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

#*****************************************************************************80
#
## MITTAG_LEFFLER_EA_VALUES: values of one-parameter Mittag Leffler function.
#
#  Discussion:
#
#    E(alpha;z) = sum ( 0 <= k < oo ) z^k / Gamma ( alpha * k + 1 )
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    02 February 2017
#
#  Author:
#
#    John Burkardt
#
#  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 A, the parameter.
#
#    Output, real X, the argument of the function.
#
#    Output, real FX, the value of the function.
#
  import numpy as np

  n_max = 25

  a_vec = np.array ( ( \
     0.25E+00, \
     0.25E+00, \
     0.25E+00, \
     0.25E+00, \
     0.25E+00, \
     1.75E+00, \
     1.75E+00, \
     1.75E+00, \
     1.75E+00, \
     1.75E+00, \
     2.25E+00, \
     2.25E+00, \
     2.25E+00, \
     2.25E+00, \
     2.25E+00, \
     1.0E+00, \
     2.0E+00, \
     3.0E+00, \
     4.0E+00, \
     5.0E+00, \
     6.0E+00, \
     7.0E+00, \
     8.0E+00, \
     9.0E+00, \
     10.0E+00 ))

  fx_vec = np.array ( ( \
      1.0, \
      0.2525646348870172, \
      0.1427989464258737, \
      0.994231091392936E-01, \
      0.762370352397216E-01, \
      1.0, \
     -0.2579027070618285, \
      0.2716853059670252, \
      0.1846579916604009E-01, \
     -0.139707389642194, \
      1.0, \
     -0.1022121843823497E+01, \
      0.1860844522589611E+01, \
      0.2644615445996891E+01, \
      0.7762512036620307, \
      0.6737946999045729E-02, \
     -0.6172728764571668, \
      0.2010457248089053, \
      0.7922864454196143, \
      0.958340222567225, \
      0.993055607747429, \
      0.999007936794713, \
      0.999875992064687, \
      0.999986221340384, \
      0.999998622134038 ))

  x_vec = np.array ( ( \
       0.0, \
      -2.5, \
      -5.0, \
      -7.5, \
     -10.0, \
       0.0, \
     -12.5, \
     -25.0, \
     -37.5, \
     -50.0, \
       0.0, \
     -25.0, \
     -50.0, \
     -75.0, \
    -100.0, \
      -5.0, \
      -5.0, \
      -5.0, \
      -5.0, \
      -5.0, \
      -5.0, \
      -5.0, \
      -5.0, \
      -5.0, \
      -5.0 ))

  if ( n_data < 0 ):
    n_data = 0

  if ( n_max <= n_data ):
    n_data = 0
    a = 0.0
    x = 0.0
    fx = 0.0
  else:
    a = a_vec[n_data]
    x = x_vec[n_data]
    fx = fx_vec[n_data]
    n_data = n_data + 1

  return n_data, a, x, fx

def mittag_leffler_ea_values_test ( ):

#*****************************************************************************80
#
## MITTAG_LEFFLER_EA_VALUES_TEST demonstrates MITTAG_LEFFLER_EA_VALUES.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    02 February 2017
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'MITTAG_LEFFLER_EA_VALUES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  MITTAG_LEFFLER_EA_VALUES stores values of' )
  print ( '  the Mittag-Leffler one parameter function E(A;X).' )
  print ( '' )
  print ( '        A             X               E(A;X)' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, a, x, fx = mittag_leffler_ea_values ( n_data )

    if ( n_data == 0 ):
      break

    print ( '  %12f  %12f  %24.16g' % ( a, x, fx ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'MITTAG_LEFFLER_EA_VALUES_TEST:' )
  print ( '  Normal end of execution.' )
  return

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