27 February 2022 08:05:29 AM HYPERSPHERE_MONTE_CARLO_TEST C++ version Test the HYPERSPHERE_MONTE_CARLO library. TEST01 Use HYPERSPHERE01_SAMPLE to estimate integrals on 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 12.56637061 10.53394337 0.8351536397 1.197273603 8.830231604 0.7000797141 0.1140714471 2 12.56637061 3.684797691 2.904776974 5.97679595 1.339212308 0.5881768868 2.842764548 4 12.56637061 5.72058541 1.844045315 5.00173989 4.60843029 0.8613956249 4.140862475 8 12.56637061 4.438333571 3.40516533 4.722871713 2.305884064 0.9183990811 2.525007427 16 12.56637061 3.164166187 6.55900895 2.843195477 1.472181725 0.9270860034 1.595256731 32 12.56637061 4.72365217 4.515612278 3.327106166 2.865585788 1.026885169 1.68892193 64 12.56637061 4.12415534 4.577289843 3.864925432 2.673812909 0.8187490184 2.284236515 128 12.56637061 4.064743193 4.682408743 3.819218678 2.461148336 0.7890431824 2.191902062 256 12.56637061 4.143237338 4.232166396 4.190966881 2.478625309 0.8430305116 2.495150277 512 12.56637061 4.096299819 4.056008521 4.414062274 2.437558834 0.769521227 2.731488894 1024 12.56637061 4.36525421 4.117059763 4.084056641 2.713015291 0.8363405364 2.475653278 2048 12.56637061 4.095044873 4.146678998 4.324646743 2.410649664 0.8255907261 2.616315416 4096 12.56637061 4.15893746 4.251544803 4.155888352 2.492424164 0.8424596298 2.495097179 8192 12.56637061 4.152243243 4.223021044 4.191106327 2.477469272 0.8468509757 2.52100033 16384 12.56637061 4.174708322 4.175795672 4.21586662 2.483721459 0.8379375879 2.535682466 32768 12.56637061 4.237593211 4.156914107 4.171863297 2.547096377 0.8401384795 2.495712834 65536 12.56637061 4.154566287 4.199326145 4.212478182 2.478998597 0.8364158369 2.528949974 Exact 12.56637061 4.188790205 4.188790205 4.188790205 2.513274123 0.837758041 2.513274123 TEST02 Use HYPERSPHERE01_SAMPLE to estimate integrals on 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 31.00627668 22.88744951 1.33943172 0.08295041635 0.003305045715 0.2657872975 0.005251377256 2 31.00627668 5.550699312 12.50956587 2.282040164 0.8878649569 0.02215197083 0.003572580849 4 31.00627668 4.335264577 5.549943155 0.4976617134 1.587410555 0.02240012908 0.009141761197 8 31.00627668 2.065457484 4.181440641 0.2892661571 2.48393322 0.02637168576 1.312300904 16 31.00627668 0.04228011129 6.785403918 0.7114584209 1.501614203 0.06526429291 0.6074045547 32 31.00627668 -2.639320918 5.468577911 0.7016673806 1.862752186 0.07518980753 0.3138681586 64 31.00627668 -0.1099792291 5.07067821 0.6558054626 1.334133355 0.05082080106 1.502816174 128 31.00627668 0.4244163044 4.936897343 0.6023988813 1.963163828 0.06765069872 0.9337204656 256 31.00627668 -0.0927212625 5.290369224 0.5873711994 2.283998873 0.05997466558 1.046637679 512 31.00627668 -0.3842674396 5.863301374 0.6833531215 1.856132806 0.06318661943 0.8690452253 1024 31.00627668 -0.4685020247 4.984846972 0.6380999471 2.161227919 0.06115631344 1.001193629 2048 31.00627668 -0.4520527703 5.155419993 0.6540498788 1.910294271 0.06777851407 0.9618179486 4096 31.00627668 0.01750880266 5.025065386 0.6502921621 1.956004223 0.06924371438 0.95803258 8192 31.00627668 0.06978945128 5.158979488 0.6462470196 1.991424158 0.06502543657 0.9492440477 16384 31.00627668 -0.1905706456 5.27999565 0.6519094591 1.900493562 0.06256916573 0.9424478726 32768 31.00627668 0.169699533 5.122081256 0.6470745907 1.970504064 0.06599403123 0.909036612 65536 31.00627668 0.03782708666 5.137583916 0.6405079526 1.940282471 0.06372742961 0.9778480809 Exact 31.00627668 0 5.16771278 0.6459640975 1.937892293 0.06459640975 0.9689461463 HYPERSPHERE_MONTE_CARLO_TEST Normal end of execution. 27 February 2022 08:05:29 AM