12 July 2023 09:02:34 AM

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     2.220446049250313e-16
   1     2.775557561562891e-16
   2     2.775557561562891e-17
   3     1.249000902703301e-16
   4     1.196959198423997e-16
   5     3.469446951953614e-17
   6      0.008772414128785593
   7     0.0006056836049176022

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     1.665334536937735e-16     4.996003610813202e-16
   2     2.220446049250313e-16     6.661338147750936e-16
   3     1.665334536937735e-16     1.665334536937738e-15
   4     2.220446049250313e-16     9.699272635055414e-15
   5     2.775557561562891e-16     9.426053687589064e-15
   6     2.324529457808922e-16      7.32226779209864e-14
   7     4.371503159461554e-16     7.389206434227901e-14
   8     8.881784197001252e-16     6.125398040357083e-13
   9     1.303211011327576e-15     1.064840354565121e-12
  10     1.304512053934559e-15     4.706140872486982e-12
  11      1.45630035808253e-15     5.078631505385482e-12
  12      5.47131784323085e-15      1.78293389271934e-11
  13     1.311385895708117e-14     3.555913674281093e-11
  14     1.311212423360519e-14     2.409723542948556e-10
  15     1.621391822886897e-14     8.912399120581262e-10
  16     1.621380980865172e-14      1.50176613011621e-09
  17     7.491359962918942e-14     4.892707991477539e-09
  18     1.361616169207741e-13     2.317872029662416e-08
  19     1.361616169207741e-13     7.986468683787245e-08
  20     1.544540930158329e-13     1.478863312362768e-07

pyramid_jaskowiec_rule_test()
  Normal end of execution.

12 July 2023 09:02:34 AM