28-Jul-2021 11:35:34 hypersphere_integrals_test() MATLAB/Octave version 9.9.0.1467703 (R2020b) Test hypersphere_integrals(). 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 4 8 4 0.000333486 0.000344615 1.11e-05 0 8 6 0.0101641 0.00976408 4.00e-04 6 8 4 8.52452e-05 9.0688e-05 5.44e-06 8 0 6 0.00995484 0.00976408 1.91e-04 4 6 6 0.000233924 0.000246153 1.22e-05 2 4 8 0.00190296 0.00195282 4.99e-05 8 4 6 8.32489e-05 9.0688e-05 7.44e-06 2 8 6 0.000584257 0.000574358 9.90e-06 6 4 8 8.321e-05 9.0688e-05 7.48e-06 0 6 4 0.0560345 0.0543999 1.63e-03 0 2 0 4.28036 4.18879 9.16e-02 0 8 8 0.00419929 0.0040205 1.79e-04 2 2 0 0.830844 0.837758 6.91e-03 6 4 8 8.321e-05 9.0688e-05 7.48e-06 8 8 8 1.65531e-06 1.84005e-06 1.85e-07 4 6 6 0.000233924 0.000246153 1.22e-05 0 8 0 1.47485 1.39626 7.86e-02 0 2 6 0.197316 0.199466 2.15e-03 0 6 2 0.204769 0.199466 5.30e-03 4 6 0 0.0548545 0.0543999 4.55e-04 HYPERSPHERE_INTEGRALS_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 0 6 6 0 4 2 1.91599e-06 2.04813e-06 1.32e-07 6 2 6 4 4 2 3.66594e-10 3.51671e-10 1.49e-11 6 6 6 2 4 4 6.39573e-12 5.49486e-12 9.01e-13 4 6 4 4 6 0 9.84471e-10 1.05501e-09 7.05e-11 6 4 4 2 2 2 1.93536e-08 1.70678e-08 2.29e-09 6 2 4 2 0 6 8.47742e-08 8.53388e-08 5.65e-10 6 4 2 4 0 2 4.4955e-07 4.09626e-07 3.99e-08 4 4 0 2 6 0 8.99843e-06 9.01178e-06 1.33e-08 6 6 4 0 6 6 3.26973e-11 2.74743e-11 5.22e-12 6 0 0 0 0 6 0.00529552 0.00540707 1.12e-04 4 0 4 2 2 6 4.23194e-07 4.09626e-07 1.36e-08 2 0 2 2 6 0 0.000370357 0.000360471 9.89e-06 0 0 6 4 6 4 2.5258e-07 2.56016e-07 3.44e-09 6 4 0 2 4 0 8.68236e-06 9.01178e-06 3.29e-07 2 4 0 0 2 2 0.00123373 0.00115351 8.02e-05 0 0 6 6 2 6 3.98236e-07 4.26694e-07 2.85e-08 6 0 2 2 6 6 1.53035e-08 1.64113e-08 1.11e-09 2 2 4 4 0 2 1.1829e-05 1.20157e-05 1.87e-07 6 6 2 4 0 6 2.07679e-09 1.75835e-09 3.18e-10 0 0 6 6 2 2 1.34547e-05 1.50196e-05 1.56e-06 hypersphere_integrals_test(): Normal end of execution. 28-Jul-2021 11:35:34