Home License -- for personal use only. Not for government, academic, research, commercial, or other organizational use. 13-May-2025 14:51:52 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 9.271514 0.206622 3.088235 6.840556 0.152446 0.758946 2 12.566371 3.139949 3.657202 5.769220 1.217844 1.491580 5.007865 4 12.566371 8.360849 1.467876 2.737646 5.737508 0.900706 0.733157 8 12.566371 4.296001 3.618405 4.651964 2.873789 0.647971 3.130784 16 12.566371 3.088980 7.269887 2.207504 1.512653 1.240971 0.969689 32 12.566371 5.891660 3.739196 2.935514 4.225226 0.923123 1.570016 64 12.566371 4.944610 3.681552 3.940208 3.126043 0.925181 2.289226 128 12.566371 3.689123 4.248879 4.628369 2.047142 0.795576 2.797641 256 12.566371 3.996480 4.394807 4.175083 2.469755 0.852208 2.587917 512 12.566371 3.937914 4.403758 4.224698 2.319302 0.839754 2.602425 1024 12.566371 3.958438 4.305841 4.302091 2.364170 0.799121 2.600603 2048 12.566371 4.151109 4.169070 4.246192 2.486822 0.836352 2.557267 4096 12.566371 4.265557 4.180688 4.120125 2.593630 0.860281 2.478800 8192 12.566371 4.222580 4.186664 4.157127 2.530954 0.857153 2.483233 16384 12.566371 4.155790 4.211712 4.198868 2.484732 0.835077 2.512750 32768 12.566371 4.195326 4.206404 4.164640 2.518064 0.845483 2.495532 65536 12.566371 4.206861 4.169260 4.190250 2.531919 0.836006 2.517760 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 6.531731 3.802176 0.969057 0.614303 0.051110 0.047585 2 31.006277 10.546126 3.729526 0.473642 3.135215 0.061817 0.556137 4 31.006277 -2.394529 7.576128 0.686982 3.124677 0.017359 0.474924 8 31.006277 -4.230232 3.442254 0.836439 1.652496 0.037070 1.015571 16 31.006277 -1.214303 3.254833 0.657961 1.933879 0.036897 0.730061 32 31.006277 1.287037 3.977684 0.549341 1.881434 0.054717 0.375992 64 31.006277 0.268836 5.473655 0.686219 2.859464 0.047010 0.535136 128 31.006277 -0.074229 4.031400 0.510851 2.069184 0.074953 1.349980 256 31.006277 -0.355115 5.306323 0.610514 1.850739 0.067187 1.142200 512 31.006277 -0.176426 5.435323 0.675679 1.783554 0.047187 1.022819 1024 31.006277 0.122526 5.096375 0.656357 2.002496 0.062856 0.980332 2048 31.006277 0.385859 5.121794 0.660668 1.970684 0.067418 0.968028 4096 31.006277 -0.220356 4.972908 0.659990 1.915619 0.066805 0.939616 8192 31.006277 -0.164336 5.227567 0.656785 1.973586 0.062108 0.922250 16384 31.006277 -0.027288 5.200320 0.652987 1.920227 0.064199 0.968124 32768 31.006277 0.015061 5.207860 0.646023 1.987365 0.063498 0.994203 65536 31.006277 -0.064491 5.131988 0.643898 1.943691 0.064359 0.954127 Exact 31.006277 0.000000 5.167713 0.645964 1.937892 0.064596 0.968946 hypersphere_monte_carlo_test(): Normal end of execution. 13-May-2025 14:51:53