06-Nov-2022 22:42:52 hypersphere_monte_carlo_test(): MATLAB/Octave version 4.2.2 Test hypersphere_monte_carlo(). hypersphere_monte_carlo_test01 hypersphere01_sample() estimates 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 4.822717 3.648683 4.094971 1.850860 1.400290 1.334418 2 12.566371 0.186676 12.379115 0.000579 0.004561 0.182101 0.000000 4 12.566371 1.628818 6.480457 4.457096 0.310458 0.674145 2.796235 8 12.566371 4.506926 6.220737 1.838707 3.119383 0.700553 0.539257 16 12.566371 4.491437 4.031897 4.043037 3.057770 0.723219 2.460463 32 12.566371 3.900496 4.588075 4.077799 2.210222 0.719391 2.335798 64 12.566371 4.300143 4.380383 3.885844 2.588011 0.809904 2.248786 128 12.566371 3.883094 4.636593 4.046684 2.311719 0.833772 2.493708 256 12.566371 4.478305 3.695999 4.392067 2.803502 0.770242 2.725671 512 12.566371 4.076764 4.130818 4.358789 2.371129 0.817910 2.623436 1024 12.566371 4.089936 4.215372 4.261063 2.406197 0.824395 2.553857 2048 12.566371 4.218333 4.210952 4.137085 2.550006 0.845531 2.483394 4096 12.566371 4.194820 4.166886 4.204665 2.520648 0.835854 2.524081 8192 12.566371 4.153096 4.174227 4.239048 2.500362 0.828494 2.577814 16384 12.566371 4.262936 4.131824 4.171610 2.578774 0.841165 2.506374 32768 12.566371 4.177090 4.187939 4.201342 2.515662 0.827313 2.532297 65536 12.566371 4.187531 4.165029 4.213810 2.513258 0.835450 2.534179 Exact 12.566371 4.188790 4.188790 4.188790 2.513274 0.837758 2.513274 hypersphere_monte_carlo_test02(): hypersphere02_sample() estimates 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 9.695314 2.694094 0.880361 6.376916 0.000366 0.000940 2 31.006277 -7.265369 15.116177 1.882003 0.190232 0.034366 0.132624 4 31.006277 -0.902913 5.104770 1.457440 0.210551 0.048126 0.321743 8 31.006277 6.472206 6.435757 0.930933 2.348282 0.067046 0.900802 16 31.006277 6.256626 5.360566 0.882915 1.101721 0.088146 0.961454 32 31.006277 1.000987 4.391682 0.779885 1.995213 0.056729 1.179314 64 31.006277 -1.421905 5.465403 0.968471 1.510184 0.060292 0.702433 128 31.006277 -0.408784 5.695387 0.672876 2.267999 0.056494 1.048542 256 31.006277 0.115384 4.647653 0.501267 1.983370 0.073137 1.144383 512 31.006277 -0.403270 4.681200 0.671911 1.945414 0.062795 0.855204 1024 31.006277 -0.239133 4.981316 0.630419 1.859110 0.065727 1.065589 2048 31.006277 -0.118253 5.059055 0.642682 1.960854 0.064175 0.983625 4096 31.006277 -0.170349 5.156708 0.654581 1.983313 0.062667 0.928065 8192 31.006277 0.080412 5.122604 0.643496 1.910183 0.065965 0.957212 16384 31.006277 -0.226333 5.057213 0.640099 2.013385 0.064003 0.947726 32768 31.006277 -0.072204 5.159677 0.646937 1.952060 0.064541 0.965328 65536 31.006277 0.053922 5.152850 0.644414 1.940707 0.064340 0.965060 Exact 31.006277 0.000000 5.167713 0.645964 1.937892 0.064596 0.968946 hypersphere_monte_carlo_test(): Normal end of execution. 06-Nov-2022 22:42:52