stats <- function ( x = NULL )

#*****************************************************************************80
#
## stats() does stats.
#
#  Discussion:
#
#    This function computes statistical quantities for a sequence of values
#    X which are supplied one at a time, like a data stream.  The statistical
#    quantities are updated every time a new value of X is supplied.
#
#    Because we are dealing with a data stream, and not saving the previous
#    data values, it is not possible to compute the median and mode.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    11 May 2021
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    real X, the next item in the sequence.
#    If X is set to Inf, then its value is ignored, and the current data
#    is returned.
#    If no argument is specified, then all internal data is reset to 0.
#
#  Output:
#
#    integer N: the number of items in the sequence.
#
#    real X_SUM: the sum of the values.
#
#    real X_MIN, X_MEAN, X_MAX: the minimum, mean, and maximum values.
#
#    real X_VAR, X_STD: the variance and standard deviation.
#
{
#
#  Persistent data is stored as attributes associated with the function.
#
  n_internal      <- attr ( stats, "n_internal" )
  x_max_internal  <- attr ( stats, "x_max_internal" )
  x_mean_internal <- attr ( stats, "x_mean_internal" )
  x_min_internal  <- attr ( stats, "x_min_internal" )
  x_std_internal  <- attr ( stats, "x_std_internal" )
  x_sum_internal  <- attr ( stats, "x_sum_internal" )
  x_var_internal  <- attr ( stats, "x_var_internal" )
#
#  Initialize the persistent data on first call, and again if x not input.
#  Note that we need to use a DOUBLE ARROW assignment here!
#  This makes the assignment "globally".
#
  if ( is.null ( n_internal ) )
  {
    n_internal      = 0
    x_max_internal  = -Inf
    x_mean_internal = 0.0
    x_min_internal  = Inf
    x_std_internal  = 0.0
    x_sum_internal  = 0.0
    x_var_internal  = 0.0
    attr ( stats, "n_internal" )      <<- n_internal
    attr ( stats, "x_max_internal" )  <<- x_max_internal
    attr ( stats, "x_mean_internal" ) <<- x_mean_internal
    attr ( stats, "x_min_internal" )  <<- x_min_internal
    attr ( stats, "x_std_internal" )  <<- x_std_internal
    attr ( stats, "x_sum_internal" )  <<- x_sum_internal
    attr ( stats, "x_var_internal" )  <<- x_var_internal
  }
#
#  Action based on input value X:
#
  if ( is.null ( x ) )
  {
    n_internal      = 0
    x_max_internal  = -Inf
    x_mean_internal = 0.0
    x_min_internal  = Inf
    x_std_internal  = 0.0
    x_sum_internal  = 0.0
    x_var_internal  = 0.0
  }
#
#  X = Inf.  Do nothing.
#  This allows user to read current memory.
#
  else if ( x == Inf )
  {
  }
#
#  X supplied, and not Inf.
#
  else
  {
    n_internal = n_internal + 1
    x_max_internal = max ( x_max_internal, x )
    x_min_internal = min ( x_min_internal, x )
    x_sum_internal = x_sum_internal + x
    x_mean_old = x_mean_internal
    x_mean_internal = x_sum_internal / n_internal
    if ( n_internal == 1 )
    {
      x_var_internal = 0.0
      x_std_internal = 0.0
    }
    else
    {
      x_var_internal = ( x_var_internal * ( n_internal - 2 ) +
        ( x - x_mean_old ) * ( x - x_mean_internal ) ) / ( n_internal - 1 )
      x_std_internal = sqrt ( x_var_internal )
    }
  }
#
#  Save values.
#
  attr ( stats, "n_internal" )      <<- n_internal
  attr ( stats, "x_max_internal" )  <<- x_max_internal
  attr ( stats, "x_mean_internal" ) <<- x_mean_internal
  attr ( stats, "x_min_internal" )  <<- x_min_internal
  attr ( stats, "x_std_internal" )  <<- x_std_internal
  attr ( stats, "x_sum_internal" )  <<- x_sum_internal
  attr ( stats, "x_var_internal" )  <<- x_var_internal
#
#  Set output values.
#
  n      = n_internal
  x_max  = x_max_internal
  x_min  = x_min_internal
  x_sum  = x_sum_internal
  x_mean = x_mean_internal
  x_var  = x_var_internal
  x_std  = x_std_internal

  output = c ( n, x_sum, x_min, x_mean, x_max, x_var, x_std )

  return ( output )
}