06 October 2025 11:40:33 AM

SPHERE_INTEGRALS_TEST():
  C++ version
  Test SPHERE_INTEGRALS().

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.

06 October 2025 11:40:33 AM