Tue Oct 19 17:33:13 2021 WEDGE_MONTE_CARLO_TEST Python version: 3.6.9 Test WEDGE_MONTE_CARLO() WEDGE01_MONOMIAL_INTEGRAL_TEST: Python version: 3.6.9 WEDGE01_MONOMIAL_INTEGRAL computes the integral of a monomial over the interior of the unit wedge in 3D. Compare with a Monte Carlo estimate. Number of sample points used is 500000 E1 E2 E3 MC-Estimate Exact Error 0 1 0 0.333558 0.333333 0.000224871 1 1 0 0.0833686 0.0833333 3.52782e-05 2 1 0 0.0333684 0.0333333 3.5027e-05 3 1 0 0.0166867 0.0166667 1.99907e-05 4 1 0 0.00953272 0.00952381 8.91196e-06 5 1 0 0.00595506 0.00595238 2.67932e-06 0 2 0 0.166892 0.166667 0.000224978 1 2 0 0.0333287 0.0333333 4.64929e-06 2 2 0 0.0111192 0.0111111 8.13783e-06 3 2 0 0.0047687 0.0047619 6.79699e-06 4 2 0 0.00238483 0.00238095 3.87825e-06 0 3 0 0.100239 0.1 0.000238723 1 3 0 0.0166565 0.0166667 1.01346e-05 2 3 0 0.00476235 0.0047619 4.48175e-07 3 3 0 0.00178774 0.00178571 2.02879e-06 0 4 0 0.0669127 0.0666667 0.000246033 1 4 0 0.00951584 0.00952381 7.96478e-06 2 4 0 0.00237949 0.00238095 1.46331e-06 0 5 0 0.047863 0.047619 0.000243984 1 5 0 0.00594755 0.00595238 4.83533e-06 0 6 0 0.0359496 0.0357143 0.000235267 0 1 1 0.00028089 0 0.00028089 1 1 1 7.45269e-05 0 7.45269e-05 2 1 1 4.70496e-05 0 4.70496e-05 3 1 1 3.26239e-05 0 3.26239e-05 4 1 1 2.25158e-05 0 2.25158e-05 0 2 1 0.000198979 0 0.000198979 1 2 1 2.72958e-05 0 2.72958e-05 2 2 1 1.26937e-05 0 1.26937e-05 3 2 1 8.22253e-06 0 8.22253e-06 0 3 1 0.000158962 0 0.000158962 1 3 1 1.532e-05 0 1.532e-05 2 3 1 4.53686e-06 0 4.53686e-06 0 4 1 0.000129398 0 0.000129398 1 4 1 1.10551e-05 0 1.10551e-05 0 5 1 0.000105294 0 0.000105294 0 1 2 0.111139 0.111111 2.79011e-05 1 1 2 0.0277522 0.0277778 2.55805e-05 2 1 2 0.0111027 0.0111111 8.41644e-06 3 1 2 0.00555234 0.00555556 3.21324e-06 0 2 2 0.0556266 0.0555556 7.10647e-05 1 2 2 0.011094 0.0111111 1.71389e-05 2 2 2 0.00369825 0.0037037 5.44884e-06 0 3 2 0.0334203 0.0333333 8.69973e-05 1 3 2 0.00554463 0.00555556 1.09226e-05 0 4 2 0.0223122 0.0222222 8.9934e-05 0 1 3 0.000114143 0 0.000114143 1 1 3 3.69002e-05 0 3.69002e-05 2 1 3 2.70383e-05 0 2.70383e-05 0 2 3 9.14223e-05 0 9.14223e-05 1 2 3 1.35099e-05 0 1.35099e-05 0 3 3 7.59361e-05 0 7.59361e-05 0 1 4 0.0667081 0.0666667 4.14153e-05 1 1 4 0.0166401 0.0166667 2.65837e-05 0 2 4 0.0334091 0.0333333 7.57529e-05 0 1 5 6.11518e-05 0 6.11518e-05 WEDGE01_MONOMIAL_INTEGRAL_TEST: Normal end of execution. WEDGE01_MONTE_CARLO_TEST Python version: 3.6.9 Use WEDGE01_SAMPLE for a Monte Carlo estimate of an integral over the interior of the unit wedge in 3D. N 1 X Y Z X^2 XY Z^2 X^3 1 1 0.22813 0.600842 -0.774051 0.0520434 0.13707 0.599156 0.0118727 2 1 0.108729 0.29842 -0.107681 0.0121237 0.0311415 0.298603 0.00138381 4 1 0.211851 0.488017 0.295811 0.0822816 0.0937622 0.15027 0.0396721 8 1 0.197701 0.531194 -0.153115 0.0563392 0.0881971 0.375083 0.019368 16 1 0.37834 0.227585 0.110803 0.200077 0.0602014 0.348486 0.119699 32 1 0.308416 0.267021 -0.0795001 0.141944 0.0731566 0.288632 0.0774507 64 1 0.271057 0.33714 0.0271814 0.112329 0.07325 0.366671 0.0571399 128 1 0.319477 0.330751 -0.0357285 0.159152 0.0774645 0.340374 0.0951998 256 1 0.352433 0.316257 -0.0366362 0.179976 0.0795239 0.373265 0.107243 512 1 0.342843 0.327289 -0.00402771 0.176147 0.0834154 0.333793 0.108209 1024 1 0.334283 0.334251 -0.0250692 0.164975 0.0845115 0.331741 0.0982079 2048 1 0.326378 0.341233 -0.0198329 0.160819 0.084041 0.329321 0.0949697 4096 1 0.330734 0.333052 -0.00429428 0.164582 0.0827991 0.329855 0.0983306 8192 1 0.332088 0.336875 0.00244876 0.165334 0.0840769 0.32781 0.0988201 16384 1 0.333336 0.32885 -0.0108586 0.166396 0.0823086 0.334185 0.0995894 32768 1 0.333922 0.332305 0.000764176 0.167511 0.0830195 0.332513 0.100882 65536 1 0.331762 0.336817 0.00141006 0.165422 0.083762 0.333184 0.0990803 Exact 1 0.333333 0.333333 0 0.166667 0.0833333 0.333333 0.1 WEDGE01_MONTE_CARLO_TEST Normal end of execution. WEDGE01_SAMPLE_TEST Python version: 3.6.9 WEDGE01_SAMPLE samples the unit wedge. Sample points in the unit wedge. Row: 0 1 2 Col 0 : 0.431747 0.231746 -0.546095 1 : 0.59944 0.19689 0.166494 2 : 0.217237 0.464181 0.241355 3 : 0.0396118 0.68902 -0.925281 4 : 0.771068 0.127093 0.853293 5 : 0.666805 0.057591 -0.54533 6 : 0.455141 0.496735 -0.40307 7 : 0.297539 0.13262 0.542554 8 : 0.0687328 0.897709 0.619859 9 : 0.681361 0.0540367 -0.561675 WEDGE01_SAMPLE_TEST Normal end of execution. WEDGE01_VOLUME_TEST Python version: 3.6.9 WEDGE01_VOLUME returns the volume of the unit wedge. WEDGE01_VOLUME() = 1 WEDGE01_VOLUME_TEST Normal end of execution. WEDGE_MONTE_CARLO_TEST Normal end of execution. Tue Oct 19 17:33:53 2021