10 July 2023 10:46:02 PM

triangle_witherden_rule_test():
  C version
  Test triangle_witherden_rule().

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

  Number of nodes N = 7

     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

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

  Number of nodes N = 7

  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 a quadrature rule 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     2.775557561562891e-17     1.665334536937735e-16
   3     1.110223024625157e-16      3.33066907387547e-16
   4     1.110223024625157e-16     4.163336342344337e-16
   5     5.551115123125783e-17     3.642919299551295e-16
   6     5.551115123125783e-17     4.163336342344337e-16
   7     2.775557561562891e-17     6.245004513516506e-16
   8     5.551115123125783e-17     6.245004513516507e-16
   9     1.665334536937735e-16     1.144917494144692e-15
  10     2.220446049250313e-16     1.144917494144693e-15
  11     4.440892098500626e-16     1.502704211064909e-15
  12     4.440892098500626e-16      2.84147705365001e-15
  13     4.440892098500626e-16     2.706168622523819e-15
  14     6.938893903907228e-17     3.122502256758253e-15
  15     6.938893903907228e-17     2.289275946544198e-15
  16      3.33066907387547e-16     9.156737867943576e-15
  17     2.775557561562891e-17     2.123301534595612e-15
  18     4.440892098500626e-16     3.856290287096442e-15
  19     2.775557561562891e-16     6.739400704169895e-15
  20     1.110223024625157e-16     7.212980213111564e-15

triangle_witherden_rule_test()
  Normal end of execution.

10 July 2023 10:46:02 PM