3 January 2014 10:14:26.243 PM HYPERSPHERE_MONTE_CARLO_PRB FORTRAN77 version Test the HYPERSPHERE_MONTE_CARLO library. 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 11.3240 0.897789 0.344608 10.2044 0.809027 0.945019E-02 2 12.5664 6.82292 3.00201 2.74144 4.77046 1.34968 1.17718 4 12.5664 1.37309 3.92356 7.26972 0.454756 0.184124 5.89584 8 12.5664 1.62306 7.08669 3.85662 0.781676 0.333392 2.11514 16 12.5664 3.40245 4.20245 4.96147 1.72428 1.04306 3.42187 32 12.5664 4.26103 3.24737 5.05797 2.28422 0.742707 3.07812 64 12.5664 3.86475 4.34508 4.35654 2.39759 0.727493 2.86162 128 12.5664 4.30924 3.72341 4.53372 2.62785 0.848620 2.87410 256 12.5664 4.22226 4.20108 4.14303 2.62393 0.848376 2.63735 512 12.5664 3.88884 4.35113 4.32640 2.23850 0.792462 2.65146 1024 12.5664 4.25477 4.16352 4.14808 2.56793 0.891570 2.57269 2048 12.5664 4.12273 4.41842 4.02523 2.45425 0.867904 2.41710 4096 12.5664 4.29241 4.19838 4.07558 2.62444 0.860534 2.46934 8192 12.5664 4.23964 4.19549 4.13124 2.57097 0.852451 2.50829 16384 12.5664 4.17086 4.23147 4.16404 2.51568 0.847836 2.54305 32768 12.5664 4.20219 4.19912 4.16506 2.54564 0.839862 2.53371 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_PRB Normal end of execution. 3 January 2014 10:14:26.314 PM