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

#*****************************************************************************80
#
## ELLIPTIC_INC_FK_VALUES: values of the incomplete elliptic integral F(PHI,K).
#
#  Discussion:
#
#    This is the incomplete elliptic integral of the first kind.
#
#      F(PHI,K) = integral ( 0 <= T <= PHI ) 
#        dT / sqrt ( 1 - K^2 * sin ( T )^2 )
#
#  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, K, the arguments.
#
#    Output, real FK, the value of the function.
#
  import numpy as np

  n_max = 20

  fk_vec = np.array ( [ \
       0.4340870330108736, \
        1.307312511398114, \
       0.8005154258533936, \
       0.4656721451084328, \
      0.06969849613441773, \
      0.09712646708750489, \
       0.6632598061016007, \
          2.2308677858579, \
        1.439846282888019, \
       0.2043389243773096, \
        1.537183574881771, \
       0.2749229901565622, \
       0.4828388342828284, \
       0.1812848567886627, \
        1.360729522341841, \
         1.09039680912027, \
        1.355363051581808, \
        1.445462819732441, \
       0.3125355489354676, \
       0.6775731623807174 ] )

  k_vec = np.array ( [ \
        2.712952582080266, \
       0.1279518954120547, \
       -1.429437513650137, \
       -1.981659235625333, \
        3.894801879555818, \
       -1.042486024983672, \
       0.8641142168759754, \
       -1.049058412826877, \
      -0.3024062128402472, \
       -6.574288841527263, \
       0.6987397421988888, \
        -5.12558591600033, \
        2.074947853793764, \
       -1.670886158426681, \
      -0.4843595000931672, \
       0.1393061679635559, \
      -0.0946527302537008, \
       0.1977207111754007, \
        1.788159919089993, \
       -1.077780624681256 ] )

  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
    fk = 0.0
    k = 0.0
    phi = 0.0
  else:
    fk = fk_vec[n_data]
    k = k_vec[n_data]
    phi = phi_vec[n_data]
    n_data = n_data + 1

  return n_data, phi, k, fk

def elliptic_inc_fk_values_test ( ):

#*****************************************************************************80
#
## ELLIPTIC_INC_FK_VALUES_TEST tests ELLIPTIC_INC_FK_VALUES.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    23 June 2018
#
#  Author:
#
#    John Burkardt
#
  print ( '' )
  print ( 'ELLIPTIC_INC_FK_VALUES_TEST:' )
  print ( '  ELLIPTIC_INC_FK_VALUES stores values of' )
  print ( '  the incomplete elliptic integral of the first' )
  print ( '  kind, with parameters PHI, K.' )
  print ( '' )
  print ( '    PHI        K            F(PHI,K)' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, phi, k, fk = elliptic_inc_fk_values ( n_data )

    if ( n_data == 0 ):
      break

    print ( '  %12f  %12f  %24.16f' % ( phi, k, fk ) )

  return

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