function [ suborder_xyz, suborder_w ] = triangle_nco_subrule ( rule, suborder_num )

%% TRIANGLE_NCO_SUBRULE returns a compressed NCO rule.
%
%  Modified:
%
%    30 January 2007
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Peter Silvester,
%    Symmetric Quadrature Formulae for Simplexes,
%    Mathematics of Computation,
%    Volume 24, Number 109, January 1970, pages 95-100.
%
%  Parameters:
%
%    Input, integer RULE, the index of the rule.
%
%    Input, integer SUBORDER_NUM, the number of suborders of the rule.
%
%    Output, real SUBORDER_XYZ(3,SUBORDER_NUM),
%    the barycentric coordinates of the abscissas.
%
%    Output, real SUBORDER_W(SUBORDER_NUM), the suborder weights.
%
  if ( rule == 1 )

    suborder_xyz_n(1:3,1:suborder_num) = [ ...
      0,  0, 0 ]';

    suborder_xyz_d = 0;

    suborder_w_n(1:suborder_num) = [ 1 ];

    suborder_w_d = 1;

  elseif ( rule == 2 )

    suborder_xyz_n(1:3,1:suborder_num) = [ ...
      1, 0, 0 ]';

    suborder_xyz_d = 1;

    suborder_w_n(1:suborder_num) = [ 1 ];

    suborder_w_d = 3;

  elseif ( rule == 3 )

    suborder_xyz_n(1:3,1:suborder_num) = [ ...
      2, 0, 0; ...
      1, 1, 0 ]';

    suborder_xyz_d = 2;

    suborder_w_n(1:suborder_num) = [ 7, -3 ];

     suborder_w_d = 12;

  elseif ( rule == 4 )

    suborder_xyz_n(1:3,1:suborder_num) = [ ...
      3, 0, 0; ...
      2, 1, 0; ...
      1, 1, 1 ]';

    suborder_xyz_d = 3;

    suborder_w_n(1:suborder_num) = [ 8, 3, -12 ];

     suborder_w_d = 30;

  elseif ( rule == 5 )

    suborder_xyz_n(1:3,1:suborder_num) = [ ...
      4, 0, 0; ...
      3, 1, 0; ...
      2, 2, 0; ...
      2, 1, 1 ]';

    suborder_xyz_d = 4;

    suborder_w_n(1:suborder_num) = [ 307, -316, 629, -64 ];

     suborder_w_d = 720;

  elseif ( rule == 6 )

    suborder_xyz_n(1:3,1:suborder_num) = [ ...
      5, 0, 0; ...
      4, 1, 0; ...
      3, 2, 0; ...
      3, 1, 1; ...
      2, 2, 1 ]';

    suborder_xyz_d = 5;

    suborder_w_n(1:suborder_num) = [ 71, -13, 57, -167, 113 ];

    suborder_w_d = 315;

  elseif ( rule == 7 )

    suborder_xyz_n(1:3,1:suborder_num) = [ ...
      6, 0, 0; ...
      5, 1, 0; ...
      4, 2, 0; ...
      4, 1, 1; ...
      3, 3, 0; ...
      3, 2, 1; ...
      2, 2, 2 ]';

    suborder_xyz_d = 6;

    suborder_w_n(1:suborder_num) = [ 767, -1257, 2901, 387, -3035, -915, 3509 ];

    suborder_w_d = 2240;

  elseif ( rule == 8 )

    suborder_xyz_n(1:3,1:suborder_num) = [ ...
      7, 0, 0; ...
      6, 1, 0; ...
      5, 2, 0; ...
      5, 1, 1; ...
      4, 3, 0; ...
      4, 2, 1; ...
      3, 3, 1; ...
      3, 2, 2 ]';

    suborder_xyz_d = 7;

    suborder_w_n(1:suborder_num) = [ ...
      898, -662, 1573, -2522, -191, 2989, -5726, 1444 ];

    suborder_w_d = 4536;

  elseif ( rule == 9 )

    suborder_xyz_n(1:3,1:suborder_num) = [ ...
      8, 0, 0; ...
      7, 1, 0; ...
      6, 2, 0; ...
      6, 1, 1; ...
      5, 3, 0; ...
      5, 2, 1; ...
      4, 4, 0; ...
      4, 3, 1; ...
      4, 2, 2; ...
      3, 3, 2 ]';

    suborder_xyz_d = 8;

    suborder_w_n(1:suborder_num) = [ ...
      1051445, -2366706, 6493915, 1818134, -9986439,-3757007, 12368047, ...
       478257, 10685542, -6437608 ];

    suborder_w_d = 3628800;

  else

    fprintf ( 1, '\n' );
    fprintf ( 1, 'NCO_TRIANGLE_SUBRULE - Fatal error!\n' );
    fprintf ( 1, '  Illegal RULE = %d\n', rule );
    error ( 'NCO_TRIANGLE_SUBRULE - Fatal error!' )

  end

  suborder_xyz(1:3,1:suborder_num) = ...
    ( 1 + suborder_xyz_n(1:3,1:suborder_num) ) / ( 3 + suborder_xyz_d );

  suborder_w(1:suborder_num) = ...
    suborder_w_n(1:suborder_num) / suborder_w_d;