function [ n_data, x, fx ] = 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:
%
%    24 February 2005
%
%  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 FX, the value of the function.
%
  n_max = 22;

  fx_vec = [ ...
    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 = [ ...
    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;
  end

  n_data = n_data + 1;

  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);
  end

  return
end
