26 February 2022 06:56:10 PM HYPERBALL_INTEGRALS_TEST C version Test the HYPERBALL_INTEGRALS library. TEST01 Use the Monte Carlo method to estimate integrals over the interior of the unit hyperball in M dimensions. Spatial dimension M = 3 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 0 2 0.00944719 0.00976408 3.17e-04 4 2 8 0.000106546 0.000114872 8.33e-06 8 2 4 0.000113351 0.000114872 1.52e-06 0 8 4 0.0017592 0.00195282 1.94e-04 0 0 6 0.201203 0.199466 1.74e-03 2 6 8 2.91293e-05 3.02293e-05 1.10e-06 0 2 0 0.817859 0.837758 1.99e-02 4 6 4 4.88858e-05 4.92307e-05 3.45e-07 6 2 0 0.0194586 0.0181333 1.33e-03 8 8 2 1.00818e-05 1.00764e-05 5.40e-09 8 4 8 1.28466e-06 1.31432e-06 2.97e-08 2 2 8 0.000617766 0.000650939 3.32e-05 6 0 4 0.00401111 0.00418461 1.73e-04 8 4 0 0.00211512 0.00195282 1.62e-04 6 0 0 0.206377 0.199466 6.91e-03 8 2 0 0.0106769 0.00976408 9.13e-04 8 4 2 0.000116982 0.000114872 2.11e-06 2 6 0 0.0174516 0.0181333 6.82e-04 2 8 8 9.7552e-06 1.00764e-05 3.21e-07 0 2 2 0.116416 0.11968 3.26e-03 TEST02 Use the Monte Carlo method to estimate integrals over the interior of the unit hyperball in M dimensions. Spatial dimension M = 6 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 0 2 4 4 0 6 3.50057e-07 4.09626e-07 5.96e-08 6 0 2 2 6 6 4.57443e-10 5.86118e-10 1.29e-10 0 0 4 6 6 6 1.32607e-09 1.75835e-09 4.32e-10 2 4 6 2 6 6 1.40123e-12 1.83162e-12 4.30e-13 6 2 0 0 6 0 1.47968e-05 1.50196e-05 2.23e-07 2 0 2 6 4 4 1.6326e-08 1.70678e-08 7.42e-10 2 6 4 0 0 0 5.78593e-05 6.00785e-05 2.22e-06 4 6 4 0 4 2 1.97856e-09 1.96936e-09 9.20e-12 6 0 4 0 6 4 9.10346e-09 9.84678e-09 7.43e-10 4 2 4 4 0 0 2.08824e-06 1.80236e-06 2.86e-07 2 0 2 6 0 6 6.96057e-07 6.8271e-07 1.33e-08 0 4 4 2 2 6 1.41946e-08 1.70678e-08 2.87e-09 6 2 0 2 6 4 3.36529e-09 3.28226e-09 8.30e-11 0 6 2 4 2 2 1.15718e-07 1.36542e-07 2.08e-08 0 6 4 0 6 0 2.04727e-06 2.04813e-06 8.61e-10 2 0 6 0 4 0 5.66048e-05 6.00785e-05 3.47e-06 6 0 2 4 0 4 4.25947e-07 4.09626e-07 1.63e-08 0 2 2 4 2 4 5.07457e-07 6.00785e-07 9.33e-08 2 4 6 6 2 0 3.30373e-09 3.28226e-09 2.15e-11 4 6 0 2 4 2 1.61164e-08 1.70678e-08 9.51e-10 HYPERBALL_INTEGRALS_TEST Normal end of execution. 26 February 2022 06:56:10 PM