07-Jan-2022 18:09:00 circle_monte_carlo_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 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 0.983086 5.3001 0.153816 0.829269 4.47083 0.0240666 2 6.28319 3.69513 2.58805 2.23667 1.45847 1.12959 1.39014 4 6.28319 2.96341 3.31978 1.86981 1.0936 2.22618 1.23328 8 6.28319 4.7773 1.50588 4.31257 0.464737 1.04114 4.04014 16 6.28319 2.66036 3.62283 1.79593 0.864425 2.7584 1.39629 32 6.28319 2.78804 3.49514 2.1617 0.626345 2.8688 1.88122 64 6.28319 3.07489 3.2083 2.31594 0.758943 2.44936 1.92643 128 6.28319 3.15282 3.13037 2.3789 0.773918 2.35645 1.97093 256 6.28319 3.10289 3.18029 2.29038 0.812507 2.36779 1.89637 512 6.28319 3.01072 3.27246 2.20354 0.807178 2.46528 1.80122 1024 6.28319 3.17224 3.11095 2.37649 0.795744 2.3152 1.97164 2048 6.28319 3.1981 3.08509 2.41346 0.784636 2.30045 2.01589 4096 6.28319 3.1179 3.16528 2.32596 0.791943 2.37334 1.9325 8192 6.28319 3.15006 3.13313 2.36271 0.787344 2.34578 1.96551 16384 6.28319 3.12617 3.15701 2.33625 0.789919 2.36709 1.94174 32768 6.28319 3.14915 3.13404 2.36538 0.783773 2.35026 1.97238 65536 6.28319 3.13039 3.1528 2.34814 0.782248 2.37055 1.95781 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. 07-Jan-2022 18:09:00