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  #ifndef __OPENCV_CORE_OPERATIONS_HPP__
  #define __OPENCV_CORE_OPERATIONS_HPP__
  
  #ifndef __cplusplus
  #  error operations.hpp header must be compiled as C++
  #endif
  
  #include <cstdio>
  
  //! @cond IGNORED
  
  namespace cv
  {
  
  ////////////////////////////// Matx methods depending on core API /////////////////////////////
  
  namespace internal
  {
  
  template<typename _Tp, int m> struct Matx_FastInvOp
  {
      bool operator()(const Matx<_Tp, m, m>& a, Matx<_Tp, m, m>& b, int method) const
      {
          Matx<_Tp, m, m> temp = a;
  
          // assume that b is all 0's on input => make it a unity matrix
          for( int i = 0; i < m; i++ )
              b(i, i) = (_Tp)1;
  
          if( method == DECOMP_CHOLESKY )
              return Cholesky(temp.val, m*sizeof(_Tp), m, b.val, m*sizeof(_Tp), m);
  
          return LU(temp.val, m*sizeof(_Tp), m, b.val, m*sizeof(_Tp), m) != 0;
      }
  };
  
  template<typename _Tp> struct Matx_FastInvOp<_Tp, 2>
  {
      bool operator()(const Matx<_Tp, 2, 2>& a, Matx<_Tp, 2, 2>& b, int) const
      {
          _Tp d = determinant(a);
          if( d == 0 )
              return false;
          d = 1/d;
          b(1,1) = a(0,0)*d;
          b(0,0) = a(1,1)*d;
          b(0,1) = -a(0,1)*d;
          b(1,0) = -a(1,0)*d;
          return true;
      }
  };
  
  template<typename _Tp> struct Matx_FastInvOp<_Tp, 3>
  {
      bool operator()(const Matx<_Tp, 3, 3>& a, Matx<_Tp, 3, 3>& b, int) const
      {
          _Tp d = (_Tp)determinant(a);
          if( d == 0 )
              return false;
          d = 1/d;
          b(0,0) = (a(1,1) * a(2,2) - a(1,2) * a(2,1)) * d;
          b(0,1) = (a(0,2) * a(2,1) - a(0,1) * a(2,2)) * d;
          b(0,2) = (a(0,1) * a(1,2) - a(0,2) * a(1,1)) * d;
  
          b(1,0) = (a(1,2) * a(2,0) - a(1,0) * a(2,2)) * d;
          b(1,1) = (a(0,0) * a(2,2) - a(0,2) * a(2,0)) * d;
          b(1,2) = (a(0,2) * a(1,0) - a(0,0) * a(1,2)) * d;
  
          b(2,0) = (a(1,0) * a(2,1) - a(1,1) * a(2,0)) * d;
          b(2,1) = (a(0,1) * a(2,0) - a(0,0) * a(2,1)) * d;
          b(2,2) = (a(0,0) * a(1,1) - a(0,1) * a(1,0)) * d;
          return true;
      }
  };
  
  
  template<typename _Tp, int m, int n> struct Matx_FastSolveOp
  {
      bool operator()(const Matx<_Tp, m, m>& a, const Matx<_Tp, m, n>& b,
                      Matx<_Tp, m, n>& x, int method) const
      {
          Matx<_Tp, m, m> temp = a;
          x = b;
          if( method == DECOMP_CHOLESKY )
              return Cholesky(temp.val, m*sizeof(_Tp), m, x.val, n*sizeof(_Tp), n);
  
          return LU(temp.val, m*sizeof(_Tp), m, x.val, n*sizeof(_Tp), n) != 0;
      }
  };
  
  template<typename _Tp> struct Matx_FastSolveOp<_Tp, 2, 1>
  {
      bool operator()(const Matx<_Tp, 2, 2>& a, const Matx<_Tp, 2, 1>& b,
                      Matx<_Tp, 2, 1>& x, int) const
      {
          _Tp d = determinant(a);
          if( d == 0 )
              return false;
          d = 1/d;
          x(0) = (b(0)*a(1,1) - b(1)*a(0,1))*d;
          x(1) = (b(1)*a(0,0) - b(0)*a(1,0))*d;
          return true;
      }
  };
  
  template<typename _Tp> struct Matx_FastSolveOp<_Tp, 3, 1>
  {
      bool operator()(const Matx<_Tp, 3, 3>& a, const Matx<_Tp, 3, 1>& b,
                      Matx<_Tp, 3, 1>& x, int) const
      {
          _Tp d = (_Tp)determinant(a);
          if( d == 0 )
              return false;
          d = 1/d;
          x(0) = d*(b(0)*(a(1,1)*a(2,2) - a(1,2)*a(2,1)) -
                  a(0,1)*(b(1)*a(2,2) - a(1,2)*b(2)) +
                  a(0,2)*(b(1)*a(2,1) - a(1,1)*b(2)));
  
          x(1) = d*(a(0,0)*(b(1)*a(2,2) - a(1,2)*b(2)) -
                  b(0)*(a(1,0)*a(2,2) - a(1,2)*a(2,0)) +
                  a(0,2)*(a(1,0)*b(2) - b(1)*a(2,0)));
  
          x(2) = d*(a(0,0)*(a(1,1)*b(2) - b(1)*a(2,1)) -
                  a(0,1)*(a(1,0)*b(2) - b(1)*a(2,0)) +
                  b(0)*(a(1,0)*a(2,1) - a(1,1)*a(2,0)));
          return true;
      }
  };
  
  } // internal
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp,m,n> Matx<_Tp,m,n>::randu(_Tp a, _Tp b)
  {
      Matx<_Tp,m,n> M;
      cv::randu(M, Scalar(a), Scalar(b));
      return M;
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp,m,n> Matx<_Tp,m,n>::randn(_Tp a, _Tp b)
  {
      Matx<_Tp,m,n> M;
      cv::randn(M, Scalar(a), Scalar(b));
      return M;
  }
  
  template<typename _Tp, int m, int n> inline
  Matx<_Tp, n, m> Matx<_Tp, m, n>::inv(int method, bool *p_is_ok /*= NULL*/) const
  {
      Matx<_Tp, n, m> b;
      bool ok;
      if( method == DECOMP_LU || method == DECOMP_CHOLESKY )
          ok = cv::internal::Matx_FastInvOp<_Tp, m>()(*this, b, method);
      else
      {
          Mat A(*this, false), B(b, false);
          ok = (invert(A, B, method) != 0);
      }
      if( NULL != p_is_ok ) { *p_is_ok = ok; }
      return ok ? b : Matx<_Tp, n, m>::zeros();
  }
  
  template<typename _Tp, int m, int n> template<int l> inline
  Matx<_Tp, n, l> Matx<_Tp, m, n>::solve(const Matx<_Tp, m, l>& rhs, int method) const
  {
      Matx<_Tp, n, l> x;
      bool ok;
      if( method == DECOMP_LU || method == DECOMP_CHOLESKY )
          ok = cv::internal::Matx_FastSolveOp<_Tp, m, l>()(*this, rhs, x, method);
      else
      {
          Mat A(*this, false), B(rhs, false), X(x, false);
          ok = cv::solve(A, B, X, method);
      }
  
      return ok ? x : Matx<_Tp, n, l>::zeros();
  }
  
  
  
  ////////////////////////// Augmenting algebraic & logical operations //////////////////////////
  
  #define CV_MAT_AUG_OPERATOR1(op, cvop, A, B) \
      static inline A& operator op (A& a, const B& b) { cvop; return a; }
  
  #define CV_MAT_AUG_OPERATOR(op, cvop, A, B)   \
      CV_MAT_AUG_OPERATOR1(op, cvop, A, B)      \
      CV_MAT_AUG_OPERATOR1(op, cvop, const A, B)
  
  #define CV_MAT_AUG_OPERATOR_T(op, cvop, A, B)                   \
      template<typename _Tp> CV_MAT_AUG_OPERATOR1(op, cvop, A, B) \
      template<typename _Tp> CV_MAT_AUG_OPERATOR1(op, cvop, const A, B)
  
  CV_MAT_AUG_OPERATOR  (+=, cv::add(a,b,a), Mat, Mat)
  CV_MAT_AUG_OPERATOR  (+=, cv::add(a,b,a), Mat, Scalar)
  CV_MAT_AUG_OPERATOR_T(+=, cv::add(a,b,a), Mat_<_Tp>, Mat)
  CV_MAT_AUG_OPERATOR_T(+=, cv::add(a,b,a), Mat_<_Tp>, Scalar)
  CV_MAT_AUG_OPERATOR_T(+=, cv::add(a,b,a), Mat_<_Tp>, Mat_<_Tp>)
  
  CV_MAT_AUG_OPERATOR  (-=, cv::subtract(a,b,a), Mat, Mat)
  CV_MAT_AUG_OPERATOR  (-=, cv::subtract(a,b,a), Mat, Scalar)
  CV_MAT_AUG_OPERATOR_T(-=, cv::subtract(a,b,a), Mat_<_Tp>, Mat)
  CV_MAT_AUG_OPERATOR_T(-=, cv::subtract(a,b,a), Mat_<_Tp>, Scalar)
  CV_MAT_AUG_OPERATOR_T(-=, cv::subtract(a,b,a), Mat_<_Tp>, Mat_<_Tp>)
  
  CV_MAT_AUG_OPERATOR  (*=, cv::gemm(a, b, 1, Mat(), 0, a, 0), Mat, Mat)
  CV_MAT_AUG_OPERATOR_T(*=, cv::gemm(a, b, 1, Mat(), 0, a, 0), Mat_<_Tp>, Mat)
  CV_MAT_AUG_OPERATOR_T(*=, cv::gemm(a, b, 1, Mat(), 0, a, 0), Mat_<_Tp>, Mat_<_Tp>)
  CV_MAT_AUG_OPERATOR  (*=, a.convertTo(a, -1, b), Mat, double)
  CV_MAT_AUG_OPERATOR_T(*=, a.convertTo(a, -1, b), Mat_<_Tp>, double)
  
  CV_MAT_AUG_OPERATOR  (/=, cv::divide(a,b,a), Mat, Mat)
  CV_MAT_AUG_OPERATOR_T(/=, cv::divide(a,b,a), Mat_<_Tp>, Mat)
  CV_MAT_AUG_OPERATOR_T(/=, cv::divide(a,b,a), Mat_<_Tp>, Mat_<_Tp>)
  CV_MAT_AUG_OPERATOR  (/=, a.convertTo((Mat&)a, -1, 1./b), Mat, double)
  CV_MAT_AUG_OPERATOR_T(/=, a.convertTo((Mat&)a, -1, 1./b), Mat_<_Tp>, double)
  
  CV_MAT_AUG_OPERATOR  (&=, cv::bitwise_and(a,b,a), Mat, Mat)
  CV_MAT_AUG_OPERATOR  (&=, cv::bitwise_and(a,b,a), Mat, Scalar)
  CV_MAT_AUG_OPERATOR_T(&=, cv::bitwise_and(a,b,a), Mat_<_Tp>, Mat)
  CV_MAT_AUG_OPERATOR_T(&=, cv::bitwise_and(a,b,a), Mat_<_Tp>, Scalar)
  CV_MAT_AUG_OPERATOR_T(&=, cv::bitwise_and(a,b,a), Mat_<_Tp>, Mat_<_Tp>)
  
  CV_MAT_AUG_OPERATOR  (|=, cv::bitwise_or(a,b,a), Mat, Mat)
  CV_MAT_AUG_OPERATOR  (|=, cv::bitwise_or(a,b,a), Mat, Scalar)
  CV_MAT_AUG_OPERATOR_T(|=, cv::bitwise_or(a,b,a), Mat_<_Tp>, Mat)
  CV_MAT_AUG_OPERATOR_T(|=, cv::bitwise_or(a,b,a), Mat_<_Tp>, Scalar)
  CV_MAT_AUG_OPERATOR_T(|=, cv::bitwise_or(a,b,a), Mat_<_Tp>, Mat_<_Tp>)
  
  CV_MAT_AUG_OPERATOR  (^=, cv::bitwise_xor(a,b,a), Mat, Mat)
  CV_MAT_AUG_OPERATOR  (^=, cv::bitwise_xor(a,b,a), Mat, Scalar)
  CV_MAT_AUG_OPERATOR_T(^=, cv::bitwise_xor(a,b,a), Mat_<_Tp>, Mat)
  CV_MAT_AUG_OPERATOR_T(^=, cv::bitwise_xor(a,b,a), Mat_<_Tp>, Scalar)
  CV_MAT_AUG_OPERATOR_T(^=, cv::bitwise_xor(a,b,a), Mat_<_Tp>, Mat_<_Tp>)
  
  #undef CV_MAT_AUG_OPERATOR_T
  #undef CV_MAT_AUG_OPERATOR
  #undef CV_MAT_AUG_OPERATOR1
  
  
  
  ///////////////////////////////////////////// SVD /////////////////////////////////////////////
  
  inline SVD::SVD() {}
  inline SVD::SVD( InputArray m, int flags ) { operator ()(m, flags); }
  inline void SVD::solveZ( InputArray m, OutputArray _dst )
  {
      Mat mtx = m.getMat();
      SVD svd(mtx, (mtx.rows >= mtx.cols ? 0 : SVD::FULL_UV));
      _dst.create(svd.vt.cols, 1, svd.vt.type());
      Mat dst = _dst.getMat();
      svd.vt.row(svd.vt.rows-1).reshape(1,svd.vt.cols).copyTo(dst);
  }
  
  template<typename _Tp, int m, int n, int nm> inline void
      SVD::compute( const Matx<_Tp, m, n>& a, Matx<_Tp, nm, 1>& w, Matx<_Tp, m, nm>& u, Matx<_Tp, n, nm>& vt )
  {
      CV_StaticAssert( nm == MIN(m, n), "Invalid size of output vector.");
      Mat _a(a, false), _u(u, false), _w(w, false), _vt(vt, false);
      SVD::compute(_a, _w, _u, _vt);
      CV_Assert(_w.data == (uchar*)&w.val[0] && _u.data == (uchar*)&u.val[0] && _vt.data == (uchar*)&vt.val[0]);
  }
  
  template<typename _Tp, int m, int n, int nm> inline void
  SVD::compute( const Matx<_Tp, m, n>& a, Matx<_Tp, nm, 1>& w )
  {
      CV_StaticAssert( nm == MIN(m, n), "Invalid size of output vector.");
      Mat _a(a, false), _w(w, false);
      SVD::compute(_a, _w);
      CV_Assert(_w.data == (uchar*)&w.val[0]);
  }
  
  template<typename _Tp, int m, int n, int nm, int nb> inline void
  SVD::backSubst( const Matx<_Tp, nm, 1>& w, const Matx<_Tp, m, nm>& u,
                  const Matx<_Tp, n, nm>& vt, const Matx<_Tp, m, nb>& rhs,
                  Matx<_Tp, n, nb>& dst )
  {
      CV_StaticAssert( nm == MIN(m, n), "Invalid size of output vector.");
      Mat _u(u, false), _w(w, false), _vt(vt, false), _rhs(rhs, false), _dst(dst, false);
      SVD::backSubst(_w, _u, _vt, _rhs, _dst);
      CV_Assert(_dst.data == (uchar*)&dst.val[0]);
  }
  
  
  
  /////////////////////////////////// Multiply-with-Carry RNG ///////////////////////////////////
  
  inline RNG::RNG()              { state = 0xffffffff; }
  inline RNG::RNG(uint64 _state) { state = _state ? _state : 0xffffffff; }
  
  inline RNG::operator uchar()    { return (uchar)next(); }
  inline RNG::operator schar()    { return (schar)next(); }
  inline RNG::operator ushort()   { return (ushort)next(); }
  inline RNG::operator short()    { return (short)next(); }
  inline RNG::operator int()      { return (int)next(); }
  inline RNG::operator unsigned() { return next(); }
  inline RNG::operator float()    { return next()*2.3283064365386962890625e-10f; }
  inline RNG::operator double()   { unsigned t = next(); return (((uint64)t << 32) | next()) * 5.4210108624275221700372640043497e-20; }
  
  inline unsigned RNG::operator ()(unsigned N) { return (unsigned)uniform(0,N); }
  inline unsigned RNG::operator ()()           { return next(); }
  
  inline int    RNG::uniform(int a, int b)       { return a == b ? a : (int)(next() % (b - a) + a); }
  inline float  RNG::uniform(float a, float b)   { return ((float)*this)*(b - a) + a; }
  inline double RNG::uniform(double a, double b) { return ((double)*this)*(b - a) + a; }
  
  inline unsigned RNG::next()
  {
      state = (uint64)(unsigned)state* /*CV_RNG_COEFF*/ 4164903690U + (unsigned)(state >> 32);
      return (unsigned)state;
  }
  
  //! returns the next unifomly-distributed random number of the specified type
  template<typename _Tp> static inline _Tp randu()
  {
    return (_Tp)theRNG();
  }
  
  ///////////////////////////////// Formatted string generation /////////////////////////////////
  
  CV_EXPORTS String format( const char* fmt, ... );
  
  ///////////////////////////////// Formatted output of cv::Mat /////////////////////////////////
  
  static inline
  Ptr<Formatted> format(InputArray mtx, int fmt)
  {
      return Formatter::get(fmt)->format(mtx.getMat());
  }
  
  static inline
  int print(Ptr<Formatted> fmtd, FILE* stream = stdout)
  {
      int written = 0;
      fmtd->reset();
      for(const char* str = fmtd->next(); str; str = fmtd->next())
          written += fputs(str, stream);
  
      return written;
  }
  
  static inline
  int print(const Mat& mtx, FILE* stream = stdout)
  {
      return print(Formatter::get()->format(mtx), stream);
  }
  
  static inline
  int print(const UMat& mtx, FILE* stream = stdout)
  {
      return print(Formatter::get()->format(mtx.getMat(ACCESS_READ)), stream);
  }
  
  template<typename _Tp> static inline
  int print(const std::vector<Point_<_Tp> >& vec, FILE* stream = stdout)
  {
      return print(Formatter::get()->format(Mat(vec)), stream);
  }
  
  template<typename _Tp> static inline
  int print(const std::vector<Point3_<_Tp> >& vec, FILE* stream = stdout)
  {
      return print(Formatter::get()->format(Mat(vec)), stream);
  }
  
  template<typename _Tp, int m, int n> static inline
  int print(const Matx<_Tp, m, n>& matx, FILE* stream = stdout)
  {
      return print(Formatter::get()->format(cv::Mat(matx)), stream);
  }
  
  //! @endcond
  
  /****************************************************************************************\
  *                                  Auxiliary algorithms                                  *
  \****************************************************************************************/
  
  /** @brief Splits an element set into equivalency classes.
  
  The generic function partition implements an \f$O(N^2)\f$ algorithm for splitting a set of \f$N\f$ elements
  into one or more equivalency classes, as described in
  <http://en.wikipedia.org/wiki/Disjoint-set_data_structure> . The function returns the number of
  equivalency classes.
  @param _vec Set of elements stored as a vector.
  @param labels Output vector of labels. It contains as many elements as vec. Each label labels[i] is
  a 0-based cluster index of `vec[i]`.
  @param predicate Equivalence predicate (pointer to a boolean function of two arguments or an
  instance of the class that has the method bool operator()(const _Tp& a, const _Tp& b) ). The
  predicate returns true when the elements are certainly in the same class, and returns false if they
  may or may not be in the same class.
  @ingroup core_cluster
  */
  template<typename _Tp, class _EqPredicate> int
  partition( const std::vector<_Tp>& _vec, std::vector<int>& labels,
            _EqPredicate predicate=_EqPredicate())
  {
      int i, j, N = (int)_vec.size();
      const _Tp* vec = &_vec[0];
  
      const int PARENT=0;
      const int RANK=1;
  
      std::vector<int> _nodes(N*2);
      int (*nodes)[2] = (int(*)[2])&_nodes[0];
  
      // The first O(N) pass: create N single-vertex trees
      for(i = 0; i < N; i++)
      {
          nodes[i][PARENT]=-1;
          nodes[i][RANK] = 0;
      }
  
      // The main O(N^2) pass: merge connected components
      for( i = 0; i < N; i++ )
      {
          int root = i;
  
          // find root
          while( nodes[root][PARENT] >= 0 )
              root = nodes[root][PARENT];
  
          for( j = 0; j < N; j++ )
          {
              if( i == j || !predicate(vec[i], vec[j]))
                  continue;
              int root2 = j;
  
              while( nodes[root2][PARENT] >= 0 )
                  root2 = nodes[root2][PARENT];
  
              if( root2 != root )
              {
                  // unite both trees
                  int rank = nodes[root][RANK], rank2 = nodes[root2][RANK];
                  if( rank > rank2 )
                      nodes[root2][PARENT] = root;
                  else
                  {
                      nodes[root][PARENT] = root2;
                      nodes[root2][RANK] += rank == rank2;
                      root = root2;
                  }
                  CV_Assert( nodes[root][PARENT] < 0 );
  
                  int k = j, parent;
  
                  // compress the path from node2 to root
                  while( (parent = nodes[k][PARENT]) >= 0 )
                  {
                      nodes[k][PARENT] = root;
                      k = parent;
                  }
  
                  // compress the path from node to root
                  k = i;
                  while( (parent = nodes[k][PARENT]) >= 0 )
                  {
                      nodes[k][PARENT] = root;
                      k = parent;
                  }
              }
          }
      }
  
      // Final O(N) pass: enumerate classes
      labels.resize(N);
      int nclasses = 0;
  
      for( i = 0; i < N; i++ )
      {
          int root = i;
          while( nodes[root][PARENT] >= 0 )
              root = nodes[root][PARENT];
          // re-use the rank as the class label
          if( nodes[root][RANK] >= 0 )
              nodes[root][RANK] = ~nclasses++;
          labels[i] = ~nodes[root][RANK];
      }
  
      return nclasses;
  }
  
  } // cv
  
  #endif
  