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

#*****************************************************************************80
#
## ELLIPTIC_INC_PIM_VALUES: values of incomplete elliptic integral Pi(PHI,N,M).
#
#  Discussion:
#
#    This is the incomplete elliptic integral of the third kind.
#
#      Pi(PHI,N,M) = integral ( 0 <= T <= PHI ) 
#        dT / (1 - N sin^2(T) ) sqrt ( 1 - M * sin ( T )^2 )
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    24 June 2018
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Milton Abramowitz, 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, N, M, the arguments of the function.
#
#    Output, real PIM, the value of the function.
#
  import numpy as np

  n_max = 20

  m_vec = np.array ( [ \
       7.330122710928245, \
      0.1108806690614566, \
      0.2828355944410993, \
      0.6382999794812498, \
       2.294718938593894, \
       42062.55329826538, \
        39.2394337789563, \
    0.008002151065098688, \
      0.7190579590867517, \
      0.9703767630929055, \
       1.098881295982823, \
       1.398066725917478, \
       4.641021931654496, \
       4.455969064311461, \
      0.3131448239736511, \
      0.3686443684703166, \
     0.06678210908100803, \
      0.9635538974026796, \
       1.060208762696207, \
      0.4687160847955397 ] )

  n_vec = np.array ( [ \
       8.064681366127422, \
     -0.2840588974558835, \
      -5.034023488967104, \
      -1.244606253942751, \
       1.465981775919188, \
       95338.12857321106, \
      -44.43130633436311, \
     -0.8029374966926196, \
       5.218883222649502, \
       2.345821782626782, \
       0.157358332363011, \
       1.926593468907062, \
       6.113982855261652, \
       1.805710621498681, \
     -0.4072847419780592, \
     -0.9416404038595624, \
      0.7009655305226739, \
      -1.019830985340273, \
     -0.4510798219577842, \
      0.6028821390092596  ] )

  phi_vec = np.array ( [ \
      0.3430906586047127, \
      0.8823091382756705, \
      0.4046022501376546, \
      0.9958310121985398, \
       0.630370432896175, \
    0.002887706662908567, \
      0.1485105463502483, \
       1.320800086884777, \
      0.4088829927466769, \
       0.552337007372852, \
       1.087095515757691, \
      0.7128175949111615, \
      0.2968093345769761, \
      0.2910907344062498, \
      0.9695030752034163, \
       1.122288759723523, \
       1.295911610809573, \
       1.116491437736542, \
       1.170719322533712, \
       1.199360682338851 ] )

  pim_vec = np.array ( [ \
         1.0469349800785, \
       0.842114448140669, \
      0.3321642201520043, \
      0.8483033529960849, \
       1.055753817656772, \
    0.005108896144265593, \
      0.1426848042785896, \
       1.031350958206424, \
      0.7131013701418496, \
      0.8268044665355507, \
        1.57632867896015, \
       1.542817120857211, \
      0.4144629799126912, \
      0.3313231611366746, \
      0.9195822851915201, \
      0.9422320754002217, \
       2.036599002815859, \
       1.076799231499882, \
       1.416084462957852, \
       1.824124922310891 ] )

  if ( n_data < 0 ):
    n_data = 0

  if ( n_max <= n_data ):
    n_data = 0
    m = 0.0
    n = 0.0
    phi = 0.0
    pim = 0.0
  else:
    m = m_vec[n_data]
    n = n_vec[n_data]
    phi = phi_vec[n_data]
    pim = pim_vec[n_data]
    n_data = n_data + 1

  return n_data, phi, n, m, pim

def elliptic_inc_pim_values_test ( ):

#*****************************************************************************80
#
## ELLIPTIC_INC_PIM_VALUES_TEST tests ELLIPTIC_INC_PIM_VALUES.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    23 June 2018
#
#  Author:
#
#    John Burkardt
#
  print ( '' )
  print ( 'ELLIPTIC_INC_PIM_VALUES_TEST:' )
  print ( '  ELLIPTIC_INC_PIM_VALUES stores values of' )
  print ( '  the incomplete elliptic integral of the third' )
  print ( '  kind, with parameters PHI, N and M.' )
  print ( '' )
  print ( '    PHI           N             M            Pi(PHI,N,M)' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, phi, n, m, pim = elliptic_inc_pim_values ( n_data )

    if ( n_data == 0 ):
      break

    print ( '  %12f  %12f  %12f  %24.16f' % ( phi, n, m, pim ) )

  return

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