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

#*****************************************************************************80
#
## ZETA_VALUES returns some values of the Riemann Zeta function.
#
#  Discussion:
#
#    ZETA(N) = sum ( 1 <= I < Infinity ) 1 / I^N
#
#    In Mathematica, the function can be evaluated by:
#
#      Zeta[n]
#
#  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, the argument of the Zeta function.
#
#    Output, real F, the value of the Zeta function.
#
  import numpy as np

  n_max = 15

  n_vec = np.array ( ( \
     2, \
     3, \
     4, \
     5, \
     6, \
     7, \
     8, \
     9, \
    10, \
    11, \
    12, \
    16, \
    20, \
    30, \
    40 ))

  f_vec = np.array ( ( \
     0.164493406684822643647E+01, \
     0.120205690315959428540E+01, \
     0.108232323371113819152E+01, \
     0.103692775514336992633E+01, \
     0.101734306198444913971E+01, \
     0.100834927738192282684E+01, \
     0.100407735619794433939E+01, \
     0.100200839292608221442E+01, \
     0.100099457512781808534E+01, \
     0.100049418860411946456E+01, \
     0.100024608655330804830E+01, \
     0.100001528225940865187E+01, \
     0.100000095396203387280E+01, \
     0.100000000093132743242E+01, \
     0.100000000000090949478E+01 ))

  if ( n_data < 0 ):
    n_data = 0

  if ( n_max <= n_data ):
    n_data = 0
    n = 0
    f = 0.0
  else:
    n = n_vec[n_data]
    f = f_vec[n_data]
    n_data = n_data + 1

  return n_data, n, f

def zeta_values_test ( ):

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

  print ( '' )
  print ( 'ZETA_VALUES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  ZETA_VALUES stores values of the ZETA function.' )
  print ( '' )
  print ( '      N         ZETA(N)' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, n, f = zeta_values ( n_data )

    if ( n_data == 0 ):
      break

    print ( '  %6d  %24.16f' % ( n, f ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'ZETA_VALUES_TEST:' )
  print ( '  Normal end of execution.' )
  return

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