08-Jan-2022 09:34:55 simplex_integrals_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test simplex_integrals(). SIMPLEX_INTEGRALS_TEST01 Estimate monomial integrals using Monte Carlo over the interior of the unit simplex in M dimensions. Number of sample points used is 4192 We randomly choose the exponents. Ex Ey Ez MC-Estimate Exact Error 0 3 1 0.00115598 0.00119048 3.45e-05 3 1 0 0.00124824 0.00119048 5.78e-05 2 2 1 0.000104016 9.92063e-05 4.81e-06 4 4 4 1.15702e-08 1.05714e-08 9.99e-10 2 0 1 0.00282701 0.00277778 4.92e-05 1 0 2 0.00280211 0.00277778 2.43e-05 1 3 2 3.41687e-05 3.30688e-05 1.10e-06 1 4 0 0.000580135 0.000595238 1.51e-05 1 0 4 0.000605514 0.000595238 1.03e-05 3 3 1 1.03654e-05 9.92063e-06 4.45e-07 0 3 1 0.00115598 0.00119048 3.45e-05 3 2 2 7.05072e-06 6.61376e-06 4.37e-07 3 3 0 0.000100395 9.92063e-05 1.19e-06 3 4 3 1.50006e-07 1.3875e-07 1.13e-08 0 4 4 1.32582e-05 1.443e-05 1.17e-06 0 2 1 0.0027375 0.00277778 4.03e-05 3 2 4 6.37894e-07 6.01251e-07 3.66e-08 4 2 1 1.39966e-05 1.32275e-05 7.69e-07 1 1 4 6.70353e-05 6.61376e-05 8.98e-07 3 3 1 1.03654e-05 9.92063e-06 4.45e-07 SIMPLEX_INTEGRALS_TEST02 Estimate monomial integrals using Monte Carlo over the interior of the unit simplex in M dimensions. Number of sample points used is 4192 We randomly choose the exponents. E1 E2 E3 E4 E5 E6 MC-Estimate Exact Error 4 2 3 0 4 0 6.85433e-14 5.6821e-14 1.17e-14 0 4 2 4 4 1 5.75136e-16 5.41153e-16 3.40e-17 3 0 4 2 3 2 1.43308e-15 1.42053e-15 1.26e-17 2 0 3 3 2 4 1.35795e-15 1.42053e-15 6.26e-17 1 1 4 2 0 2 4.28552e-12 4.5883e-12 3.03e-13 4 1 0 1 4 4 6.43316e-15 5.6821e-15 7.51e-16 4 0 3 4 0 0 8.92706e-12 9.7164e-12 7.89e-13 0 4 4 3 1 3 3.88031e-16 4.05865e-16 1.78e-17 0 1 1 3 0 2 1.6267e-09 1.92709e-09 3.00e-10 2 0 2 3 3 0 6.15973e-12 6.88245e-12 7.23e-13 0 3 1 0 3 1 3.81435e-10 4.12947e-10 3.15e-11 0 2 4 4 3 4 6.65387e-18 6.41683e-18 2.37e-19 0 3 3 2 4 1 1.44707e-14 1.42053e-14 2.65e-16 0 1 2 1 4 2 5.10296e-12 4.5883e-12 5.15e-13 0 4 0 3 2 0 2.051e-10 2.20238e-10 1.51e-11 2 2 2 3 3 4 6.47452e-18 6.14946e-18 3.25e-19 3 1 4 3 2 4 1.49478e-18 1.60421e-18 1.09e-19 1 4 0 2 4 0 3.16872e-12 3.2388e-12 7.01e-14 1 2 1 0 3 1 1.3861e-10 1.37649e-10 9.61e-13 3 2 1 1 4 1 4.99067e-14 4.49833e-14 4.92e-15 simplex_integrals_test(): Normal end of execution. 08-Jan-2022 09:34:56