28-Jul-2021 11:36:52 hypersphere_monte_carlo_test(): MATLAB/Octave version 9.9.0.1467703 (R2020b) Test hypersphere_monte_carlo(). TEST01 Use HYPERSPHERE01_SAMPLE to estimate integrals over the surface of the unit hypersphere in M dimensions. Spatial dimension M = 3 N 1 X^2 Y^2 Z^2 X^4 X^2Y^2 Z^4 1 12.566371 0.414954 4.827445 7.323972 0.013702 0.159407 4.268581 2 12.566371 1.918107 0.306140 10.342124 0.533125 0.073506 8.808455 4 12.566371 4.337562 1.758939 6.469869 1.958886 0.766084 4.535904 8 12.566371 3.120904 3.609357 5.836110 1.821631 0.454273 3.669051 16 12.566371 3.673973 3.192372 5.700026 2.201957 0.661221 4.056516 32 12.566371 5.003332 4.256956 3.306082 3.272778 0.875090 1.610098 64 12.566371 3.979986 4.660357 3.926027 2.543459 0.721436 2.340244 128 12.566371 3.902341 4.779900 3.884129 2.181078 0.915884 2.250096 256 12.566371 4.290056 4.167940 4.108374 2.584960 0.833644 2.404789 512 12.566371 4.319225 4.256895 3.990251 2.608388 0.875256 2.373155 1024 12.566371 4.186398 4.215361 4.164612 2.565787 0.789765 2.485559 2048 12.566371 4.129446 4.327102 4.109823 2.462833 0.845201 2.438067 4096 12.566371 4.241162 4.140645 4.184563 2.542846 0.840866 2.493621 8192 12.566371 4.167920 4.179935 4.218515 2.500641 0.839851 2.553697 16384 12.566371 4.226704 4.205244 4.134423 2.544964 0.841785 2.468357 32768 12.566371 4.186059 4.188174 4.192138 2.516220 0.837528 2.518934 65536 12.566371 4.166347 4.212841 4.187183 2.496701 0.837692 2.515112 Exact 12.566371 4.188790 4.188790 4.188790 2.513274 0.837758 2.513274 TEST01 Use HYPERSPHERE02_SAMPLE to estimate integrals over the surface of the unit hypersphere in M dimensions. Spatial dimension M = 6 N 1 U V^2 V^2W^2 X^4 Y^2Z^2 Z^6 1 31.006277 -17.648201 2.269348 0.034076 9.298413 0.000766 0.001730 2 31.006277 -0.087436 1.996163 0.185127 6.158931 0.008294 0.832039 4 31.006277 -2.656694 3.954295 0.504365 2.718897 0.115243 0.038218 8 31.006277 0.352803 8.987638 1.008960 0.456764 0.067778 0.177633 16 31.006277 -6.399318 3.428532 0.591373 1.095735 0.058060 0.863084 32 31.006277 2.815280 4.460362 0.724937 2.737492 0.031764 0.507541 64 31.006277 -2.821639 4.235746 0.587111 1.781198 0.065019 1.450318 128 31.006277 0.896472 5.183449 0.755890 1.599935 0.081718 1.157393 256 31.006277 -0.635795 5.378407 0.727866 1.694500 0.069715 0.959391 512 31.006277 0.816391 5.158205 0.667059 2.005743 0.069826 0.720726 1024 31.006277 -0.147991 5.017864 0.615961 1.894353 0.068039 0.998399 2048 31.006277 0.231581 5.124153 0.614544 2.001175 0.062238 0.943360 4096 31.006277 0.102821 5.069334 0.653656 1.952074 0.064493 0.984416 8192 31.006277 0.051349 5.155394 0.643924 1.932108 0.064429 0.955429 16384 31.006277 -0.276848 5.175743 0.639828 1.921287 0.065803 0.973540 32768 31.006277 0.044325 5.124637 0.628725 1.950738 0.065825 0.999210 65536 31.006277 0.081088 5.169941 0.647626 1.940601 0.064593 0.955272 Exact 31.006277 0.000000 5.167713 0.645964 1.937892 0.064596 0.968946 hypersphere_monte_carlo_test(): Normal end of execution. 28-Jul-2021 11:36:52