07-Jan-2019 08:54:00 DISK_MONTE_CARLO_TEST MATLAB version 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 (-2.815817, 4.563176) 0.829509 2.161685 ( 0.616954,-0.846929) 0.066119 0.013734 (-2.424222,-3.900432) 0.043829 0.006035 ( 1.339657,-4.382728) 0.449539 0.634870 (-0.986937, 2.546735) 0.797287 1.997005 (-4.981616, 3.975041) 0.350752 0.386501 (-4.054552,-4.863831) 0.859097 2.318644 ( 3.408475,-3.768961) 0.007512 0.000177 (-2.396970, 4.124837) 0.113664 0.040588 (-1.483713, 3.228873) 0.267132 0.224183 DISK_SAMPLE_TEST Use DISK_SAMPLE to estimate 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 0.47599 0.210192 0.0721182 0.0318466 0.0140631 0.0109268 2 3.14159 1.73168 1.07349 1.19108 0.300499 0.725323 0.917328 4 3.14159 0.530975 0.490591 0.143572 0.0301652 0.2349 0.0431326 8 3.14159 0.726601 0.550568 0.253437 0.166811 0.193653 0.0962167 16 3.14159 0.83617 0.461501 0.535368 0.106842 0.1664 0.388239 32 3.14159 0.939212 0.717655 0.540707 0.120774 0.333415 0.375648 64 3.14159 0.770507 0.85233 0.381658 0.141415 0.463464 0.241444 128 3.14159 0.813217 0.659644 0.41285 0.105768 0.302171 0.254905 256 3.14159 0.790912 0.858681 0.399831 0.138701 0.44323 0.258527 512 3.14159 0.765811 0.807335 0.373852 0.138586 0.396512 0.229205 1024 3.14159 0.76508 0.775703 0.379359 0.124548 0.392603 0.236835 2048 3.14159 0.791923 0.784789 0.401137 0.127464 0.401916 0.253723 4096 3.14159 0.789652 0.781106 0.392809 0.13394 0.388011 0.244168 8192 3.14159 0.787569 0.760929 0.395181 0.126653 0.374784 0.248592 16384 3.14159 0.783454 0.782018 0.388764 0.129473 0.391897 0.240684 32768 3.14159 0.780569 0.791597 0.387422 0.131147 0.39734 0.24089 65536 3.14159 0.783274 0.782328 0.392463 0.129609 0.390335 0.246167 Exact 3.14159 0.785398 0.785398 0.392699 0.1309 0.392699 0.245437 DISK_SAMPLE_TEST Use DISK_SAMPLE to estimate 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 1.12339 0.178449 0.401708 0.063811 0.0101363 0.143645 2 3.14159 5.31253 0.606388 17.7008 1.39602 0.132801 59.4144 4 3.14159 5.43591 0.34645 12.0484 0.328436 0.0824161 29.9756 8 3.14159 5.51129 0.202086 14.0306 0.573936 0.0277403 39.4931 16 3.14159 3.12507 0.786554 4.81976 0.992123 0.377123 9.18406 32 3.14159 2.70984 0.91289 4.71902 0.830092 0.467098 10.4784 64 3.14159 3.7849 0.741377 8.09506 0.819718 0.361704 21.0752 128 3.14159 4.30279 0.729396 9.29578 0.934301 0.34751 24.1659 256 3.14159 3.90733 0.846749 8.1787 0.992894 0.454495 20.6063 512 3.14159 3.54163 0.799297 7.14053 0.862468 0.412322 17.9753 1024 3.14159 3.88608 0.777723 8.04607 0.883265 0.39818 20.3926 2048 3.14159 3.9804 0.786966 8.52174 0.918179 0.39732 22.2376 4096 3.14159 3.86036 0.777113 8.11141 0.889348 0.381459 20.8344 8192 3.14159 3.9131 0.776188 8.1433 0.912371 0.38535 20.6135 16384 3.14159 3.88021 0.793906 8.07253 0.914393 0.397309 20.4991 32768 3.14159 3.93899 0.793539 8.27052 0.926546 0.398722 21.1402 65536 3.14159 3.9233 0.780739 8.2315 0.910425 0.389206 21.0024 DISK_SAMPLE_TEST Use DISK_SAMPLE to estimate 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 163.123 115.166 941.11 664.429 469.09 5429.56 2 28.2743 19.0162 548.169 16.5145 321.236 11231.8 16.1175 4 28.2743 84.3103 222.151 378.308 507.461 2704.54 2069.57 8 28.2743 83.4093 206.559 824.172 756.499 2169.29 9300.67 16 28.2743 66.4958 117.806 496.208 293.738 920.604 6039.56 32 28.2743 87.5622 172.83 697.545 445.62 2649.03 7326.54 64 28.2743 72.6661 173.019 397.219 419.936 2339.46 3100.26 128 28.2743 99.2776 149.896 800.925 480.442 1698.27 8060.5 256 28.2743 102.701 184.949 850.808 564.237 2336.14 8793.26 512 28.2743 90.345 182.961 676.589 541.174 2423.66 6722.36 1024 28.2743 91.3329 174.667 657.528 515.374 2179.66 6118.18 2048 28.2743 92.8059 177.792 710.676 540.491 2294.45 7035.58 4096 28.2743 94.5003 179.702 724.255 547.667 2295.24 7163.53 8192 28.2743 90.1804 178.331 674.192 518.014 2290.13 6596.44 16384 28.2743 90.9163 176.716 684.028 520.875 2269.7 6731.33 32768 28.2743 91.8127 176.567 695.33 526.02 2268.98 6877.97 65536 28.2743 91.691 176.694 694.576 524.581 2258.85 6867.15 DISK_MONTE_CARLO_TEST Normal end of execution. 07-Jan-2019 08:54:06