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

#*****************************************************************************80
#
## LERCH_VALUES returns some values of the Lerch transcendent function.
#
#  Discussion:
#
#    The Lerch function is defined as
#
#      Phi(z,s,a) = Sum ( 0 <= k < Infinity ) z^k / ( a + k )^s
#
#    omitting any terms with ( a + k ) = 0.
#
#    In Mathematica, the function can be evaluated by:
#
#      LerchPhi[z,s,a]
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    19 February 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    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, real Z, the parameters of the function.
#
#    Output, integer S, the parameters of the function.
#
#    Output, real A, the parameters of the function.
#
#    Output, real F, the value of the function.
#
  import numpy as np

  n_max = 12

  a_vec = np.array ( ( \
     0.0E+00, \
     0.0E+00, \
     0.0E+00, \
     1.0E+00, \
     1.0E+00, \
     1.0E+00, \
     2.0E+00, \
     2.0E+00, \
     2.0E+00, \
     3.0E+00, \
     3.0E+00, \
     3.0E+00 ))

  f_vec = np.array ( ( \
     0.1644934066848226E+01, \
     0.1202056903159594E+01, \
     0.1000994575127818E+01, \
     0.1164481052930025E+01, \
     0.1074426387216080E+01, \
     0.1000492641212014E+01, \
     0.2959190697935714E+00, \
     0.1394507503935608E+00, \
     0.9823175058446061E-03, \
     0.1177910993911311E+00, \
     0.3868447922298962E-01, \
     0.1703149614186634E-04 ))

  s_vec = np.array ( ( \
     2, 3, 10, \
     2, 3, 10, \
     2, 3, 10, \
     2, 3, 10 ))

  z_vec = np.array ( ( \
     0.1000000000000000E+01, \
     0.1000000000000000E+01, \
     0.1000000000000000E+01, \
     0.5000000000000000E+00, \
     0.5000000000000000E+00, \
     0.5000000000000000E+00, \
     0.3333333333333333E+00, \
     0.3333333333333333E+00, \
     0.3333333333333333E+00, \
     0.1000000000000000E+00, \
     0.1000000000000000E+00, \
     0.1000000000000000E+00 ))

  if ( n_data < 0 ):
    n_data = 0

  if ( n_max <= n_data ):
    n_data = 0
    z = 0.0
    s = 0
    a = 0.0
    f = 0.0
  else:
    z = z_vec[n_data]
    s = s_vec[n_data]
    a = a_vec[n_data]
    f = f_vec[n_data]
    n_data = n_data + 1

  return n_data, z, s, a, f

def lerch_values_test ( ):

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

  print ( '' )
  print ( 'LERCH_VALUES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  LERCH_VALUES stores values of the Lerch function.' )
  print ( '' )
  print ( '        Z            S        A               F' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, z, s, a, f = lerch_values ( n_data )

    if ( n_data == 0 ):
      break

    print ( '  %12f  %6d  %12f  %24.16f' % ( z, s, a, f ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'LERCH_VALUES_TEST:' )
  print ( '  Normal end of execution.' )
  return

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