function [ n_data, a, b, fx ] = arithmetic_geometric_mean_values ( n_data )

%*****************************************************************************80
%
%% AGM_VALUES returns some values of the AGM.
%
%  Discussion:
%
%    The AGM is defined for nonnegative A and B.
%
%    The AGM of numbers A and B is defined by setting
%
%      A(0) = A,
%      B(0) = B
%
%      A(N+1) = ( A(N) + B(N) ) / 2
%      B(N+1) = sqrt ( A(N) * B(N) )
%
%    The two sequences both converge to AGM(A,B).
%
%    In Mathematica, the AGM can be evaluated by
%
%      ArithmeticGeometricMean [ a, b ]
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    09 February 2008
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Stephen Wolfram,
%    The Mathematica Book,
%    Fourth Edition,
%    Wolfram Media / Cambridge University Press, 1999.
%
%  Parameters:
%
%    Input, 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, 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 A, B, the argument ofs the function.
%
%    Output, real FX, the value of the function.
%
  n_max = 14;

  a_vec = [ ...
     22.0, ...
     83.0, ...
     42.0, ...
     26.0, ...
      4.0, ...
      6.0, ...
     40.0, ...
     80.0, ...
     90.0, ...
      9.0, ...
     53.0, ...
      1.0, ...
      1.0, ...
      1.0, ...
      1.5 ];
  b_vec = [ ...
     96.0, ...
     56.0, ...
      7.0, ...
     11.0, ...
     63.0, ...
     45.0, ...
     75.0, ...
      0.0, ...
     35.0, ...
      1.0, ...
     53.0, ...
      2.0, ...
      4.0, ...
      8.0, ...
      8.0 ];
  fx_vec = [ ...
     52.274641198704240049, ...
     68.836530059858524345, ...
     20.659301196734009322, ...
     17.696854873743648823, ...
     23.867049721753300163, ...
     20.717015982805991662, ...
     56.127842255616681863, ...
      0.000000000000000000, ...
     59.269565081229636528, ...
     3.9362355036495554780, ...
     53.000000000000000000, ...
     1.4567910310469068692, ...
     2.2430285802876025701, ...
     3.6157561775973627487, ...
     4.0816924080221632670 ];

  if ( n_data < 0 )
    n_data = 0;
  end

  n_data = n_data + 1;

  if ( n_max < n_data )
    n_data = 0;
    a = 0.0;
    b = 0.0;
    fx = 0.0;
  else
    a = a_vec(n_data);
    b = b_vec(n_data);
    fx = fx_vec(n_data);
  end

  return
end
