27 February 2022 07:44:45 AM

SPHERE_INTEGRALS_TEST:
  C++ version
  Test the SPHERE_INTEGRALS library.

TEST01
  Estimate monomial integrands using Monte Carlo
  over the surface of the unit sphere in 3D.

  Number of sample points used is 8192

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

  Ex  Ey  Ez     MC-Estimate           Exact      Error

   8   2   6     0.000576973     0.000574358     2.61503e-06
   4   6   4     0.000825674     0.000836921     1.12468e-05
   0   2   6        0.200907        0.199466      0.00144093
   2   6   0        0.194165        0.199466      0.00530161
   8   6   6     2.15884e-05     2.15924e-05      3.9661e-09
   4   6   6     0.000245113     0.000246153     1.04055e-06
   4   4   2       0.0106654         0.01088     0.000214615
   2   2   0        0.828991        0.837758      0.00876719
   6   4   4     0.000832578     0.000836921     4.34361e-06
   4   2   6      0.00421285      0.00418461     2.82486e-05
   4   2   2       0.0395759       0.0398932     0.000317343
   8   2   2      0.00971765      0.00976408     4.64286e-05
   6   4   0       0.0543348       0.0543999     6.50345e-05
   4   2   4       0.0108986         0.01088     1.86243e-05
   6   2   6      0.00140246      0.00139487     7.58949e-06
   0   4   2        0.356252        0.359039      0.00278668
   6   4   8     9.14311e-05      9.0688e-05     7.43012e-07
   0   4   8       0.0293621       0.0292922     6.98223e-05
   0   8   0         1.39732         1.39626      0.00105301
   8   4   8     3.05228e-05     3.02293e-05     2.93414e-07

SPHERE_INTEGRALS_TEST
  Normal end of execution.

27 February 2022 07:44:45 AM