12 July 2023 10:07:52 PM

pyramid_witherden_rule_test():
  C version
  Test pyramid_witherden_rule().

pyramid_witherden_rule_test01():
  Quadrature rule for the unit pyramid.
  Precision p = 5

  Number of nodes N = 15

     I      W          X           Y           Z

     0   0.0684354           0           0    0.729858
     1    0.169397           0           0    0.300401
     2   0.0587045           0           0  6.49177e-09
     3   0.0764413    0.706526           0       0.125
     4   0.0764413           0    0.706526       0.125
     5   0.0764413   -0.706526           0       0.125
     6   0.0764413           0   -0.706526       0.125
     7   0.0396709    0.705117    0.705117   0.0611119
     8   0.0396709    0.705117   -0.705117   0.0611119
     9   0.0396709   -0.705117    0.705117   0.0611119
    10   0.0396709   -0.705117   -0.705117   0.0611119
    11   0.0597536    0.432883    0.432883    0.423601
    12   0.0597536    0.432883   -0.432883    0.423601
    13   0.0597536   -0.432883    0.432883    0.423601
    14   0.0597536   -0.432883   -0.432883    0.423601

  Weight Sum = 1

pyramid_witherden_rule_test02():
  Test the precision of a quadrature rule for the unit pyramid.

  Number of nodes N = 15

  Stated precision of rule    = 5
  Number of quadrature points = 15

  Degree  Maximum error

   0     2.220446049250313e-16
   1     1.110223024625157e-16
   2     5.551115123125783e-17
   3      1.52655665885959e-16
   4     1.266348137463069e-16
   5     3.122502256758253e-17
   6        0.0100361111063078
   7     0.0007024040490240255

pyramid_witherden_rule_test03():
  Test the precision of quadrature rules for the unit pyramid.
  Check rules of precision p = 0 through 10
  for error in approximating integrals of monomials.

              maximum                   maximum
   p          absolute                  relative
              error                     error

   0                         0                         0
   1     1.665334536937735e-16     4.996003610813202e-16
   2     6.661338147750939e-16     4.996003610813204e-16
   3     1.249000902703301e-16     1.873501354054955e-15
   4     2.220446049250313e-16     9.835882108788589e-15
   5     2.220446049250313e-16     9.972491582521764e-15
   6       2.3635607360184e-16     7.445216318458507e-14
   7     6.661338147750939e-16     7.389206434227901e-14
   8     1.554312234475219e-15     6.164441515841027e-13
   9     1.554312234475219e-15     1.067657924960871e-12
  10      1.29844052176864e-15     4.704004214936884e-12

pyramid_witherden_rule_test()
  Normal end of execution.

12 July 2023 10:07:52 PM