01-Feb-2019 13:22:25 HYPERSPHERE_MONTE_CARLO_TEST MATLAB version Test HYPERSPHERE_MONTE_CARLO. TEST01 Use HYPERSPHERE01_SAMPLE to estimate 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 1.336983 7.696116 3.533272 0.142247 0.818818 0.993446 2 12.566371 5.748476 2.833179 3.984716 3.620353 1.335932 2.335646 4 12.566371 3.898071 6.849679 1.818621 2.738812 0.453929 0.980904 8 12.566371 4.642867 3.779666 4.143838 2.925583 0.872751 2.593609 16 12.566371 5.263329 3.000832 4.302209 3.298450 0.710540 2.484926 32 12.566371 5.198260 3.284200 4.083911 3.394286 0.827203 2.413955 64 12.566371 3.702391 4.820884 4.043096 2.160163 0.937532 2.508285 128 12.566371 4.230923 3.888350 4.447098 2.461462 0.864902 2.758277 256 12.566371 4.288453 4.259343 4.018575 2.676486 0.784630 2.294439 512 12.566371 4.155020 4.501145 3.910206 2.486289 0.876220 2.296390 1024 12.566371 4.413851 4.205051 3.947469 2.655566 0.907917 2.319064 2048 12.566371 4.309458 4.019189 4.237723 2.600009 0.847430 2.557968 4096 12.566371 4.232080 4.223925 4.110365 2.562060 0.860209 2.483800 8192 12.566371 4.161427 4.212238 4.192706 2.512442 0.833882 2.526083 16384 12.566371 4.189870 4.164386 4.212115 2.513694 0.828536 2.531057 32768 12.566371 4.207787 4.171158 4.187425 2.534187 0.835050 2.509363 65536 12.566371 4.175873 4.196902 4.193595 2.504683 0.840296 2.527796 Exact 12.566371 4.188790 4.188790 4.188790 2.513274 0.837758 2.513274 TEST01 Use HYPERSPHERE02_SAMPLE to estimate 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 -24.417815 0.003652 0.000267 0.812166 0.033106 0.000069 2 31.006277 -9.526481 2.940108 2.133603 0.000041 0.068959 0.004447 4 31.006277 -6.490685 3.085534 0.231457 0.640522 0.167042 0.127897 8 31.006277 -2.888262 7.645301 0.670186 1.003647 0.179566 1.177908 16 31.006277 -1.022545 4.634738 0.844364 1.266210 0.072928 0.988452 32 31.006277 -1.414052 7.322700 0.884101 0.938092 0.046687 0.788132 64 31.006277 1.669828 4.913967 0.841028 2.395132 0.080991 0.537903 128 31.006277 0.367357 4.583763 0.548695 1.704299 0.075105 1.479499 256 31.006277 -0.241734 5.279473 0.539576 2.212735 0.070363 0.990215 512 31.006277 -0.087821 5.484298 0.603797 2.065967 0.065181 0.791267 1024 31.006277 0.736098 4.997720 0.617776 2.136271 0.070685 0.826258 2048 31.006277 0.437539 5.052125 0.634728 1.888777 0.063629 0.936403 4096 31.006277 0.072476 5.064007 0.617181 1.974664 0.066160 1.044870 8192 31.006277 -0.017841 5.186762 0.645893 1.969306 0.062575 0.982554 16384 31.006277 0.067743 5.118520 0.637274 1.960717 0.065114 0.990224 32768 31.006277 -0.017483 5.221437 0.647653 1.923848 0.063465 0.979795 65536 31.006277 -0.025495 5.157164 0.651372 1.952732 0.065356 0.968567 Exact 31.006277 0.000000 5.167713 0.645964 1.937892 0.064596 0.968946 HYPERSPHERE_MONTE_CARLO_TEST Normal end of execution. 01-Feb-2019 13:22:26