04-Nov-2022 08:37:05 disk_monte_carlo_test(): MATLAB/Octave version 4.2.2 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 (-3.426580, 4.622078) 0.809822 2.060294 (-4.282690,-3.206698) 0.704414 1.558855 ( 0.111271,-1.195573) 0.024965 0.001958 ( 3.233438,-3.956820) 0.517448 0.841169 ( 1.964857,-3.312286) 0.532859 0.892020 ( 2.696501, 2.670168) 0.155102 0.075576 ( 2.371013, 3.611627) 0.631039 1.251013 ( 2.672469, 0.489123) 0.056794 0.010133 ( 3.656133, 1.501171) 0.670241 1.411276 ( 0.768684, 1.785355) 0.362297 0.412363 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 0.824834 0.699477 0.216562 0.183649 0.155739 0.056859 2 3.14159 0.158906 1.15168 0.0152337 0.0695842 0.440038 0.00149851 4 3.14159 0.588294 0.4743 0.154475 0.081457 0.105285 0.0452699 8 3.14159 0.860783 1.28224 0.642254 0.0969432 0.853347 0.564006 16 3.14159 0.752032 0.478778 0.366855 0.0914103 0.173414 0.224656 32 3.14159 0.837401 0.964556 0.46622 0.151149 0.502967 0.30329 64 3.14159 0.991731 0.768359 0.531986 0.170484 0.356811 0.328291 128 3.14159 0.811078 0.792424 0.412842 0.133007 0.391643 0.26296 256 3.14159 0.829164 0.804893 0.430861 0.126985 0.412542 0.273278 512 3.14159 0.79573 0.732421 0.387981 0.133807 0.352996 0.233899 1024 3.14159 0.799689 0.789328 0.3923 0.13812 0.388013 0.239971 2048 3.14159 0.766497 0.788938 0.375703 0.129819 0.389649 0.233724 4096 3.14159 0.775456 0.779435 0.386875 0.128709 0.387979 0.241882 8192 3.14159 0.793839 0.779231 0.399111 0.130462 0.390511 0.25026 16384 3.14159 0.788911 0.789004 0.396346 0.131157 0.39665 0.249337 32768 3.14159 0.781144 0.787008 0.38885 0.130793 0.393953 0.242413 65536 3.14159 0.784956 0.784663 0.392058 0.13012 0.392251 0.24491 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 0.0221462 0.00264953 0.000156117 1.86775e-05 2.23454e-06 1.10052e-06 2 3.14159 1.31994 0.663509 1.0675 0.384527 0.161938 0.879526 4 3.14159 4.66484 1.18025 8.99729 1.21865 0.877094 20.8541 8 3.14159 5.43113 1.35814 11.6671 2.40822 0.823625 27.1442 16 3.14159 3.50361 0.43635 6.50192 0.453649 0.1248 14.6765 32 3.14159 3.39773 0.914508 6.65082 0.97994 0.527267 17.2145 64 3.14159 3.50262 0.749507 6.57367 0.957345 0.406921 14.3748 128 3.14159 3.60422 0.728499 7.00116 0.749228 0.39521 16.6529 256 3.14159 4.05256 0.806206 8.18156 1.01139 0.387573 19.9455 512 3.14159 3.77418 0.818632 7.93121 0.901146 0.408962 20.4778 1024 3.14159 3.72334 0.819636 7.57198 0.91242 0.419337 18.984 2048 3.14159 3.9185 0.78622 8.31155 0.90221 0.392349 21.5244 4096 3.14159 3.97224 0.800522 8.37688 0.945361 0.405707 21.3761 8192 3.14159 3.93652 0.782523 8.28058 0.914985 0.389771 21.1512 16384 3.14159 3.9189 0.787071 8.19852 0.909677 0.393687 20.8769 32768 3.14159 3.92647 0.784431 8.27637 0.910214 0.392368 21.2074 65536 3.14159 3.9115 0.788062 8.19108 0.920566 0.395084 20.8524 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 70.5329 689.487 175.951 1719.99 16813.6 438.925 2 28.2743 30.5385 84.6841 64.2624 98.2201 255.095 136.975 4 28.2743 140.907 261.374 1118.51 1910.75 4529.83 10180.5 8 28.2743 64.7838 332.712 490.827 761.982 5205.64 4894.81 16 28.2743 84.1507 182.223 696.445 616.844 2634.6 8069.34 32 28.2743 89.9987 202.685 713.803 627.281 2625.12 7761.01 64 28.2743 69.5539 161.09 454.984 427.882 1784.85 4119.24 128 28.2743 94.1067 171.697 733.236 510.851 2086.46 7636.84 256 28.2743 82.2718 160.517 564.884 426.073 1966.17 5215.96 512 28.2743 93.2759 191.694 706.274 574.787 2592.21 7019.33 1024 28.2743 94.9059 167.788 763.245 499.508 2076.32 7915.12 2048 28.2743 94.5364 182.133 730.346 576.262 2342.5 7330.12 4096 28.2743 92.9059 178.022 712.944 528.359 2267.36 7137.61 8192 28.2743 91.8082 176.767 698.429 518.359 2272.64 6908.21 16384 28.2743 92.5103 177.742 705.491 537.376 2273.46 7041.24 32768 28.2743 92.0614 176.591 695.103 527.222 2267.04 6849.52 65536 28.2743 92.27 176.45 699.295 530.778 2260.7 6919.76 disk_monte_carlo_test(): Normal end of execution. 04-Nov-2022 08:37:06