Home License -- for personal use only. Not for government, academic, research, commercial, or other organizational use. 08-Oct-2025 00:37:23 simplex_monte_carlo_test(): MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7 Test simplex_monte_carlo(). TEST01 SIMPLEX_UNIT_SAMPLE computes a Monte Carlo estimate of an integral over the interior of the unit simplex in 3D. N 1 X Y Z X^2 XY XZ Y^2 YZ Z^2 1 0.166667 0.0698421 0.0527121 0.0267274 0.0292675 0.0220891 0.0112002 0.0166714 0.00845314 0.00428613 2 0.166667 0.0233442 0.0617997 0.03879 0.00327237 0.00841238 0.00555179 0.0453128 0.0034754 0.0143402 4 0.166667 0.0504208 0.063245 0.0358288 0.0274147 0.0112451 0.00740579 0.0318345 0.0147603 0.00909715 8 0.166667 0.0462136 0.038089 0.0327491 0.0192614 0.00995719 0.00813502 0.00999387 0.0088766 0.00960744 16 0.166667 0.0539945 0.0337921 0.0340083 0.0280154 0.0087499 0.006536 0.0100365 0.00610396 0.0122659 32 0.166667 0.0398481 0.0420081 0.0445332 0.0165741 0.00831916 0.0086545 0.0153264 0.00988601 0.0173157 64 0.166667 0.040683 0.0458422 0.040912 0.0168028 0.00861461 0.0089001 0.0188018 0.00902244 0.0147173 128 0.166667 0.0450458 0.0406306 0.0446794 0.0181299 0.00870116 0.0100991 0.0162713 0.00867716 0.0184776 256 0.166667 0.0390677 0.0448694 0.0407451 0.0152996 0.00817322 0.00778614 0.0188238 0.00907413 0.0154607 512 0.166667 0.040219 0.0401599 0.0416577 0.015906 0.00811562 0.0076635 0.0151517 0.00797968 0.0173312 1024 0.166667 0.0412399 0.0434406 0.041674 0.016602 0.00850519 0.00839407 0.0181238 0.0085284 0.0166064 2048 0.166667 0.0419707 0.0416527 0.0413375 0.0168855 0.008372 0.00839266 0.0165296 0.00826252 0.0164488 4096 0.166667 0.0408248 0.0415202 0.0424036 0.0162402 0.00812114 0.00834977 0.0166741 0.00844821 0.017084 8192 0.166667 0.0418966 0.0415562 0.0415938 0.0168096 0.00837567 0.00845473 0.0166219 0.00817631 0.0165681 16384 0.166667 0.0419199 0.0414921 0.0416047 0.0167809 0.00834395 0.00832786 0.0165729 0.00823668 0.016729 32768 0.166667 0.0417845 0.0416376 0.0415946 0.0167151 0.00839502 0.00830969 0.016576 0.00834532 0.016623 65536 0.166667 0.0417785 0.0417618 0.0413916 0.0167678 0.00837268 0.00827691 0.0167084 0.00831692 0.016503 Exact 0.166667 0.0416667 0.0416667 0.0416667 0.0166667 0.00833333 0.00833333 0.0166667 0.00833333 0.0166667 TEST02 SIMPLEX_UNIT_SAMPLE computes a Monte Carlo estimate of an integral over the interior of the unit simplex in 6D. N 1 U V^2 V^2W^2 X^4 Y^2Z^2 Z^6 1 0.00138889 0.000303952 1.93405e-05 1.01059e-06 4.01315e-07 4.42364e-11 1.45901e-12 2 0.00138889 0.000112729 4.36414e-05 5.23222e-06 1.89746e-05 2.12899e-11 4.32896e-10 4 0.00138889 0.000190715 5.42875e-06 6.26367e-07 2.74819e-06 2.10956e-09 4.98684e-08 8 0.00138889 0.000103579 2.34504e-05 4.40726e-07 2.14595e-06 2.82428e-09 5.22842e-07 16 0.00138889 0.000162732 2.56501e-05 1.19672e-06 2.9573e-05 7.12308e-09 6.93807e-07 32 0.00138889 0.000170916 4.932e-05 2.46522e-06 4.93613e-06 1.36998e-08 4.86273e-07 64 0.00138889 0.00021023 3.78387e-05 8.39262e-07 3.05473e-06 2.59037e-08 8.19681e-07 128 0.00138889 0.000213346 5.42729e-05 1.02783e-06 4.79345e-06 1.7456e-08 1.5162e-06 256 0.00138889 0.000206777 4.34641e-05 9.93023e-07 5.05426e-06 1.49044e-08 7.69242e-07 512 0.00138889 0.00019196 5.27415e-05 9.46829e-07 5.4029e-06 1.45187e-08 2.29972e-06 1024 0.00138889 0.00019949 5.21022e-05 9.60932e-07 6.1925e-06 1.82921e-08 2.0506e-06 2048 0.00138889 0.000198163 5.07171e-05 1.14692e-06 5.60739e-06 1.54696e-08 1.75571e-06 4096 0.00138889 0.000196486 5.07593e-05 1.09322e-06 6.67042e-06 1.66499e-08 1.60396e-06 8192 0.00138889 0.000198732 4.84502e-05 1.06444e-06 6.46268e-06 1.66168e-08 1.61349e-06 16384 0.00138889 0.000199242 4.96877e-05 1.08094e-06 6.83887e-06 1.73802e-08 1.43613e-06 32768 0.00138889 0.000199804 4.94577e-05 1.1035e-06 6.82208e-06 1.6912e-08 1.40816e-06 65536 0.00138889 0.000199003 4.95532e-05 1.08301e-06 6.74194e-06 1.68599e-08 1.52629e-06 Exact 0.00138889 0.000198413 4.96032e-05 1.10229e-06 6.61376e-06 1.67014e-08 1.50313e-06 TEST03 SIMPLEX_GENERAL_SAMPLE computes a Monte Carlo estimate of an integral over the interior of a general simplex in 3D. Simplex vertices: 1 0 0 2 0 0 1 2 0 1 0 3 N 1 X Y Z X^2 XY XZ Y^2 YZ Z^2 1 1 1.13647 0.20706 1.891 1.29156 0.235317 2.14906 0.0428738 0.391549 3.57586 2 1 1.26759 0.190547 1.55166 1.62206 0.225482 1.90286 0.0531599 0.362855 2.67555 4 1 1.3037 0.805396 0.534089 1.72429 1.03286 0.690886 0.679622 0.412091 0.313596 8 1 1.23731 0.464112 0.780539 1.55792 0.579275 0.909853 0.344479 0.176943 1.35959 16 1 1.30208 0.548139 0.563477 1.73084 0.67761 0.727229 0.459876 0.209171 0.597121 32 1 1.23185 0.556444 0.875714 1.54692 0.649305 1.0574 0.510679 0.36571 1.09969 64 1 1.27057 0.48429 0.765597 1.65343 0.593701 0.933297 0.396437 0.281733 0.919806 128 1 1.25896 0.488419 0.815392 1.62315 0.594297 0.977467 0.369009 0.324007 1.05248 256 1 1.2476 0.530218 0.724656 1.59606 0.628426 0.867434 0.452771 0.300673 0.855413 512 1 1.24228 0.499032 0.765426 1.58274 0.594419 0.916221 0.417758 0.287895 0.961333 1024 1 1.25762 0.518171 0.731085 1.62081 0.623104 0.881309 0.421794 0.308625 0.853693 2048 1 1.25143 0.503752 0.738579 1.60326 0.606829 0.885703 0.397828 0.295843 0.881201 4096 1 1.24926 0.495176 0.77897 1.59892 0.593735 0.931921 0.395395 0.304316 0.969432 8192 1 1.24969 0.505198 0.740239 1.599 0.605861 0.887009 0.408649 0.299586 0.882645 16384 1 1.24842 0.504302 0.748976 1.59657 0.603645 0.898045 0.40876 0.3012 0.89809 32768 1 1.24872 0.502722 0.748571 1.5967 0.602514 0.897272 0.402582 0.303689 0.894161 65536 1 1.2513 0.49706 0.752415 1.60369 0.596883 0.903267 0.39591 0.299705 0.904679 simplex_monte_carlo_test(): Normal end of execution. 08-Oct-2025 00:37:25