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

#*****************************************************************************80
#
## ELLIPTIC_INC_EA_VALUES: values of the incomplete elliptic integral E(PHI,A).
#
#  Discussion:
#
#    This is one form of the incomplete elliptic integral of the second kind.
#
#      E(PHI,A) = integral ( 0 <= T <= PHI ) 
#        sqrt ( 1 - sin^2 ( A ) * sin^2 ( T ) ) dT
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    23 June 2018
#
#  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, real PHI, A, the arguments of the function.
#
#    Output, real EA, the value of the function.
#
  import numpy as np

  n_max = 20

  a_vec = np.array ( [ \
         123.0821233267548, \
         11.26931745051486, \
        -94.88806452075445, \
        -99.71407853545323, \
         57.05881039324191, \
        -19.71363287074183, \
         56.31230299738043, \
        -91.55605346417718, \
        -27.00654574696468, \
        -169.2293728595904, \
         61.96859564803047, \
        -158.7324398933148, \
         105.0883958999383, \
        -48.95883872360177, \
        -42.58568835110901, \
         11.65603284687828, \
        -8.398113719173338, \
         17.69362213019626, \
          73.8803420626852, \
        -69.82492339645128 ] )

  ea_vec = np.array ( [ \
        0.3384181367348019, \
         1.292924624509506, \
        0.6074183768796306, \
        0.3939726730783567, \
       0.06880814097089803, \
        0.0969436473376824, \
        0.6025937791452033, \
        0.9500549494837583, \
         1.342783372140486, \
        0.1484915631401388, \
         1.085432887050926, \
        0.1932136916085597, \
        0.3983689593057807, \
        0.1780054133336934, \
         1.164525270273536, \
         1.080167047541845, \
         1.346684963830312, \
         1.402100272685504, \
        0.2928091845544553, \
        0.5889342583405707 ] )

  phi_vec = np.array ( [ \
        0.3430906586047127, \
         1.302990057703935, \
        0.6523628380743488, \
        0.4046022501376546, \
       0.06884642871852312, \
        0.0969609046794745, \
         0.630370432896175, \
         1.252375418911598, \
         1.409796082144801, \
        0.1485105463502483, \
         1.349466184634646, \
        0.1933711786970301, \
        0.4088829927466769, \
        0.1785430666405224, \
         1.292588374416351, \
         1.087095515757691, \
         1.352794600489329, \
         1.432530166308616, \
        0.2968093345769761, \
        0.6235880396594726 ] )

  if ( n_data < 0 ):
    n_data = 0

  if ( n_max <= n_data ):
    n_data = 0
    a = 0.0
    ea = 0.0
    phi = 0.0
  else:
    a = a_vec[n_data]
    ea = ea_vec[n_data]
    phi = phi_vec[n_data]
    n_data = n_data + 1

  return n_data, phi, a, ea

def elliptic_inc_ea_values_test ( ):

#*****************************************************************************80
#
## ELLIPTIC_INC_EA_VALUES_TEST tests ELLIPTIC_INC_EA_VALUES.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    23 June 2018
#
#  Author:
#
#    John Burkardt
#
  print ( '' )
  print ( 'ELLIPTIC_INC_EA_VALUES_TEST:' )
  print ( '  ELLIPTIC_INC_EA_VALUES stores values of' )
  print ( '  the incomplete elliptic integral of the second' )
  print ( '  kind, with parameters PHI, A.' )
  print ( '' )
  print ( '    PHI        A            E(PHI,A)' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, phi, a, ea = elliptic_inc_ea_values ( n_data )

    if ( n_data == 0 ):
      break

    print ( '  %12f  %12f  %24.16f' % ( phi, a, ea ) )

  return

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