#! /usr/bin/env python
#
def bessel_i0_spherical_values ( n_data ):

#*****************************************************************************80
#
## BESSEL_I0_SPHERICAL_VALUES returns some values of the Spherical Bessel function i0.
#
#  Discussion:
#
#    In Mathematica, the function can be evaluated by:
#
#      Sqrt[Pi/(2*x)] * BesselI[1/2,x]
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    30 December 2014
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Milton Abramowitz, Irene Stegun,
#    Handbook of Mathematical Functions,
#    National Bureau of Standards, 1964,
#    LC: QA47.A34,
#    ISBN: 0-486-61272-4.
#
#    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 X, the argument of the function.
#
#    Output, real FX, the value of the function.
#
  import numpy as np

  n_max = 21

  fx_vec = np.array ( ( \
    1.001667500198440E+00, \
    1.006680012705470E+00, \
    1.026880814507039E+00, \
    1.061089303580402E+00, \
    1.110132477734529E+00, \
    1.175201193643801E+00, \
    1.257884462843477E+00, \
    1.360215358179667E+00, \
    1.484729970750144E+00, \
    1.634541271164267E+00, \
    1.813430203923509E+00, \
    2.025956895698133E+00, \
    2.277595505698373E+00, \
    2.574897010920645E+00, \
    2.925685126512827E+00, \
    3.339291642469967E+00, \
    3.826838748926716E+00, \
    4.401577467270101E+00, \
    5.079293155726485E+00, \
    5.878791279137455E+00, \
    6.822479299281938E+00 ) )

  x_vec = np.array ( ( \
     0.1E+00, \
     0.2E+00, \
     0.4E+00, \
     0.6E+00, \
     0.8E+00, \
     1.0E+00, \
     1.2E+00, \
     1.4E+00, \
     1.6E+00, \
     1.8E+00, \
     2.0E+00, \
     2.2E+00, \
     2.4E+00, \
     2.6E+00, \
     2.8E+00, \
     3.0E+00, \
     3.2E+00, \
     3.4E+00, \
     3.6E+00, \
     3.8E+00, \
     4.0E+00  ) )

  if ( n_data < 0 ):
    n_data = 0

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

  return n_data, x, fx

def bessel_i0_spherical_values_test ( ):

#*****************************************************************************80
#
## BESSEL_I0_SPHERICAL_VALUES_TEST tests BESSEL_I0_SPHERICAL_VALUES.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    30 December 2014
#
#  Author:
#
#    John Burkardt
#
  print ( '' )
  print ( 'BESSEL_I0_SPHERICAL_VALUES_TEST:' )
  print ( '  BESSEL_I0_SPHERICAL_VALUES: values of the spherical Bessel I function. of order 0.' )
  print ( '' )
  print ( '      X        Spherical I(0,X)' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, x, fx = bessel_i0_spherical_values ( n_data )

    if ( n_data == 0 ):
      break

    print ( '  %12f  %24.16g' % ( x, fx ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'BESSEL_I0_SPHERICAL_VALUES_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  bessel_i0_spherical_values_test ( )
  timestamp ( )