13 April 2020 12:39:33 PM SIMPLEX_INTEGRALS_TEST C++ version Test the SIMPLEX_INTEGRALS library. 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 0 1 0.000596497 0.000595238 1.2591e-06 2 1 4 1.21848e-05 1.32275e-05 1.04267e-06 4 1 2 1.3095e-05 1.32275e-05 1.3251e-07 0 4 2 0.000133047 0.000132275 7.71569e-07 0 0 3 0.00828332 0.00833333 5.00154e-05 1 3 4 3.44193e-06 3.6075e-06 1.65571e-07 0 1 0 0.0416317 0.0416667 3.49308e-05 2 3 2 6.43774e-06 6.61376e-06 1.76012e-07 3 1 0 0.00123659 0.00119048 4.6109e-05 4 4 1 1.22501e-06 1.2025e-06 2.25112e-08 4 2 4 1.71043e-07 1.85e-07 1.39575e-08 1 1 4 6.22057e-05 6.61376e-05 3.93189e-06 3 0 2 0.000283257 0.000297619 1.43624e-05 4 2 0 0.000138185 0.000132275 5.90954e-06 3 0 0 0.00855041 0.00833333 0.000217079 4 1 0 0.000628507 0.000595238 3.32689e-05 4 2 1 1.37709e-05 1.32275e-05 5.43377e-07 1 3 0 0.00118823 0.00119048 2.24457e-06 1 4 4 1.17146e-06 1.2025e-06 3.10369e-08 0 1 1 0.00827531 0.00833333 5.80222e-05 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 0 1 3 2 0 3 4.97645e-11 5.50596e-11 5.29507e-12 4 0 2 2 4 4 5.22484e-17 4.91957e-17 3.05266e-18 0 0 3 4 4 4 1.53487e-15 1.62346e-15 8.85885e-17 1 2 4 1 3 4 1.53435e-16 1.35288e-16 1.81466e-17 4 1 0 0 4 0 3.61894e-10 4.40477e-10 7.85823e-11 1 0 2 3 2 2 2.2951e-12 2.29415e-12 9.55383e-16 2 4 3 0 0 1 1.48624e-11 1.37649e-11 1.09747e-12 2 3 2 0 3 1 4.28496e-13 4.0485e-13 2.3646e-14 4 0 2 0 3 3 2.91592e-13 2.699e-13 2.16924e-14 3 1 2 2 1 0 1.75541e-11 1.83532e-11 7.9911e-13 2 0 1 4 0 3 1.26258e-11 1.37649e-11 1.13912e-12 1 2 2 1 1 4 2.73927e-13 2.699e-13 4.02706e-15 4 2 1 1 4 3 1.4812e-16 1.35288e-16 1.28314e-17 1 4 2 2 1 2 3.02289e-14 2.99889e-14 2.40072e-16 0 4 3 0 3 1 2.40506e-12 2.4291e-12 2.40428e-14 1 0 3 0 2 0 2.55856e-08 2.50521e-08 5.3345e-10 4 0 2 2 0 2 8.70665e-12 9.1766e-12 4.69946e-13 0 1 2 3 1 2 1.77891e-11 1.83532e-11 5.64083e-13 2 3 4 3 1 0 1.27687e-14 1.42053e-14 1.43659e-15 3 4 1 2 3 1 7.82207e-16 7.10263e-16 7.19439e-17 SIMPLEX_INTEGRALS_TEST Normal end of execution. 13 April 2020 12:39:33 PM