13 September 2021 8:59:04.700 AM HYPERBALL_MONTE_CARLO_TEST FORTRAN90 version Test the HYPERBALL_MONTE_CARLO library. TEST01 Use the Monte Carlo method to estimate integrals over the interior of the unit hyperball in M dimensions. Spatial dimension M = 3 N 1 X^2 Y^2 Z^2 X^4 X^2Y^2 Z^4 1 4.18879 1.68589 0.114235 1.42007 0.678530 0.459769E-01 0.481429 2 4.18879 1.44305 0.782942 0.929587 0.697465 0.989313E-01 0.408254 4 4.18879 0.700199 0.900729 0.332015 0.281062 0.402324E-01 0.421967E-01 8 4.18879 0.999760 0.766127 0.587573 0.518166 0.160063 0.129834 16 4.18879 0.988886 0.501597 1.02689 0.490428 0.122149 0.549423 32 4.18879 0.820140 0.687820 0.807452 0.272309 0.865106E-01 0.347215 64 4.18879 0.890282 0.675129 0.932994 0.367417 0.122173 0.410159 128 4.18879 0.765899 0.850553 0.728828 0.289856 0.108107 0.261386 256 4.18879 0.820312 0.899123 0.848078 0.355523 0.124432 0.361600 512 4.18879 0.874296 0.804186 0.808239 0.350535 0.121983 0.323836 1024 4.18879 0.809715 0.827331 0.852285 0.322147 0.119140 0.370798 2048 4.18879 0.872450 0.829759 0.801796 0.385347 0.117825 0.333076 4096 4.18879 0.814217 0.830534 0.847215 0.342307 0.115726 0.367261 8192 4.18879 0.832937 0.847957 0.840755 0.358216 0.120832 0.361733 16384 4.18879 0.829688 0.832933 0.844100 0.355063 0.117429 0.363123 32768 4.18879 0.835980 0.839264 0.836147 0.358740 0.119142 0.356689 65536 4.18879 0.837005 0.837963 0.838678 0.359032 0.119486 0.359171 Exact 4.18879 0.837758 0.837758 0.837758 0.359039 0.119680 0.359039 TEST02 Use the Monte Carlo method to estimate integrals over the interior of the unit hyperball in M dimensions. Spatial dimension M = 6 N 1 U V^2 V^2W^2 X^4 Y^2Z^2 Z^6 1 5.16771 2.03829 1.32016 0.124239 0.894066E-04 0.195402E-01 0.863293E-02 2 5.16771 -0.238829 0.306743 0.655296E-03 0.907107E-01 0.458790E-02 0.947720E-03 4 5.16771 -0.749725 0.244834 0.278963E-01 0.206307E-01 0.244090E-02 0.113188E-01 8 5.16771 -0.261442E-01 0.448346 0.455767E-01 0.681386E-01 0.145605E-01 0.335252E-01 16 5.16771 0.126051 0.502833 0.492064E-01 0.376326 0.383069E-02 0.392142E-01 32 5.16771 -0.320669E-01 0.432882 0.367893E-01 0.112255 0.467015E-02 0.105743 64 5.16771 -0.101648 0.628624 0.801834E-01 0.152955 0.405811E-02 0.125388 128 5.16771 0.455858E-02 0.524327 0.493291E-01 0.242552 0.550176E-02 0.102099 256 5.16771 -0.392123 0.705884 0.651906E-01 0.165311 0.540985E-02 0.859365E-01 512 5.16771 0.180914 0.614776 0.637865E-01 0.175448 0.453243E-02 0.917898E-01 1024 5.16771 0.616016E-01 0.646195 0.654430E-01 0.204676 0.505813E-02 0.792169E-01 2048 5.16771 0.819939E-02 0.636433 0.610591E-01 0.190862 0.575149E-02 0.879690E-01 4096 5.16771 0.121438E-01 0.638690 0.655790E-01 0.184197 0.557545E-02 0.784393E-01 8192 5.16771 0.179130E-01 0.639317 0.645805E-01 0.197575 0.524642E-02 0.841601E-01 16384 5.16771 -0.292803E-02 0.644473 0.645479E-01 0.190949 0.539686E-02 0.796421E-01 32768 5.16771 -0.856853E-03 0.643970 0.640245E-01 0.197664 0.532875E-02 0.808999E-01 65536 5.16771 0.506865E-02 0.642733 0.642014E-01 0.194511 0.534259E-02 0.796326E-01 Exact 5.16771 0.00000 0.645964 0.645964E-01 0.193789 0.538303E-02 0.807455E-01 HYPERBALL_MONTE_CARLO_TEST Normal end of execution. 13 September 2021 8:59:04.810 AM