function [ a, b, c, w ] = rule15 ( )

%*****************************************************************************80
%
%% rule15() returns the rule of precision 15.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    09 June 2023
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Hong Xiao, Zydrunas Gimbutas,
%    A numerical algorithm for the construction of efficient
%    quadrature rules in two and higher dimensions, 
%    Computers and Mathematics with Applications,
%    Volume 59, 2010, pages 663-676.
%
%  Output:
%
%    real a(n), b(n), c(n): the barycentric coordinates of quadrature points.
%
%    real w(n): the quadrature weights.
%
  a = [ ...
          0.1299782299330778, ...
          0.7400435401338442, ...
          0.1299782299330779, ...
          0.3333333333333333, ...
          0.4600769492970597, ...
          0.4600769492970597, ...
          0.0798461014058805, ...
          0.1823217834071913, ...
          0.7330839951106168, ...
          0.0845942214821919, ...
          0.7330839951106169, ...
          0.1823217834071914, ...
          0.0845942214821916, ...
          0.1502003840652387, ...
          0.8337725261484157, ...
          0.0160270897863456, ...
          0.8337725261484158, ...
          0.1502003840652388, ...
          0.0160270897863453, ...
          0.3231113151637127, ...
          0.5792382424060449, ...
          0.0976504424302423, ...
          0.5792382424060449, ...
          0.3231113151637127, ...
          0.0976504424302423, ...
          0.4916858166302972, ...
          0.4916858166302972, ...
          0.0166283667394055, ...
          0.2215323407951419, ...
          0.5569353184097160, ...
          0.2215323407951421, ...
          0.3969337374090606, ...
          0.3969337374090606, ...
          0.2061325251818788, ...
          0.3079476814836729, ...
          0.6735980666116939, ...
          0.0184542519046332, ...
          0.6735980666116940, ...
          0.3079476814836729, ...
          0.0184542519046331, ...
          0.0563419176961000, ...
          0.8873161646077997, ...
          0.0563419176961004, ...
          0.0380352293011093, ...
          0.9608512354248769, ...
          0.0011135352740139, ...
          0.9608512354248770, ...
          0.0380352293011093, ...
          0.0011135352740135 ];

  b = [ ...
          0.1299782299330780, ...
          0.1299782299330778, ...
          0.7400435401338445, ...
          0.3333333333333334, ...
          0.0798461014058806, ...
          0.4600769492970598, ...
          0.4600769492970599, ...
          0.0845942214821918, ...
          0.1823217834071913, ...
          0.7330839951106169, ...
          0.0845942214821918, ...
          0.7330839951106171, ...
          0.1823217834071916, ...
          0.0160270897863455, ...
          0.1502003840652387, ...
          0.8337725261484159, ...
          0.0160270897863455, ...
          0.8337725261484159, ...
          0.1502003840652391, ...
          0.0976504424302424, ...
          0.3231113151637127, ...
          0.5792382424060452, ...
          0.0976504424302424, ...
          0.5792382424060450, ...
          0.3231113151637129, ...
          0.0166283667394056, ...
          0.4916858166302973, ...
          0.4916858166302975, ...
          0.2215323407951421, ...
          0.2215323407951420, ...
          0.5569353184097161, ...
          0.2061325251818789, ...
          0.3969337374090606, ...
          0.3969337374090607, ...
          0.0184542519046332, ...
          0.3079476814836729, ...
          0.6735980666116942, ...
          0.0184542519046332, ...
          0.6735980666116941, ...
          0.3079476814836731, ...
          0.0563419176961003, ...
          0.0563419176960999, ...
          0.8873161646077998, ...
          0.0011135352740137, ...
          0.0380352293011093, ...
          0.9608512354248772, ...
          0.0011135352740137, ...
          0.9608512354248772, ...
          0.0380352293011096 ];

  c = [ ...
          0.7400435401338443, ...
          0.1299782299330780, ...
          0.1299782299330775, ...
          0.3333333333333333, ...
          0.4600769492970597, ...
          0.0798461014058806, ...
          0.4600769492970595, ...
          0.7330839951106168, ...
          0.0845942214821918, ...
          0.1823217834071911, ...
          0.1823217834071912, ...
          0.0845942214821916, ...
          0.7330839951106169, ...
          0.8337725261484158, ...
          0.0160270897863456, ...
          0.1502003840652385, ...
          0.1502003840652387, ...
          0.0160270897863453, ...
          0.8337725261484157, ...
          0.5792382424060450, ...
          0.0976504424302423, ...
          0.3231113151637125, ...
          0.3231113151637127, ...
          0.0976504424302423, ...
          0.5792382424060449, ...
          0.4916858166302972, ...
          0.0166283667394055, ...
          0.4916858166302970, ...
          0.5569353184097159, ...
          0.2215323407951420, ...
          0.2215323407951418, ...
          0.3969337374090605, ...
          0.2061325251818788, ...
          0.3969337374090605, ...
          0.6735980666116940, ...
          0.0184542519046332, ...
          0.3079476814836727, ...
          0.3079476814836729, ...
          0.0184542519046330, ...
          0.6735980666116937, ...
          0.8873161646077997, ...
          0.0563419176961003, ...
          0.0563419176960998, ...
          0.9608512354248770, ...
          0.0011135352740138, ...
          0.0380352293011089, ...
          0.0380352293011092, ...
          0.0011135352740136, ...
          0.9608512354248769 ];

  w = [ ...
          0.0073975040670461, ...
          0.0073975040670461, ...
          0.0073975040670461, ...
          0.0297304197480713, ...
          0.0215940879364384, ...
          0.0215940879364384, ...
          0.0215940879364384, ...
          0.0242300087831256, ...
          0.0242300087831256, ...
          0.0242300087831256, ...
          0.0242300087831256, ...
          0.0242300087831256, ...
          0.0242300087831256, ...
          0.0112285042988781, ...
          0.0112285042988781, ...
          0.0112285042988781, ...
          0.0112285042988781, ...
          0.0112285042988781, ...
          0.0112285042988781, ...
          0.0310752204705109, ...
          0.0310752204705109, ...
          0.0310752204705109, ...
          0.0310752204705109, ...
          0.0310752204705109, ...
          0.0310752204705109, ...
          0.0158322763500218, ...
          0.0158322763500218, ...
          0.0158322763500218, ...
          0.0462872861051981, ...
          0.0462872861051981, ...
          0.0462872861051981, ...
          0.0463360413912072, ...
          0.0463360413912072, ...
          0.0463360413912072, ...
          0.0164367620928279, ...
          0.0164367620928279, ...
          0.0164367620928279, ...
          0.0164367620928279, ...
          0.0164367620928279, ...
          0.0164367620928279, ...
          0.0150844742475971, ...
          0.0150844742475971, ...
          0.0150844742475971, ...
          0.0024752660145579, ...
          0.0024752660145579, ...
          0.0024752660145579, ...
          0.0024752660145579, ...
          0.0024752660145579, ...
          0.0024752660145579 ];

  return
end
