06 October 2025 11:20:07 AM

HYPERSPHERE_INTEGRALS_TEST():
  C++ version
  Test HYPERSPHERE_INTEGRALS().

TEST01
  Estimate monomial integrals using Monte Carlo
  over the surface of the unit hypersphere in 3D.

  Number of sample points used is 4192

  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   6   0       0.0101008      0.00976408  0.000336707
   0   4   6       0.0523806       0.0543999  0.00201931
   8   8   4      3.0704e-05     3.02293e-05  4.74664e-07
   0   6   0         1.77434          1.7952   0.0208579
   8   6   0       0.0101008      0.00976408  0.000336707
   8   0   8      0.00390143       0.0040205  0.000119069
   6   8   0       0.0097385      0.00976408  2.55797e-05
   2   0   8        0.129394        0.126933   0.0024606
   2   6   0         0.19463        0.199466  0.00483577
   0   8   4       0.0277834       0.0292922  0.00150887
   2   4   4       0.0106938         0.01088  0.000186218
   6   0   8      0.00950729      0.00976408  0.000256789
   2   0   2        0.833768        0.837758   0.0039901
   8   2   8     0.000206441     0.000211605  5.16396e-06
   6   6   0       0.0212456        0.020923  0.000322554
   8   8   4      3.0704e-05     3.02293e-05  4.74664e-07
   0   8   8      0.00373499       0.0040205  0.000285513
   2   6   4      0.00406454      0.00418461  0.000120069
   0   8   0         1.38603         1.39626   0.0102358
   0   8   6      0.00910394      0.00976408  0.000660144

TEST02
  Estimate monomial integrals using Monte Carlo
  over the surface of the unit hypersphere in 6D.

  Number of sample points used is 4192

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

  E1  E2  E3  E4  E5  E6     MC-Estimate           Exact      Error

   6   6   6   6   6   6     9.72609e-16     1.10755e-15  1.34939e-16
   2   0   6   4   0   4      9.4212e-06     9.01178e-06  4.0942e-07
   4   4   2   4   0   6     4.92505e-08     5.12033e-08  1.95275e-09
   4   4   0   6   4   6      9.5141e-10     1.05501e-09  1.03603e-10
   0   2   4   2   6   6     6.94566e-08     8.53388e-08  1.58822e-08
   4   6   2   2   6   2     3.10547e-09     3.28226e-09  1.76787e-10
   0   6   6   2   0   0     0.000294144     0.000300393  6.24902e-06
   0   2   4   0   4   0      0.00347433      0.00346052  1.38102e-05
   6   2   2   6   6   0     1.57771e-08     1.64113e-08  6.34216e-10
   2   0   0   0   4   0        0.191455        0.193789    0.002334
   0   6   6   0   0   2     0.000303096     0.000300393  2.70345e-06
   2   6   4   4   2   4     1.84291e-09     1.96936e-09  1.26445e-10
   6   0   2   4   2   6     8.78755e-08     8.53388e-08  2.53669e-09
   2   4   0   4   6   0     9.47199e-06     9.01178e-06  4.60211e-07
   4   6   2   0   6   0     1.98882e-06     2.04813e-06  5.93151e-08
   0   2   2   2   0   6     0.000369649     0.000360471  9.17839e-06
   2   0   6   0   6   6     4.02629e-07     4.26694e-07  2.40648e-08
   0   0   4   6   4   4     1.05238e-06     1.22888e-06  1.76497e-07
   0   0   2   4   6   2     5.15405e-05     6.00785e-05   8.538e-06
   6   2   6   6   6   2     8.39922e-12     9.15809e-12  7.58873e-13

HYPERSPHERE_INTEGRALS_TEST():
  Normal end of execution.

06 October 2025 11:20:07 AM