12-Jul-2023 20:25:01

pyramid_jaskowiec_rule_test():
  MATLAB/Octave version 5.2.0
  Test pyramid_jaskowiec_rule().

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

     I      W          X           Y           Z

     1   0.0677344           0           0    0.730709
     2   0.0647089           0           0  0.00619723
     3    0.177272           0           0    0.268446
     4   0.0591078    0.753441           0       0.125
     5   0.0591078           0    0.753441       0.125
     6   0.0591078   -0.753441           0       0.125
     7   0.0591078           0   -0.753441       0.125
     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   0.0653755   -0.417152   -0.417152    0.421822
    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
    15    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,

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

  Degree  Maximum error

   0                         0
   1     1.665334536937735e-16
   2     5.551115123125783e-17
   3     1.110223024625157e-16
   4     1.196959198423997e-16
   5     3.816391647148976e-17
   6      0.008772414128785599
   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     2.220446049250313e-16     1.665334536937738e-15
   4     2.220446049250313e-16     9.699272635055414e-15
   5     1.665334536937735e-16     9.426053687589064e-15
   6     2.324529457808922e-16      7.32226779209864e-14
   7     4.388850394221322e-16     7.340027023683954e-14
   8     7.062492951570576e-16     6.120165409622123e-13
   9     1.302777330458582e-15     1.064853771567006e-12
  10     1.304945734803553e-15     4.705225162108368e-12
  11     1.455866677213535e-15     5.078651854505006e-12
  12     5.467848396278896e-15     1.782916723149741e-11
  13     1.311342527621218e-14     3.555959305640025e-11
  14     1.311342527621218e-14     2.409713164897596e-10
  15     1.621337612778273e-14     8.912397545341386e-10
  16     1.621348454799998e-14     1.501765526846641e-09
  17     7.491251542701693e-14     4.892706124214592e-09
  18      1.36161698235937e-13     2.317871994213597e-08
  19     1.361616779071463e-13     7.986468620093834e-08
  20     1.544540455819879e-13     1.478863313753901e-07

pyramid_jaskowiec_rule_test():
  Normal end of execution.

12-Jul-2023 20:25:06