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

#*****************************************************************************80
#
## LAMBERT_W_VALUES returns some values of the Lambert W function.
#
#  Discussion:
#
#    The function W(X) is defined implicitly by:
#
#      W(X) * e^W(X) = X
#
#    The function is also known as the "Omega" function.
#
#    In Mathematica, the function can be evaluated by:
#
#      W = ProductLog [ X ]
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    17 February 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Brian Hayes,
#    "Why W?",
#    The American Scientist,
#    Volume 93, March-April 2005, pages 104-108.
#
#    Eric Weisstein,
#    "Lambert's W-Function",
#    CRC Concise Encyclopedia of Mathematics,
#    CRC Press, 1998.
#
#    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 F, the value of the function.
#
  import numpy as np

  n_max = 22

  f_vec = np.array ( ( \
    0.0000000000000000E+00, \
    0.3517337112491958E+00, \
    0.5671432904097839E+00, \
    0.7258613577662263E+00, \
    0.8526055020137255E+00, \
    0.9585863567287029E+00, \
    0.1000000000000000E+01, \
    0.1049908894964040E+01, \
    0.1130289326974136E+01, \
    0.1202167873197043E+01, \
    0.1267237814307435E+01, \
    0.1326724665242200E+01, \
    0.1381545379445041E+01, \
    0.1432404775898300E+01, \
    0.1479856830173851E+01, \
    0.1524345204984144E+01, \
    0.1566230953782388E+01, \
    0.1605811996320178E+01, \
    0.1745528002740699E+01, \
    0.3385630140290050E+01, \
    0.5249602852401596E+01, \
    0.1138335808614005E+02 ))

  x_vec = np.array ( ( \
    0.0000000000000000E+00, \
    0.5000000000000000E+00, \
    0.1000000000000000E+01, \
    0.1500000000000000E+01, \
    0.2000000000000000E+01, \
    0.2500000000000000E+01, \
    0.2718281828459045E+01, \
    0.3000000000000000E+01, \
    0.3500000000000000E+01, \
    0.4000000000000000E+01, \
    0.4500000000000000E+01, \
    0.5000000000000000E+01, \
    0.5500000000000000E+01, \
    0.6000000000000000E+01, \
    0.6500000000000000E+01, \
    0.7000000000000000E+01, \
    0.7500000000000000E+01, \
    0.8000000000000000E+01, \
    0.1000000000000000E+02, \
    0.1000000000000000E+03, \
    0.1000000000000000E+04, \
    0.1000000000000000E+07 ))

  if ( n_data < 0 ):
    n_data = 0

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

  return n_data, x, f

def lambert_w_values_test ( ):

#*****************************************************************************80
#
## LAMBERT_W_VALUES_TEST demonstrates the use of LAMBERT_W_VALUES.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    17 February 2015
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'LAMBERT_W_VALUES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  LAMBERT_W_VALUES stores values of the Lambert W function.' )
  print ( '' )
  print ( '      X         LAMBERT_W(X)' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, x, f = lambert_w_values ( n_data )

    if ( n_data == 0 ):
      break

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

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