Home License -- for personal use only. Not for government, academic, research, commercial, or other organizational use. 07-Oct-2025 21:49:05 hypersphere_monte_carlo_test(): MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7 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 1.751193 1.209889 9.605289 0.244038 0.168605 7.341942 2 12.566371 5.087342 0.874136 6.604892 3.554896 0.600610 5.501045 4 12.566371 0.399174 5.409207 6.757989 0.016109 0.186487 4.464341 8 12.566371 3.886828 3.373682 5.305861 2.196778 0.384106 3.147660 16 12.566371 3.984934 3.127497 5.453940 2.129182 0.793647 3.667714 32 12.566371 2.735096 5.188753 4.642522 1.325068 0.746323 2.934280 64 12.566371 4.861231 4.217469 3.487671 3.010315 1.019314 1.916757 128 12.566371 3.850035 4.728964 3.987371 2.208639 0.973830 2.320018 256 12.566371 4.280097 4.211452 4.074822 2.564756 0.808587 2.405126 512 12.566371 4.134130 4.202300 4.229940 2.484009 0.834722 2.573943 1024 12.566371 4.363279 4.034218 4.168874 2.648983 0.860097 2.539846 2048 12.566371 4.116553 4.193644 4.256173 2.422009 0.844155 2.563047 4096 12.566371 4.209237 4.145684 4.211449 2.536690 0.834853 2.542178 8192 12.566371 4.173583 4.196540 4.196248 2.496590 0.854374 2.538275 16384 12.566371 4.197375 4.249440 4.119555 2.520146 0.847468 2.458382 32768 12.566371 4.177944 4.211066 4.177361 2.498051 0.848436 2.511363 65536 12.566371 4.225784 4.154098 4.186489 2.541963 0.837383 2.507453 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 -12.144046 4.468450 1.844317 0.219069 0.010506 0.000046 2 31.006277 -11.785302 6.533098 0.259908 0.021379 0.150963 0.551074 4 31.006277 11.796039 1.759011 0.093404 1.233532 0.018828 4.040485 8 31.006277 -13.713356 5.702264 0.718718 1.024739 0.060626 0.563662 16 31.006277 -1.931233 5.047517 0.422840 1.536524 0.045459 1.835708 32 31.006277 -2.161307 4.820950 0.495407 3.291673 0.060526 0.414000 64 31.006277 -1.510539 5.434378 0.720059 1.493656 0.065646 0.962830 128 31.006277 1.180253 4.752926 0.580413 2.060476 0.064435 1.097727 256 31.006277 1.166703 5.037304 0.612980 1.807042 0.069448 1.027347 512 31.006277 -0.439588 5.403318 0.685895 1.921271 0.060705 0.954602 1024 31.006277 0.285092 5.128717 0.651119 1.755836 0.068478 0.890683 2048 31.006277 -0.024846 5.134175 0.616020 1.982522 0.066788 0.899893 4096 31.006277 0.189136 5.246303 0.655709 1.988905 0.063457 0.945098 8192 31.006277 0.212193 5.158340 0.649462 1.945141 0.063489 0.948487 16384 31.006277 0.010998 5.183249 0.639907 1.939607 0.065800 0.922031 32768 31.006277 0.025154 5.161432 0.650782 1.919399 0.064830 0.962961 65536 31.006277 0.080950 5.176588 0.652850 1.937115 0.065001 0.976224 Exact 31.006277 0.000000 5.167713 0.645964 1.937892 0.064596 0.968946 hypersphere_monte_carlo_test(): Normal end of execution. 07-Oct-2025 21:49:05