07-Jan-2022 21:45:19 hyperball_monte_carlo_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 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^2 ans = 52 Z^2 X^4 X^2Y^2 Z^4 1 4.18879 0.13021 1.51482 2.29822 0.00404764 0.0470889 1.26094 2 4.18879 0.0427576 1.79932 0.822169 0.000525828 0.0148834 0.280792 4 4.18879 0.985336 0.459551 1.65454 0.330294 0.154091 0.944113 8 4.18879 0.709477 0.972526 0.686575 0.285109 0.168356 0.244712 16 4.18879 0.726163 0.825975 0.922468 0.266247 0.073732 0.450392 32 4.18879 0.663482 0.800301 0.995057 0.234325 0.120865 0.481546 64 4.18879 0.869874 0.820555 0.833975 0.359719 0.102759 0.346786 128 4.18879 0.88648 0.733562 0.91777 0.371962 0.124863 0.353847 256 4.18879 0.898277 0.819722 0.841008 0.419525 0.121199 0.377282 512 4.18879 0.829889 0.883331 0.836566 0.359027 0.134191 0.35738 1024 4.18879 0.844258 0.862491 0.776249 0.366722 0.124249 0.31542 2048 4.18879 0.820789 0.836938 0.85377 0.342689 0.122347 0.37775 4096 4.18879 0.828418 0.864249 0.858048 0.348521 0.124249 0.368133 8192 4.18879 0.832945 0.82887 0.839417 0.355433 0.117157 0.364418 16384 4.18879 0.83827 0.834364 0.83407 0.359957 0.116989 0.354266 32768 4.18879 0.83808 0.837594 0.839141 0.359462 0.119599 0.359072 65536 4.18879 0.840322 0.837246 0.837067 0.360879 0.119471 0.357493 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 1.1873 0.0786914 0.0167702 2.14938 3.41564e-05 6.07013e-06 2 5.16771 0.341647 0.487188 0.0578699 0.325407 0.00260455 0.000159343 4 5.16771 -0.710882 0.0517364 0.00539816 0.354635 0.00412311 0.000863042 8 5.16771 0.355333 1.27004 0.139063 0.428395 0.00208217 0.37357 16 5.16771 1.08526 0.411639 0.047788 0.165713 0.00321791 0.338533 32 5.16771 -0.0219615 0.485949 0.0590505 0.192442 0.007146 0.128713 64 5.16771 -0.0216426 0.567472 0.0494539 0.167202 0.00666958 0.0977567 128 5.16771 -0.14429 0.529962 0.0521641 0.173248 0.00495521 0.064302 256 5.16771 -0.0447805 0.654786 0.0669782 0.175796 0.00557079 0.0900523 512 5.16771 -0.110071 0.668654 0.0702357 0.192336 0.0052966 0.0805218 1024 5.16771 0.000373873 0.668706 0.0608921 0.184433 0.00544337 0.0837678 2048 5.16771 0.0406819 0.67134 0.0668651 0.178038 0.00526684 0.0790798 4096 5.16771 -0.0114136 0.650691 0.0647661 0.191941 0.00531212 0.083653 8192 5.16771 0.0122893 0.646025 0.0629162 0.191666 0.0057659 0.0794132 16384 5.16771 -0.0108003 0.641268 0.0661224 0.19168 0.00540528 0.0784683 32768 5.16771 -0.00510976 0.654161 0.0639864 0.194184 0.00547429 0.0807093 65536 5.16771 -6.24896e-05 0.646278 0.0642547 0.193154 0.00534841 0.080788 Exact 5.16771 0 0.645964 0.0645964 0.193789 0.00538303 0.0807455 hyperball_monte_carlo_test(): Normal end of execution. 07-Jan-2022 21:45:20