29-Oct-2022 11:31:01 circle_monte_carlo_test(): MATLAB/Octave version 4.2.2. Test circle_monte_carlo(). circle01_sample_random_test(): circle01_sample_random() randomly samples the unit circle. Use it to estimate integrals. N 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 1 6.28319 6.15778 0.125407 6.03487 0.122904 0.00250302 5.91442 2 6.28319 2.55577 3.72741 1.69907 0.856697 2.87072 1.22763 4 6.28319 2.48674 3.79644 1.19238 1.29436 2.50208 0.641313 8 6.28319 1.57541 4.70778 0.692246 0.883164 3.82461 0.35831 16 6.28319 2.78086 3.50233 2.0444 0.736457 2.76587 1.7274 32 6.28319 2.7604 3.52279 2.02678 0.733615 2.78917 1.71803 64 6.28319 2.90594 3.37725 2.01075 0.895186 2.48206 1.57089 128 6.28319 2.88918 3.39401 2.12545 0.763727 2.63028 1.77077 256 6.28319 3.12802 3.15517 2.32964 0.798376 2.35679 1.91477 512 6.28319 3.09778 3.18541 2.27448 0.823293 2.36212 1.86938 1024 6.28319 2.99937 3.28382 2.21781 0.781556 2.50226 1.83609 2048 6.28319 3.11643 3.16676 2.35323 0.7632 2.40356 1.97219 4096 6.28319 3.17506 3.10813 2.39977 0.775294 2.33283 2.01249 8192 6.28319 3.14568 3.13751 2.37248 0.773202 2.36431 1.98643 16384 6.28319 3.14822 3.13496 2.36373 0.78449 2.35047 1.97013 32768 6.28319 3.1513 3.13188 2.36385 0.787451 2.34443 1.97022 65536 6.28319 3.13148 3.15171 2.34691 0.784568 2.36714 1.95521 Exact 6.28319 3.14159 3.14159 2.35619 0.785398 2.35619 1.9635 circle01_sample_ergodic_test(): circle01_sample_ergodic() ergodically samples the unit circle. Use it to estimate integrals. N 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 1 6.28319 6.28319 0 6.28319 0 0 6.28319 2 6.28319 4.84972 1.43347 4.07032 0.779395 0.654073 3.64655 4 6.28319 3.01837 3.26482 2.25052 0.767845 2.49697 1.90297 8 6.28319 3.04968 3.23351 2.3008 0.748871 2.48464 1.95871 16 6.28319 3.11752 3.16567 2.37908 0.738438 2.42723 2.0164 32 6.28319 3.21906 3.06412 2.43708 0.781985 2.28214 2.04792 64 6.28319 3.16393 3.11926 2.38392 0.78001 2.33925 1.9937 128 6.28319 3.16442 3.11877 2.385 0.779418 2.33935 1.99556 256 6.28319 3.15606 3.12713 2.37107 0.784992 2.34214 1.97789 512 6.28319 3.14012 3.14307 2.3555 0.784619 2.35845 1.96372 1024 6.28319 3.14162 3.14157 2.35699 0.784632 2.35693 1.96467 2048 6.28319 3.14328 3.1399 2.35789 0.785389 2.35451 1.96516 4096 6.28319 3.14146 3.14173 2.35608 0.785374 2.35635 1.96344 8192 6.28319 3.1415 3.14168 2.35615 0.785351 2.35633 1.96351 16384 6.28319 3.14159 3.14159 2.35624 0.78535 2.35624 1.96357 32768 6.28319 3.1417 3.14149 2.3563 0.785398 2.35609 1.9636 65536 6.28319 3.14159 3.1416 2.35619 0.785397 2.3562 1.96349 Exact 6.28319 3.14159 3.14159 2.35619 0.785398 2.35619 1.9635 circle_monte_carlo_test(): Normal end of execution. 29-Oct-2022 11:31:04