#! /usr/bin/env python
#
def stirling2_values ( n_data ):

#*****************************************************************************80
#
## STIRLING2_VALUES returns some values of the Stirling numbers, kind 2.
#
#  Discussion:
#
#    S2(N,M) represents the number of distinct partitions of N elements
#    into M nonempty sets.  For a fixed N, the sum of the Stirling
#    numbers S2(N,M) is represented by B(N), called "Bell's number",
#    and represents the number of distinct partitions of N elements.
#
#    For example, with 4 objects, there are:
#
#    1 partition into 1 set:
#
#      (A,B,C,D)
#
#    7 partitions into 2 sets:
#
#      (A,B,C) (D)
#      (A,B,D) (C)
#      (A,C,D) (B)
#      (A) (B,C,D)
#      (A,B) (C,D)
#      (A,C) (B,D)
#      (A,D) (B,C)
#
#    6 partitions into 3 sets:
#
#      (A,B) (C) (D)
#      (A) (B,C) (D)
#      (A) (B) (C,D)
#      (A,C) (B) (D)
#      (A,D) (B) (C)
#      (A) (B,D) (C)
#
#    1 partition into 4 sets:
#
#      (A) (B) (C) (D)
#
#    So S2(4,1) = 1, S2(4,2) = 7, S2(4,3) = 6, S2(4,4) = 1, and B(4) = 15.
#
#
#  First terms:
#
#    N/M: 1    2    3    4    5    6    7    8
#
#    1    1    0    0    0    0    0    0    0
#    2    1    1    0    0    0    0    0    0
#    3    1    3    1    0    0    0    0    0
#    4    1    7    6    1    0    0    0    0
#    5    1   15   25   10    1    0    0    0
#    6    1   31   90   65   15    1    0    0
#    7    1   63  301  350  140   21    1    0
#    8    1  127  966 1701 1050  266   28    1
#
#    In Mathematica, the function can be evaluated by:
#
#      StirlingS2[n,m]
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    22 February 2015
#
#  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, M, the arguments of the function.
#
#    Output, integer F, the value of the function.
#
  import numpy as np

  n_max = 16

  f_vec = np.array ( ( \
           0, \
           1, \
           3, \
           7, \
          15, \
          31, \
          63, \
         127, \
         255, \
         511, \
         966, \
        1701, \
        1050, \
         266, \
          28, \
           1 ))

  m_vec = np.array ( ( \
     2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4, 5, 6, 7, 8 ))

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

  if ( n_data < 0 ):
    n_data = 0

  if ( n_max <= n_data ):
    n_data = 0
    n = 0
    m = 0
    f = 0
  else:
    n = n_vec[n_data]
    m = m_vec[n_data]
    f = f_vec[n_data]
    n_data = n_data + 1

  return n_data, n, m, f

def stirling2_values_test ( ):

#*****************************************************************************80
#
## STIRLING2_VALUES_TEST demonstrates the use of STIRLING2_VALUES.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    22 February 2015
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'STIRLING2_VALUES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  STIRLING2_VALUES stores values of the STIRLING2 function.' )
  print ( '' )
  print ( '             N             M        STIRLING2(N,M)' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, n, m, f = stirling2_values ( n_data )

    if ( n_data == 0 ):
      break

    print ( '  %12d  %12d  %12d' % ( n, m, f ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'STIRLING2_VALUES_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  stirling2_values_test ( )
  timestamp ( )