function [ w, xyz ] = pyramid_unit_o13 ( )

%*****************************************************************************80
%
%% pyramid_unit_o13() returns a 13 point quadrature rule for the unit pyramid.
%
%  Discussion:
%
%    The integration region is defined as:
%
%    - ( 1 - Z ) <= X <= 1 - Z
%    - ( 1 - Z ) <= Y <= 1 - Z
%              0 <= Z <= 1.
%
%    When Z is zero, the integration region is a square lying in the (X,Y) 
%    plane, centered at (0,0,0) with "radius" 1.  As Z increases to 1, the 
%    radius of the square diminishes, and when Z reaches 1, the square has 
%    contracted to the single point (0,0,1).
%
%  Licensing:
%
%    This code is distributed under the MIT license. 
%
%  Modified:
%
%    13 April 2009
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Carlos Felippa,
%    A compendium of FEM integration formulas for symbolic work,
%    Engineering Computation,
%    Volume 21, Number 8, 2004, pages 867-890.
%
%  Output:
%
%    real W(13), the weights.
%
%    real XYZ(3,13), the abscissas.
%
  w(1:13,1) = [ ...
   0.063061594202898550725, ...
   0.063061594202898550725, ...
   0.063061594202898550725, ...
   0.063061594202898550725, ...
   0.042101946815575556199, ...
   0.042101946815575556199, ...
   0.042101946815575556199, ...
   0.042101946815575556199, ...
   0.13172030707666776585, ...
   0.13172030707666776585, ...
   0.13172030707666776585, ...
   0.13172030707666776585, ...
   0.05246460761943250889 ];

  xyz(1:3,1:13) = [ ...
  -0.38510399211870384331,  -0.38510399211870384331,  0.428571428571428571429; ...
   0.38510399211870384331,  -0.38510399211870384331,  0.428571428571428571429; ...
   0.38510399211870384331,   0.38510399211870384331,  0.428571428571428571429; ...
  -0.38510399211870384331,   0.38510399211870384331,  0.428571428571428571429; ...
  -0.40345831960728204766,   0.00000000000000000000,  0.33928571428571428571; ...
   0.40345831960728204766,   0.00000000000000000000,  0.33928571428571428571; ...
   0.00000000000000000000,  -0.40345831960728204766,  0.33928571428571428571; ...
   0.00000000000000000000,   0.40345831960728204766,  0.33928571428571428571; ...
  -0.53157877436961973359,  -0.53157877436961973359,  0.08496732026143790850; ...
   0.53157877436961973359,  -0.53157877436961973359,  0.08496732026143790850; ...
   0.53157877436961973359,   0.53157877436961973359,  0.08496732026143790850; ...
  -0.53157877436961973359,   0.53157877436961973359,  0.08496732026143790850; ...
   0.00000000000000000000,   0.00000000000000000000,  0.76219701803768503595 ]';

  return
end
