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