function [ x, y, z, w ] = rule11 ( )

%*****************************************************************************80
%
%% rule11() returns the rule of precision 11.
%
%  Discussion:
%
%    The data is given for the following triangle:
%
%     (0,1) 
%       |   \ 
%       |    \ 
%       |     \ 
%       |      \ 
%     (0,0)----(1,0)
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    23 April 2023
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Freddie Witherden, Peter Vincent,
%    On the identification of symmetric quadrature rules for finite element methods,
%    Computers and Mathematics with Applications,
%    Volume 69, pages 1232-1241, 2015.
%
%  Output:
%
%    real x(n), y(n), z(n): the barycentric coordinates of quadrature points.
%
%    real w(n): the quadrature weights.
%
  x = [ ...
      0.3333333333333334, ...
      0.0284854176143719, ...
      0.9430291647712562, ...
      0.0284854176143719, ...
      0.2102199567031783, ...
      0.5795600865936434, ...
      0.2102199567031783, ...
      0.1026354827122464, ...
      0.7947290345755071, ...
      0.1026354827122464, ...
      0.4958919009658909, ...
      0.0082161980682182, ...
      0.4958919009658909, ...
      0.4384659267643522, ...
      0.1230681464712956, ...
      0.4384659267643522, ...
      0.1493247886520824, ...
      0.8433497836618531, ...
      0.0073254276860645, ...
      0.8433497836618531, ...
      0.0073254276860645, ...
      0.1493247886520824, ...
      0.0460105001654300, ...
      0.6644083741968642, ...
      0.2895811256377059, ...
      0.6644083741968642, ...
      0.2895811256377059, ...
      0.0460105001654300 ];

  y = [ ...
      0.3333333333333334, ...
      0.9430291647712562, ...
      0.0284854176143719, ...
      0.0284854176143719, ...
      0.5795600865936434, ...
      0.2102199567031783, ...
      0.2102199567031783, ...
      0.7947290345755071, ...
      0.1026354827122464, ...
      0.1026354827122464, ...
      0.0082161980682182, ...
      0.4958919009658909, ...
      0.4958919009658909, ...
      0.1230681464712956, ...
      0.4384659267643522, ...
      0.4384659267643522, ...
      0.8433497836618531, ...
      0.1493247886520824, ...
      0.8433497836618531, ...
      0.0073254276860645, ...
      0.1493247886520824, ...
      0.0073254276860645, ...
      0.6644083741968642, ...
      0.0460105001654300, ...
      0.6644083741968642, ...
      0.2895811256377059, ...
      0.0460105001654300, ...
      0.2895811256377059 ];

  z = [ ...
      0.3333333333333333, ...
      0.0284854176143720, ...
      0.0284854176143719, ...
      0.9430291647712563, ...
      0.2102199567031783, ...
      0.2102199567031783, ...
      0.5795600865936434, ...
      0.1026354827122464, ...
      0.1026354827122464, ...
      0.7947290345755071, ...
      0.4958919009658910, ...
      0.4958919009658909, ...
      0.0082161980682182, ...
      0.4384659267643521, ...
      0.4384659267643522, ...
      0.1230681464712955, ...
      0.0073254276860646, ...
      0.0073254276860645, ...
      0.1493247886520824, ...
      0.1493247886520824, ...
      0.8433497836618531, ...
      0.8433497836618532, ...
      0.2895811256377059, ...
      0.2895811256377059, ...
      0.0460105001654300, ...
      0.0460105001654300, ...
      0.6644083741968642, ...
      0.6644083741968642 ];

  w = [ ...
      0.0428805898661121, ...
      0.0052159352564473, ...
      0.0052159352564473, ...
      0.0052159352564473, ...
      0.0352578420558583, ...
      0.0352578420558583, ...
      0.0352578420558583, ...
      0.0193153796185097, ...
      0.0193153796185097, ...
      0.0193153796185097, ...
      0.0083031365272927, ...
      0.0083031365272927, ...
      0.0083031365272927, ...
      0.0336580770397341, ...
      0.0336580770397341, ...
      0.0336580770397341, ...
      0.0051451447864766, ...
      0.0051451447864766, ...
      0.0051451447864766, ...
      0.0051451447864766, ...
      0.0051451447864766, ...
      0.0051451447864766, ...
      0.0201662383202503, ...
      0.0201662383202503, ...
      0.0201662383202503, ...
      0.0201662383202503, ...
      0.0201662383202503, ...
      0.0201662383202503 ];
%
%  The weights should sum to 1, not 1/2!
%
  w = w * 2.0;

  return
end
