18 March 2020 12:16:36 PM HYPERSPHERE_INTEGRALS_TEST C++ version Test the HYPERSPHERE_INTEGRALS library. 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. 18 March 2020 12:16:36 PM