31-Jan-2019 22:17:29 HYPERBALL_INTEGRALS_TEST MATLAB version Test HYPERBALL_INTEGRALS. HYPERBALL_INTEGRALS_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 2 8 8 9.83951e-06 1.00764e-05 2.37e-07 4 4 0 0.0106403 0.01088 2.40e-04 2 0 0 0.835923 0.837758 1.83e-03 6 0 4 0.0040831 0.00418461 1.02e-04 4 6 6 1.26799e-05 1.29554e-05 2.76e-07 0 8 2 0.0106439 0.00976408 8.80e-04 0 0 8 0.124122 0.126933 2.81e-03 8 0 0 0.125298 0.126933 1.64e-03 2 8 0 0.00943474 0.00976408 3.29e-04 2 8 2 0.000659226 0.000650939 8.29e-06 6 4 8 4.25563e-06 4.31848e-06 6.28e-08 4 8 4 1.8137e-05 1.81376e-05 5.74e-10 0 6 2 0.0191658 0.0181333 1.03e-03 0 4 2 0.0405876 0.0398932 6.94e-04 6 2 2 0.00140508 0.00139487 1.02e-05 6 0 2 0.0175474 0.0181333 5.86e-04 8 8 0 0.00020666 0.000211605 4.95e-06 6 0 6 0.00140957 0.00139487 1.47e-05 6 2 8 3.07589e-05 3.02293e-05 5.30e-07 6 6 4 1.31195e-05 1.29554e-05 1.64e-07 HYPERBALL_INTEGRALS_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 6 6 4 2 0 8.10625e-08 8.53388e-08 4.28e-09 2 0 0 4 0 2 0.00111579 0.00115351 3.77e-05 2 6 6 0 6 2 6.64721e-10 5.86118e-10 7.86e-11 0 0 6 6 0 0 0.00026114 0.000300393 3.93e-05 2 6 0 2 6 2 2.52576e-08 2.84463e-08 3.19e-09 4 4 6 2 6 4 1.09816e-12 1.09897e-12 8.14e-16 0 6 2 0 4 2 3.41589e-06 3.00393e-06 4.12e-07 4 2 0 4 0 2 1.13169e-05 1.20157e-05 6.99e-07 6 6 0 4 0 6 1.93842e-09 1.75835e-09 1.80e-10 4 2 6 6 6 2 1.79834e-12 1.83162e-12 3.33e-14 6 4 0 4 0 2 4.33371e-07 4.09626e-07 2.37e-08 2 6 0 0 0 0 0.00611996 0.00576754 3.52e-04 2 0 0 0 4 6 5.59198e-05 6.00785e-05 4.16e-06 4 0 6 4 2 6 3.5455e-10 3.51671e-10 2.88e-12 6 6 4 0 2 2 4.27945e-09 3.28226e-09 9.97e-10 6 4 2 0 6 6 6.40488e-11 5.86118e-11 5.44e-12 4 2 4 2 4 6 6.53503e-11 7.03342e-11 4.98e-12 0 4 6 2 4 2 1.46782e-08 1.70678e-08 2.39e-09 2 6 6 6 0 2 5.21902e-10 5.86118e-10 6.42e-11 0 6 2 6 4 6 4.58553e-11 5.86118e-11 1.28e-11 HYPERBALL_INTEGRALS_TEST Normal end of execution. 31-Jan-2019 22:17:29