13 September 2021 9:02:56.020 AM HYPERSPHERE_MONTE_CARLO_TEST FORTRAN90 version Test the HYPERSPHERE_MONTE_CARLO library. TEST01 Use HYPERSPHERE01_SAMPLE to estimate integrals on the surface of the unit hypersphere. Spatial dimension = 3 N 1 X^2 Y^2 Z^2 X^4 X^2Y^2 Z^4 1 12.5664 10.9607 1.17570 0.429944 9.56024 1.02548 0.147101E-01 2 12.5664 1.15869 2.12169 9.28599 0.192606 0.281352E-01 6.93981 4 12.5664 5.85826 3.51793 3.19018 3.66783 1.72001 2.15473 8 12.5664 3.67131 4.57396 4.32110 2.26931 0.739249 2.44318 16 12.5664 3.18804 4.93520 4.44313 1.99356 0.579651 3.17544 32 12.5664 4.27899 4.77591 3.51147 2.67032 0.606391 1.85446 64 12.5664 4.32148 4.45194 3.79295 2.42185 1.02615 2.17893 128 12.5664 4.57830 3.71014 4.27794 2.98648 0.786975 2.65997 256 12.5664 4.19514 4.25849 4.11274 2.55969 0.868213 2.45018 512 12.5664 4.19879 4.22150 4.14607 2.54113 0.880051 2.52060 1024 12.5664 4.23708 4.17210 4.15718 2.53583 0.856382 2.45400 2048 12.5664 4.26775 4.02966 4.26896 2.58606 0.830569 2.58613 4096 12.5664 4.23886 4.20749 4.12001 2.54499 0.845557 2.43224 8192 12.5664 4.23711 4.14429 4.18497 2.55664 0.831448 2.49331 16384 12.5664 4.19593 4.23720 4.13324 2.51191 0.852356 2.45645 32768 12.5664 4.17195 4.19516 4.19926 2.50209 0.831512 2.51939 65536 12.5664 4.21219 4.18801 4.16618 2.53732 0.840334 2.49451 Exact 12.5664 4.18879 4.18879 4.18879 2.51327 0.837758 2.51327 TEST02 Use HYPERSPHERE01_SAMPLE to estimate integrals on the surface of the unit hypersphere. Spatial dimension = 6 N 1 U V^2 V^2W^2 X^4 Y^2Z^2 Z^6 1 31.0063 -5.42508 2.20516 0.943813 2.32228 0.227772E-04 0.235145 2 31.0063 -12.7719 6.44889 0.815272 0.551081 0.317043E-01 0.324429 4 31.0063 -7.38025 8.49788 0.244476 2.95381 0.231801E-02 0.695154 8 31.0063 2.04476 2.25733 0.524661 0.298994 0.825159E-01 3.80914 16 31.0063 5.28653 5.39624 0.434818 2.04492 0.659087E-01 0.901989 32 31.0063 0.823561 5.41740 0.335843 2.32217 0.806290E-01 0.628354 64 31.0063 1.61196 5.83848 0.616039 2.01952 0.371781E-01 1.20124 128 31.0063 0.762599E-01 5.07409 0.621163 1.31717 0.698968E-01 1.39095 256 31.0063 0.593159 4.88231 0.614084 1.70767 0.673186E-01 1.28926 512 31.0063 -0.187725 4.86364 0.585796 2.16465 0.643552E-01 0.745117 1024 31.0063 0.325380 4.87021 0.639277 2.10069 0.683795E-01 0.854987 2048 31.0063 -0.633992 5.15311 0.628688 2.07876 0.634172E-01 0.975605 4096 31.0063 0.167378 5.08270 0.646228 1.93626 0.653858E-01 0.952721 8192 31.0063 0.416262E-01 5.11056 0.649249 1.92448 0.653295E-01 0.951680 16384 31.0063 0.708857E-01 5.11858 0.643863 1.98286 0.632219E-01 0.941134 32768 31.0063 -0.882159E-01 5.13881 0.649989 1.92813 0.643011E-01 0.937667 65536 31.0063 -0.654528E-01 5.15137 0.645875 1.93313 0.643508E-01 0.974385 Exact 31.0063 0.00000 5.16771 0.645964 1.93789 0.645964E-01 0.968946 HYPERSPHERE_MONTE_CARLO_TEST Normal end of execution. 13 September 2021 9:02:56.104 AM