29-Jul-2021 15:34:10 simplex_monte_carlo_test(): MATLAB/Octave version 9.9.0.1467703 (R2020b) 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 0.0138931 0.00670873 0.139921 0.00115811 0.00055923 0.0116636 0.000270042 0.00563217 0.117468 2 0.166667 0.0100315 0.0430758 0.101513 0.000844415 0.00411375 0.00398721 0.0207481 0.0128179 0.0805567 4 0.166667 0.042889 0.0541526 0.0193019 0.0228871 0.0071916 0.0071369 0.0327393 0.00372591 0.00283377 8 0.166667 0.0291446 0.0503304 0.0395192 0.0087006 0.00868316 0.00695424 0.0170393 0.0112774 0.0145954 16 0.166667 0.0393181 0.0307049 0.0492834 0.0133995 0.00556866 0.0116719 0.0125112 0.00522182 0.0222317 32 0.166667 0.035436 0.0411527 0.0384955 0.0115932 0.00825278 0.0060597 0.0153385 0.00762204 0.0127798 64 0.166667 0.0463906 0.0385162 0.0407268 0.0192518 0.00921571 0.00976232 0.0141134 0.00754058 0.0151911 128 0.166667 0.0394493 0.0419948 0.0395991 0.0153031 0.00870208 0.00805723 0.0156542 0.0081594 0.0146995 256 0.166667 0.0446094 0.037874 0.0436913 0.0183092 0.00857241 0.00890481 0.0136964 0.00798744 0.0185387 512 0.166667 0.0416737 0.0416556 0.0425025 0.0167268 0.00818584 0.00859684 0.0167546 0.00839764 0.0173391 1024 0.166667 0.0433568 0.0416119 0.0413768 0.0176627 0.00871555 0.00856798 0.0162784 0.00845037 0.0164856 2048 0.166667 0.0424473 0.0417037 0.0413477 0.0175108 0.00845349 0.0082949 0.0165759 0.0083556 0.0165242 4096 0.166667 0.0423029 0.0407107 0.0415887 0.0170752 0.00830372 0.00838269 0.0161204 0.00814978 0.0165823 8192 0.166667 0.0412722 0.0418391 0.0412241 0.0164347 0.00832757 0.00820977 0.0166824 0.00828607 0.0163194 16384 0.166667 0.0418224 0.0415933 0.0419878 0.0168996 0.00828968 0.00835835 0.0165834 0.00844704 0.0168838 32768 0.166667 0.0416293 0.0416903 0.0416957 0.016677 0.00829567 0.00838859 0.0166903 0.00837972 0.0166224 65536 0.166667 0.0415177 0.0414991 0.0419067 0.0165855 0.00827288 0.00834567 0.0164915 0.0083729 0.0168014 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 0.000151677 3.02616e-06 6.84306e-10 2.90163e-08 4.00825e-10 1.47833e-11 2 0.00138889 0.000236489 6.17655e-06 9.12101e-08 2.43187e-07 2.69836e-11 1.4413e-07 4 0.00138889 8.96688e-05 3.64328e-05 1.92421e-07 5.85661e-05 1.61333e-09 1.96073e-08 8 0.00138889 0.000208243 4.5766e-05 1.15885e-06 1.45859e-05 3.73088e-09 4.02696e-06 16 0.00138889 0.000244941 1.4303e-05 2.9552e-07 2.88092e-06 1.96549e-08 3.53269e-06 32 0.00138889 0.000199954 6.79311e-05 1.38193e-06 8.35132e-06 8.53668e-09 3.58231e-06 64 0.00138889 0.000168435 5.31344e-05 1.01873e-06 3.62471e-06 1.2503e-08 3.08998e-06 128 0.00138889 0.000167181 4.44604e-05 9.54285e-07 4.18278e-06 1.15259e-08 2.49649e-06 256 0.00138889 0.000193772 5.15427e-05 1.04427e-06 5.56705e-06 2.03159e-08 1.93968e-06 512 0.00138889 0.000198411 5.35746e-05 1.10105e-06 6.00691e-06 1.27046e-08 1.42544e-06 1024 0.00138889 0.000199742 5.00323e-05 1.08282e-06 6.30065e-06 1.78876e-08 1.79041e-06 2048 0.00138889 0.000193449 4.99572e-05 1.11597e-06 6.61877e-06 1.50723e-08 1.7059e-06 4096 0.00138889 0.000196931 4.92221e-05 1.10349e-06 6.99003e-06 1.67812e-08 1.68758e-06 8192 0.00138889 0.000196339 5.03512e-05 1.10044e-06 6.73962e-06 1.61621e-08 1.44188e-06 16384 0.00138889 0.000199736 4.80895e-05 1.10043e-06 6.63518e-06 1.70189e-08 1.52325e-06 32768 0.00138889 0.000199811 4.87167e-05 1.0854e-06 6.45914e-06 1.65159e-08 1.5309e-06 65536 0.00138889 0.000199693 5.01043e-05 1.10242e-06 6.46112e-06 1.66505e-08 1.4381e-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 1.21296 0.242944 1.87913 1.47127 0.294681 2.27931 0.0590215 0.456522 3.53113 2 1 1.38451 0.383471 0.319978 1.92529 0.495976 0.426606 0.2919 0.190711 0.134317 4 1 1.27577 0.409634 0.462834 1.63057 0.528583 0.590334 0.206258 0.205412 0.232539 8 1 1.26168 0.46201 0.768371 1.60984 0.565647 0.945753 0.296655 0.294932 0.984773 16 1 1.3143 0.4221 0.645827 1.76888 0.536001 0.781872 0.249686 0.28224 0.675617 32 1 1.26897 0.50513 0.619846 1.66921 0.614796 0.718985 0.38785 0.23727 0.760544 64 1 1.27411 0.427143 0.737434 1.65457 0.533966 0.895265 0.298831 0.251852 0.883539 128 1 1.23908 0.526977 0.778052 1.56673 0.635592 0.932173 0.406079 0.344859 0.948196 256 1 1.25223 0.490418 0.799349 1.6049 0.597709 0.953853 0.365021 0.307494 1.01644 512 1 1.2411 0.517227 0.749639 1.5757 0.617136 0.895104 0.415308 0.32165 0.888485 1024 1 1.25615 0.502471 0.750296 1.61815 0.60444 0.901941 0.405299 0.306345 0.89724 2048 1 1.25162 0.505038 0.751035 1.6049 0.608207 0.899316 0.406244 0.298345 0.917404 4096 1 1.24497 0.505441 0.75117 1.58613 0.605672 0.898265 0.409312 0.304548 0.897063 8192 1 1.24985 0.502117 0.756651 1.60053 0.602172 0.906062 0.404529 0.303078 0.917274 16384 1 1.25 0.498737 0.748996 1.60053 0.598407 0.898186 0.3959 0.301114 0.896788 32768 1 1.25034 0.498611 0.750758 1.6009 0.59864 0.90042 0.397604 0.300345 0.90153 65536 1 1.249 0.500376 0.752626 1.5973 0.599985 0.902914 0.400669 0.301445 0.905161 simplex_monte_carlo_test(): Normal end of execution. 29-Jul-2021 15:34:11