13 April 2020 01:44:35 PM SIMPLEX_MONTE_CARLO_TEST C++ version Test the SIMPLEX_MONTE_CARLO library. TEST01 Use SIMPLEX_UNIT_SAMPLE for 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 0.108836 0.00319531 0.0133722 0.0710712 0.00208659 0.00873222 6.12602e-05 0.00025637 0.00107289 2 0.166667 0.0465888 0.0369168 0.0481681 0.0171202 0.00619286 0.0160657 0.0123334 0.00804945 0.0155724 4 0.166667 0.0184118 0.00891519 0.0451976 0.00408874 0.000514367 0.00618915 0.000844536 0.00239784 0.0163394 8 0.166667 0.0360005 0.0372846 0.0420662 0.0129251 0.00505735 0.00705661 0.0146145 0.00582353 0.019257 16 0.166667 0.0437533 0.0428705 0.046921 0.0191599 0.00974345 0.0100214 0.0169617 0.00989801 0.0194349 32 0.166667 0.0364091 0.0413269 0.0398156 0.0116544 0.00824662 0.0078217 0.0159309 0.00645544 0.0166135 64 0.166667 0.0410983 0.0407457 0.0477179 0.0157147 0.00840319 0.00853668 0.0157488 0.0100792 0.0209082 128 0.166667 0.0410154 0.0392559 0.0419492 0.0163329 0.00727833 0.00896483 0.0151086 0.009015 0.0153849 256 0.166667 0.0411811 0.0434836 0.0394655 0.0171697 0.00850398 0.00748752 0.0180581 0.00824735 0.0154249 512 0.166667 0.0393674 0.0429917 0.0439233 0.0155455 0.00787818 0.00837353 0.0178996 0.00867139 0.0184081 1024 0.166667 0.0416583 0.0409537 0.0418057 0.0169094 0.00809834 0.00814815 0.0162248 0.0081718 0.016949 2048 0.166667 0.0426096 0.0415558 0.0406269 0.017329 0.00872283 0.00819597 0.0162348 0.0081296 0.0159704 4096 0.166667 0.0416662 0.0417558 0.0414527 0.0166896 0.0083384 0.00836203 0.0166834 0.00832732 0.0164112 8192 0.166667 0.0417008 0.0411189 0.0422165 0.016769 0.00828496 0.00847933 0.0163504 0.0082938 0.0169832 16384 0.166667 0.0415194 0.0421521 0.0414839 0.0166988 0.0082595 0.0082619 0.0170481 0.00846335 0.0164934 32768 0.166667 0.0415293 0.0416533 0.0419026 0.0165493 0.00830354 0.00838069 0.0166469 0.00839485 0.0167151 65536 0.166667 0.0413845 0.0417127 0.0414789 0.0164739 0.00829776 0.00825136 0.0167255 0.00830295 0.0165317 Exact 0.166667 0.0416667 0.0416667 0.0416667 0.0166667 0.00833333 0.00833333 0.0166667 0.00833333 0.0166667 TEST02 Use SIMPLEX_UNIT_SAMPLE for 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 0.000290196 5.22638e-08 3.44438e-11 5.46945e-08 1.22908e-07 3.74386e-06 2 0.00138889 0.000155902 0.000192056 1.20345e-07 3.36606e-06 1.68906e-09 4.7257e-07 4 0.00138889 7.56665e-05 9.00446e-05 2.83315e-06 4.50826e-07 5.95488e-09 6.99618e-08 8 0.00138889 8.90641e-05 5.72928e-05 2.01558e-06 1.81123e-05 3.74329e-09 7.26724e-08 16 0.00138889 0.000208737 5.02954e-05 6.79761e-07 7.31319e-06 9.83494e-09 7.80523e-07 32 0.00138889 0.000162178 5.72106e-05 1.63594e-06 3.52558e-06 2.23339e-08 2.00419e-06 64 0.00138889 0.000233964 4.57502e-05 7.37006e-07 2.69552e-06 2.10692e-08 7.3948e-07 128 0.00138889 0.000208762 6.43324e-05 1.40103e-06 5.33364e-06 1.86852e-08 7.25176e-07 256 0.00138889 0.000208645 4.88095e-05 1.31562e-06 7.09597e-06 1.74711e-08 1.06163e-06 512 0.00138889 0.000206396 5.02979e-05 1.0006e-06 7.22588e-06 1.71464e-08 8.10567e-07 1024 0.00138889 0.000200898 4.57717e-05 1.08842e-06 5.8484e-06 1.86196e-08 1.53546e-06 2048 0.00138889 0.00019878 4.80666e-05 1.15229e-06 6.51354e-06 1.75557e-08 1.24638e-06 4096 0.00138889 0.000199385 5.01331e-05 1.02137e-06 6.79476e-06 1.68284e-08 1.40324e-06 8192 0.00138889 0.000198351 4.78787e-05 1.06564e-06 6.70696e-06 1.67213e-08 1.49432e-06 16384 0.00138889 0.000199584 5.10857e-05 1.13646e-06 6.42033e-06 1.71447e-08 1.70993e-06 32768 0.00138889 0.000197031 4.97478e-05 1.08659e-06 6.45824e-06 1.72107e-08 1.53712e-06 65536 0.00138889 0.000198098 4.94459e-05 1.10593e-06 6.51338e-06 1.65313e-08 1.4986e-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 1.65301 0.0383438 0.240699 2.73246 0.0633828 0.397879 0.00147025 0.00922932 0.0579361 2 1 1.27953 0.443002 0.867026 1.66179 0.517316 1.15621 0.296001 0.28978 0.840907 4 1 1.11047 0.106982 0.813557 1.24547 0.113155 0.924962 0.0202689 0.0863224 0.882329 8 1 1.216 0.447415 0.757191 1.50956 0.508103 0.88421 0.350749 0.209647 1.03988 16 1 1.26252 0.514446 0.844578 1.64 0.631367 1.02496 0.40708 0.356328 1.04948 32 1 1.21845 0.495922 0.716681 1.50684 0.594882 0.857472 0.382341 0.232396 0.897127 64 1 1.24659 0.488949 0.858922 1.58747 0.589787 1.01258 0.377971 0.362851 1.12904 128 1 1.24609 0.471071 0.755085 1.59018 0.558411 0.916452 0.362607 0.32454 0.830786 256 1 1.24709 0.521803 0.710378 1.59719 0.623851 0.845154 0.433393 0.296905 0.832943 512 1 1.2362 0.5159 0.79062 1.56568 0.610438 0.941343 0.429591 0.31217 0.994037 1024 1 1.24995 0.491444 0.752503 1.60136 0.588624 0.89917 0.389395 0.294185 0.915248 2048 1 1.25566 0.49867 0.731285 1.61529 0.603344 0.878812 0.389636 0.292666 0.8624 4096 1 1.25 0.50107 0.746148 1.60013 0.601131 0.896665 0.400401 0.299783 0.886205 8192 1 1.2502 0.493427 0.759897 1.60102 0.592847 0.912525 0.392411 0.298577 0.917092 16384 1 1.24912 0.505825 0.746711 1.59843 0.604939 0.895425 0.409154 0.304681 0.890645 32768 1 1.24918 0.499839 0.754247 1.59765 0.599482 0.905099 0.399525 0.302215 0.902617 65536 1 1.24831 0.500552 0.74662 1.59546 0.600126 0.895144 0.401411 0.298906 0.892712 SIMPLEX_MONTE_CARLO_TEST Normal end of execution. 13 April 2020 01:44:35 PM