stat.h

使用R语言的马尔科夫链蒙特卡洛模拟（MCMC）源代码程序。

    };
  }
  
   /*! 
	* \brief Calculate the variance of a Matrix
	*
	* This function calculates the variance of a matrix.
	*
	* \param A The matrix whose variance is of interest.
	*
  * \see var(cons Matrix<T,PO,PS> &A, T mu)
	* \see varc(const Matrix<T,PO,PS> &A)
	* \see sd(const Matrix<T,PO,PS> &A)
	* \see mean(const Matrix<T,PO,PS> &A)
	*/
  template <typename T, matrix_order PO, matrix_style PS>
  T
  var (const Matrix<T,PO,PS> &A)
  {
    return var(A, mean(A));
  }

  /* Calculate the variances of each column of a Matrix. */
  
  /*! 
	* \brief Calculate the variance of each column of a Matrix
	*
	* This function calculates the variance of each column of a matrix.
	*
	* \param A The matrix whose variances are of interest.
	*
	* \see var(const Matrix<T,PO,PS> &A)
  * \see var(cons Matrix<T,PO,PS> &A, T mu)
	* \see sdc(const Matrix<T,PO,PS> &A)
	* \see meanc(const Matrix<T,PO,PS> &A)
	*/
	
  SCYTHE_STATMETH_COL(var)

 /*! 
	* \brief Calculate the variance of a Matrix
	*
	* This function calculates the variance of a matrix when the mean is
  * already known.
	*
	* \param A The matrix whose variance is of interest.
  * \param mu The mean of the values in the matrix.
	*
  * \see var(cons Matrix<T,PO,PS> &A)
	* \see varc(const Matrix<T,PO,PS> &A)
	* \see sd(const Matrix<T,PO,PS> &A)
	* \see mean(const Matrix<T,PO,PS> &A)
	*/
  template <typename T, matrix_order PO, matrix_style PS>
  T
  var (const Matrix<T,PO,PS> &A, T mu)
  {
    return std::accumulate(A.begin_f(), A.end_f(), (T) 0, 
                         var_step<T, uint> (mu, A.size() - 1, 2));
  }
  
  /* Calculate the standard deviation of a Matrix (not std cause of namespace std:: */
  
  /*! 
	* \brief Calculate the standard deviation of a Matrix
	*
	* This function calculates the standard deviation of a matrix by 
	* taking the square root of the matrix's variance. 	
	*
	* \param A The matrix whose standard deviation is of interest.
	*
  * \see sd(const Matrix<T,PO,PS) &A, T mu)
	* \see sdc(const Matrix<T,PO,PS> &A)
	* \see variance(const Matrix<T,PO,PS> &A)
	*/
	
  template <typename T, matrix_order PO, matrix_style PS>
  T
  sd (const Matrix<T,PO,PS> &A)
  {
    return std::sqrt(var(A));
  }
  
  /* Calculate the standard deviation of each column of a Matrix */
   /*! 
	* \brief Calculate the standard deviation of each column of a Matrix
	*
	* This function calculates the standard deviation of each column of a matrix by 
	* taking the square root of each column's variance. 	
	*
	* \param A The matrix whose standard deviations are of interest.
	*
	* \see sd(const Matrix<T,PO,PS> &A)
	* \see variancec(const Matrix<T,PO,PS> &A)
	*/
	
  SCYTHE_STATMETH_COL(sd)

  /*! 
	* \brief Calculate the standard deviation of a Matrix
	*
	* This function calculates the standard deviation of a matrix
  * when the matrix's mean is already known.
	*
	* \param A The matrix whose standard deviation is of interest.
  * \param mu The matrix mean.
	*
  * \see sd(const Matrix<T,PO,PS) &A)
	* \see sdc(const Matrix<T,PO,PS> &A)
	* \see variance(const Matrix<T,PO,PS> &A)
	*/
	
  template <typename T, matrix_order PO, matrix_style PS>
  T
  sd (const Matrix<T,PO,PS> &A, T mu)
  {
    return std::sqrt(var(A, mu));
  }

  /* Calculate the skew of a Matrix */

  /*! 
	 * \brief Calculate the skew of a Matrix
	 *
	 * This function calculates the skew of a matrix.
	 *
	 * \param A The matrix whose skew is of interest.
	 *
	 * \see skewc(const Matrix<T,PO,PS> &A)
	 * \see kurtosis(const Matrix<T,PO,PS> &A)
	 */

  template <typename T, matrix_order PO, matrix_style PS>
  T
  skew (const Matrix<T,PO,PS> &A)
  {
    T mu = mean(A);
    T sde = sd(A, mu);
    return std::accumulate(A.begin_f(), A.end_f(), (T) 0, 
              var_step<T, T> (mu, A.size() * std::pow(sde, 3), 3));
  }

  /* Calculate the skew of each column of a Matrix. */
  
   /*! 
	* \brief Calculate the skew of each column of a Matrix
	*
	* This function calculates the skew of each column of a matrix.
	*
	* \param A The matrix whose skews are of interest.
	*
	* \see skew(const Matrix<T,PO,PS> &A)
	* \see kurtosisc(const Matrix<T,PO,PS> &A)
	*/

  SCYTHE_STATMETH_COL(skew)
  
  /* Calculate the kurtosis of a Matrix */
    
   /*! 
	* \brief Calculate the kurtosis of a Matrix
	*
	* This function calculates the kurtosis of a matrix.
	*
	* \param A The matrix whose kurtosis is of interest.
	*
	* \see skew(const Matrix<T,PO,PS> &A)
	* \see kurtosisc(const Matrix<T,PO,PS> &A)
	*/
  template <typename T, matrix_order PO, matrix_style PS>
  T
  kurtosis (const Matrix<T,PO,PS> &A)
  {
    T mu = mean(A);
    T sde = sd(A, mu);
    return (std::accumulate(A.begin_f(), A.end_f(), (T) 0, 
              var_step<T, T> (mu, A.size() * std::pow(sde, 4), 4))
            - 3);
  }
  
  /* Calculate the kurtosis of each column of a Matrix. */
  
   /*! 
	* \brief Calculate the kurtosis of each column of a Matrix
	*
	* This function calculates the kurtosis of each column of a matrix.
	*
	* \param A The matrix whose kurtoses are of interest.
	*
	* \see skewc(const Matrix<T,PO,PS> &A)
	* \see kurtosis(const Matrix<T,PO,PS> &A)
	*/

  SCYTHE_STATMETH_COL(kurtosis)

  /* Calculates the maximum element in a Matrix */
  /*! 
	* \brief Calculate the maximum element in a Matrix
	*
	* This function identifies the maximum element in a matrix.
	*
	* \param A The matrix whose maximum element is of interest.
	*
	* \see min(const Matrix<T,PO,PS> &A)
	* \see maxc (const Matrix<T,PO,PS> &A)

	*/
	
  template <typename T, matrix_order PO, matrix_style PS>
  T
  max (const Matrix<T,PO,PS> &A)
  {
    return *(max_element(A.begin_f(), A.end_f()));
  }

   /*! 
	* \brief Calculate the maximum of each column of a Matrix
	*
	* This function identifies the maximum of each column in a matrix.
	*
	* \param A The matrix whose maximae are of interest.
	*
	* \see max(const Matrix<T,PO,PS> &A)
	* \see minc(const Matrix<T,PO,PS> &A)
	*/
  
  SCYTHE_STATMETH_COL(max)

  /* Calculates the minimum element in a Matrix */
  
	/*! 
	* \brief Calculate the maximum element in a Matrix
	*
	* This function identifies the maximum element in a matrix.
	*
	* \param A The matrix whose maximum element is of interest.
	*
	* \see max(const Matrix<T,PO,PS> &A)
	* \see minc(const Matrix<T,PO,PS> &A)
	*/
  template <typename T, matrix_order PO, matrix_style PS>
  T
  min (const Matrix<T,PO,PS> &A)
  {
    return *(min_element(A.begin_f(), A.end_f()));
  }
  
   /*! 
	* \brief Calculate the minimum of each column of a Matrix
	*
	* This function identifies the minimum of each column in a matrix.
	*
	* \param A The matrix whose minimae are of interest.
	*
	* \see min(const Matrix<T,PO,PS> &A)
	* \see maxc(const Matrix<T,PO,PS> &A)
	*/
  
  SCYTHE_STATMETH_COL(min)

  /* Find the index of the max element */  
	/*! 
	* \brief Calculate the index of the maximum element in a Matrix
	*
	* This function identifies the index of the maximum element in a matrix.
	*
	* \param A The matrix whose maximum element indices are of interest.
	*
	* \see minind(const Matrix<T,PO,PS> &A)
	* \see max(const Matrix<T,PO,PS> &A)
	* \see maxindc(const Matrix<T,PO,PS> &A)
	*/

  template <typename T, matrix_order PO, matrix_style PS>
  unsigned int
  maxind (const Matrix<T,PO,PS> &A)
  {
    return (max_element(A.begin_f(), A.end_f())).get_index();
  }
  
   /*! 
	* \brief Calculate the index of the maximum for each column of a Matrix
	*
	* This function identifies the index of the maximum for each column of a Matrix.
	*
	* \param A The matrix whose maximum indices are of interest.
	*
	* \see maxc(const Matrix<T,PO,PS> &A)
	* \see minindc(const Matrix<T,PO,PS> &A)
	*/

  SCYTHE_STATMETH_COL(maxind)
  
  /* Find the index of the min element */
  
  /*! 
	* \brief Calculate the index of the minimum element in a Matrix
	*
	* This function identifies the index of the minimum element in a matrix.
	*
	* \param A The matrix whose minimum element indices are of interest.
	*
	* \see maxind(const Matrix<T,PO,PS> &A)
	* \see min(const Matrix<T,PO,PS> &A)
	* \see minindc(const Matrix <T> &A)
	*/
  template <typename T, matrix_order PO, matrix_style PS>
  unsigned int
  minind (const Matrix<T,PO,PS> &A)
  {
    return (min_element(A.begin_f(), A.end_f())).get_index();
  }

    /*! 
	* \brief Calculate the index of the minimum for each column of a Matrix
	*
	* This function identifies the index of the minimum for each column of a Matrix.
	*
	* \param A The matrix whose minimum indices are of interest.
	*
	* \see minc(const Matrix<T,PO,PS> &A)
	* \see maxindc(const Matrix<T,PO,PS> &A)
	*/
  SCYTHE_STATMETH_COL(minind)

} // end namespace scythe


#endif /* SCYTHE_STAT_H */