31-Jan-2019 22:32:58 HYPERBALL_MONTE_CARLO_TEST MATLAB version Test 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 0.461259 1.18886 0.655042 0.0507927 0.130914 0.102435 2 4.18879 2.20303 1.48286 0.17341 1.77385 0.22175 0.00763818 4 4.18879 0.3166 1.1627 0.69097 0.0280131 0.100722 0.131717 8 4.18879 0.770255 0.785885 0.496738 0.37721 0.0761832 0.167346 16 4.18879 0.971365 0.639305 0.617656 0.533526 0.0815172 0.225873 32 4.18879 0.814321 0.634161 0.96266 0.347757 0.133598 0.443839 64 4.18879 0.906047 0.854695 0.776138 0.455333 0.130438 0.302421 128 4.18879 0.943762 0.954913 0.838029 0.472804 0.144016 0.387496 256 4.18879 0.848113 0.822631 0.900585 0.357368 0.115655 0.389434 512 4.18879 0.828613 0.830253 0.873495 0.356411 0.121238 0.398114 1024 4.18879 0.811715 0.828925 0.868354 0.339422 0.11778 0.384687 2048 4.18879 0.833419 0.820693 0.797641 0.356849 0.118321 0.331975 4096 4.18879 0.850484 0.805808 0.846489 0.362231 0.11894 0.363186 8192 4.18879 0.834723 0.855811 0.834317 0.357217 0.122296 0.352931 16384 4.18879 0.827123 0.840527 0.851411 0.349223 0.119897 0.36659 32768 4.18879 0.836469 0.837841 0.845335 0.358472 0.120544 0.363438 65536 4.18879 0.837893 0.839658 0.838634 0.35865 0.120076 0.360434 Exact 4.18879 0.837758 0.837758 0.837758 0.359039 0.11968 0.359039 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 2.79901 0.120755 0.0320285 0.00690986 9.87137e-05 3.16113e-05 2 5.16771 -0.57149 0.293342 0.170255 0.271744 2.60982e-05 5.58291e-07 4 5.16771 -0.279778 0.623651 0.0810514 0.779915 0.000618039 0.00897805 8 5.16771 0.255952 0.218145 0.0186323 0.659832 0.00250608 0.00500613 16 5.16771 0.346619 0.495884 0.0397796 0.366304 0.00315855 0.26885 32 5.16771 0.113231 0.824358 0.101111 0.297606 0.00139085 0.0842669 64 5.16771 0.0639861 0.665368 0.071364 0.241507 0.00413323 0.147151 128 5.16771 0.276801 0.689519 0.0647158 0.225491 0.00809441 0.0574316 256 5.16771 0.0500191 0.67486 0.0791635 0.15683 0.00501851 0.109614 512 5.16771 0.0977458 0.657873 0.0666419 0.184941 0.00513758 0.0764639 1024 5.16771 0.0408428 0.673262 0.0673144 0.177005 0.00572069 0.08292 2048 5.16771 0.0491676 0.630574 0.0644603 0.191926 0.0055962 0.0685449 4096 5.16771 0.0485198 0.664904 0.0701552 0.193349 0.00522243 0.083794 8192 5.16771 -0.00799636 0.65078 0.0660861 0.194349 0.00538144 0.0788404 16384 5.16771 0.0167012 0.64635 0.0641625 0.19524 0.00545644 0.0806157 32768 5.16771 -0.00569121 0.644045 0.065072 0.193422 0.00539826 0.0813297 65536 5.16771 -0.00145247 0.64794 0.0641957 0.192135 0.00540707 0.0805035 Exact 5.16771 0 0.645964 0.0645964 0.193789 0.00538303 0.0807455 HYPERBALL_MONTE_CARLO_TEST Normal end of execution. 31-Jan-2019 22:33:02