function [ x, y, z, w ] = rule14 ( )

%*****************************************************************************80
%
%% rule14() returns the rule of precision 14.
%
%  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 = [ ...
      0.1772055324125434, ...
      0.6455889351749131, ...
      0.1772055324125434, ...
      0.4176447193404539, ...
      0.1647105613190922, ...
      0.4176447193404539, ...
      0.0617998830908726, ...
      0.8764002338182548, ...
      0.0617998830908726, ...
      0.4889639103621786, ...
      0.0220721792756427, ...
      0.4889639103621786, ...
      0.2734775283088386, ...
      0.4530449433823227, ...
      0.2734775283088386, ...
      0.0193909612487010, ...
      0.9612180775025979, ...
      0.0193909612487010, ...
      0.2983728821362578, ...
      0.6869801678080878, ...
      0.0146469500556544, ...
      0.6869801678080878, ...
      0.0146469500556544, ...
      0.2983728821362578, ...
      0.0571247574036479, ...
      0.7706085547749965, ...
      0.1722666878213556, ...
      0.7706085547749965, ...
      0.1722666878213556, ...
      0.0571247574036479, ...
      0.3368614597963450, ...
      0.5702222908466832, ...
      0.0929162493569718, ...
      0.5702222908466832, ...
      0.0929162493569718, ...
      0.3368614597963450, ...
      0.0012683309328720, ...
      0.8797571713701711, ...
      0.1189744976969568, ...
      0.8797571713701711, ...
      0.1189744976969568, ...
      0.0012683309328720 ];

  y = [ ...
      0.6455889351749131, ...
      0.1772055324125434, ...
      0.1772055324125434, ...
      0.1647105613190922, ...
      0.4176447193404539, ...
      0.4176447193404539, ...
      0.8764002338182548, ...
      0.0617998830908726, ...
      0.0617998830908726, ...
      0.0220721792756427, ...
      0.4889639103621786, ...
      0.4889639103621786, ...
      0.4530449433823227, ...
      0.2734775283088386, ...
      0.2734775283088386, ...
      0.9612180775025979, ...
      0.0193909612487010, ...
      0.0193909612487010, ...
      0.6869801678080878, ...
      0.2983728821362578, ...
      0.6869801678080878, ...
      0.0146469500556544, ...
      0.2983728821362578, ...
      0.0146469500556544, ...
      0.7706085547749965, ...
      0.0571247574036479, ...
      0.7706085547749965, ...
      0.1722666878213556, ...
      0.0571247574036479, ...
      0.1722666878213556, ...
      0.5702222908466832, ...
      0.3368614597963450, ...
      0.5702222908466832, ...
      0.0929162493569718, ...
      0.3368614597963450, ...
      0.0929162493569718, ...
      0.8797571713701711, ...
      0.0012683309328720, ...
      0.8797571713701711, ...
      0.1189744976969568, ...
      0.0012683309328720, ...
      0.1189744976969568 ];

  z = [ ...
      0.1772055324125434, ...
      0.1772055324125434, ...
      0.6455889351749131, ...
      0.4176447193404538, ...
      0.4176447193404538, ...
      0.1647105613190921, ...
      0.0617998830908726, ...
      0.0617998830908726, ...
      0.8764002338182548, ...
      0.4889639103621787, ...
      0.4889639103621787, ...
      0.0220721792756428, ...
      0.2734775283088386, ...
      0.2734775283088386, ...
      0.4530449433823227, ...
      0.0193909612487010, ...
      0.0193909612487010, ...
      0.9612180775025978, ...
      0.0146469500556544, ...
      0.0146469500556544, ...
      0.2983728821362578, ...
      0.2983728821362578, ...
      0.6869801678080878, ...
      0.6869801678080878, ...
      0.1722666878213556, ...
      0.1722666878213556, ...
      0.0571247574036480, ...
      0.0571247574036480, ...
      0.7706085547749966, ...
      0.7706085547749965, ...
      0.0929162493569718, ...
      0.0929162493569718, ...
      0.3368614597963450, ...
      0.3368614597963450, ...
      0.5702222908466832, ...
      0.5702222908466832, ...
      0.1189744976969569, ...
      0.1189744976969569, ...
      0.0012683309328720, ...
      0.0012683309328721, ...
      0.8797571713701711, ...
      0.8797571713701711 ];

  w = [ ...
      0.0210812943684965, ...
      0.0210812943684965, ...
      0.0210812943684965, ...
      0.0163941767720627, ...
      0.0163941767720627, ...
      0.0163941767720627, ...
      0.0072168498348883, ...
      0.0072168498348883, ...
      0.0072168498348883, ...
      0.0109417906847144, ...
      0.0109417906847144, ...
      0.0109417906847144, ...
      0.0258870522536458, ...
      0.0258870522536458, ...
      0.0258870522536458, ...
      0.0024617018012000, ...
      0.0024617018012000, ...
      0.0024617018012000, ...
      0.0072181540567669, ...
      0.0072181540567669, ...
      0.0072181540567669, ...
      0.0072181540567669, ...
      0.0072181540567669, ...
      0.0072181540567669, ...
      0.0123328766062818, ...
      0.0123328766062818, ...
      0.0123328766062818, ...
      0.0123328766062818, ...
      0.0123328766062818, ...
      0.0123328766062818, ...
      0.0192857553935303, ...
      0.0192857553935303, ...
      0.0192857553935303, ...
      0.0192857553935303, ...
      0.0192857553935303, ...
      0.0192857553935303, ...
      0.0025051144192503, ...
      0.0025051144192503, ...
      0.0025051144192503, ...
      0.0025051144192503, ...
      0.0025051144192503, ...
      0.0025051144192503 ];
%
%  The weights should sum to 1, not 1/2!
%
  w = w * 2.0;

  return
end
