30 April 2020 05:21:58 PM TETRAHEDRON_MONTE_CARLO_TEST C++ version Test the TETRAHEDRON_MONTE_CARLO library. TEST01 Sample using TETRAHEDRON_UNIT_SAMPLE_01 Integrate TETRAHEDRON_UNIT_INTEGRAND_03 Integration region is the unit tetrahedron. Use an increasing number of points P_NUM. Note that the sample routine is a "bad" sampler. P_NUM X^2 X*Y X*Z Y^2 Y*Z Z^2 1 0.00120763 0.00528746 0.00458634 0.0231505 0.0200807 0.017418 2 0.0200559 0.00481267 0.0125281 0.0241942 0.00427564 0.00789573 4 0.0302268 0.0231009 0.00718381 0.0307148 0.0102074 0.0075206 8 0.0117702 0.0106626 0.00950056 0.0199444 0.0116801 0.0123572 16 0.0132896 0.00902844 0.00813869 0.0101117 0.00730063 0.010756 32 0.0147432 0.0104011 0.0109008 0.0136417 0.00856791 0.0152403 64 0.0134063 0.00950749 0.0081138 0.0129571 0.0089201 0.011106 128 0.0142174 0.00976202 0.00948439 0.015123 0.00946042 0.0118131 256 0.0144301 0.00908613 0.00985396 0.0123813 0.00905926 0.0151476 512 0.0142517 0.00950238 0.00934722 0.0135979 0.00861832 0.0125197 1024 0.0139837 0.00943655 0.00915851 0.0142043 0.00938047 0.013934 2048 0.013459 0.00924911 0.00937593 0.013531 0.00944727 0.0142939 4096 0.013454 0.00931752 0.00937959 0.0136518 0.00928029 0.0139004 8192 0.0135961 0.00949325 0.00926899 0.0137752 0.00926235 0.0134578 16384 0.0138082 0.00925538 0.00937326 0.013622 0.00932962 0.0136365 32768 0.0137786 0.00935584 0.00932879 0.013713 0.00927055 0.0134594 65536 0.0137548 0.00937239 0.00940389 0.013658 0.00935064 0.0137592 TEST02 Sample using TETRAHEDRON_UNIT_SAMPLE_02 Integrate TETRAHEDRON_UNIT_INTEGRAND_03 Integration region is the unit tetrahedron. Use an increasing number of points P_NUM. Note that the sample routine is a good sampler. P_NUM X^2 X*Y X*Z Y^2 Y*Z Z^2 1 0.00268006 0.000923216 0.0138385 0.000318026 0.00476701 0.0714547 2 0.0279388 0.0203075 0.00280425 0.0153809 0.00189399 0.000315035 4 0.0252599 0.00641717 0.0102405 0.0194421 0.00490141 0.0330667 8 0.0411817 0.0133023 0.00815115 0.0188628 0.00530985 0.00406394 16 0.0162033 0.00546692 0.0075859 0.00858323 0.00786344 0.0169424 32 0.012731 0.00855491 0.00570481 0.0236266 0.0118318 0.0192896 64 0.0135433 0.00755872 0.0074547 0.022653 0.00879154 0.017511 128 0.0201186 0.00936979 0.00925194 0.0142647 0.00854525 0.016082 256 0.0172159 0.00846661 0.00788278 0.0167369 0.0078286 0.0164737 512 0.0169019 0.00837163 0.00844684 0.0170946 0.00803322 0.0158228 1024 0.0176071 0.00835279 0.00851073 0.0166157 0.00810487 0.016211 2048 0.0164696 0.00854378 0.00815693 0.0169153 0.00826185 0.0163875 4096 0.0164776 0.00856374 0.00823639 0.0171876 0.00854875 0.016834 8192 0.017023 0.00836067 0.00839444 0.016277 0.00835697 0.016518 16384 0.0166148 0.00840943 0.00831745 0.0165876 0.00837075 0.0168483 32768 0.0165732 0.00833576 0.00829823 0.0166856 0.00834954 0.0165646 65536 0.0166837 0.00832516 0.00834317 0.0167211 0.00828953 0.0166479 TEST03 Sample using TETRAHEDRON_UNIT_SAMPLE_03 Integrate TETRAHEDRON_UNIT_INTEGRAND_03 Integration region is the unit tetrahedron. Use an increasing number of points P_NUM. Note that the sample routine is a good sampler. P_NUM X^2 X*Y X*Z Y^2 Y*Z Z^2 1 0.02637 0.000881743 0.00665648 2.94831e-05 0.000222575 0.00168027 2 0.0135749 0.0171669 0.0133528 0.0222438 0.0192891 0.0239396 4 0.0481305 0.0142144 0.00503491 0.0245073 0.00383041 0.00151703 8 0.0140793 0.00496968 0.0153538 0.0118848 0.00989156 0.0217565 16 0.0158204 0.0084914 0.0070563 0.0205308 0.00911986 0.0238999 32 0.0158471 0.00719333 0.00680947 0.0161667 0.00897796 0.0135959 64 0.0224717 0.00846362 0.00810511 0.0153362 0.00866248 0.0171957 128 0.0123761 0.0078325 0.00820489 0.0154607 0.00856506 0.0181744 256 0.0160873 0.00866279 0.00786049 0.0187582 0.00874858 0.0193828 512 0.0156889 0.00835191 0.00856512 0.0171408 0.00857428 0.0170312 1024 0.0173688 0.00809484 0.00820148 0.0152979 0.0080098 0.0160049 2048 0.0170081 0.00870171 0.00849897 0.0165675 0.00862529 0.0167969 4096 0.0165166 0.00821636 0.00825902 0.0164795 0.00859219 0.0162134 8192 0.0164993 0.00837596 0.00830946 0.0169553 0.00834807 0.0165908 16384 0.0167675 0.00837675 0.00842485 0.0164294 0.00828018 0.0167963 32768 0.0170165 0.00840034 0.00839122 0.0165714 0.00827328 0.0164725 65536 0.0166177 0.00835167 0.0083632 0.0166437 0.00834775 0.016775 TEST04 Sample using TETRAHEDRON_UNIT_SAMPLE_04 Integrate TETRAHEDRON_UNIT_INTEGRAND_03 Integration region is the unit tetrahedron. Use an increasing number of points P_NUM. Note that the sample routine is a good sampler. P_NUM X^2 X*Y X*Z Y^2 Y*Z Z^2 1 0.0710712 0.00208659 0.00873222 6.12602e-05 0.00025637 0.00107289 2 0.0171202 0.00619286 0.0160657 0.0123334 0.00804945 0.0155724 4 0.00408874 0.000514367 0.00618915 0.000844536 0.00239784 0.0163394 8 0.0129251 0.00505735 0.00705661 0.0146145 0.00582353 0.019257 16 0.0191599 0.00974345 0.0100214 0.0169617 0.00989801 0.0194349 32 0.0116544 0.00824662 0.0078217 0.0159309 0.00645544 0.0166135 64 0.0157147 0.00840319 0.00853668 0.0157488 0.0100792 0.0209082 128 0.0163329 0.00727833 0.00896483 0.0151086 0.009015 0.0153849 256 0.0171697 0.00850398 0.00748752 0.0180581 0.00824735 0.0154249 512 0.0155455 0.00787818 0.00837353 0.0178996 0.00867139 0.0184081 1024 0.0169094 0.00809834 0.00814815 0.0162248 0.0081718 0.016949 2048 0.017329 0.00872283 0.00819597 0.0162348 0.0081296 0.0159704 4096 0.0166896 0.0083384 0.00836203 0.0166834 0.00832732 0.0164112 8192 0.016769 0.00828496 0.00847933 0.0163504 0.0082938 0.0169832 16384 0.0166988 0.0082595 0.0082619 0.0170481 0.00846335 0.0164934 32768 0.0165493 0.00830354 0.00838069 0.0166469 0.00839485 0.0167151 65536 0.0164739 0.00829776 0.00825136 0.0167255 0.00830295 0.0165317 TEST05 Sample using TETRAHEDRON_UNIT_SAMPLE_01 Integrate TETRAHEDRON_UNIT_INTEGRAND_USER Integration region is over a general tetrahedron. Use an increasing number of points P_NUM. Note that the sample routine is a bad sampler. Tetrahedron vertices: Row: 1 2 3 Col 1 1 2 3 2 4 1 2 3 2 4 4 4 3 2 5 P_NUM 1 2.66667 7.6778 13.7878 103.741 200.441 1312.25 2 2.66667 6.93816 11.8166 103.243 150.069 743.623 4 2.66667 6.70436 9.83229 62.4656 104.451 525.091 8 2.66667 6.8862 12.9335 99.68 164.234 921.71 16 2.66667 6.66585 13.4448 131.04 198.773 1137.92 32 2.66667 6.56024 14.186 115.168 180.886 1029.82 64 2.66667 6.71544 13.1642 121.007 186.444 1056.42 128 2.66667 6.708 13.3033 114.847 179.695 1016.56 256 2.66667 6.56816 14.3419 119.389 188.172 1089.71 512 2.66667 6.64847 13.5685 118.347 183.471 1039.43 1024 2.66667 6.67085 13.8278 116.518 184.198 1061.06 2048 2.66667 6.66462 13.9966 118.496 187.356 1084.39 4096 2.66667 6.66805 13.8892 118.207 186.16 1071.06 8192 2.66667 6.67925 13.7513 117.713 185.204 1062.86 16384 2.66667 6.65784 13.8357 118.013 185.366 1063.25 32768 2.66667 6.66645 13.777 117.857 185.093 1060.93 65536 2.66667 6.65865 13.8546 117.775 185.325 1064.42 TEST06 Sample using TETRAHEDRON_UNIT_SAMPLE_02 Integrate TETRAHEDRON_UNIT_INTEGRAND_USER Integration region is over a general tetrahedron. Use an increasing number of points P_NUM. Note that the sample routine is a good sampler. Tetrahedron vertices: Row: 1 2 3 Col 1 1 2 3 2 4 1 2 3 2 4 4 4 3 2 5 P_NUM 1 2.66667 5.69411 28.4423 165.668 291.701 2034.2 2 2.66667 6.51468 8.93777 118.134 150.885 718.697 4 2.66667 6.19914 17.0327 109.214 169.404 979.345 8 2.66667 6.07435 10.8644 91.1631 125.795 597.644 16 2.66667 6.58213 14.8176 138.959 212.066 1265.82 32 2.66667 7.08617 13.7129 109.369 181.802 1108.66 64 2.66667 6.99382 13.8693 117.883 188.286 1129.83 128 2.66667 6.44703 14.2029 117.603 180.628 1039.81 256 2.66667 6.66884 14.0756 122.582 189.245 1112.02 512 2.66667 6.66243 13.9483 121.549 186.055 1075.62 1024 2.66667 6.63379 14.0866 121.409 186.875 1089.28 2048 2.66667 6.69753 14.014 120.808 187.436 1097.25 4096 2.66667 6.68815 14.0897 119.581 186.116 1089.33 8192 2.66667 6.64382 14.1376 121.371 187.517 1095.1 16384 2.66667 6.66318 14.1684 121.178 187.748 1098.66 32768 2.66667 6.67313 14.1089 121.38 187.791 1097.59 65536 2.66667 6.66584 14.129 121.332 187.572 1095.7 TEST07 Sample using TETRAHEDRON_UNIT_SAMPLE_03 Integrate TETRAHEDRON_UNIT_INTEGRAND_USER Integration region is over a general tetrahedron. Use an increasing number of points P_NUM. Note that the sample routine is a good sampler. Tetrahedron vertices: Row: 1 2 3 Col 1 1 2 3 2 4 1 2 3 2 4 4 4 3 2 5 P_NUM 1 2.66667 5.64628 12.7606 179.011 204.011 944.926 2 2.66667 6.59073 14.936 75.8828 145.819 877.504 4 2.66667 6.11369 9.60174 90.9592 117.016 540.867 8 2.66667 6.2276 16.8085 126.994 194.491 1103.34 16 2.66667 6.83121 15.061 113.757 189.221 1181.61 32 2.66667 6.75845 13.4764 124.801 190.873 1109.54 64 2.66667 6.45893 14.3274 116.526 181.917 1076.53 128 2.66667 6.73687 14.6675 127.749 199.75 1188.25 256 2.66667 6.72831 14.4185 115.852 184.599 1098.27 512 2.66667 6.70378 14.2006 121.124 188.358 1104.28 1024 2.66667 6.62242 14.0462 123.947 188.926 1095.63 2048 2.66667 6.64365 14.1396 119.073 185.099 1079.84 4096 2.66667 6.68155 14.0636 121.846 188.593 1103.27 8192 2.66667 6.68069 14.0939 120.889 187.249 1094.26 16384 2.66667 6.65365 14.1756 121.389 187.729 1096.72 32768 2.66667 6.65017 14.1029 121.016 186.844 1089.39 65536 2.66667 6.66274 14.1661 121.438 187.897 1098.79 TEST08 Sample using TETRAHEDRON_UNIT_SAMPLE_04 Integrate TETRAHEDRON_UNIT_INTEGRAND_USER Integration region is over a general tetrahedron. Use an increasing number of points P_NUM. Note that the sample routine is a good sampler. Tetrahedron vertices: Row: 1 2 3 Col 1 1 2 3 2 4 1 2 3 2 4 4 4 3 2 5 P_NUM 1 2.66667 4.35443 12.227 119.932 117.919 412.31 2 2.66667 6.32914 15.1483 113.208 174.274 944.219 4 2.66667 6.8303 16.7872 222.124 319.214 2031.77 8 2.66667 6.77148 14.7585 132.574 202.633 1188.02 16 2.66667 6.53509 14.8106 115.319 183.954 1102.36 32 2.66667 6.85909 14.0232 129.133 198.553 1160.64 64 2.66667 6.5733 15.1119 119.661 190.145 1138.23 128 2.66667 6.64442 14.1732 126.706 193.131 1122.17 256 2.66667 6.7465 13.6836 120.799 186.569 1092.28 512 2.66667 6.72534 14.4469 120.381 189.235 1120.69 1024 2.66667 6.6533 14.2181 122.354 189.051 1107.8 2048 2.66667 6.65135 13.9689 120.94 186.566 1086.55 4096 2.66667 6.67153 14.0845 121.306 187.561 1095.23 8192 2.66667 6.64801 14.2565 122.065 188.938 1107.56 16384 2.66667 6.68207 14.0656 120.758 186.971 1092.56 32768 2.66667 6.66707 14.1632 121.352 187.984 1099.81 65536 2.66667 6.67944 14.1006 121.789 188.274 1100.8 TETRAHEDRON_MONTE_CARLO_TEST Normal end of execution. 30 April 2020 05:21:58 PM