13 July 2023  10:07:10.230 AM

pyramid_witherden_rule_test():
  Fortran90 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

     1    0.684354E-01     0.00000         0.00000        0.729858    
     2    0.169397         0.00000         0.00000        0.300401    
     3    0.587045E-01     0.00000         0.00000        0.649177E-08
     4    0.764413E-01    0.706526         0.00000        0.125000    
     5    0.764413E-01     0.00000        0.706526        0.125000    
     6    0.764413E-01   -0.706526         0.00000        0.125000    
     7    0.764413E-01     0.00000       -0.706526        0.125000    
     8    0.396709E-01    0.705117        0.705117        0.611119E-01
     9    0.396709E-01    0.705117       -0.705117        0.611119E-01
    10    0.396709E-01   -0.705117        0.705117        0.611119E-01
    11    0.396709E-01   -0.705117       -0.705117        0.611119E-01
    12    0.597536E-01    0.432883        0.432883        0.423601    
    13    0.597536E-01    0.432883       -0.432883        0.423601    
    14    0.597536E-01   -0.432883        0.432883        0.423601    
    15    0.597536E-01   -0.432883       -0.432883        0.423601    

  Weight Sum    1.00000    

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    0.2220446049250313E-15
   1    0.1110223024625157E-15
   2    0.5551115123125783E-16
   3    0.1526556658859590E-15
   4    0.1266348137463069E-15
   5    0.3122502256758253E-16
   6    0.1003611110630780E-01
   7    0.7024040490240255E-03

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     0.000000000000000         0.000000000000000    
   1    0.1665334536937735E-15    0.4996003610813202E-15
   2    0.6661338147750939E-15    0.4996003610813204E-15
   3    0.1249000902703301E-15    0.1873501354054955E-14
   4    0.2220446049250313E-15    0.9835882108788589E-14
   5    0.2220446049250313E-15    0.9972491582521764E-14
   6    0.2363560736018400E-15    0.7445216318458507E-13
   7    0.6661338147750939E-15    0.7390572528965232E-13
   8    0.1554312234475219E-14    0.6162428965558349E-12
   9    0.1554312234475219E-14    0.1067657924960871E-11
  10    0.1298006840899646E-14    0.4704004214936884E-11

pyramid_witherden_rule_test():
  Normal end of execution.

13 July 2023  10:07:10.231 AM