Tue May 20 21:35:10 2025 disk_monte_carlo_test(): python version: 3.10.12 numpy version: 1.26.4 Test disk_monte_carlo(). disk_area_test(): disk_area() returns the area of the unit disk. ( CX CY ) R Area (-4.326392, 3.681114) 0.390144 0.478190 (-0.754090, 0.588405) 0.237439 0.177114 (-2.214479,-0.197533) 0.313626 0.309011 ( 0.541792,-4.402134) 0.949810 2.834152 (-3.719582,-2.352346) 0.933270 2.736306 ( 3.328210, 1.873898) 0.408262 0.523635 (-4.086786, 1.669955) 0.238652 0.178929 (-3.449547,-0.180183) 0.011025 0.000382 ( 4.069078, 3.830132) 0.978598 3.008559 (-1.605978, 2.038248) 0.741410 1.726897 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 0.959106 0.048216 0.292808 0.01472 0.000740001 0.0893922 2 3.14159 0.165116 1.3524 0.00895341 0.067198 0.636908 0.000499508 4 3.14159 0.169479 0.491209 0.0192246 0.0214658 0.190442 0.00267631 8 3.14159 1.24325 0.345775 0.790694 0.0565011 0.170874 0.557087 16 3.14159 0.953868 0.557682 0.431841 0.133959 0.238306 0.220506 32 3.14159 0.651563 0.892843 0.296984 0.0944427 0.531726 0.161902 64 3.14159 0.624591 0.935502 0.281172 0.150702 0.46781 0.165538 128 3.14159 0.760968 0.690781 0.368364 0.145169 0.28698 0.218367 256 3.14159 0.811357 0.761118 0.416238 0.125831 0.384393 0.265484 512 3.14159 0.804528 0.830085 0.397478 0.145826 0.422414 0.244012 1024 3.14159 0.770501 0.829646 0.368988 0.142977 0.428451 0.223027 2048 3.14159 0.785507 0.755184 0.395212 0.128179 0.367603 0.247998 4096 3.14159 0.801277 0.771156 0.40535 0.131182 0.381628 0.255269 8192 3.14159 0.788244 0.791773 0.395646 0.132556 0.396767 0.247718 16384 3.14159 0.778843 0.783273 0.385785 0.131219 0.391168 0.238824 32768 3.14159 0.785875 0.785684 0.392817 0.130324 0.394137 0.245287 65536 3.14159 0.78386 0.787365 0.39276 0.130273 0.394118 0.246202 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 0.000440267 0.00906696 6.16996e-08 1.27066e-06 2.61682e-05 8.64666e-12 2 3.14159 6.07019 0.441691 15.9595 0.932188 0.0635653 47.1857 4 3.14159 1.60033 1.16617 1.44939 0.845245 0.781051 1.38131 8 3.14159 1.9816 0.510454 2.12528 0.586334 0.256417 2.8939 16 3.14159 3.84235 0.695425 7.82735 1.07117 0.398218 20.0419 32 3.14159 3.99019 0.745519 7.20764 0.924961 0.396125 15.2413 64 3.14159 4.11736 1.07079 8.78419 1.17251 0.586582 21.9739 128 3.14159 3.73656 0.850272 7.86904 0.89017 0.419974 20.1908 256 3.14159 3.80525 0.764181 7.96469 0.88467 0.381837 20.2793 512 3.14159 4.00279 0.783108 8.64296 0.94727 0.387783 22.6025 1024 3.14159 4.02056 0.75939 8.48832 0.863116 0.370049 21.7673 2048 3.14159 3.8712 0.751626 8.17758 0.885964 0.365999 21.0654 4096 3.14159 3.9009 0.778166 8.20158 0.899253 0.384476 21.0128 8192 3.14159 3.97044 0.76742 8.4108 0.894278 0.381235 21.6384 16384 3.14159 3.9147 0.792861 8.19024 0.921263 0.397169 20.8157 32768 3.14159 3.97085 0.788907 8.37963 0.929078 0.394359 21.4544 65536 3.14159 3.94027 0.78563 8.28358 0.920792 0.392729 21.1864 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 32.5247 95.7551 37.4141 110.15 324.288 43.0384 2 28.2743 108.454 435.217 702.502 1749.05 6721.3 4892.51 4 28.2743 142.349 264.412 1121.06 1858.79 3775.71 10907.5 8 28.2743 51.1455 269.848 244.503 480.624 3630.48 1334.24 16 28.2743 104.065 219.835 831.653 815.13 3337.2 8636.75 32 28.2743 73.9088 176.373 514.809 341.754 2466.36 4990.88 64 28.2743 102.838 180.665 856.659 513.17 2389.23 8758.67 128 28.2743 96.9496 174.671 718.445 535.841 2251.94 6765.22 256 28.2743 89.5276 164.518 680.992 493.988 2092.67 6636.65 512 28.2743 86.9705 167.74 632.219 470.72 2112.99 6082.78 1024 28.2743 97.2056 172.728 781.369 531.849 2167.47 8034.58 2048 28.2743 92.4301 172.394 705.709 513.121 2206.61 7066.02 4096 28.2743 92.8628 177.461 716.48 538.336 2280.83 7169.16 8192 28.2743 91.8717 178.928 696.533 532.945 2308.22 6901.67 16384 28.2743 92.7044 176.054 704.818 525.675 2260.71 6968.56 32768 28.2743 91.3244 177.055 689.859 528.192 2267.42 6800.99 65536 28.2743 92.2084 177.268 699.534 529.404 2276.97 6915.03 disk_monte_carlo_test(): Normal end of execution. Tue May 20 21:35:13 2025