29-Dec-2022 22:20:58 disk01_integrands_test(): MATLAB/Octave version 4.2.2 Test disk01_integrands(). disk01_integrands_test01(): Use a simple Monte Carlo approach to estimate the integral of X^EX inside the disk of radius 1 centered at the origin. N EX Exact Approximate Error 1 2 0.7854 0.0002 7.8524e-01 2 2 0.7854 0.2548 5.3057e-01 4 2 0.7854 0.4500 3.3545e-01 8 2 0.7854 0.7018 8.3616e-02 16 2 0.7854 0.8217 3.6264e-02 32 2 0.7854 0.8383 5.2869e-02 64 2 0.7854 0.8154 3.0019e-02 128 2 0.7854 0.8013 1.5887e-02 256 2 0.7854 0.8047 1.9258e-02 512 2 0.7854 0.7758 9.5515e-03 1024 2 0.7854 0.8018 1.6413e-02 2048 2 0.7854 0.7633 2.2061e-02 4096 2 0.7854 0.7986 1.3207e-02 8192 2 0.7854 0.7734 1.2035e-02 16384 2 0.7854 0.7857 2.8899e-04 32768 2 0.7854 0.7857 3.2654e-04 65536 2 0.7854 0.7848 5.8079e-04 131072 2 0.7854 0.7874 1.9992e-03 262144 2 0.7854 0.7860 6.0256e-04 524288 2 0.7854 0.7847 6.7430e-04 1048576 2 0.7854 0.7854 3.0482e-05 1 4 0.3927 0.1229 2.6984e-01 2 4 0.3927 0.0582 3.3449e-01 4 4 0.3927 0.1829 2.0984e-01 8 4 0.3927 0.2400 1.5273e-01 16 4 0.3927 0.1799 2.1279e-01 32 4 0.3927 0.2255 1.6723e-01 64 4 0.3927 0.4700 7.7309e-02 128 4 0.3927 0.3014 9.1299e-02 256 4 0.3927 0.4167 2.3957e-02 512 4 0.3927 0.3875 5.1819e-03 1024 4 0.3927 0.3900 2.6594e-03 2048 4 0.3927 0.3916 1.0950e-03 4096 4 0.3927 0.3904 2.2832e-03 8192 4 0.3927 0.3892 3.4653e-03 16384 4 0.3927 0.3905 2.2136e-03 32768 4 0.3927 0.3913 1.3851e-03 65536 4 0.3927 0.3927 3.0993e-05 131072 4 0.3927 0.3924 3.4132e-04 262144 4 0.3927 0.3920 7.3743e-04 524288 4 0.3927 0.3923 4.0052e-04 1048576 4 0.3927 0.3927 3.0914e-05 1 6 0.2454 0.0995 1.4597e-01 2 6 0.2454 0.0124 2.3302e-01 4 6 0.2454 0.0393 2.0615e-01 8 6 0.2454 0.2088 3.6654e-02 16 6 0.2454 0.3230 7.7612e-02 32 6 0.2454 0.3136 6.8167e-02 64 6 0.2454 0.1808 6.4682e-02 128 6 0.2454 0.2317 1.3733e-02 256 6 0.2454 0.2732 2.7715e-02 512 6 0.2454 0.2499 4.4773e-03 1024 6 0.2454 0.2465 1.0907e-03 2048 6 0.2454 0.2510 5.5649e-03 4096 6 0.2454 0.2490 3.5277e-03 8192 6 0.2454 0.2500 4.6018e-03 16384 6 0.2454 0.2349 1.0495e-02 32768 6 0.2454 0.2470 1.5585e-03 65536 6 0.2454 0.2437 1.7675e-03 131072 6 0.2454 0.2468 1.3602e-03 262144 6 0.2454 0.2464 9.2201e-04 524288 6 0.2454 0.2459 4.7247e-04 1048576 6 0.2454 0.2459 4.5343e-04 disk01_integrands_test02(): Use a simple Monte Carlo approach to estimate the integral of R^EX over the disk of radius 1 centered at the origin. N E Exact Approximate Error 1 1 2.0944 1.5451 5.4930e-01 2 1 2.0944 2.0805 1.3931e-02 4 1 2.0944 2.6970 6.0259e-01 8 1 2.0944 1.5721 5.2225e-01 16 1 2.0944 1.8949 1.9945e-01 32 1 2.0944 1.9346 1.5982e-01 64 1 2.0944 2.1375 4.3102e-02 128 1 2.0944 2.1759 8.1511e-02 256 1 2.0944 2.0342 6.0241e-02 512 1 2.0944 2.0857 8.6628e-03 1024 1 2.0944 2.0760 1.8355e-02 2048 1 2.0944 2.1130 1.8617e-02 4096 1 2.0944 2.0845 9.8774e-03 8192 1 2.0944 2.0838 1.0605e-02 16384 1 2.0944 2.0929 1.5239e-03 32768 1 2.0944 2.0962 1.7821e-03 65536 1 2.0944 2.0916 2.8149e-03 131072 1 2.0944 2.0962 1.7607e-03 262144 1 2.0944 2.0922 2.1814e-03 524288 1 2.0944 2.0950 6.3703e-04 1048576 1 2.0944 2.0945 1.0693e-04 1 3 1.2566 0.0702 1.1864e+00 2 3 1.2566 1.0675 1.8916e-01 4 3 1.2566 1.4168 1.6019e-01 8 3 1.2566 1.1588 9.7818e-02 16 3 1.2566 0.8670 3.8965e-01 32 3 1.2566 1.3870 1.3035e-01 64 3 1.2566 1.2947 3.8033e-02 128 3 1.2566 1.2405 1.6170e-02 256 3 1.2566 1.3805 1.2384e-01 512 3 1.2566 1.2431 1.3553e-02 1024 3 1.2566 1.2453 1.1316e-02 2048 3 1.2566 1.2849 2.8277e-02 4096 3 1.2566 1.2639 7.2431e-03 8192 3 1.2566 1.2547 1.9240e-03 16384 3 1.2566 1.2610 4.3344e-03 32768 3 1.2566 1.2555 1.1523e-03 65536 3 1.2566 1.2599 3.3115e-03 131072 3 1.2566 1.2510 5.6127e-03 262144 3 1.2566 1.2549 1.7688e-03 524288 3 1.2566 1.2572 5.8232e-04 1048576 3 1.2566 1.2591 2.4213e-03 1 5 0.8976 0.0013 8.9629e-01 2 5 0.8976 1.0127 1.1511e-01 4 5 0.8976 1.2743 3.7670e-01 8 5 0.8976 0.2827 6.1491e-01 16 5 0.8976 0.8079 8.9694e-02 32 5 0.8976 0.9524 5.4798e-02 64 5 0.8976 1.0768 1.7919e-01 128 5 0.8976 0.9274 2.9786e-02 256 5 0.8976 0.8859 1.1685e-02 512 5 0.8976 0.8526 4.4970e-02 1024 5 0.8976 0.8883 9.2881e-03 2048 5 0.8976 0.8564 4.1160e-02 4096 5 0.8976 0.8862 1.1357e-02 8192 5 0.8976 0.8982 6.3447e-04 16384 5 0.8976 0.9106 1.2955e-02 32768 5 0.8976 0.8978 2.3187e-04 65536 5 0.8976 0.8986 1.0239e-03 131072 5 0.8976 0.8984 8.4504e-04 262144 5 0.8976 0.8984 8.1115e-04 524288 5 0.8976 0.8971 4.8103e-04 1048576 5 0.8976 0.8969 7.1978e-04 disk01_integrands_test03(): Use a simple Monte Carlo approach to estimate the integral of exp(X) over the disk of radius 1 centered at the origin. N Exact Approximate Error 1 3.5510 4.1449 5.9385e-01 2 3.5510 3.5313 1.9721e-02 4 3.5510 3.2986 2.5236e-01 8 3.5510 3.7913 2.4026e-01 16 3.5510 2.9705 5.8050e-01 32 3.5510 3.5950 4.3983e-02 64 3.5510 3.5672 1.6170e-02 128 3.5510 3.4367 1.1428e-01 256 3.5510 3.6296 7.8640e-02 512 3.5510 3.5279 2.3144e-02 1024 3.5510 3.5410 9.9592e-03 2048 3.5510 3.5414 9.6450e-03 4096 3.5510 3.5472 3.8070e-03 8192 3.5510 3.5327 1.8280e-02 16384 3.5510 3.5452 5.7979e-03 32768 3.5510 3.5430 7.9510e-03 65536 3.5510 3.5620 1.1033e-02 131072 3.5510 3.5530 2.0263e-03 262144 3.5510 3.5544 3.4170e-03 524288 3.5510 3.5512 2.2527e-04 1048576 3.5510 3.5494 1.6226e-03 disk01_integrands_test(): Normal end of execution. 29-Dec-2022 22:21:00