11-Jul-2023 09:35:15

triangle_witherden_rule_test():
  MATLAB/Octave version 5.2.0
  Test triangle_witherden_rule().

triangle_witherden_rule_test01():
  Quadrature rule for the triangle,
  given in barycentric coordinates.
  Precision p = 5

     I      W          A           B           C

     1       0.225    0.333333    0.333333    0.333333
     2    0.125939    0.101287    0.797427    0.101287
     3    0.125939    0.797427    0.101287    0.101287
     4    0.125939    0.101287    0.101287    0.797427
     5    0.132394    0.470142   0.0597159    0.470142
     6    0.132394   0.0597159    0.470142    0.470142
     7    0.132394    0.470142    0.470142   0.0597159

  Weight Sum    1

triangle_witherden_rule_test02():
  Test the precision of a quadrature rule for the unit triangle,

  Stated precision of rule    = 5
  Number of quadrature points = 7

  Degree  Maximum error

   0        0.0000000000000001
   1        0.0000000000000000
   2        0.0000000000000000
   3        0.0000000000000000
   4        0.0000000000000000
   5        0.0000000000000000
   6        0.0000818846056941
   7        0.0002540522381792

triangle_witherden_rule_test03():
  Test the precision of quadrature rules for the unit triangle,
  Check rules of precision p = 0 through 20
  for error in approximating integrals of monomials.

              maximum                   maximum
   p          absolute                  relative
              error                     error
   0                         0                         0
   1     5.551115123125783e-17      3.33066907387547e-16
   2     1.110223024625157e-16     4.996003610813204e-16
   3     2.220446049250313e-16     6.938893903907228e-16
   4     2.220446049250313e-16     8.326672684688674e-16
   5     1.110223024625157e-16     5.464378949326943e-16
   6     1.110223024625157e-16     2.220446049250313e-16
   7     1.110223024625157e-16     1.623701173514291e-15
   8     1.665334536937735e-16     1.405126015541214e-15
   9      3.33066907387547e-16     1.690542237448022e-15
  10     2.775557561562891e-17     1.373900992973631e-15
  11     2.220446049250313e-16     5.412337245047638e-15
  12     1.110223024625157e-16     2.367897544708342e-15
  13     1.110223024625157e-16     2.663884737796884e-15
  14     1.110223024625157e-15     1.040834085586084e-14
  15     2.775557561562891e-17     2.038545723827452e-15
  16     8.881784197001252e-16     1.552664247173041e-14
  17     1.110223024625157e-16     9.789044574937122e-15
  18     3.885780586188048e-16     1.878705524482882e-14
  19     4.440892098500626e-16     4.735795089416683e-15
  20      3.33066907387547e-16     9.016225266389453e-15

triangle_witherden_rule_test():
  Normal end of execution.

11-Jul-2023 09:35:15