03-Nov-2022 13:20:27 annulus_monte_carlo_test(): MATLAB/Octave version 4.2.2 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 ( 4.425572, 1.299327) 0.486530 0.803610 1.285156 (-0.468116, 0.926560) 0.527916 0.551003 0.078257 ( 0.582174, 2.982875) 0.529708 0.980420 2.138272 ( 4.661345,-1.841539) 0.354445 1.049361 3.064709 ( 2.633893,-3.994422) 0.998588 1.332638 2.446504 ( 4.357589, 1.836463) 0.406458 0.991726 2.570805 (-3.865649, 1.952939) 0.881920 1.043297 0.976046 ( 3.256239, 1.513230) 0.670253 1.619242 6.825761 ( 3.122509,-2.495587) 0.477865 1.176322 3.629731 ( 2.719113,-0.825473) 0.456520 0.679982 0.797854 annulus_sample_test(): annulus_sample() samples 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 0.0368075 0.780988 0.000431244 0.00915021 0.194151 5.05254e-06 2 3.14159 2.19895 0.217829 1.56341 0.158578 0.0166418 1.12827 4 3.14159 1.10235 0.528973 0.749539 0.080012 0.138144 0.51995 8 3.14159 0.641788 1.21177 0.23213 0.191297 0.7193 0.104468 16 3.14159 0.881275 0.866043 0.444467 0.165756 0.432499 0.275086 32 3.14159 0.788167 1.01663 0.362816 0.179203 0.517513 0.201367 64 3.14159 0.683643 0.828788 0.292859 0.121726 0.432201 0.14708 128 3.14159 0.783143 0.70063 0.42325 0.108447 0.349209 0.282893 256 3.14159 0.762168 0.767038 0.371346 0.116277 0.384126 0.229738 512 3.14159 0.817636 0.806155 0.432549 0.133074 0.426795 0.282827 1024 3.14159 0.781469 0.803064 0.398474 0.126864 0.409921 0.252219 2048 3.14159 0.811096 0.763116 0.404081 0.130937 0.378889 0.251384 4096 3.14159 0.779355 0.781773 0.389413 0.130509 0.389134 0.243566 8192 3.14159 0.788082 0.793551 0.396067 0.134174 0.395263 0.248491 16384 3.14159 0.776735 0.78332 0.386982 0.128739 0.394015 0.241449 32768 3.14159 0.788903 0.783533 0.395788 0.131187 0.391295 0.247671 65536 3.14159 0.779007 0.788654 0.386316 0.130595 0.395736 0.240116 Exact 3.14159 0.785398 0.785398 0.392699 0.1309 0.392699 0.245437 annulus_sample_test(): annulus_sample() samples 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 0.691604 0.92395 0.203004 0.271203 0.362315 0.0595869 2 2.35619 0.946706 0.731607 0.546687 0.276715 0.228954 0.353297 4 2.35619 1.0762 0.599266 0.710157 0.198159 0.180363 0.520841 8 2.35619 0.945279 0.640706 0.48211 0.218426 0.270987 0.277996 16 2.35619 0.759079 0.725769 0.362711 0.1264 0.386271 0.196644 32 2.35619 0.710713 0.773866 0.343393 0.171435 0.35211 0.203768 64 2.35619 0.773981 0.686423 0.415439 0.107274 0.365221 0.263669 128 2.35619 0.856406 0.697673 0.47983 0.1464 0.365851 0.314294 256 2.35619 0.757698 0.744175 0.399596 0.143456 0.38562 0.254366 512 2.35619 0.738422 0.736442 0.38789 0.134162 0.365921 0.244496 1024 2.35619 0.712348 0.752177 0.363556 0.127273 0.403637 0.223241 2048 2.35619 0.745393 0.732348 0.402149 0.126274 0.381319 0.260599 4096 2.35619 0.732297 0.736797 0.384732 0.128193 0.384081 0.243363 8192 2.35619 0.74526 0.728166 0.391614 0.129663 0.379687 0.246944 16384 2.35619 0.735708 0.733037 0.385533 0.128078 0.383677 0.243428 32768 2.35619 0.737485 0.735954 0.386599 0.12924 0.386311 0.244177 65536 2.35619 0.735746 0.735607 0.385912 0.129068 0.385939 0.244021 annulus_sample_test(): annulus_sample() samples 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 1.10565 1.7581 0.389123 0.618746 0.98387 0.136948 2 3.14159 3.71338 0.592969 6.74069 0.203274 0.217228 13.5264 4 3.14159 3.73231 0.689379 11.0236 0.797427 0.341457 38.9 8 3.14159 4.44884 0.437339 11.364 0.361931 0.164877 34.4247 16 3.14159 3.50592 1.18103 6.10638 1.35283 0.752606 13.2449 32 3.14159 3.92023 1.10205 7.65168 1.2556 0.611183 18.3 64 3.14159 3.93223 0.877037 8.25746 1.02358 0.400431 20.6884 128 3.14159 3.83259 0.783208 8.22023 0.851318 0.429992 21.7066 256 3.14159 4.12234 0.811599 8.86859 0.942528 0.410414 22.7807 512 3.14159 3.96996 0.766467 8.34556 0.95363 0.370722 21.1794 1024 3.14159 3.87865 0.817172 8.2159 0.951822 0.416375 21.3294 2048 3.14159 3.88384 0.780437 8.06391 0.901736 0.39223 20.4052 4096 3.14159 3.88828 0.807401 8.07072 0.946304 0.407449 20.3635 8192 3.14159 3.92119 0.793994 8.25577 0.914561 0.395899 21.1624 16384 3.14159 3.93286 0.784813 8.29662 0.918661 0.39196 21.244 32768 3.14159 3.93211 0.785439 8.27889 0.917201 0.392905 21.2031 65536 3.14159 3.90905 0.78194 8.18909 0.910831 0.390868 20.8859 annulus_monte_carlo_test(): Normal end of execution. 03-Nov-2022 13:20:27