13-Oct-2022 16:32:33 simplex_integrals_test(): MATLAB/Octave version 4.2.2 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 4 4 4 1.02836e-08 1.05714e-08 2.88e-10 0 1 4 0.000589787 0.000595238 5.45e-06 0 3 0 0.00834581 0.00833333 1.25e-05 1 0 0 0.0416337 0.0416667 3.29e-05 3 0 0 0.00821066 0.00833333 1.23e-04 0 0 1 0.0412863 0.0416667 3.80e-04 4 1 4 1.19799e-06 1.2025e-06 4.51e-09 4 2 1 1.26922e-05 1.32275e-05 5.35e-07 0 1 0 0.0416583 0.0416667 8.33e-06 0 2 0 0.0166806 0.0166667 1.39e-05 2 1 4 1.31699e-05 1.32275e-05 5.76e-08 1 3 4 3.55579e-06 3.6075e-06 5.17e-08 1 1 1 0.00137132 0.00138889 1.76e-05 3 1 1 0.000145308 0.00014881 3.50e-06 1 4 4 1.19048e-06 1.2025e-06 1.20e-08 3 2 2 6.3954e-06 6.61376e-06 2.18e-07 4 3 4 3.80677e-08 3.96429e-08 1.58e-09 2 2 2 2.15712e-05 2.20459e-05 4.75e-07 3 1 0 0.0011703 0.00119048 2.02e-05 0 3 2 0.000293374 0.000297619 4.25e-06 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 2 4 2 0 0 2 8.58892e-12 9.1766e-12 5.88e-13 1 2 1 1 0 2 5.99259e-10 6.42362e-10 4.31e-11 3 3 2 4 3 4 1.25798e-20 1.60421e-20 3.46e-21 2 0 2 3 3 4 1.49946e-15 1.42053e-15 7.89e-17 4 3 1 3 0 4 3.52558e-16 4.05865e-16 5.33e-17 0 3 4 0 3 2 2.86542e-13 2.699e-13 1.66e-14 2 4 1 2 0 4 1.79964e-14 1.89403e-14 9.44e-16 1 1 2 1 1 2 4.33685e-11 4.5883e-11 2.51e-12 2 4 2 0 0 4 2.93725e-13 3.59867e-13 6.61e-14 3 2 4 0 3 2 1.39848e-15 1.42053e-15 2.20e-17 2 0 2 4 0 0 1.23784e-09 1.10119e-09 1.37e-10 3 3 0 1 1 2 3.08613e-12 3.44122e-12 3.55e-13 3 4 2 1 1 0 8.30457e-13 8.097e-13 2.08e-14 0 2 3 2 3 3 6.83548e-15 7.10263e-15 2.67e-16 1 0 2 3 3 2 4.26111e-13 4.0485e-13 2.13e-14 1 2 3 3 1 2 2.0069e-14 2.24917e-14 2.42e-15 0 4 4 4 2 2 4.31883e-17 4.91957e-17 6.01e-18 1 2 1 0 4 4 1.88487e-13 1.79933e-13 8.55e-15 1 4 3 1 2 2 4.57078e-15 4.73509e-15 1.64e-16 3 2 4 1 3 1 7.1682e-16 7.10263e-16 6.56e-18 simplex_integrals_test(): Normal end of execution. 13-Oct-2022 16:32:33