06-Apr-2019 19:32:03 triangle_monte_carlo_test MATLAB version Test triangle_monte_carlo. TRIANGLE_MONTE_CARLO_TEST01 Sample using TRIANGLE_UNIT_SAMPLE_01 Integrate TRIANGLE_UNIT_INTEGRAND_03 Integration region is the unit triangle. Use an increasing number of points P_NUM. Note that the sample routine is a "bad" sampler. P_NUM X^2 X*Y Y^2 1 0.085647 0.022552 0.005938 2 0.003842 0.025211 0.170507 4 0.148535 0.048548 0.044776 8 0.032848 0.028801 0.082816 16 0.058606 0.052418 0.087528 32 0.076864 0.046485 0.072984 64 0.084645 0.042792 0.066866 128 0.066181 0.047870 0.073128 256 0.075407 0.048925 0.076650 512 0.069244 0.048309 0.074254 1024 0.073724 0.046008 0.068599 2048 0.072352 0.046955 0.072684 4096 0.070714 0.047255 0.072863 8192 0.071836 0.048022 0.071839 16384 0.071982 0.047376 0.070696 32768 0.071921 0.047343 0.071015 65536 0.071517 0.047364 0.071883 TRIANGLE_MONTE_CARLO_TEST02 Sample using TRIANGLE_UNIT_SAMPLE_02 Integrate TRIANGLE_UNIT_INTEGRAND_03 Integration region is the unit triangle. Use an increasing number of points P_NUM. Note that the sample routine is a good" sampler. P_NUM X^2 X*Y Y^2 1 0.015266 0.068285 0.305435 2 0.105490 0.070516 0.050387 4 0.095877 0.037573 0.053814 8 0.154186 0.042506 0.080097 16 0.067588 0.023865 0.039467 32 0.108318 0.051178 0.091483 64 0.073199 0.038644 0.098501 128 0.079182 0.043000 0.092229 256 0.079103 0.044560 0.092125 512 0.083758 0.041470 0.077927 1024 0.083544 0.041214 0.082083 2048 0.085097 0.041066 0.079867 4096 0.085221 0.041875 0.081875 8192 0.082750 0.041749 0.082597 16384 0.083314 0.042101 0.083734 32768 0.082638 0.041562 0.083170 65536 0.083404 0.041684 0.083168 TRIANGLE_MONTE_CARLO_TEST03 Sample using TRIANGLE_UNIT_SAMPLE_03 Integrate TRIANGLE_UNIT_INTEGRAND_03 Integration region is the unit triangle. Use an increasing number of points P_NUM. Note that the sample routine is a good" sampler. P_NUM X^2 X*Y Y^2 1 0.022811 0.002359 0.000244 2 0.099475 0.058771 0.153654 4 0.016470 0.015451 0.076764 8 0.071986 0.036150 0.194047 16 0.110788 0.051911 0.048713 32 0.087319 0.031378 0.083433 64 0.072996 0.046682 0.098894 128 0.088528 0.040540 0.070282 256 0.078389 0.040934 0.084555 512 0.081068 0.043319 0.089937 1024 0.084207 0.042004 0.081274 2048 0.084243 0.042013 0.082905 4096 0.081746 0.041588 0.085415 8192 0.082658 0.041849 0.083700 16384 0.083258 0.041171 0.082616 32768 0.082521 0.041803 0.084152 65536 0.083276 0.041542 0.083121 TRIANGLE_MONTE_CARLO_TEST04 Sample using TRIANGLE_UNIT_SAMPLE_04 Integrate TRIANGLE_UNIT_INTEGRAND_03 Integration region is the unit triangle. Use an increasing number of points P_NUM. Note that the sample routine is a good" sampler. P_NUM X^2 X*Y Y^2 1 0.005685 0.046273 0.376613 2 0.160594 0.046190 0.015052 4 0.010603 0.031404 0.157445 8 0.106672 0.070913 0.085843 16 0.121936 0.031995 0.046612 32 0.063821 0.036786 0.100393 64 0.089258 0.039896 0.086867 128 0.090285 0.042779 0.079963 256 0.092418 0.037899 0.072977 512 0.085600 0.042156 0.077511 1024 0.080565 0.041469 0.091284 2048 0.084655 0.041731 0.081736 4096 0.082708 0.041430 0.082961 8192 0.082952 0.041451 0.082734 16384 0.083615 0.041925 0.083132 32768 0.082651 0.041919 0.084645 65536 0.083935 0.041810 0.083314 TRIANGLE_MONTE_CARLO_TEST05 Sample using TRIANGLE_UNIT_SAMPLE_01 Integrate TRIANGLE_INTEGRAND_USER Integration region is over a general triangle. Use an increasing number of points P_NUM. Note that the sample routine is a "bad" sampler. Triangle vertices: Row: 1 2 Col 1 4.000000 1.000000 2 8.000000 3.000000 3 0.000000 9.000000 P_NUM 1 20.000000 50.546545 100.702477 127.747662 254.508115 507.049441 643.225300 3238.719039 2 20.000000 99.967783 96.527607 503.497994 478.674321 469.675314 2392.002868 11456.548810 4 20.000000 73.718971 75.474023 333.971008 216.488176 369.682137 864.602240 2700.465846 8 20.000000 71.776522 103.765910 306.763699 343.555231 561.730443 1356.362063 6243.547428 16 20.000000 84.813340 86.332079 395.770678 335.738051 411.335206 1469.374148 5994.764409 32 20.000000 80.108470 84.735303 355.033905 318.833541 385.607233 1346.683685 5482.785607 64 20.000000 77.562834 86.798859 334.896771 310.710637 419.677172 1285.060272 5386.182553 128 20.000000 81.062735 87.106624 352.111449 335.943672 406.468821 1390.877231 5938.291934 256 20.000000 82.314369 84.771865 369.732336 324.924605 397.183603 1381.776266 5672.304655 512 20.000000 80.706942 86.714427 358.075060 325.117369 410.554085 1365.948433 5644.469645 1024 20.000000 78.652731 87.211101 340.577331 319.850004 413.985647 1316.155529 5490.335769 2048 20.000000 80.184626 86.667964 352.582047 324.215144 410.217457 1352.954677 5631.355966 4096 20.000000 80.226025 86.690539 352.758234 325.286362 407.839246 1358.227658 5647.717913 8192 20.000000 80.253577 86.386189 352.820185 323.362652 406.705069 1346.300690 5580.299300 16384 20.000000 79.745787 86.817754 348.333787 323.074462 410.720643 1337.351505 5575.927364 32768 20.000000 79.718467 86.788170 349.028582 322.408092 410.367128 1336.685377 5557.212306 65536 20.000000 79.995824 86.747458 351.045216 323.681918 409.929078 1345.556505 5597.073069 TRIANGLE_MONTE_CARLO_TEST06 Sample using TRIANGLE_UNIT_SAMPLE_02 Integrate TRIANGLE_INTEGRAND_USER Integration region is over a general triangle. Use an increasing number of points P_NUM. Note that the sample routine is a "good" sampler. Triangle vertices: Row: 1 2 Col 1 4.000000 1.000000 2 8.000000 3.000000 3 0.000000 9.000000 P_NUM 1 20.000000 139.031942 58.252456 966.494050 404.947604 169.667431 2815.032600 8199.128116 2 20.000000 83.254982 72.069820 377.024934 269.308356 290.650036 1103.011302 3637.049413 4 20.000000 70.460795 87.169797 295.311931 275.844636 416.274554 1086.165014 4317.759527 8 20.000000 82.854279 71.511653 412.544240 244.921621 340.490091 1111.225882 3523.949597 16 20.000000 59.621218 106.043530 205.384704 290.298275 610.282085 940.681249 4651.337471 32 20.000000 88.215672 74.429031 434.534400 299.501941 325.273407 1402.954526 4994.151366 64 20.000000 83.267958 87.524386 397.938552 330.568850 433.061183 1485.616177 6139.740100 128 20.000000 82.868351 84.861820 396.861394 316.023852 408.147210 1423.762159 5642.135969 256 20.000000 83.138368 84.908172 400.539788 313.262009 414.621300 1397.356791 5435.558581 512 20.000000 78.106704 87.844586 359.262759 300.154461 447.083902 1276.509163 5051.927567 1024 20.000000 79.234565 86.840573 369.108926 303.500900 433.466083 1319.587335 5202.927419 2048 20.000000 78.899521 87.045831 364.051258 303.273785 437.376293 1303.057312 5191.920559 4096 20.000000 79.987634 86.207968 371.341887 306.205132 428.610421 1326.023848 5272.983488 8192 20.000000 79.811741 86.844535 371.286631 306.841480 434.299262 1328.304907 5290.767596 16384 20.000000 80.341323 86.356768 375.458190 307.465055 429.951079 1339.494854 5314.952611 32768 20.000000 79.802312 86.951714 372.201678 306.460598 436.045385 1329.968311 5284.781897 65536 20.000000 80.023024 86.636611 373.000633 307.039376 432.801444 1333.660223 5305.686111 TRIANGLE_MONTE_CARLO_TEST07 Sample using TRIANGLE_UNIT_SAMPLE_03 Integrate TRIANGLE_INTEGRAND_USER Integration region is over a general triangle. Use an increasing number of points P_NUM. Note that the sample routine is a "good" sampler. Triangle vertices: Row: 1 2 Col 1 4.000000 1.000000 2 8.000000 3.000000 3 0.000000 9.000000 P_NUM 1 20.000000 20.621175 143.174668 21.261642 147.621492 1024.949277 152.206430 1089.605251 2 20.000000 108.611158 62.117777 607.473063 348.281504 199.719435 2005.643920 6804.789882 4 20.000000 63.525853 119.597638 246.609925 348.877607 744.792473 1238.970549 6517.756089 8 20.000000 104.754936 74.976785 635.374845 350.833892 332.110985 2047.436473 7052.170106 16 20.000000 76.368706 82.897482 328.503224 269.252198 425.259211 1067.795691 3999.225786 32 20.000000 76.333423 89.740626 349.799581 304.590819 459.503134 1317.021042 5372.818665 64 20.000000 84.966779 84.784146 419.389742 317.071838 414.647218 1465.318924 5542.685356 128 20.000000 76.036507 87.859896 340.363902 293.369009 444.990333 1213.314668 4826.660599 256 20.000000 79.268372 87.612290 371.421274 306.643941 436.643201 1326.968083 5256.340268 512 20.000000 82.516001 85.506234 393.017220 313.717004 422.498513 1397.927025 5518.735284 1024 20.000000 79.638864 86.814284 369.482667 305.065984 436.555926 1313.328317 5237.953869 2048 20.000000 80.130785 86.371465 373.705133 306.283069 431.061064 1331.611757 5285.390229 4096 20.000000 80.649786 86.665172 377.444966 310.825971 431.939758 1359.606651 5428.642941 8192 20.000000 80.165658 86.658676 374.304406 307.678582 432.685950 1338.744403 5320.963960 16384 20.000000 79.601297 86.974480 370.180650 306.295904 435.746144 1326.729635 5281.050150 32768 20.000000 80.187115 86.734214 375.260822 307.335882 434.175062 1339.171267 5313.627434 65536 20.000000 79.937563 86.747463 372.432002 307.026768 433.854149 1333.212250 5304.567684 TRIANGLE_MONTE_CARLO_TEST08 Sample using TRIANGLE_UNIT_SAMPLE_04 Integrate TRIANGLE_INTEGRAND_USER Integration region is over a general triangle. Use an increasing number of points P_NUM. Note that the sample routine is a "good" sampler. Triangle vertices: Row: 1 2 Col 1 4.000000 1.000000 2 8.000000 3.000000 3 0.000000 9.000000 P_NUM 1 20.000000 147.392465 58.792299 1086.226944 433.277098 172.826723 3193.088983 9386.452168 2 20.000000 72.016547 70.063653 259.559696 251.099245 251.311936 900.730353 3201.585299 4 20.000000 88.274122 100.790470 490.238166 368.060056 568.682949 1770.710494 7122.473741 8 20.000000 93.802114 66.583951 469.564517 293.247562 247.510348 1394.895054 4518.594892 16 20.000000 69.080272 88.440599 279.272544 263.526924 474.069064 969.052728 3953.525002 32 20.000000 81.187772 89.607623 392.024839 326.756655 442.144560 1478.258170 5906.278174 64 20.000000 81.517922 84.789815 381.639177 312.191451 413.007196 1397.457321 5598.426859 128 20.000000 80.441650 84.290624 371.999892 304.301561 407.775864 1313.826030 5170.562386 256 20.000000 76.192927 88.241768 342.988985 293.921977 455.559901 1227.505138 4973.931266 512 20.000000 78.613114 86.949548 361.131489 300.740074 437.721976 1278.921566 5080.144225 1024 20.000000 82.370237 85.873746 391.411053 316.971069 422.665271 1410.738801 5644.448896 2048 20.000000 79.896564 86.366057 370.254586 306.884007 429.253381 1327.433208 5291.010332 4096 20.000000 79.829175 86.684869 371.373272 307.478756 430.613494 1334.702884 5311.059062 8192 20.000000 79.657532 87.000412 371.002974 305.983210 436.671639 1325.371108 5266.286218 16384 20.000000 80.093975 86.552022 373.657982 306.631294 432.690019 1333.515762 5294.147376 32768 20.000000 80.412830 86.507166 376.899507 307.850243 431.571743 1345.208722 5329.844988 65536 20.000000 80.133240 86.405302 374.035757 306.629188 430.689993 1333.911804 5292.636669 triangle_monte_carlo_test Normal end of execution. 06-Apr-2019 19:33:28