13-Oct-2022 16:51:02 simplex_monte_carlo_test(): MATLAB/Octave version 4.2.2 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 0.0665621 0.0634351 0.0307158 0.0265831 0.0253342 0.012267 0.0241441 0.0116907 0.00566075 2 0.166667 0.0834898 0.000728371 0.0302263 0.0475742 0.000438634 0.0153619 4.12929e-06 0.000134922 0.00549022 4 0.166667 0.0429036 0.0329344 0.037148 0.0140167 0.00595422 0.00959069 0.0119422 0.00895922 0.0103406 8 0.166667 0.0323614 0.0451094 0.0581696 0.0107821 0.00792689 0.00892553 0.0150135 0.0153888 0.0248751 16 0.166667 0.0392576 0.0426058 0.0541299 0.0154627 0.00863383 0.00976303 0.0156671 0.0112483 0.0245011 32 0.166667 0.0254975 0.0424237 0.0547814 0.00584506 0.00560501 0.00793315 0.0161081 0.0109085 0.0249459 64 0.166667 0.0447362 0.0496056 0.0397789 0.0175356 0.0111586 0.00863166 0.0207809 0.00977657 0.015046 128 0.166667 0.0396632 0.0442056 0.0376424 0.0144781 0.00859807 0.00750849 0.0187491 0.00762257 0.0138573 256 0.166667 0.044412 0.0414099 0.0395378 0.0174851 0.00887213 0.00869614 0.0173091 0.00696704 0.0158769 512 0.166667 0.0422989 0.0405008 0.0416309 0.0164382 0.00852498 0.00843946 0.0154876 0.0079992 0.0165297 1024 0.166667 0.0414458 0.0418415 0.0417485 0.0167089 0.00832819 0.00832664 0.0166983 0.00831273 0.0166526 2048 0.166667 0.0412379 0.0397257 0.0435683 0.0163796 0.00792518 0.00859323 0.0155312 0.00819592 0.0180565 4096 0.166667 0.0418731 0.0416618 0.0415514 0.0168883 0.00836173 0.00836519 0.0167664 0.00836059 0.016468 8192 0.166667 0.0412507 0.0420531 0.0417425 0.0162606 0.00837033 0.00831133 0.0169427 0.00836837 0.0167359 16384 0.166667 0.041608 0.0417359 0.0417546 0.0166891 0.00835285 0.00825385 0.0167087 0.00833884 0.0168127 32768 0.166667 0.0417917 0.041657 0.0418834 0.016827 0.008314 0.00838166 0.0166789 0.00835311 0.0168347 65536 0.166667 0.0416794 0.0419005 0.0416534 0.0166872 0.0083838 0.00832828 0.0168183 0.00833348 0.0166814 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 0.000409752 7.27122e-06 3.03414e-07 3.05674e-06 3.84812e-10 9.49844e-10 2 0.00138889 0.00036399 0.000112808 1.07264e-06 7.12987e-07 6.87549e-10 1.03038e-08 4 0.00138889 0.000215427 2.18359e-05 2.08234e-07 8.61191e-06 1.95718e-09 1.14856e-08 8 0.00138889 0.000165633 7.41775e-05 1.75498e-06 1.078e-05 1.95047e-08 2.07529e-09 16 0.00138889 0.00019246 8.21105e-05 2.37076e-06 2.66629e-06 1.22813e-08 4.71535e-07 32 0.00138889 0.000179129 7.10225e-05 4.1459e-07 5.56675e-06 6.45756e-09 1.40535e-06 64 0.00138889 0.00018204 5.71181e-05 1.41326e-06 1.05473e-05 1.79124e-08 3.8339e-07 128 0.00138889 0.000180003 5.16825e-05 1.21981e-06 5.57454e-06 1.48649e-08 1.34278e-06 256 0.00138889 0.000201215 4.42347e-05 1.53318e-06 7.62132e-06 1.74968e-08 3.20538e-06 512 0.00138889 0.000204267 4.51328e-05 8.89733e-07 5.3408e-06 1.74585e-08 1.59309e-06 1024 0.00138889 0.000196297 4.76113e-05 9.16374e-07 6.51756e-06 1.62164e-08 1.72323e-06 2048 0.00138889 0.000199686 5.04611e-05 1.0907e-06 7.04089e-06 1.79509e-08 1.36413e-06 4096 0.00138889 0.000200475 4.76127e-05 1.05541e-06 7.45543e-06 1.68354e-08 1.49748e-06 8192 0.00138889 0.000196783 4.78701e-05 1.09102e-06 6.44027e-06 1.7537e-08 1.60584e-06 16384 0.00138889 0.000198567 5.0611e-05 1.11538e-06 6.69128e-06 1.66158e-08 1.4524e-06 32768 0.00138889 0.000200501 4.94318e-05 1.1043e-06 6.8078e-06 1.71636e-08 1.45311e-06 65536 0.00138889 0.000197782 4.96403e-05 1.09735e-06 6.63959e-06 1.66868e-08 1.51852e-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 1.43217 0.406357 0.19497 2.0511 0.581971 0.279229 0.165126 0.0792273 0.0380132 2 1 1.14282 0.469944 1.27118 1.31417 0.498108 1.5213 0.407242 0.269272 2.19349 4 1 1.22151 0.311182 0.841151 1.50553 0.375734 1.04102 0.156919 0.259451 0.764857 8 1 1.4356 0.416381 0.422249 2.10368 0.565177 0.56982 0.260651 0.207703 0.238797 16 1 1.30319 0.542206 0.550782 1.72578 0.690677 0.702683 0.365078 0.270608 0.497742 32 1 1.23885 0.664871 0.607884 1.56398 0.790364 0.739957 0.603195 0.325158 0.623655 64 1 1.27302 0.473949 0.738853 1.65802 0.579467 0.894618 0.378705 0.244736 0.984382 128 1 1.24157 0.460537 0.808683 1.57401 0.551907 0.969771 0.361645 0.287399 0.994022 256 1 1.25247 0.51477 0.754787 1.61254 0.611209 0.911102 0.421132 0.309982 0.878059 512 1 1.23501 0.519817 0.735382 1.56215 0.616088 0.874531 0.426414 0.307205 0.883565 1024 1 1.24361 0.52824 0.756714 1.58226 0.630928 0.905533 0.435319 0.310624 0.931822 2048 1 1.24573 0.490201 0.765338 1.58888 0.588119 0.915966 0.384455 0.295237 0.926268 4096 1 1.2481 0.495701 0.752015 1.59609 0.592155 0.900911 0.394181 0.305409 0.899581 8192 1 1.2495 0.497512 0.755999 1.59854 0.596375 0.907614 0.397137 0.299301 0.911118 16384 1 1.25048 0.504463 0.746956 1.60122 0.60527 0.896188 0.406722 0.30072 0.893737 32768 1 1.24912 0.501419 0.747919 1.59754 0.601829 0.897213 0.400397 0.30027 0.896411 65536 1 1.25023 0.501056 0.745178 1.6005 0.601182 0.894665 0.40209 0.299055 0.89096 simplex_monte_carlo_test(): Normal end of execution. 13-Oct-2022 16:51:27