16 January 2014 09:17:58 AM SIMPLEX_MONTE_CARLO_PRB C++ version Test the SIMPLEX_MONTE_CARLO library. TEST01 Use SIMPLEX01_SAMPLE for a Monte Carlo estimate of an integral over the interior of the unit simplex in 3D. N 1 X Y Z X^2 XY XZ Y^2 YZ Z^2 1 0.166667 0.108836 0.00319531 0.0133722 0.0710712 0.00208659 0.00873222 6.12602e-05 0.00025637 0.00107289 2 0.166667 0.0465888 0.0369168 0.0481681 0.0171202 0.00619286 0.0160657 0.0123334 0.00804945 0.0155724 4 0.166667 0.0184118 0.00891519 0.0451976 0.00408874 0.000514367 0.00618915 0.000844536 0.00239784 0.0163394 8 0.166667 0.0360005 0.0372846 0.0420662 0.0129251 0.00505735 0.00705661 0.0146145 0.00582353 0.019257 16 0.166667 0.0437533 0.0428705 0.046921 0.0191599 0.00974345 0.0100214 0.0169617 0.00989801 0.0194349 32 0.166667 0.0364091 0.0413269 0.0398156 0.0116544 0.00824662 0.0078217 0.0159309 0.00645544 0.0166135 64 0.166667 0.0410983 0.0407457 0.0477179 0.0157147 0.00840319 0.00853668 0.0157488 0.0100792 0.0209082 128 0.166667 0.0410154 0.0392559 0.0419492 0.0163329 0.00727833 0.00896483 0.0151086 0.009015 0.0153849 256 0.166667 0.0411811 0.0434836 0.0394655 0.0171697 0.00850398 0.00748752 0.0180581 0.00824735 0.0154249 512 0.166667 0.0393674 0.0429917 0.0439233 0.0155455 0.00787818 0.00837353 0.0178996 0.00867139 0.0184081 1024 0.166667 0.0416583 0.0409537 0.0418057 0.0169094 0.00809834 0.00814815 0.0162248 0.0081718 0.016949 2048 0.166667 0.0426096 0.0415558 0.0406269 0.017329 0.00872283 0.00819597 0.0162348 0.0081296 0.0159704 4096 0.166667 0.0416662 0.0417558 0.0414527 0.0166896 0.0083384 0.00836203 0.0166834 0.00832732 0.0164112 8192 0.166667 0.0417008 0.0411189 0.0422165 0.016769 0.00828496 0.00847933 0.0163504 0.0082938 0.0169832 16384 0.166667 0.0415194 0.0421521 0.0414839 0.0166988 0.0082595 0.0082619 0.0170481 0.00846335 0.0164934 32768 0.166667 0.0415293 0.0416533 0.0419026 0.0165493 0.00830354 0.00838069 0.0166469 0.00839485 0.0167151 65536 0.166667 0.0413845 0.0417127 0.0414789 0.0164739 0.00829776 0.00825136 0.0167255 0.00830295 0.0165317 Exact 0.166667 0.0416667 0.0416667 0.0416667 0.0166667 0.00833333 0.00833333 0.0166667 0.00833333 0.0166667 TEST02 Use SIMPLEX01_SAMPLE for a Monte Carlo estimate of an integral over the interior of the unit simplex in 6D. N 1 U V^2 V^2W^2 X^4 Y^2Z^2 Z^6 1 0.00138889 0.000290196 5.22638e-08 3.44438e-11 5.46945e-08 1.22908e-07 3.74386e-06 2 0.00138889 0.000155902 0.000192056 1.20345e-07 3.36606e-06 1.68906e-09 4.7257e-07 4 0.00138889 7.56665e-05 9.00446e-05 2.83315e-06 4.50826e-07 5.95488e-09 6.99618e-08 8 0.00138889 8.90641e-05 5.72928e-05 2.01558e-06 1.81123e-05 3.74329e-09 7.26724e-08 16 0.00138889 0.000208737 5.02954e-05 6.79761e-07 7.31319e-06 9.83494e-09 7.80523e-07 32 0.00138889 0.000162178 5.72106e-05 1.63594e-06 3.52558e-06 2.23339e-08 2.00419e-06 64 0.00138889 0.000233964 4.57502e-05 7.37006e-07 2.69552e-06 2.10692e-08 7.3948e-07 128 0.00138889 0.000208762 6.43324e-05 1.40103e-06 5.33364e-06 1.86852e-08 7.25176e-07 256 0.00138889 0.000208645 4.88095e-05 1.31562e-06 7.09597e-06 1.74711e-08 1.06163e-06 512 0.00138889 0.000206396 5.02979e-05 1.0006e-06 7.22588e-06 1.71464e-08 8.10567e-07 1024 0.00138889 0.000200898 4.57717e-05 1.08842e-06 5.8484e-06 1.86196e-08 1.53546e-06 2048 0.00138889 0.00019878 4.80666e-05 1.15229e-06 6.51354e-06 1.75557e-08 1.24638e-06 4096 0.00138889 0.000199385 5.01331e-05 1.02137e-06 6.79476e-06 1.68284e-08 1.40324e-06 8192 0.00138889 0.000198351 4.78787e-05 1.06564e-06 6.70696e-06 1.67213e-08 1.49432e-06 16384 0.00138889 0.000199584 5.10857e-05 1.13646e-06 6.42033e-06 1.71447e-08 1.70993e-06 32768 0.00138889 0.000197031 4.97478e-05 1.08659e-06 6.45824e-06 1.72107e-08 1.53712e-06 65536 0.00138889 0.000198098 4.94459e-05 1.10593e-06 6.51338e-06 1.65313e-08 1.4986e-06 Exact 0.00138889 0.000198413 4.96032e-05 1.10229e-06 6.61376e-06 1.67014e-08 1.50313e-06 SIMPLEX_MONTE_CARLO_PRB Normal end of execution. 16 January 2014 09:17:58 AM