06-Nov-2022 11:07:26 hyperball_monte_carlo_test(): MATLAB/Octave version 4.2.2 Test hyperball_monte_carlo(). hyperball_monte_carlo_test01() Use the Monte Carlo method to estimate integrals over the interior of the unit hyperball in M dimensions. n Spatial dimension M = 3 N 1 X^2 Y^2ans = 52 Z^2 X^4 X^2Y^2 Z^4 1 4.18879 0.165668 0.028834 0.769027 0.00655219 0.00114039 0.141187 2 4.18879 0.181752 1.66508 0.588189 0.00976134 0.1015 0.133685 4 4.18879 0.531727 0.593056 0.928541 0.0839517 0.059415 0.384114 8 4.18879 0.467111 1.05897 0.570382 0.147164 0.103173 0.246191 16 4.18879 1.01087 0.938904 0.428031 0.50817 0.149002 0.095776 32 4.18879 0.694259 0.504294 1.08174 0.288381 0.0605118 0.455109 64 4.18879 0.972587 0.974479 0.985536 0.375675 0.177912 0.482418 128 4.18879 0.90742 0.733717 0.789815 0.407944 0.0890446 0.317579 256 4.18879 0.865778 0.843606 0.780642 0.392492 0.124424 0.326748 512 4.18879 0.873552 0.760477 0.841354 0.375308 0.118868 0.340839 1024 4.18879 0.784554 0.854519 0.862215 0.312417 0.115856 0.364391 2048 4.18879 0.856246 0.818166 0.840161 0.372394 0.118942 0.360463 4096 4.18879 0.841281 0.826831 0.837875 0.36709 0.117261 0.35964 8192 4.18879 0.836782 0.834132 0.841126 0.356356 0.119476 0.35743 16384 4.18879 0.838232 0.842318 0.830578 0.359769 0.121158 0.354306 32768 4.18879 0.829498 0.839639 0.838325 0.35298 0.119803 0.360639 65536 4.18879 0.833396 0.834714 0.839667 0.357597 0.118651 0.360708 Exact 4.18879 0.837758 0.837758 0.837758 0.359039 0.11968 0.359039 hyperball_monte_carlo_test02 Use the Monte Carlo method to estimate integrals over the interior of the unit hyperball in M dimensions. n Spatial dimension M = 6 N 1 U V^2 V^2W^2 X^4 Y^2Z^2 Z^6 1 5.16771 0.972819 0.134061 0.0102914 0.46894 2.41829e-05 1.10633e-05 2 5.16771 -0.0960642 0.561936 0.0701675 0.000986648 0.00121934 0.104817 4 5.16771 0.374635 1.92875 0.0489696 0.164724 0.00214781 0.0153816 8 5.16771 0.98689 0.857585 0.107043 0.218839 0.00272022 0.0832444 16 5.16771 -0.257125 0.767909 0.0645073 0.248096 0.00281502 0.0246474 32 5.16771 -0.0571143 0.683203 0.0957067 0.235576 0.00352004 0.115521 64 5.16771 0.0743273 0.856889 0.0982224 0.188634 0.00357299 0.045987 128 5.16771 -0.0500785 0.620123 0.065197 0.217097 0.00428743 0.0724895 256 5.16771 -0.00397397 0.644439 0.0631046 0.15016 0.00611772 0.0819243 512 5.16771 0.0815399 0.655485 0.063298 0.194585 0.00570113 0.0701658 1024 5.16771 -0.0441845 0.629442 0.0701063 0.170666 0.00565088 0.0883143 2048 5.16771 0.0137975 0.657229 0.0642921 0.18397 0.00552187 0.0729231 4096 5.16771 0.017946 0.645645 0.0633908 0.196618 0.00523418 0.0797541 8192 5.16771 -0.0129135 0.655811 0.0657576 0.193452 0.00542332 0.0803172 16384 5.16771 0.000425875 0.650697 0.0658709 0.18756 0.00539005 0.0800182 32768 5.16771 -0.00499311 0.650812 0.0660932 0.192356 0.00536114 0.0797154 65536 5.16771 0.0089246 0.647044 0.0641694 0.192806 0.00541524 0.0788599 Exact 5.16771 0 0.645964 0.0645964 0.193789 0.00538303 0.0807455 hyperball_monte_carlo_test(): Normal end of execution. 06-Nov-2022 11:07:30