function elliptic_inc_ek_test ( )

%*****************************************************************************80
%
%% ELLIPTIC_INC_EK_TEST tests ELLIPTIC_INC_EK.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    21 June 2018
%
%  Author:
%
%    John Burkardt
%
  fprintf ( 1, '\n' );
  fprintf ( 1, 'ELLIPTIC_INC_EK_TEST:\n' );
  fprintf ( 1, '  ELLIPTIC_INC_EK returns values of\n' );
  fprintf ( 1, '  the incomplete elliptic integral of the\n' );
  fprintf ( 1, '  second kind, with parameters PHI, K.\n' );
  fprintf ( 1, '  Compare with MATLAB ellipticE(phi,k^2)\n' );
  fprintf ( 1, '\n' );
  fprintf ( 1, '          Phi             K                ellipticE(phi,k^2)  elliptic_inc_ek(phi,k)\n' );
  fprintf ( 1, '\n' );

  seed = 123456789;

  for i = 1 : 20

    [ phi, seed ] = r8_uniform_ab ( 0.0, 0.5 * pi, seed );
    kbound = abs ( 1.0 / sin ( phi ) );
    [ k, seed ] = r8_uniform_ab ( - kbound, + kbound, seed );
    fx1 = ellipticE ( phi, k^2 );
    fx2 = elliptic_inc_ek ( phi, k );

    fprintf ( 1, '  %14.6f  %14.6f  %24.16g  %24.16g\n', phi, k, fx1, fx2 );

  end

  return
end
