13-Dec-2018 10:57:08 CIRCLE_MONTE_CARLO_TEST MATLAB version Test the CIRCLE_MONTE_CARLO library. 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 0.244176 6.03901 0.00948912 0.234687 5.80432 0.000368764 2 6.28319 3.63178 2.65141 2.86244 0.76933 1.88208 2.53685 4 6.28319 3.83126 2.45192 3.12087 0.710389 1.74154 2.5537 8 6.28319 3.51264 2.77054 2.67251 0.840136 1.93041 2.15783 16 6.28319 3.0875 3.19568 2.17034 0.917164 2.27852 1.7465 32 6.28319 2.69825 3.58493 1.86613 0.832123 2.75281 1.42816 64 6.28319 3.08747 3.19572 2.31135 0.776114 2.4196 1.93519 128 6.28319 3.48751 2.79568 2.66339 0.824118 1.97156 2.22291 256 6.28319 3.15363 3.12956 2.41053 0.743103 2.38645 2.04418 512 6.28319 3.24432 3.03887 2.45557 0.788744 2.25012 2.06643 1024 6.28319 3.09144 3.19174 2.31783 0.773612 2.41813 1.93114 2048 6.28319 3.11979 3.16339 2.37492 0.744877 2.41852 2.00411 4096 6.28319 3.13302 3.15017 2.33952 0.793495 2.35668 1.93821 8192 6.28319 3.14973 3.13346 2.36981 0.779918 2.35354 1.97784 16384 6.28319 3.14761 3.13557 2.36642 0.781195 2.35438 1.97398 32768 6.28319 3.13992 3.14326 2.35215 0.787771 2.35549 1.95857 65536 6.28319 3.14611 3.13708 2.36048 0.785628 2.35145 1.96673 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. 13-Dec-2018 10:57:16