 30};
    SparseMat_<double> M(3, sz);
    ...
    M.ref(1, 2, 3) = M(4, 5, 6) + M(7, 8, 9);
@endcode
 */
template <typename _Tp> class SparseMat_ : public SparseMat {
public:
  typedef SparseMatIterator_<_Tp> iterator;
  typedef SparseMatConstIterator_<_Tp> const_iterator;

  //! the default constructor
  SparseMat_();
  //! the full constructor equivalent to SparseMat(dims, _sizes,
  //! DataType<_Tp>::type)
  SparseMat_(int dims, const int *_sizes);
  //! the copy constructor. If DataType<_Tp>.type != m.type(), the m elements
  //! are converted
  SparseMat_(const SparseMat &m);
  //! the copy constructor. This is O(1) operation - no data is copied
  SparseMat_(const SparseMat_ &m);
  //! converts dense matrix to the sparse form
  SparseMat_(const Mat &m);
  //! converts the old-style sparse matrix to the C++ class. All the elements
  //! are copied
  // SparseMat_(const CvSparseMat* m);
  //! the assignment operator. If DataType<_Tp>.type != m.type(), the m elements
  //! are converted
  SparseMat_ &operator=(const SparseMat &m);
  //! the assignment operator. This is O(1) operation - no data is copied
  SparseMat_ &operator=(const SparseMat_ &m);
  //! converts dense matrix to the sparse form
  SparseMat_ &operator=(const Mat &m);

  //! makes full copy of the matrix. All the elements are duplicated
  CV_NODISCARD_STD SparseMat_ clone() const;
  //! equivalent to cv::SparseMat::create(dims, _sizes, DataType<_Tp>::type)
  void create(int dims, const int *_sizes);
  //! converts sparse matrix to the old-style CvSparseMat. All the elements are
  //! copied
  // operator CvSparseMat*() const;

  //! returns type of the matrix elements
  int type() const;
  //! returns depth of the matrix elements
  int depth() const;
  //! returns the number of channels in each matrix element
  int channels() const;

  //! equivalent to SparseMat::ref<_Tp>(i0, hashval)
  _Tp &ref(int i0, size_t *hashval = 0);
  //! equivalent to SparseMat::ref<_Tp>(i0, i1, hashval)
  _Tp &ref(int i0, int i1, size_t *hashval = 0);
  //! equivalent to SparseMat::ref<_Tp>(i0, i1, i2, hashval)
  _Tp &ref(int i0, int i1, int i2, size_t *hashval = 0);
  //! equivalent to SparseMat::ref<_Tp>(idx, hashval)
  _Tp &ref(const int *idx, size_t *hashval = 0);

  //! equivalent to SparseMat::value<_Tp>(i0, hashval)
  _Tp operator()(int i0, size_t *hashval = 0) const;
  //! equivalent to SparseMat::value<_Tp>(i0, i1, hashval)
  _Tp operator()(int i0, int i1, size_t *hashval = 0) const;
  //! equivalent to SparseMat::value<_Tp>(i0, i1, i2, hashval)
  _Tp operator()(int i0, int i1, int i2, size_t *hashval = 0) const;
  //! equivalent to SparseMat::value<_Tp>(idx, hashval)
  _Tp operator()(const int *idx, size_t *hashval = 0) const;

  //! returns sparse matrix iterator pointing to the first sparse matrix element
  SparseMatIterator_<_Tp> begin();
  //! returns read-only sparse matrix iterator pointing to the first sparse
  //! matrix element
  SparseMatConstIterator_<_Tp> begin() const;
  //! returns sparse matrix iterator pointing to the element following the last
  //! sparse matrix element
  SparseMatIterator_<_Tp> end();
  //! returns read-only sparse matrix iterator pointing to the element following
  //! the last sparse matrix element
  SparseMatConstIterator_<_Tp> end() const;
};

////////////////////////////////// MatConstIterator
/////////////////////////////////////

class CV_EXPORTS MatConstIterator {
public:
  typedef uchar *value_type;
  typedef ptrdiff_t difference_type;
  typedef const uchar **pointer;
  typedef uchar *reference;

  typedef std::random_access_iterator_tag iterator_category;

  //! default constructor
  MatConstIterator();
  //! constructor that sets the iterator to the beginning of the matrix
  MatConstIterator(const Mat *_m);
  //! constructor that sets the iterator to the specified element of the matrix
  MatConstIterator(const Mat *_m, int _row, int _col = 0);
  //! constructor that sets the iterator to the specified element of the matrix
  MatConstIterator(const Mat *_m, Point _pt);
  //! constructor that sets the iterator to the specified element of the matrix
  MatConstIterator(const Mat *_m, const int *_idx);
  //! copy constructor
  MatConstIterator(const MatConstIterator &it);

  //! copy operator
  MatConstIterator &operator=(const MatConstIterator &it);
  //! returns the current matrix element
  const uchar *operator*() const;
  //! returns the i-th matrix element, relative to the current
  const uchar *operator[](ptrdiff_t i) const;

  //! shifts the iterator forward by the specified number of elements
  MatConstIterator &operator+=(ptrdiff_t ofs);
  //! shifts the iterator backward by the specified number of elements
  MatConstIterator &operator-=(ptrdiff_t ofs);
  //! decrements the iterator
  MatConstIterator &operator--();
  //! decrements the iterator
  MatConstIterator operator--(int);
  //! increments the iterator
  MatConstIterator &operator++();
  //! increments the iterator
  MatConstIterator operator++(int);
  //! returns the current iterator position
  Point pos() const;
  //! returns the current iterator position
  void pos(int *_idx) const;

  ptrdiff_t lpos() const;
  void seek(ptrdiff_t ofs, bool relative = false);
  void seek(const int *_idx, bool relative = false);

  const Mat *m;
  size_t elemSize;
  const uchar *ptr;
  const uchar *sliceStart;
  const uchar *sliceEnd;
};

////////////////////////////////// MatConstIterator_
////////////////////////////////////

/** @brief Matrix read-only iterator
 */
template <typename _Tp> class MatConstIterator_ : public MatConstIterator {
public:
  typedef _Tp value_type;
  typedef ptrdiff_t difference_type;
  typedef const _Tp *pointer;
  typedef const _Tp &reference;

  typedef std::random_access_iterator_tag iterator_category;

  //! default constructor
  MatConstIterator_();
  //! constructor that sets the iterator to the beginning of the matrix
  MatConstIterator_(const Mat_<_Tp> *_m);
  //! constructor that sets the iterator to the specified element of the matrix
  MatConstIterator_(const Mat_<_Tp> *_m, int _row, int _col = 0);
  //! constructor that sets the iterator to the specified element of the matrix
  MatConstIterator_(const Mat_<_Tp> *_m, Point _pt);
  //! constructor that sets the iterator to the specified element of the matrix
  MatConstIterator_(const Mat_<_Tp> *_m, const int *_idx);
  //! copy constructor
  MatConstIterator_(const MatConstIterator_ &it);

  //! copy operator
  MatConstIterator_ &operator=(const MatConstIterator_ &it);
  //! returns the current matrix element
  const _Tp &operator*() const;
  //! returns the i-th matrix element, relative to the current
  const _Tp &operator[](ptrdiff_t i) const;

  //! shifts the iterator forward by the specified number of elements
  MatConstIterator_ &operator+=(ptrdiff_t ofs);
  //! shifts the iterator backward by the specified number of elements
  MatConstIterator_ &operator-=(ptrdiff_t ofs);
  //! decrements the iterator
  MatConstIterator_ &operator--();
  //! decrements the iterator
  MatConstIterator_ operator--(int);
  //! increments the iterator
  MatConstIterator_ &operator++();
  //! increments the iterator
  MatConstIterator_ operator++(int);
  //! returns the current iterator position
  Point pos() const;
};

//////////////////////////////////// MatIterator_
///////////////////////////////////////

/** @brief Matrix read-write iterator
 */
template <typename _Tp> class MatIterator_ : public MatConstIterator_<_Tp> {
public:
  typedef _Tp *pointer;
  typedef _Tp &reference;

  typedef std::random_access_iterator_tag iterator_category;

  //! the default constructor
  MatIterator_();
  //! constructor that sets the iterator to the beginning of the matrix
  MatIterator_(Mat_<_Tp> *_m);
  //! constructor that sets the iterator to the specified element of the matrix
  MatIterator_(Mat_<_Tp> *_m, int _row, int _col = 0);
  //! constructor that sets the iterator to the specified element of the matrix
  MatIterator_(Mat_<_Tp> *_m, Point _pt);
  //! constructor that sets the iterator to the specified element of the matrix
  MatIterator_(Mat_<_Tp> *_m, const int *_idx);
  //! copy constructor
  MatIterator_(const MatIterator_ &it);
  //! copy operator
  MatIterator_ &operator=(const MatIterator_<_Tp> &it);

  //! returns the current matrix element
  _Tp &operator*() const;
  //! returns the i-th matrix element, relative to the current
  _Tp &operator[](ptrdiff_t i) const;

  //! shifts the iterator forward by the specified number of elements
  MatIterator_ &operator+=(ptrdiff_t ofs);
  //! shifts the iterator backward by the specified number of elements
  MatIterator_ &operator-=(ptrdiff_t ofs);
  //! decrements the iterator
  MatIterator_ &operator--();
  //! decrements the iterator
  MatIterator_ operator--(int);
  //! increments the iterator
  MatIterator_ &operator++();
  //! increments the iterator
  MatIterator_ operator++(int);
};

/////////////////////////////// SparseMatConstIterator
//////////////////////////////////

/**  @brief Read-Only Sparse Matrix Iterator.

 Here is how to use the iterator to compute the sum of floating-point sparse
 matrix elements:

 \code
 SparseMatConstIterator it = m.begin(), it_end = m.end();
 double s = 0;
 CV_Assert( m.type() == CV_32F );
 for( ; it != it_end; ++it )
    s += it.value<float>();
 \endcode
*/
class CV_EXPORTS SparseMatConstIterator {
public:
  //! the default constructor
  SparseMatConstIterator();
  //! the full constructor setting the iterator to the first sparse matrix
  //! element
  SparseMatConstIterator(const SparseMat *_m);
  //! the copy constructor
  SparseMatConstIterator(const SparseMatConstIterator &it);

  //! the assignment operator
  SparseMatConstIterator &operator=(const SparseMatConstIterator &it);

  //! template method returning the current matrix element
  template <typename _Tp> const _Tp &value() const;
  //! returns the current node of the sparse matrix. it.node->idx is the current
  //! element index
  const SparseMat::Node *node() const;

  //! moves iterator to the previous element
  SparseMatConstIterator &operator--();
  //! moves iterator to the previous element
  SparseMatConstIterator operator--(int);
  //! moves iterator to the next element
  SparseMatConstIterator &operator++();
  //! moves iterator to the next element
  SparseMatConstIterator operator++(int);

  //! moves iterator to the element after the last element
  void seekEnd();

  const SparseMat *m;
  size_t hashidx;
  uchar *ptr;
};

////////////////////////////////// SparseMatIterator
////////////////////////////////////

/** @brief  Read-write Sparse Matrix Iterator

 The class is similar to cv::SparseMatConstIterator,
 but can be used for in-place modification of the matrix elements.
*/
class CV_EXPORTS SparseMatIterator : public SparseMatConstIterator {
public:
  //! the default constructor
  SparseMatIterator();
  //! the full constructor setting the iterator to the first sparse matrix
  //! element
  SparseMatIterator(SparseMat *_m);
  //! the full constructor setting the iterator to the specified sparse matrix
  //! element
  SparseMatIterator(SparseMat *_m, const int *idx);
  //! the copy constructor
  SparseMatIterator(const SparseMatIterator &it);

  //! the assignment operator
  SparseMatIterator &operator=(const SparseMatIterator &it);
  //! returns read-write reference to the current sparse matrix element
  template <typename _Tp> _Tp &value() const;
  //! returns pointer to the current sparse matrix node. it.node->idx is the
  //! index of the current element (do not modify it!)
  SparseMat::Node *node() const;

  //! moves iterator to the next element
  SparseMatIterator &operator++();
  //! moves iterator to the next element
  SparseMatIterator operator++(int);
};

/////////////////////////////// SparseMatConstIterator_
/////////////////////////////////

/** @brief  Template Read-Only Sparse Matrix Iterator Class.

 This is the derived from SparseMatConstIterator class that
 introduces more convenient operator *() for accessing the current element.
*/
template <typename _Tp>
class SparseMatConstIterator_ : public SparseMatConstIterator {
public:
  typedef std::forward_iterator_tag iterator_category;

  //! the default constructor
  SparseMatConstIterator_();
  //! the full constructor setting the iterator to the first sparse matrix
  //! element
  SparseMatConstIterator_(const SparseMat_<_Tp> *_m);
  SparseMatConstIterator_(const SparseMat *_m);
  //! the copy constructor
  SparseMatConstIterator_(const SparseMatConstIterator_ &it);

  //! the assignment operator
  SparseMatConstIterator_ &operator=(const SparseMatConstIterator_ &it);
  //! the element access operator
  const _Tp &operator*() const;

  //! moves iterator to the next element
  SparseMatConstIterator_ &operator++();
  //! moves iterator to the next element
  SparseMatConstIterator_ operator++(int);
};

///////////////////////////////// SparseMatIterator_
////////////////////////////////////

/** @brief  Template Read-Write Sparse Matrix Iterator Class.

 This is the derived from cv::SparseMatConstIterator_ class that
 introduces more convenient operator *() for accessing the current element.
*/
template <typename _Tp>
class SparseMatIterator_ : public SparseMatConstIterator_<_Tp> {
public:
  typedef std::forward_iterator_tag iterator_category;

  //! the default constructor
  SparseMatIterator_();
  //! the full constructor setting the iterator to the first sparse matrix
  //! element
  SparseMatIterator_(SparseMat_<_Tp> *_m);
  SparseMatIterator_(SparseMat *_m);
  //! the copy constructor
  SparseMatIterator_(const SparseMatIterator_ &it);

  //! the assignment operator
  SparseMatIterator_ &operator=(const SparseMatIterator_ &it);
  //! returns the reference to the current element
  _Tp &operator*() const;

  //! moves the iterator to the next element
  SparseMatIterator_ &operator++();
  //! moves the iterator to the next element
  SparseMatIterator_ operator++(int);
};

/////////////////////////////////// NAryMatIterator
/////////////////////////////////////

/** @brief n-ary multi-dimensional array iterator.

Use the class to implement unary, binary, and, generally, n-ary element-wise
operations on multi-dimensional arrays. Some of the arguments of an n-ary
function may be continuous arrays, some may be not. It is possible to use
conventional MatIterator 's for each array but incrementing all of the iterators
after each small operations may be a big overhead. In this case consider using
NAryMatIterator to iterate through several matrices simultaneously as long as
they have the same geometry (dimensionality and all the dimension sizes are the
same). On each iteration `it.planes[0]`, `it.planes[1]`,... will be the slices
of the corresponding matrices.

The example below illustrates how you can compute a normalized and threshold 3D
color histogram:
@code
    void computeNormalizedColorHist(const Mat& image, Mat& hist, int N, double
minProb)
    {
        const int histSize[] = {N, N, N};

        // make sure that the histogram has a proper size and type
        hist.create(3, histSize, CV_32F);

        // and clear it
        hist = Scalar(0);

        // the loop below assumes that the image
        // is a 8-bit 3-channel. check it.
        CV_Assert(image.type() == CV_8UC3);
        MatConstIterator_<Vec3b> it = image.begin<Vec3b>(),
                                 it_end = image.end<Vec3b>();
        for( ; it != it_end; ++it )
        {
            const Vec3b& pix = *it;
            hist.at<float>(pix[0]*N/256, pix[1]*N/256, pix[2]*N/256) += 1.f;
        }

        minProb *= image.rows*image.cols;

        // initialize iterator (the style is different from STL).
        // after initialization the iterator will contain
        // the number of slices or planes the iterator will go through.
        // it simultaneously increments iterators for several matrices
        // supplied as a null terminated list of pointers
        const Mat* arrays[] = {&hist, 0};
        Mat planes[1];
        NAryMatIterator itNAry(arrays, planes, 1);
        double s = 0;
        // iterate through the matrix. on each iteration
        // itNAry.planes[i] (of type Mat) will be set to the current plane
        // of the i-th n-dim matrix passed to the iterator constructor.
        for(int p = 0; p < itNAry.nplanes; p++, ++itNAry)
        {
            threshold(itNAry.planes[0], itNAry.planes[0], minProb, 0,
THRESH_TOZERO); s += sum(itNAry.planes[0])[0];
        }

        s = 1./s;
        itNAry = NAryMatIterator(arrays, planes, 1);
        for(int p = 0; p < itNAry.nplanes; p++, ++itNAry)
            itNAry.planes[0] *= s;
    }
@endcode
 */
class CV_EXPORTS NAryMatIterator {
public:
  //! the default constructor
  NAryMatIterator();
  //! the full constructor taking arbitrary number of n-dim matrices
  NAryMatIterator(const Mat **arrays, uchar **ptrs, int narrays = -1);
  //! the full constructor taking arbitrary number of n-dim matrices
  NAryMatIterator(const Mat **arrays, Mat *planes, int narrays = -1);
  //! the separate iterator initialization method
  void init(const Mat **arrays, Mat *planes, uchar **ptrs, int narrays = -1);

  //! proceeds to the next plane of every iterated matrix
  NAryMatIterator &operator++();
  //! proceeds to the next plane of every iterated matrix (postfix increment
  //! operator)
  NAryMatIterator operator++(int);

  //! the iterated arrays
  const Mat **arrays;
  //! the current planes
  Mat *planes;
  //! data pointers
  uchar **ptrs;
  //! the number of arrays
  int narrays;
  //! the number of hyper-planes that the iterator steps through
  size_t nplanes;
  //! the size of each segment (in elements)
  size_t size;

protected:
  int iterdepth;
  size_t idx;
};

///////////////////////////////// Matrix Expressions
////////////////////////////////////

class CV_EXPORTS MatOp {
public:
  MatOp();
  virtual ~MatOp();

  virtual bool elementWise(const MatExpr &expr) const;
  virtual void assign(const MatExpr &expr, Mat &m, int type = -1) const = 0;
  virtual void roi(const MatExpr &expr, const Range &rowRange,
                   const Range &colRange, MatExpr &res) const;
  virtual void diag(const MatExpr &expr, int d, MatExpr &res) const;
  virtual void augAssignAdd(const MatExpr &expr, Mat &m) const;
  virtual void augAssignSubtract(const MatExpr &expr, Mat &m) const;
  virtual void augAssignMultiply(const MatExpr &expr, Mat &m) const;
  virtual void augAssignDivide(const MatExpr &expr, Mat &m) const;
  virtual void augAssignAnd(const MatExpr &expr, Mat &m) const;
  virtual void augAssignOr(const MatExpr &expr, Mat &m) const;
  virtual void augAssignXor(const MatExpr &expr, Mat &m) const;

  virtual void add(const MatExpr &expr1, const MatExpr &expr2,
                   MatExpr &res) const;
  virtual void add(const MatExpr &expr1, const Scalar &s, MatExpr &res) const;

  virtual void subtract(const MatExpr &expr1, const MatExpr &expr2,
                        MatExpr &res) const;
  virtual void subtract(const Scalar &s, const MatExpr &expr,
                        MatExpr &res) const;

  virtual void multiply(const MatExpr &expr1, const MatExpr &expr2,
                        MatExpr &res, double scale = 1) const;
  virtual void multiply(const MatExpr &expr1, double s, MatExpr &res) const;

  virtual void divide(const MatExpr &expr1, const MatExpr &expr2, MatExpr &res,
                      double scale = 1) const;
  virtual void divide(double s, const MatExpr &expr, MatExpr &res) const;

  virtual void abs(const MatExpr &expr, MatExpr &res) const;

  virtual void transpose(const MatExpr &expr, MatExpr &res) const;
  virtual void matmul(const MatExpr &expr1, const MatExpr &expr2,
                      MatExpr &res) const;
  virtual void invert(const MatExpr &expr, int method, MatExpr &res) const;

  virtual Size size(const MatExpr &expr) const;
  virtual int type(const MatExpr &expr) const;
};

/** @brief Matrix expression representation
@anchor MatrixExpressions
This is a list of implemented matrix operations that can be combined in
arbitrary complex expressions (here A, B stand for matrices ( Mat ), s for a
scalar ( Scalar ), alpha for a real-valued scalar ( double )):
-   Addition, subtraction, negation: `A+B`, `A-B`, `A+s`, `A-s`, `s+A`, `s-A`,
`-A`
-   Scaling: `A*alpha`
-   Per-element multiplication and division: `A.mul(B)`, `A/B`, `alpha/A`
-   Matrix multiplication: `A*B`
-   Transposition: `A.t()` (means A<sup>T</sup>)
-   Matrix inversion and pseudo-inversion, solving linear systems and
least-squares problems: `A.inv([method]) (~ A<sup>-1</sup>)`, `A.inv([method])*B
(~ X: AX=B)`
-   Comparison: `A cmpop B`, `A cmpop alpha`, `alpha cmpop A`, where *cmpop* is
one of
  `>`, `>=`, `==`, `!=`, `<=`, `<`. The result of comparison is an 8-bit single
channel mask whose elements are set to 255 (if the particular element or pair of
elements satisfy the condition) or 0.
-   Bitwise logical operations: `A logicop B`, `A logicop s`, `s logicop A`,
`~A`, where *logicop* is one of
  `&`, `|`, `^`.
-   Element-wise minimum and maximum: `min(A, B)`, `min(A, alpha)`, `max(A, B)`,
`max(A, alpha)`
-   Element-wise absolute value: `abs(A)`
-   Cross-product, dot-product: `A.cross(B)`, `A.dot(B)`
-   Any function of matrix or matrices and scalars that returns a matrix or a
scalar, such as norm, mean, sum, countNonZero, trace, determinant, repeat, and
others.
-   Matrix initializers ( Mat::eye(), Mat::zeros(), Mat::ones() ), matrix
comma-separated initializers, matrix constructors and operators that extract
sub-matrices (see Mat description).
-   Mat_<destination_type>() constructors to cast the result to the proper type.
@note Comma-separated initializers and probably some other operations may
require additional explicit Mat() or Mat_<T>() constructor calls to resolve a
possible ambiguity.

Here are examples of matrix expressions:
@code
    // compute pseudo-inverse of A, equivalent to A.inv(DECOMP_SVD)
    SVD svd(A);
    Mat pinvA = svd.vt.t()*Mat::diag(1./svd.w)*svd.u.t();

    // compute the new vector of parameters in the Levenberg-Marquardt algorithm
    x -= (A.t()*A +
lambda*Mat::eye(A.cols,A.cols,A.type())).inv(DECOMP_CHOLESKY)*(A.t()*err);

    // sharpen image using "unsharp mask" algorithm
    Mat blurred; double sigma = 1, threshold = 5, amount = 1;
    GaussianBlur(img, blurred, Size(), sigma, sigma);
    Mat lowContrastMask = abs(img - blurred) < threshold;
    Mat sharpened = img*(1+amount) + blurred*(-amount);
    img.copyTo(sharpened, lowContrastMask);
@endcode
*/
class CV_EXPORTS MatExpr {
public:
  MatExpr();
  explicit MatExpr(const Mat &m);

  MatExpr(const MatOp *_op, int _flags, const Mat &_a = Mat(),
          const Mat &_b = Mat(), const Mat &_c = Mat(), double _alpha = 1,
          double _beta = 1, const Scalar &_s = Scalar());

  operator Mat() const;
  template <typename _Tp> operator Mat_<_Tp>() const;

  Size size() const;
  int type() const;

  MatExpr row(int y) const;
  MatExpr col(int x) const;
  MatExpr diag(int d = 0) const;
  MatExpr operator()(const Range &rowRange, const Range &colRange) const;
  MatExpr operator()(const Rect &roi) const;

  MatExpr t() const;
  MatExpr inv(int method = DECOMP_LU) const;
  MatExpr mul(const MatExpr &e, double scale = 1) const;
  MatExpr mul(const Mat &m, double scale = 1) const;

  Mat cross(const Mat &m) const;
  double dot(const Mat &m) const;

  void swap(MatExpr &b);

  const MatOp *op;
  int flags;

  Mat a, b, c;
  double alpha, beta;
  Scalar s;
};

//! @} core_basic

//! @relates cv::MatExpr
//! @{
CV_EXPORTS MatExpr operator+(const Mat &a, const Mat &b);
CV_EXPORTS MatExpr operator+(const Mat &a, const Scalar &s);
CV_EXPORTS MatExpr operator+(const Scalar &s, const Mat &a);
CV_EXPORTS MatExpr operator+(const MatExpr &e, const Mat &m);
CV_EXPORTS MatExpr operator+(const Mat &m, const MatExpr &e);
CV_EXPORTS MatExpr operator+(const MatExpr &e, const Scalar &s);
CV_EXPORTS MatExpr operator+(const Scalar &s, const MatExpr &e);
CV_EXPORTS MatExpr operator+(const MatExpr &e1, const MatExpr &e2);
template <typename _Tp, int m, int n>
static inline MatExpr operator+(const Mat &a, const Matx<_Tp, m, n> &b) {
  return a + Mat(b);
}
template <typename _Tp, int m, int n>
static inline MatExpr operator+(const Matx<_Tp, m, n> &a, const Mat &b) {
  return Mat(a) + b;
}

CV_EXPORTS MatExpr operator-(const Mat &a, const Mat &b);
CV_EXPORTS MatExpr operator-(const Mat &a, const Scalar &s);
CV_EXPORTS MatExpr operator-(const Scalar &s, const Mat &a);
CV_EXPORTS MatExpr operator-(const MatExpr &e, const Mat &m);
CV_EXPORTS MatExpr operator-(const Mat &m, const MatExpr &e);
CV_EXPORTS MatExpr operator-(const MatExpr &e, const Scalar &s);
CV_EXPORTS MatExpr operator-(const Scalar &s, const MatExpr &e);
CV_EXPORTS MatExpr operator-(const MatExpr &e1, const MatExpr &e2);
template <typename _Tp, int m, int n>
static inline MatExpr operator-(const Mat &a, const Matx<_Tp, m, n> &b) {
  return a - Mat(b);
}
template <typename _Tp, int m, int n>
static inline MatExpr operator-(const Matx<_Tp, m, n> &a, const Mat &b) {
  return Mat(a) - b;
}

CV_EXPORTS MatExpr operator-(const Mat &m);
CV_EXPORTS MatExpr operator-(const MatExpr &e);

CV_EXPORTS MatExpr operator*(const Mat &a, const Mat &b);
CV_EXPORTS MatExpr operator*(const Mat &a, double s);
CV_EXPORTS MatExpr operator*(double s, const Mat &a);
CV_EXPORTS MatExpr operator*(const MatExpr &e, const Mat &m);
CV_EXPORTS MatExpr operator*(const Mat &m, const MatExpr &e);
CV_EXPORTS MatExpr operator*(const MatExpr &e, double s);
CV_EXPORTS MatExpr operator*(double s, const MatExpr &e);
CV_EXPORTS MatExpr operator*(const MatExpr &e1, const MatExpr &e2);
template <typename _Tp, int m, int n>
static inline MatExpr operator*(const Mat &a, const Matx<_Tp, m, n> &b) {
  return a * Mat(b);
}
template <typename _Tp, int m, int n>
static inline MatExpr operator*(const Matx<_Tp, m, n> &a, const Mat &b) {
  return Mat(a) * b;
}

CV_EXPORTS MatExpr operator/(const Mat &a, const Mat &b);
CV_EXPORTS MatExpr operator/(const Mat &a, double s);
CV_EXPORTS MatExpr operator/(double s, const Mat &a);
CV_EXPORTS MatExpr operator/(const MatExpr &e, const Mat &m);
CV_EXPORTS MatExpr operator/(const Mat &m, const MatExpr &e);
CV_EXPORTS MatExpr operator/(const MatExpr &e, double s);
CV_EXPORTS MatExpr operator/(double s, const MatExpr &e);
CV_EXPORTS MatExpr operator/(const MatExpr &e1, const MatExpr &e2);
template <typename _Tp, int m, int n>
static inline MatExpr operator/(const Mat &a, const Matx<_Tp, m, n> &b) {
  return a / Mat(b);
}
template <typename _Tp, int m, int n>
static inline MatExpr operator/(const Matx<_Tp, m, n> &a, const Mat &b) {
  return Mat(a) / b;
}

CV_EXPORTS MatExpr operator<(const Mat &a, const Mat &b);
CV_EXPORTS MatExpr operator<(const Mat &a, double s);
CV_EXPORTS MatExpr operator<(double s, const Mat &a);
template <typename _Tp, int m, int n>
static inline MatExpr operator<(const Mat &a, const Matx<_Tp, m, n> &b) {
  return a < Mat(b);
}
template <typename _Tp, int m, int n>
static inline MatExpr operator<(const Matx<_Tp, m, n> &a, const Mat &b) {
  return Mat(a) < b;
}

CV_EXPORTS MatExpr operator<=(const Mat &a, const Mat &b);
CV_EXPORTS MatExpr operator<=(const Mat &a, double s);
CV_EXPORTS MatExpr operator<=(double s, const Mat &a);
template <typename _Tp, int m, int n>
static inline MatExpr operator<=(const Mat &a, const Matx<_Tp, m, n> &b) {
  return a <= Mat(b);
}
template <typename _Tp, int m, int n>
static inline MatExpr operator<=(const Matx<_Tp, m, n> &a, const Mat &b) {
  return Mat(a) <= b;
}

CV_EXPORTS MatExpr operator==(const Mat &a, const Mat &b);
CV_EXPORTS MatExpr operator==(const Mat &a, double s);
CV_EXPORTS MatExpr operator==(double s, const Mat &a);
template <typename _Tp, int m, int n>
static inline MatExpr operator==(const Mat &a, const Matx<_Tp, m, n> &b) {
  return a == Mat(b);
}
template <typename _Tp, int m, int n>
static inline MatExpr operator==(const Matx<_Tp, m, n> &a, const Mat &b) {
  return Mat(a) == b;
}

CV_EXPORTS MatExpr operator!=(const Mat &a, const Mat &b);
CV_EXPORTS MatExpr operator!=(const Mat &a, double s);
CV_EXPORTS MatExpr operator!=(double s, const Mat &a);
template <typename _Tp, int m, int n>
static inline MatExpr operator!=(const Mat &a, const Matx<_Tp, m, n> &b) {
  return a != Mat(b);
}
template <typename _Tp, int m, int n>
static inline MatExpr operator!=(const Matx<_Tp, m, n> &a, const Mat &b) {
  return Mat(a) != b;
}

CV_EXPORTS MatExpr operator>=(const Mat &a, const Mat &b);
CV_EXPORTS MatExpr operator>=(const Mat &a, double s);
CV_EXPORTS MatExpr operator>=(double s, const Mat &a);
template <typename _Tp, int m, int n>
static inline MatExpr operator>=(const Mat &a, const Matx<_Tp, m, n> &b) {
  return a >= Mat(b);
}
template <typename _Tp, int m, int n>
static inline MatExpr operator>=(const Matx<_Tp, m, n> &a, const Mat &b) {
  return Mat(a) >= b;
}

CV_EXPORTS MatExpr operator>(const Mat &a, const Mat &b);
CV_EXPORTS MatExpr operator>(const Mat &a, double s);
CV_EXPORTS MatExpr operator>(double s, const Mat &a);
template <typename _Tp, int m, int n>
static inline MatExpr operator>(const Mat &a, const Matx<_Tp, m, n> &b) {
  return a > Mat(b);
}
template <typename _Tp, int m, int n>
static inline MatExpr operator>(const Matx<_Tp, m, n> &a, const Mat &b) {
  return Mat(a) > b;
}

CV_EXPORTS MatExpr operator&(const Mat &a, const Mat &b);
CV_EXPORTS MatExpr operator&(const Mat &a, const Scalar &s);
CV_EXPORTS MatExpr operator&(const Scalar &s, const Mat &a);
template <typename _Tp, int m, int n>
static inline MatExpr operator&(const Mat &a, const Matx<_Tp, m, n> &b) {
  return a & Mat(b);
}
template <typename _Tp, int m, int n>
static inline MatExpr operator&(const Matx<_Tp, m, n> &a, const Mat &b) {
  return Mat(a) & b;
}

CV_EXPORTS MatExpr operator|(const Mat &a, const Mat &b);
CV_EXPORTS MatExpr operator|(const Mat &a, const Scalar &s);
CV_EXPORTS MatExpr operator|(const Scalar &s, const Mat &a);
template <typename _Tp, int m, int n>
static inline MatExpr operator|(const Mat &a, const Matx<_Tp, m, n> &b) {
  return a | Mat(b);
}
template <typename _Tp, int m, int n>
static inline MatExpr operator|(const Matx<_Tp, m, n> &a, const Mat &b) {
  return Mat(a) | b;
}

CV_EXPORTS MatExpr operator^(const Mat &a, const Mat &b);
CV_EXPORTS MatExpr operator^(const Mat &a, const Scalar &s);
CV_EXPORTS MatExpr operator^(const Scalar &s, const Mat &a);
template <typename _Tp, int m, int n>
static inline MatExpr operator^(const Mat &a, const Matx<_Tp, m, n> &b) {
  return a ^ Mat(b);
}
template <typename _Tp, int m, int n>
static inline MatExpr operator^(const Matx<_Tp, m, n> &a, const Mat &b) {
  return Mat(a) ^ b;
}

CV_EXPORTS MatExpr operator~(const Mat &m);

CV_EXPORTS MatExpr min(const Mat &a, const Mat &b);
CV_EXPORTS MatExpr min(const Mat &a, double s);
CV_EXPORTS MatExpr min(double s, const Mat &a);
template <typename _Tp, int m, int n>
static inline MatExpr min(const Mat &a, const Matx<_Tp, m, n> &b) {
  return min(a, Mat(b));
}
template <typename _Tp, int m, int n>
static inline MatExpr min(const Matx<_Tp, m, n> &a, const Mat &b) {
  return min(Mat(a), b);
}

CV_EXPORTS MatExpr max(const Mat &a, const Mat &b);
CV_EXPORTS MatExpr max(const Mat &a, double s);
CV_EXPORTS MatExpr max(double s, const Mat &a);
template <typename _Tp, int m, int n>
static inline MatExpr max(const Mat &a, const Matx<_Tp, m, n> &b) {
  return max(a, Mat(b));
}
template <typename _Tp, int m, int n>
static inline MatExpr max(const Matx<_Tp, m, n> &a, const Mat &b) {
  return max(Mat(a), b);
}

/** @brief Calculates an absolute value of each matrix element.

abs is a meta-function that is expanded to one of absdiff or convertScaleAbs
forms:
- C = abs(A-B) is equivalent to `absdiff(A, B, C)`
- C = abs(A) is equivalent to `absdiff(A, Scalar::all(0), C)`
- C = `Mat_<Vec<uchar,n> >(abs(A*alpha + beta))` is equivalent to
`convertScaleAbs(A, C, alpha, beta)`

The output matrix has the same size and the same type as the input one except
for the last case, where C is depth=CV_8U .
@param m matrix.
@sa @ref MatrixExpressions, absdiff, convertScaleAbs
 */
CV_EXPORTS MatExpr abs(const Mat &m);
/** @overload
@param e matrix expression.
*/
CV_EXPORTS MatExpr abs(const MatExpr &e);
//! @} relates cv::MatExpr

} // namespace cv

#include "opencv2/core/mat.inl.hpp"

#endif // OPENCV_CORE_MAT_HPP