12 July 2023 02:56:55 PM

pyramid_jaskowiec_rule_test():
  C++ version
  Test pyramid_jaskowiec_rule().

pyramid_jaskowiec_rule_test01():
  Quadrature rule for the unit pyramid.
  Precision p = 5

  Number of nodes N = 15

     I      W          X           Y           Z

     0   0.0677344           0           0    0.730709
     1   0.0647089           0           0  0.00619723
     2    0.177272           0           0    0.268446
     3   0.0591078    0.753441           0       0.125
     4   0.0591078           0    0.753441       0.125
     5   0.0591078   -0.753441           0       0.125
     6   0.0591078           0   -0.753441       0.125
     7   0.0653755    0.417152    0.417152    0.421822
     8   0.0653755   -0.417152    0.417152    0.421822
     9   0.0653755    0.417152   -0.417152    0.421822
    10   0.0653755   -0.417152   -0.417152    0.421822
    11    0.048088    0.674023    0.674023   0.0657957
    12    0.048088   -0.674023    0.674023   0.0657957
    13    0.048088    0.674023   -0.674023   0.0657957
    14    0.048088   -0.674023   -0.674023   0.0657957

  Weight Sum = 1

pyramid_jaskowiec_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               2.22045e-16
   1               2.77556e-16
   2               2.77556e-17
   3                 1.249e-16
   4               1.19696e-16
   5               3.46945e-17
   6                0.00877241
   7               0.000605684

pyramid_jaskowiec_rule_test03():
  Test the precision of quadrature rules for the unit pyramid.
  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               1.66533e-16                 4.996e-16
   2               2.22045e-16               6.66134e-16
   3               1.66533e-16               1.66533e-15
   4               2.22045e-16               9.69927e-15
   5               2.77556e-16               9.42605e-15
   6               2.32453e-16               7.32227e-14
   7                4.3715e-16               7.38921e-14
   8               8.88178e-16                6.1254e-13
   9               1.30321e-15               1.06484e-12
  10               1.30451e-15               4.70614e-12
  11                1.4563e-15               5.07863e-12
  12               5.47132e-15               1.78293e-11
  13               1.31139e-14               3.55591e-11
  14               1.31121e-14               2.40972e-10
  15               1.62139e-14                8.9124e-10
  16               1.62138e-14               1.50177e-09
  17               7.49136e-14               4.89271e-09
  18               1.36162e-13               2.31787e-08
  19               1.36162e-13               7.98647e-08
  20               1.54454e-13               1.47886e-07

pyramid_jaskowiec_rule_test()
  Normal end of execution.

12 July 2023 02:56:55 PM