8 September 2023  12:05:07.201 PM      
 
ball_integrals_test():
  FORTRAN77 version
  Test ball_integrals().

TEST01
  Estimate monomial integrals using Monte Carlo
  over the interior of the unit ball in 3D.

  Number of sample points used is   4192

  If any exponent is odd, the integral is zero.
  We restrict this test to randomly chosen even exponents.

  Ex  Ey  Ez     MC-Estimate           Exact      Error

   6   0   4    0.394126E-02    0.418461E-02    0.24E-03
   6   6   0    0.142603E-02    0.139487E-02    0.31E-04
   8   0   2    0.965872E-02    0.976408E-02    0.11E-03
   0   4   0    0.364398        0.359039        0.54E-02
   0   8   4    0.187776E-02    0.195282E-02    0.75E-04
   8   4   6    0.387801E-05    0.431848E-05    0.44E-06
   8   8   4    0.129103E-05    0.131432E-05    0.23E-07
   8   0   4    0.184647E-02    0.195282E-02    0.11E-03
   2   2   4    0.351040E-02    0.362666E-02    0.12E-03
   8   8   8    0.667825E-07    0.681499E-07    0.14E-08
   2   4   2    0.352597E-02    0.362666E-02    0.10E-03
   2   0   8    0.968985E-02    0.976408E-02    0.74E-04
   4   4   2    0.804125E-03    0.836921E-03    0.33E-04
   0   2   2    0.117002        0.119680        0.27E-02
   6   6   8    0.890667E-06    0.938800E-06    0.48E-07
   4   6   8    0.416897E-05    0.431848E-05    0.15E-06
   0   4   4    0.106290E-01    0.108800E-01    0.25E-03
   4   2   8    0.106263E-03    0.114872E-03    0.86E-05
   4   0   4    0.103571E-01    0.108800E-01    0.52E-03
   6   4   4    0.463140E-04    0.492307E-04    0.29E-05
 
ball_integrals_test():
  Normal end of execution.
 
 8 September 2023  12:05:07.204 PM