Tue May 20 22:43:32 2025

triangle_witherden_rule_test():
  python version: 3.10.12
  numpy version:  1.26.4
  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

     0       0.225    0.333333    0.333333    0.333333
     1    0.125939    0.101287    0.797427    0.101287
     2    0.125939    0.797427    0.101287    0.101287
     3    0.125939    0.101287    0.101287    0.797427
     4    0.132394    0.470142   0.0597159    0.470142
     5    0.132394   0.0597159    0.470142    0.470142
     6    0.132394    0.470142    0.470142   0.0597159

  Weight Sum     1.0000000000000002

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     1.110223024625157e-16
   1     5.551115123125783e-17
   2     2.775557561562891e-17
   3     2.081668171172169e-17
   4     6.938893903907228e-18
   5     1.387778780781446e-17
   6     8.188460569411721e-05
   7     0.0002540522381792171

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     6.661338147750939e-16
   3     2.220446049250313e-16     8.326672684688674e-16
   4     2.220446049250313e-16     8.326672684688674e-16
   5     1.110223024625157e-16     5.828670879282072e-16
   6     5.551115123125783e-17     4.163336342344337e-16
   7     1.110223024625157e-16     1.623701173514291e-15
   8     2.220446049250313e-16     1.405126015541214e-15
   9     3.885780586188048e-16     1.690542237448022e-15
  10     5.551115123125783e-17     1.405126015541214e-15
  11     6.245004513516506e-17     5.547645676173829e-15
  12     1.110223024625157e-16     2.210037708394452e-15
  13     5.551115123125783e-17     2.663884737796884e-15
  14     1.332267629550188e-15     1.040834085586084e-14
  15     2.775557561562891e-17     2.038545723827452e-15
  16     7.771561172376096e-16     1.552664247173041e-14
  17     4.510281037539698e-17     9.789044574937122e-15
  18     4.440892098500626e-16     1.878705524482882e-14
  19     6.106226635438361e-16     4.735795089416683e-15
  20     7.216449660063518e-16     9.141450617311529e-15

triangle_witherden_rule_test():
  Normal end of execution.
Tue May 20 22:43:32 2025