function [ a, b, c, w ] = rule19 ( )

%*****************************************************************************80
%
%% rule19() returns the rule of precision 19.
%
%  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 = [ ...
          0.1424222825711269, ...
          0.8525725750765226, ...
          0.0050051423523504, ...
          0.8525725750765226, ...
          0.1424222825711269, ...
          0.0050051423523502, ...
          0.0525262798541034, ...
          0.8949474402917929, ...
          0.0525262798541039, ...
          0.0600838999627024, ...
          0.9301390385986208, ...
          0.0097770614386771, ...
          0.9301390385986208, ...
          0.0600838999627025, ...
          0.0097770614386767, ...
          0.1307006699605345, ...
          0.8301568806048565, ...
          0.0391424494346090, ...
          0.8301568806048566, ...
          0.1307006699605346, ...
          0.0391424494346087, ...
          0.3113183832239869, ...
          0.5593688070080342, ...
          0.1293128097679790, ...
          0.5593688070080342, ...
          0.3113183832239869, ...
          0.1293128097679789, ...
          0.1114480557169985, ...
          0.7771038885660025, ...
          0.1114480557169988, ...
          0.0116390273279224, ...
          0.9767219453441548, ...
          0.0116390273279229, ...
          0.2551621331531247, ...
          0.4896757336937503, ...
          0.2551621331531249, ...
          0.2214339418891134, ...
          0.7040048688065315, ...
          0.0745611893043552, ...
          0.7040048688065313, ...
          0.2214339418891134, ...
          0.0745611893043550, ...
          0.4039697179663860, ...
          0.4039697179663860, ...
          0.1920605640672278, ...
          0.3540259269997119, ...
          0.6050857585353100, ...
          0.0408883144649781, ...
          0.6050857585353100, ...
          0.3540259269997119, ...
          0.0408883144649780, ...
          0.1781710060796274, ...
          0.6436579878407451, ...
          0.1781710060796276, ...
          0.4591943889568276, ...
          0.4591943889568276, ...
          0.0816112220863447, ...
          0.3333333333333333, ...
          0.4925124498658742, ...
          0.4925124498658742, ...
          0.0149751002682516, ...
          0.2418941040068926, ...
          0.7431822570856689, ...
          0.0149236389074385, ...
          0.7431822570856689, ...
          0.2418941040068927, ...
          0.0149236389074383, ...
          0.3646204143387100, ...
          0.6333104818121875, ...
          0.0020691038491024, ...
          0.6333104818121876, ...
          0.3646204143387101, ...
          0.0020691038491022 ];

  b = [ ...
          0.0050051423523504, ...
          0.1424222825711269, ...
          0.8525725750765228, ...
          0.0050051423523504, ...
          0.8525725750765228, ...
          0.1424222825711273, ...
          0.0525262798541037, ...
          0.0525262798541034, ...
          0.8949474402917930, ...
          0.0097770614386769, ...
          0.0600838999627023, ...
          0.9301390385986208, ...
          0.0097770614386769, ...
          0.9301390385986208, ...
          0.0600838999627027, ...
          0.0391424494346089, ...
          0.1307006699605346, ...
          0.8301568806048567, ...
          0.0391424494346089, ...
          0.8301568806048567, ...
          0.1307006699605348, ...
          0.1293128097679790, ...
          0.3113183832239869, ...
          0.5593688070080343, ...
          0.1293128097679790, ...
          0.5593688070080343, ...
          0.3113183832239870, ...
          0.1114480557169988, ...
          0.1114480557169985, ...
          0.7771038885660028, ...
          0.0116390273279228, ...
          0.0116390273279224, ...
          0.9767219453441548, ...
          0.2551621331531249, ...
          0.2551621331531249, ...
          0.4896757336937504, ...
          0.0745611893043552, ...
          0.2214339418891134, ...
          0.7040048688065317, ...
          0.0745611893043552, ...
          0.7040048688065317, ...
          0.2214339418891137, ...
          0.1920605640672279, ...
          0.4039697179663861, ...
          0.4039697179663862, ...
          0.0408883144649781, ...
          0.3540259269997119, ...
          0.6050857585353102, ...
          0.0408883144649781, ...
          0.6050857585353101, ...
          0.3540259269997121, ...
          0.1781710060796276, ...
          0.1781710060796274, ...
          0.6436579878407452, ...
          0.0816112220863448, ...
          0.4591943889568277, ...
          0.4591943889568278, ...
          0.3333333333333334, ...
          0.0149751002682516, ...
          0.4925124498658743, ...
          0.4925124498658744, ...
          0.0149236389074385, ...
          0.2418941040068926, ...
          0.7431822570856692, ...
          0.0149236389074385, ...
          0.7431822570856690, ...
          0.2418941040068929, ...
          0.0020691038491024, ...
          0.3646204143387101, ...
          0.6333104818121877, ...
          0.0020691038491024, ...
          0.6333104818121877, ...
          0.3646204143387103 ];

  c = [ ...
          0.8525725750765227, ...
          0.0050051423523504, ...
          0.1424222825711267, ...
          0.1424222825711269, ...
          0.0050051423523502, ...
          0.8525725750765225, ...
          0.8949474402917929, ...
          0.0525262798541037, ...
          0.0525262798541032, ...
          0.9301390385986208, ...
          0.0097770614386769, ...
          0.0600838999627021, ...
          0.0600838999627024, ...
          0.0097770614386767, ...
          0.9301390385986207, ...
          0.8301568806048566, ...
          0.0391424494346090, ...
          0.1307006699605343, ...
          0.1307006699605345, ...
          0.0391424494346087, ...
          0.8301568806048565, ...
          0.5593688070080340, ...
          0.1293128097679789, ...
          0.3113183832239867, ...
          0.3113183832239868, ...
          0.1293128097679789, ...
          0.5593688070080340, ...
          0.7771038885660027, ...
          0.1114480557169989, ...
          0.1114480557169985, ...
          0.9767219453441548, ...
          0.0116390273279228, ...
          0.0116390273279222, ...
          0.4896757336937503, ...
          0.2551621331531249, ...
          0.2551621331531247, ...
          0.7040048688065315, ...
          0.0745611893043551, ...
          0.2214339418891131, ...
          0.2214339418891135, ...
          0.0745611893043550, ...
          0.7040048688065313, ...
          0.4039697179663861, ...
          0.1920605640672278, ...
          0.4039697179663860, ...
          0.6050857585353100, ...
          0.0408883144649781, ...
          0.3540259269997117, ...
          0.3540259269997119, ...
          0.0408883144649780, ...
          0.6050857585353098, ...
          0.6436579878407449, ...
          0.1781710060796274, ...
          0.1781710060796272, ...
          0.4591943889568276, ...
          0.0816112220863447, ...
          0.4591943889568275, ...
          0.3333333333333333, ...
          0.4925124498658742, ...
          0.0149751002682516, ...
          0.4925124498658741, ...
          0.7431822570856689, ...
          0.0149236389074385, ...
          0.2418941040068923, ...
          0.2418941040068927, ...
          0.0149236389074383, ...
          0.7431822570856688, ...
          0.6333104818121876, ...
          0.0020691038491024, ...
          0.3646204143387098, ...
          0.3646204143387100, ...
          0.0020691038491022, ...
          0.6333104818121874 ];

  w = [ ...
          0.0029256924878801, ...
          0.0029256924878801, ...
          0.0029256924878801, ...
          0.0029256924878801, ...
          0.0029256924878801, ...
          0.0029256924878801, ...
          0.0071093936227949, ...
          0.0071093936227949, ...
          0.0071093936227949, ...
          0.0033273888405939, ...
          0.0033273888405939, ...
          0.0033273888405939, ...
          0.0033273888405939, ...
          0.0033273888405939, ...
          0.0033273888405939, ...
          0.0096955190816242, ...
          0.0096955190816242, ...
          0.0096955190816242, ...
          0.0096955190816242, ...
          0.0096955190816242, ...
          0.0096955190816242, ...
          0.0263462647074454, ...
          0.0263462647074454, ...
          0.0263462647074454, ...
          0.0263462647074454, ...
          0.0263462647074454, ...
          0.0263462647074454, ...
          0.0152349565170048, ...
          0.0152349565170048, ...
          0.0152349565170048, ...
          0.0017651924183085, ...
          0.0017651924183085, ...
          0.0017651924183085, ...
          0.0317528545875300, ...
          0.0317528545875300, ...
          0.0317528545875300, ...
          0.0181080745904305, ...
          0.0181080745904305, ...
          0.0181080745904305, ...
          0.0181080745904305, ...
          0.0181080745904305, ...
          0.0181080745904305, ...
          0.0315373586452396, ...
          0.0315373586452396, ...
          0.0315373586452396, ...
          0.0161022094609394, ...
          0.0161022094609394, ...
          0.0161022094609394, ...
          0.0161022094609394, ...
          0.0161022094609394, ...
          0.0161022094609394, ...
          0.0246519810535848, ...
          0.0246519810535848, ...
          0.0246519810535848, ...
          0.0229835709771232, ...
          0.0229835709771232, ...
          0.0229835709771232, ...
          0.0344691608509053, ...
          0.0103218821824189, ...
          0.0103218821824189, ...
          0.0103218821824189, ...
          0.0084559248390935, ...
          0.0084559248390935, ...
          0.0084559248390935, ...
          0.0084559248390935, ...
          0.0084559248390935, ...
          0.0084559248390935, ...
          0.0032821375148397, ...
          0.0032821375148397, ...
          0.0032821375148397, ...
          0.0032821375148397, ...
          0.0032821375148397, ...
          0.0032821375148397 ];

  return
end
