#! /usr/bin/env python
#
def bell_values ( n_data ):

#*****************************************************************************80
#
## BELL_VALUES returns some values of the Bell numbers.
#
#  Discussion:
#
#    The Bell number B(N) is the number of restricted growth functions on N.
#
#    Note that the Stirling numbers of the second kind, S^m_n, count the
#    number of partitions of N objects into M classes, and so it is
#    true that
#
#      B(N) = S^1_N + S^2_N + ... + S^N_N.
#
#    The Bell numbers were named for Eric Temple Bell.
#
#    In Mathematica, the function can be evaluated by
#
#      Sum[StirlingS2[n,m],{m,1,n}]
#
#    The Bell number B(N) is defined as the number of partitions (of
#    any size) of a set of N distinguishable objects.  
#
#    A partition of a set is a division of the objects of the set into 
#    subsets.
#
#  Example:
#
#    There are 15 partitions of a set of 4 objects:
#
#      (1234), 
#      (123) (4), 
#      (124) (3), 
#      (12) (34), 
#      (12) (3) (4), 
#      (134) (2), 
#      (13) (24), 
#      (13) (2) (4), 
#      (14) (23), 
#      (1) (234),
#      (1) (23) (4), 
#      (14) (2) (3), 
#      (1) (24) (3), 
#      (1) (2) (34), 
#      (1) (2) (3) (4).
#
#    and so B(4) = 15.
#
#  First values:
#
#     N         B(N)
#     0           1
#     1           1
#     2           2
#     3           5
#     4          15
#     5          52
#     6         203
#     7         877
#     8        4140
#     9       21147
#    10      115975
#
#  Recursion:
#
#    B(I) = sum ( 1 <= J <=I ) Binomial ( I-1, J-1 ) * B(I-J)
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    23 November 2014
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Milton Abramowitz and Irene Stegun,
#    Handbook of Mathematical Functions,
#    US Department of Commerce, 1964.
#
#    Stephen Wolfram,
#    The Mathematica Book,
#    Fourth Edition,
#    Wolfram Media / Cambridge University Press, 1999.
#
#  Parameters:
#
#    Input/output, integer N_DATA.  The user sets N_DATA to 0 before the
#    first call.  On each call, the routine increments N_DATA by 1, and
#    returns the corresponding data; when there is no more data, the
#    output value of N_DATA will be 0 again.
#
#    Output, integer N, the order of the Bell number.
#
#    Output, integer C, the value of the Bell number.
#
  import numpy as np

  n_max = 11

  c_vec = np.array ( ( 1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975 ) )

  n_vec = np.array ( ( 0,  1,  2,  3,  4, 5,  6,  7,  8,  9,  10 ) )

  if ( n_data < 0 ):
    n_data = 0

  if ( n_max <= n_data ):
    n_data = 0
    n = 0
    c = 0
  else:
    n = n_vec[n_data]
    c = c_vec[n_data]
    n_data = n_data + 1

  return n_data, n, c

def bell_values_test ( ):

#*****************************************************************************80
#
## BELL_VALUES_TEST demonstrates the use of BELL_VALUES.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    23 November 2014
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'BELL_VALUES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  BELL_VALUES returns values of' )
  print ( '  the Bell numbers.' )
  print ( '' )
  print ( '     N        BELL(N)' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, n, c = bell_values ( n_data )

    if ( n_data == 0 ):
      break

    print ( '%6d  %10d' % ( n, c ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'BELL_VALUES_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  bell_values_test ( )
  timestamp ( )