Home License -- for personal use only. Not for government, academic, research, commercial, or other organizational use. 13-May-2025 17:39:02 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 0.0593465 0.0201003 0.0274966 0.021132 0.00715729 0.00979095 0.00242413 0.00331614 0.00453637 2 0.166667 0.0344601 0.0146298 0.0781154 0.00721035 0.00335578 0.0159101 0.00256687 0.0059225 0.0372928 4 0.166667 0.049304 0.0634607 0.0334075 0.0266484 0.00711104 0.00636011 0.037703 0.0144349 0.00938771 8 0.166667 0.0312984 0.0532123 0.038529 0.0079013 0.0109395 0.00426862 0.023771 0.0084095 0.0174845 16 0.166667 0.0335871 0.0343257 0.0373432 0.00826105 0.00647617 0.00800956 0.0121614 0.00617218 0.0105948 32 0.166667 0.0410565 0.0486588 0.0439899 0.0158873 0.00794115 0.00906498 0.0237489 0.00941481 0.0181483 64 0.166667 0.0494638 0.0380773 0.0441279 0.0216535 0.00967702 0.00944997 0.0136983 0.00762638 0.0189677 128 0.166667 0.0436068 0.0366858 0.0411064 0.0180916 0.00715182 0.00887991 0.0137051 0.00769217 0.0149039 256 0.166667 0.0428275 0.0389106 0.0402813 0.0175382 0.00876129 0.00787514 0.0143573 0.00727167 0.0160822 512 0.166667 0.0418905 0.0424996 0.0420032 0.0165778 0.00880422 0.00825975 0.0173423 0.00838488 0.0168157 1024 0.166667 0.042627 0.041455 0.0410294 0.0173715 0.00851 0.00812078 0.0162513 0.00833695 0.0163296 2048 0.166667 0.0420371 0.0417411 0.0415898 0.01691 0.00832365 0.00844865 0.016959 0.00817937 0.0169889 4096 0.166667 0.0425082 0.0411225 0.0413837 0.0174439 0.00840806 0.00834787 0.0163287 0.00818553 0.0163953 8192 0.166667 0.0416229 0.0424529 0.0412074 0.0166168 0.00849319 0.00822734 0.0172056 0.00835019 0.0164606 16384 0.166667 0.0414929 0.0423614 0.0413195 0.0166132 0.00841463 0.00820985 0.0171801 0.00837947 0.0164589 32768 0.166667 0.0417073 0.0417981 0.0417297 0.0166642 0.00841657 0.00835246 0.0167619 0.00835346 0.0166847 65536 0.166667 0.0415725 0.0416684 0.0416915 0.0165953 0.00830955 0.00832843 0.0167014 0.00832954 0.0167273 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 0.000604451 4.10258e-05 6.59281e-07 3.81654e-07 1.53579e-12 3.36939e-17 2 0.00138889 0.00042562 8.25151e-07 3.07039e-09 7.46371e-06 2.71868e-10 3.53362e-12 4 0.00138889 0.000115864 2.16444e-05 3.4798e-07 5.28975e-06 3.22866e-09 1.27284e-07 8 0.00138889 0.00017347 7.31485e-05 1.82657e-06 9.30905e-07 8.62893e-09 5.36215e-07 16 0.00138889 0.00013896 3.89827e-05 1.3832e-06 4.48032e-06 8.39296e-09 5.11481e-06 32 0.00138889 0.000156857 5.67103e-05 2.29114e-06 3.15185e-06 1.04712e-08 3.77056e-07 64 0.00138889 0.000212907 5.76471e-05 1.89059e-06 4.25598e-06 3.26608e-08 2.54385e-06 128 0.00138889 0.0001872 4.3449e-05 9.89882e-07 8.1965e-06 1.36422e-08 1.9472e-06 256 0.00138889 0.000198288 4.45076e-05 1.16166e-06 7.84492e-06 2.04886e-08 9.46695e-07 512 0.00138889 0.000194962 5.28893e-05 1.14716e-06 8.39798e-06 1.54285e-08 7.04286e-07 1024 0.00138889 0.000197613 4.8561e-05 1.03329e-06 7.41738e-06 1.42478e-08 1.49411e-06 2048 0.00138889 0.000200697 4.74677e-05 1.03639e-06 6.29218e-06 1.6087e-08 1.47801e-06 4096 0.00138889 0.000197068 4.74404e-05 1.13879e-06 6.45714e-06 1.60987e-08 1.57348e-06 8192 0.00138889 0.000201137 4.97186e-05 1.07549e-06 7.19701e-06 1.74201e-08 1.5916e-06 16384 0.00138889 0.000195874 4.95893e-05 1.11676e-06 6.6948e-06 1.55292e-08 1.45213e-06 32768 0.00138889 0.000198579 5.03497e-05 1.08168e-06 6.64973e-06 1.70787e-08 1.54856e-06 65536 0.00138889 0.000198028 4.96071e-05 1.10826e-06 6.57844e-06 1.66187e-08 1.50549e-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 1.13382 0.1321 1.6367 1.28555 0.149777 1.85572 0.0174503 0.216207 2.67878 2 1 1.14571 0.19784 1.78764 1.32155 0.21319 2.03068 0.0595793 0.380117 3.2299 4 1 1.08786 0.454176 1.2119 1.18846 0.494514 1.31118 0.212645 0.520921 1.82587 8 1 1.15731 0.569722 0.75623 1.3619 0.657218 0.827489 0.517127 0.232966 1.08258 16 1 1.236 0.405298 0.988621 1.56548 0.484093 1.14689 0.311144 0.336416 1.43195 32 1 1.25219 0.387126 0.964412 1.61142 0.469765 1.14179 0.266829 0.26881 1.38176 64 1 1.292 0.533721 0.60204 1.71518 0.656567 0.737076 0.427103 0.275114 0.648489 128 1 1.23313 0.471889 0.862429 1.55195 0.564693 1.02337 0.32934 0.35686 1.0764 256 1 1.26071 0.470491 0.746323 1.62224 0.574337 0.912582 0.338598 0.309068 0.838609 512 1 1.24843 0.518933 0.758965 1.59237 0.624758 0.910145 0.429415 0.304462 0.915541 1024 1 1.24563 0.518522 0.725212 1.58902 0.619898 0.86928 0.421282 0.302376 0.853822 2048 1 1.24143 0.487601 0.772083 1.57647 0.582712 0.922769 0.384017 0.304598 0.933923 4096 1 1.25394 0.501221 0.733224 1.60956 0.604796 0.881028 0.399283 0.295985 0.867149 8192 1 1.25296 0.498933 0.746097 1.60713 0.601225 0.897032 0.394683 0.298049 0.895398 16384 1 1.24883 0.496541 0.750896 1.59663 0.595048 0.901581 0.398992 0.295778 0.904293 32768 1 1.25004 0.499583 0.74941 1.60003 0.599743 0.899276 0.398467 0.300007 0.897072 65536 1 1.25013 0.500119 0.75209 1.6001 0.600475 0.902451 0.399805 0.301298 0.901984 simplex_monte_carlo_test(): Normal end of execution. 13-May-2025 17:39:04