Tue May 20 21:17:41 2025 annulus_monte_carlo_test(): python version: 3.10.12 numpy version: 1.26.4 Test annulus_monte_carlo(). annulus_area_test(): annulus_area() computes the area of an annulus with center = (CX,CY), inner radius R1 and outer radius R2. ( CX CY ) R1 R2 Area (-3.912540, 3.697699) 0.451693 0.556315 0.331312 ( 2.207536, 4.880966) 0.915741 1.233330 2.144203 ( 1.278587, 2.948263) 0.081074 1.069988 3.576080 (-0.908584, 4.367958) 0.196096 0.996495 2.998802 (-2.805391, 2.027846) 0.160761 0.461928 0.589154 (-3.878132, 1.260656) 0.714971 1.401797 4.567411 (-2.473456,-4.954460) 0.421380 0.557024 0.416936 ( 4.430746, 3.639490) 0.557128 1.245796 3.900651 (-4.270610, 4.830156) 0.215646 1.042565 3.268632 ( 3.805074,-0.348953) 0.049542 0.162065 0.074803 annulus_sample_test(): annulus_sample() can sample an annulus uniformly. Use it to estimate integrals in the annulus centered at (0,0) with R1 = 0, R2 = 1 N 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 1 3.14159 0.26693 0.158914 0.02268 0.0135023 0.00803848 0.00192704 2 3.14159 0.265744 1.25976 0.0442018 0.208958 0.98783 0.00741401 4 3.14159 2.05204 0.11732 1.70801 0.0678782 0.014513 1.5157 8 3.14159 0.849118 0.85251 0.405584 0.107761 0.408276 0.230966 16 3.14159 0.534212 0.67151 0.203835 0.0726472 0.287445 0.104723 32 3.14159 0.991319 0.865767 0.56506 0.144173 0.475507 0.375744 64 3.14159 0.800683 0.90771 0.356621 0.185825 0.434419 0.199473 128 3.14159 0.750406 0.835273 0.39686 0.123131 0.436703 0.265579 256 3.14159 0.759357 0.867279 0.370155 0.155381 0.432248 0.224782 512 3.14159 0.793068 0.783208 0.396832 0.130706 0.387577 0.24557 1024 3.14159 0.775511 0.805467 0.389271 0.131372 0.414914 0.244144 2048 3.14159 0.809369 0.797869 0.410082 0.137268 0.403289 0.259185 4096 3.14159 0.781983 0.798447 0.388454 0.13207 0.401451 0.242528 8192 3.14159 0.797608 0.773362 0.404506 0.130565 0.380538 0.255063 16384 3.14159 0.783949 0.78152 0.393196 0.130587 0.390376 0.246217 32768 3.14159 0.785696 0.785835 0.394112 0.130264 0.392114 0.247291 65536 3.14159 0.781883 0.790071 0.388342 0.131379 0.394949 0.241261 Exact 3.14159 0.785398 0.785398 0.392699 0.1309 0.392699 0.245437 annulus_sample_test(): annulus_sample() can sample an annulus uniformly. Use it to estimate integrals in the annulus centered at (0,0) with R1 = 0.5, R2 = 1 N 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 1 2.35619 0.94866 0.783917 0.381953 0.315624 0.260813 0.153784 2 2.35619 0.348274 0.460387 0.102658 0.000198902 0.179914 0.0303038 4 2.35619 0.80538 0.76282 0.340833 0.213322 0.370922 0.15432 8 2.35619 0.506504 0.745828 0.175415 0.110931 0.34286 0.0664865 16 2.35619 0.955685 0.605315 0.587389 0.144483 0.284944 0.400382 32 2.35619 0.650129 0.788335 0.335144 0.125414 0.406871 0.202165 64 2.35619 0.716957 0.849626 0.389743 0.128806 0.490979 0.257128 128 2.35619 0.704064 0.774555 0.380081 0.123796 0.413875 0.247864 256 2.35619 0.771768 0.692631 0.395506 0.140498 0.345991 0.243037 512 2.35619 0.73525 0.744664 0.388849 0.13314 0.377502 0.247702 1024 2.35619 0.717253 0.736441 0.36856 0.128035 0.384861 0.228574 2048 2.35619 0.74368 0.720245 0.395543 0.12667 0.371745 0.252125 4096 2.35619 0.745263 0.728602 0.389912 0.131799 0.37687 0.245143 8192 2.35619 0.739016 0.738973 0.391307 0.130069 0.387157 0.250208 16384 2.35619 0.739471 0.735874 0.390934 0.128966 0.38697 0.248594 32768 2.35619 0.734257 0.738658 0.384618 0.128568 0.38885 0.242621 65536 2.35619 0.735044 0.740186 0.385787 0.129213 0.389996 0.244241 annulus_sample_test(): annulus_sample() can sample an annulus uniformly. Use it to estimate integrals in the annulus centered at (1,0) with R1 = 0, R2 = 1 N 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 1 3.14159 3.55459 0.908439 4.02187 1.02786 0.262689 4.55059 2 3.14159 2.61872 1.22521 2.21026 1.12102 0.841006 1.88805 4 3.14159 3.83433 1.1609 5.50425 1.22627 0.514947 8.45268 8 3.14159 3.44041 0.627593 7.31083 0.604965 0.287248 21.2886 16 3.14159 5.88179 0.923561 14.2644 1.81981 0.353881 37.674 32 3.14159 3.09028 0.771276 5.54018 0.838093 0.419787 12.6676 64 3.14159 4.25935 0.810985 9.42309 0.878357 0.431325 25.5564 128 3.14159 3.9259 0.807885 8.09277 0.989524 0.406301 20.6677 256 3.14159 4.26492 0.852082 9.20262 1.08065 0.479285 23.7684 512 3.14159 3.80704 0.742942 7.98745 0.884934 0.360195 20.4984 1024 3.14159 3.89259 0.74594 8.15841 0.839508 0.360768 20.8484 2048 3.14159 3.8938 0.776542 8.00583 0.914592 0.384503 20.1167 4096 3.14159 3.91152 0.780847 8.16751 0.908151 0.395852 20.7557 8192 3.14159 3.88597 0.788228 8.14005 0.918111 0.395015 20.7444 16384 3.14159 3.90633 0.789016 8.22343 0.907671 0.393873 21.0716 32768 3.14159 3.92168 0.789395 8.2011 0.922621 0.395237 20.875 65536 3.14159 3.92164 0.784028 8.22671 0.912241 0.391559 20.9969 annulus_monte_carlo_test(): Normal end of execution. Tue May 20 21:17:43 2025