Home License -- for personal use only. Not for government, academic, research, commercial, or other organizational use. 13-May-2025 13:10:00 disk_monte_carlo_test(): MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7 Test disk_monte_carlo(). disk_area_test(): disk_area() computes the area of a disk with center = (CX,CY) and radius R. ( CX CY ) R Area ( 3.147237, 4.057919) 0.126987 0.050660 ( 4.133759, 1.323592) 0.097540 0.029890 (-2.215018, 0.468815) 0.957507 2.880273 ( 4.648885,-3.423869) 0.970593 2.959538 ( 4.571669,-0.146244) 0.800280 2.012029 (-3.581137,-0.782387) 0.915736 2.634450 ( 2.922073, 4.594924) 0.655741 1.350872 (-4.642883, 3.491293) 0.933993 2.740548 ( 1.787352, 2.577401) 0.743132 1.734932 (-1.077730, 1.554779) 0.171187 0.092064 disk_sample_test(): disk_sample() estimates integrals in the disk with center (0,0) and radius 1 N 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 1 3.14159 0.00228444 1.3414 1.66115e-06 0.000975411 0.572751 1.20792e-09 2 3.14159 1.17618 0.0921874 0.880447 0.00345456 0.00489718 0.659166 4 3.14159 0.905502 0.293058 0.509783 0.0547301 0.032422 0.304058 8 3.14159 0.757819 0.617463 0.371382 0.0782458 0.224143 0.22021 16 3.14159 1.11379 0.760196 0.623268 0.206054 0.372677 0.414302 32 3.14159 0.894762 0.768189 0.432465 0.144828 0.39989 0.247721 64 3.14159 0.661674 0.739901 0.315988 0.0989612 0.366078 0.191493 128 3.14159 0.777712 0.759378 0.38188 0.115511 0.36299 0.232271 256 3.14159 0.768585 0.812736 0.380584 0.135336 0.408323 0.234587 512 3.14159 0.778546 0.745764 0.384337 0.12077 0.354208 0.238682 1024 3.14159 0.79206 0.803614 0.400229 0.134082 0.407333 0.252782 2048 3.14159 0.796963 0.8049 0.404358 0.137866 0.404751 0.257137 4096 3.14159 0.812516 0.792007 0.412717 0.133063 0.396078 0.260893 8192 3.14159 0.771919 0.800291 0.382454 0.131076 0.403852 0.237471 16384 3.14159 0.798295 0.775231 0.400884 0.131548 0.385282 0.250857 32768 3.14159 0.782244 0.784755 0.390228 0.130494 0.393045 0.243836 65536 3.14159 0.778814 0.789405 0.386783 0.130567 0.395814 0.240701 Exact 3.14159 0.785398 0.785398 0.392699 0.1309 0.392699 0.245437 disk_sample_test(): disk_sample() estimates integrals in the disk with center (1,0) and radius 1 N 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 1 3.14159 10.899 0.1021 37.8114 0.354211 0.00331819 131.177 2 3.14159 6.52881 1.69198 13.6142 3.51454 0.911317 28.4847 4 3.14159 2.16063 0.311476 2.97413 0.303209 0.041426 4.26922 8 3.14159 2.39091 0.814163 3.26991 0.634139 0.337689 5.52812 16 3.14159 3.42423 0.893279 5.46222 0.977195 0.529644 11.0151 32 3.14159 4.74721 0.872878 10.6448 1.03207 0.494753 29.0132 64 3.14159 3.52624 0.761871 6.56556 0.95726 0.374965 15.0499 128 3.14159 3.76779 0.720354 8.16216 0.857692 0.372473 21.8084 256 3.14159 3.92486 0.763326 8.05565 0.890319 0.39708 20.0497 512 3.14159 4.02782 0.799 8.72949 0.931783 0.40143 22.7702 1024 3.14159 4.07275 0.748886 8.62885 0.914473 0.366327 22.0148 2048 3.14159 3.88437 0.812445 8.13238 0.953735 0.421435 20.744 4096 3.14159 3.94623 0.789216 8.28627 0.906187 0.396069 21.2167 8192 3.14159 3.91715 0.797026 8.15747 0.93736 0.403289 20.6489 16384 3.14159 3.95855 0.789856 8.34279 0.919734 0.395539 21.3635 32768 3.14159 3.94057 0.785082 8.31235 0.914521 0.391123 21.318 65536 3.14159 3.93003 0.782572 8.27697 0.914751 0.391541 21.1767 disk_sample_test(): disk_sample() estimates integrals in the disk with center (1,2) and radius 3 N 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 1 28.2743 19.4753 0.210445 13.4146 0.144954 0.00156633 9.23993 2 28.2743 60.4306 454.585 129.45 987.974 8228.41 277.922 4 28.2743 34.8147 175.987 63.2198 319.655 1638.64 124.681 8 28.2743 77.0652 166.939 622.437 406.695 1838.01 7091.59 16 28.2743 112.035 211.462 1026.15 785.139 3200.87 12093 32 28.2743 90.2482 186.453 635.756 658.958 2735.28 6017.57 64 28.2743 85.5008 110.601 595.339 434.532 1156.57 5528.49 128 28.2743 106.949 161.152 887.473 605.34 1957.85 9419.7 256 28.2743 91.2978 179.449 677.969 538.052 2341.28 6585.5 512 28.2743 90.8563 179.564 674.322 504.674 2337.93 6607.63 1024 28.2743 91.3836 175.661 700.187 543.684 2212.63 6906.42 2048 28.2743 87.8683 175.593 649.642 501.701 2250.04 6371.87 4096 28.2743 92.0352 178.713 694.064 520.894 2318.79 6857.49 8192 28.2743 92.0558 178.028 696.542 527.481 2295.41 6878.81 16384 28.2743 93.2146 179.355 709.276 535.297 2305.36 7011.26 32768 28.2743 91.8834 176.391 696.572 528.176 2255.91 6896.24 65536 28.2743 92.3593 175.923 701.38 526.838 2251.84 6927.32 disk_monte_carlo_test(): Normal end of execution. 13-May-2025 13:10:01