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

#*****************************************************************************80
#
## BESSEL_KX_VALUES returns some values of the Kx Bessel function.
#
#  Discussion:
#
#    This set of data considers the less common case in which the
#    index of the Bessel function Kn is actually not an integer.
#    We may suggest this case by occasionally replacing the symbol
#    "Kn" by "Kx".
#
#    The modified Bessel functions In(Z) and Kn(Z) are solutions of
#    the differential equation
#
#      Z^2 W'' + Z * W' - ( Z^2 + N^2 ) * W = 0.
#
#    In Mathematica, the function can be evaluated by:
#
#      BesselK[n,x]
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    12 January 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Milton Abramowitz, Irene Stegun,
#    Handbook of Mathematical Functions,
#    National Bureau of Standards, 1964,
#    ISBN: 0-486-61272-4,
#    LC: QA47.A34.
#
#    Stephen Wolfram,
#    The Mathematica Book,
#    Fourth Edition,
#    Cambridge University Press, 1999,
#    ISBN: 0-521-64314-7,
#    LC: QA76.95.W65.
#
#  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 NU, the order of the function.
#
#    Output, real X, the argument of the function.
#
#    Output, real FX, the value of the function.
#
  import numpy as np

  n_max = 28

  fx_vec = np.array ( ( \
       2.294489339798475E+00, \
       0.4610685044478946E+00, \
       0.1199377719680614E+00, \
       0.06506594315400999E+00, \
       0.03602598513176459E+00, \
       0.003776613374642883E+00, \
       0.00001799347809370518E+00, \
       5.776373974707445E-10, \
       0.9221370088957891E+00, \
       0.1799066579520922E+00, \
       0.004531936049571459E+00, \
       0.00001979282590307570E+00, \
       3.486992497366216E-23, \
       3.227479531135262E+00, \
       0.3897977588961997E+00, \
       0.006495775004385758E+00, \
       0.00002393132586462789E+00, \
       3.627839645299048E-23, \
       0.7311451879202114E+00, \
       0.1567475478393932E+00, \
       0.004257389528177461E+00, \
       0.00001915541065869563E+00, \
       3.463337593569306E-23, \
       4.731184839919541E+00, \
       0.4976876225514758E+00, \
       0.007300864610941163E+00, \
       0.00002546421294106458E+00, \
       3.675275677913656E-23 ) )

  nu_vec = np.array ( ( \
    0.50E+00, \
    0.50E+00, \
    0.50E+00, \
    0.50E+00, \
    0.50E+00, \
    0.50E+00, \
    0.50E+00, \
    0.50E+00, \
    1.50E+00, \
    1.50E+00, \
    1.50E+00, \
    1.50E+00, \
    1.50E+00, \
    2.50E+00, \
    2.50E+00, \
    2.50E+00, \
    2.50E+00, \
    2.50E+00, \
    1.25E+00, \
    1.25E+00, \
    1.25E+00, \
    1.25E+00, \
    1.25E+00, \
    2.75E+00, \
    2.75E+00, \
    2.75E+00, \
    2.75E+00, \
    2.75E+00 ))

  x_vec = np.array ( ( \
      0.2E+00, \
      1.0E+00, \
      2.0E+00, \
      2.5E+00, \
      3.0E+00, \
      5.0E+00, \
     10.0E+00, \
     20.0E+00, \
      1.0E+00, \
      2.0E+00, \
      5.0E+00, \
     10.0E+00, \
     50.0E+00, \
      1.0E+00, \
      2.0E+00, \
      5.0E+00, \
     10.0E+00, \
     50.0E+00, \
      1.0E+00, \
      2.0E+00, \
      5.0E+00, \
     10.0E+00, \
     50.0E+00, \
      1.0E+00, \
      2.0E+00, \
      5.0E+00, \
     10.0E+00, \
     50.0E+00  ) )

  if ( n_data < 0 ):
    n_data = 0

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

  return n_data, nu, x, fx

def bessel_kx_values_test ( ):

#*****************************************************************************80
#
## BESSEL_KX_VALUES_TEST demonstrates the use of BESSEL_KX_VALUES.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    12 January 2015
#
#  Author:
#
#    John Burkardt
#
  print ( '' )
  print ( 'BESSEL_KX_VALUES_TEST:' )
  print ( '  BESSEL_KX_VALUES stores values of the Bessel K function. of real order NU.' )
  print ( '' )
  print ( '      NU          X           K(NU,X)' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, nu, x, fx = bessel_kx_values ( n_data )

    if ( n_data == 0 ):
      break

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

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