27 February 2022 09:26:15 AM HYPERBALL_MONTE_CARLO_TEST C++ version Test the HYPERBALL_MONTE_CARLO library. TEST01 Use Monte Carlo to estimate integrals over the interior of the unit hyperball in M dimensions Spatial dimension M = 3 N 1 X^2 Y^2 Z^2 X^4 X^2Y^2 Z^4 1 4.18879 1.95456 0.154962 0.222153 0.912032 0.0723078 0.0117819 2 4.18879 0.30208 1.41866 0.647801 0.0431141 0.103688 0.139884 4 4.18879 0.394127 0.422192 1.85585 0.067326 0.0688346 1.58415 8 4.18879 0.869953 1.85205 0.541987 0.345824 0.273545 0.0856052 16 4.18879 0.605462 0.628688 1.49649 0.278568 0.0311051 0.969962 32 4.18879 0.702491 0.738047 0.729994 0.255183 0.0953813 0.311035 64 4.18879 0.841256 0.921435 0.948113 0.375505 0.132859 0.436792 128 4.18879 0.697263 0.835355 0.840336 0.25897 0.108464 0.385282 256 4.18879 0.758845 0.982907 0.79947 0.282047 0.135516 0.321607 512 4.18879 0.861309 0.848892 0.889467 0.383292 0.118559 0.39702 1024 4.18879 0.824353 0.804706 0.83928 0.353982 0.116929 0.364192 2048 4.18879 0.802597 0.827287 0.837435 0.339362 0.108983 0.350441 4096 4.18879 0.814609 0.857322 0.823506 0.346262 0.121103 0.355719 8192 4.18879 0.846142 0.832733 0.830106 0.365327 0.122692 0.357038 16384 4.18879 0.825411 0.843814 0.839942 0.350532 0.120549 0.36232 32768 4.18879 0.826305 0.845943 0.836875 0.350559 0.1201 0.359654 65536 4.18879 0.838419 0.839585 0.835232 0.359812 0.120075 0.357826 Exact 4.18879 0.837758 0.837758 0.837758 0.359039 0.11968 0.359039 TEST02 Use Monte Carlo to estimate integrals over the interior of the unit hyperball in M dimensions Spatial dimension M = 6 N 1 U V^2 V^2W^2 X^4 Y^2Z^2 Z^6 1 5.16771 3.04274 0.142038 0.0055968 0.000222997 0.0114102 0.00022544 2 5.16771 1.11184 0.111952 0.0423846 0.206952 0.000276141 0.000193508 4 5.16771 0.281598 0.431241 0.024336 1.0314 0.00253869 0.0190485 8 5.16771 0.835375 0.710598 0.0960127 0.306391 0.00305187 0.0346406 16 5.16771 -0.4655 0.533704 0.0368343 0.138859 0.00560582 0.0436744 32 5.16771 -0.410588 0.629349 0.0661006 0.229327 0.00641345 0.0305731 64 5.16771 0.263124 0.616333 0.0633565 0.239756 0.00691472 0.0562121 128 5.16771 0.0714582 0.759511 0.0618515 0.194698 0.00514072 0.0694943 256 5.16771 0.298052 0.670231 0.0654164 0.223186 0.0049548 0.0733315 512 5.16771 0.158398 0.605173 0.0636747 0.176768 0.00470867 0.0707295 1024 5.16771 0.00364674 0.645884 0.062665 0.199173 0.00517182 0.0762541 2048 5.16771 -0.0279251 0.678594 0.070349 0.190501 0.00551096 0.0743479 4096 5.16771 0.00515873 0.648389 0.0634704 0.194696 0.0054127 0.0898392 8192 5.16771 -0.00600352 0.649061 0.0658245 0.195116 0.0050911 0.077415 16384 5.16771 0.016906 0.641998 0.0645766 0.19403 0.0055186 0.0788994 32768 5.16771 0.00257438 0.647711 0.0649024 0.193155 0.00533461 0.079884 65536 5.16771 -0.00529787 0.643672 0.0644957 0.193769 0.00540016 0.0807632 Exact 5.16771 0 0.645964 0.0645964 0.193789 0.00538303 0.0807455 HYPERBALL_MONTE_CARLO_TEST Normal end of execution. 27 February 2022 09:26:15 AM