Tue Oct 19 11:23:49 2021 annulus_monte_carlo_test(): Python version: 3.6.9 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 (-0.013214,-3.141475) 0.498271 0.648524 0.541328 (-1.619503,-1.512383) 0.475026 1.356062 5.068192 (-4.537017, 3.122176) 0.921112 0.949901 0.169218 (-0.216840,-1.273637) 0.417259 1.122342 3.410346 ( 3.731837, 0.864260) 0.414977 0.930111 2.176812 (-0.003329, 0.619075) 0.496877 0.898341 1.759699 (-3.007317, 2.409223) 0.299937 0.937992 2.481437 (-2.412924,-4.876059) 0.210244 0.487055 0.606391 (-3.980124, 3.435372) 0.293939 0.934759 2.473607 ( 3.468412, 0.213274) 0.188157 0.562376 0.882358 annulus_area_test(): Normal end of execution. 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 0.926846 0.0133006 0.273442 0.003924 5.6311e-05 0.0806719 2 3.14159 0.844091 1.36141 0.333429 0.279557 0.659691 0.146889 4 3.14159 1.0617 0.632982 0.448478 0.145204 0.207798 0.227627 8 3.14159 0.405696 0.792556 0.11296 0.133385 0.343593 0.0375485 16 3.14159 0.847227 0.829598 0.421093 0.15098 0.412277 0.243526 32 3.14159 0.751078 0.773884 0.419785 0.105315 0.36805 0.279837 64 3.14159 0.918121 0.791658 0.490986 0.151741 0.442189 0.318849 128 3.14159 0.733051 0.801985 0.334909 0.137284 0.382737 0.18507 256 3.14159 0.764733 0.81811 0.371257 0.148565 0.391415 0.22562 512 3.14159 0.779031 0.780261 0.376213 0.132298 0.382036 0.228936 1024 3.14159 0.799196 0.774706 0.401456 0.131296 0.375244 0.253364 2048 3.14159 0.81296 0.800199 0.418876 0.130856 0.405625 0.266541 4096 3.14159 0.77583 0.788717 0.384357 0.130984 0.394904 0.238347 8192 3.14159 0.795653 0.795736 0.400404 0.133407 0.401537 0.251305 16384 3.14159 0.791213 0.778675 0.397069 0.13065 0.388592 0.248461 32768 3.14159 0.787665 0.783753 0.395369 0.130212 0.391405 0.247862 65536 3.14159 0.787633 0.784059 0.394163 0.130434 0.391811 0.246296 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 0.24198 1.22142 0.0248512 0.125439 0.633164 0.00255221 2 2.35619 0.695651 0.398636 0.206254 0.124554 0.121703 0.0614071 4 2.35619 0.429185 1.25975 0.116862 0.183819 0.772184 0.0376173 8 2.35619 0.595916 1.13249 0.249066 0.220334 0.622164 0.125175 16 2.35619 1.0558 0.516604 0.714233 0.118181 0.232317 0.555219 32 2.35619 0.699916 0.788836 0.324231 0.171173 0.390723 0.183059 64 2.35619 0.78186 0.632067 0.414447 0.111641 0.324004 0.263283 128 2.35619 0.705663 0.751376 0.339567 0.140786 0.384118 0.197486 256 2.35619 0.732126 0.711026 0.365114 0.125355 0.374743 0.218164 512 2.35619 0.737449 0.698755 0.377028 0.124393 0.35269 0.232756 1024 2.35619 0.726622 0.734971 0.372678 0.126745 0.389012 0.229671 2048 2.35619 0.74728 0.704388 0.394028 0.12525 0.363928 0.250919 4096 2.35619 0.744672 0.735788 0.394883 0.13024 0.385187 0.252457 8192 2.35619 0.725475 0.740163 0.376404 0.127409 0.390276 0.235526 16384 2.35619 0.734122 0.741012 0.385066 0.129631 0.38884 0.243001 32768 2.35619 0.733082 0.740353 0.382776 0.129784 0.388986 0.240878 65536 2.35619 0.737687 0.739114 0.386709 0.129779 0.390005 0.244225 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 8.43766 1.23365 22.6618 3.31333 0.484435 60.8647 2 3.14159 6.66307 0.304336 15.7051 0.439405 0.0564738 39.9826 4 3.14159 4.4653 1.16231 7.34673 1.52886 0.72934 12.6416 8 3.14159 3.20718 0.518187 6.80789 0.401109 0.137119 16.8966 16 3.14159 3.38784 1.30071 6.24213 1.45242 0.906188 14.6203 32 3.14159 4.80948 0.772612 11.4362 1.10246 0.384291 31.8491 64 3.14159 2.91172 0.815625 5.25581 0.841339 0.452975 12.2347 128 3.14159 3.93078 0.812956 8.24073 1.02876 0.436026 20.3399 256 3.14159 3.7177 0.731852 7.81023 0.876439 0.348953 20.0611 512 3.14159 4.25538 0.766211 9.32585 0.948828 0.373447 24.2131 1024 3.14159 3.89775 0.84034 8.0526 0.959917 0.44193 20.2641 2048 3.14159 4.00382 0.792616 8.62839 0.927024 0.401326 22.646 4096 3.14159 3.90983 0.776474 8.16948 0.908354 0.386162 20.813 8192 3.14159 3.93381 0.788093 8.24154 0.928526 0.392694 20.9589 16384 3.14159 3.91826 0.784682 8.19775 0.920215 0.391271 20.8356 32768 3.14159 3.94415 0.785147 8.2868 0.923703 0.394267 21.1642 65536 3.14159 3.94043 0.784413 8.3016 0.920178 0.391671 21.2659 annulus_monte_carlo_test(): Normal end of execution. Tue Oct 19 11:23:51 2021