23 October 2023 10:38:33.624 AM hypersphere_monte_carlo_test(): FORTRAN77 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 12.5664 10.5339 0.835154 1.19727 8.83023 0.700080 0.114071 2 12.5664 4.28968 2.47122 5.80547 1.57859 0.709761 2.68539 4 12.5664 1.56372 3.30088 7.70177 0.672040 0.257850 6.14261 8 12.5664 1.84747 6.81078 3.90812 0.859633 0.456343 1.85661 16 12.5664 3.17624 4.98900 4.40113 1.36133 1.03992 2.89549 32 12.5664 5.07425 3.92917 3.56295 3.06785 1.00885 1.94710 64 12.5664 3.75023 4.36541 4.45073 2.22941 0.696132 2.75584 128 12.5664 4.25770 3.74421 4.56445 2.56305 0.793423 2.75939 256 12.5664 4.19827 4.28120 4.08690 2.54469 0.843342 2.47283 512 12.5664 3.94159 4.26918 4.35560 2.33799 0.768640 2.70099 1024 12.5664 4.33650 4.13726 4.09261 2.63774 0.889952 2.48749 2048 12.5664 4.08640 4.32941 4.15056 2.43336 0.836960 2.48845 4096 12.5664 4.21149 4.11647 4.23842 2.52601 0.828100 2.53557 8192 12.5664 4.18569 4.14896 4.23172 2.50069 0.837680 2.53923 16384 12.5664 4.14831 4.19980 4.21825 2.47607 0.833538 2.53489 32768 12.5664 4.15185 4.16627 4.24826 2.47339 0.825077 2.55324 Exact 12.5664 4.18879 4.18879 4.18879 2.51327 0.837758 2.51327 TEST02 Use HYPERSPHERE01_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 31.0063 22.8874 1.33943 0.829504E-01 0.330505E-02 0.265787 0.525138E-02 2 31.0063 5.55070 12.5096 2.28204 0.887865 0.221520E-01 0.357258E-02 4 31.0063 4.33526 5.54994 0.497662 1.58741 0.224001E-01 0.914176E-02 8 31.0063 2.06546 4.18144 0.289266 2.48393 0.263717E-01 1.31230 16 31.0063 0.422801E-01 6.78540 0.711458 1.50161 0.652643E-01 0.607405 32 31.0063 -2.63932 5.46858 0.701667 1.86275 0.751898E-01 0.313868 64 31.0063 -0.109979 5.07068 0.655805 1.33413 0.508208E-01 1.50282 128 31.0063 0.424416 4.93690 0.602399 1.96316 0.676507E-01 0.933720 256 31.0063 -0.927213E-01 5.29037 0.587371 2.28400 0.599747E-01 1.04664 512 31.0063 -0.384267 5.86330 0.683353 1.85613 0.631866E-01 0.869045 1024 31.0063 -0.468502 4.98485 0.638100 2.16123 0.611563E-01 1.00119 2048 31.0063 -0.452053 5.15542 0.654050 1.91029 0.677785E-01 0.961818 4096 31.0063 0.175088E-01 5.02507 0.650292 1.95600 0.692437E-01 0.958033 8192 31.0063 0.697895E-01 5.15898 0.646247 1.99142 0.650254E-01 0.949244 16384 31.0063 -0.190571 5.28000 0.651909 1.90049 0.625692E-01 0.942448 32768 31.0063 0.169700 5.12208 0.647075 1.97050 0.659940E-01 0.909037 Exact 31.0063 0.00000 5.16771 0.645964 1.93789 0.645964E-01 0.968946 hypersphere_monte_carlo_test(): Normal end of execution. 23 October 2023 10:38:33.665 AM