Tue May 20 21:35:03 2025 disk01_integrands_test(): python version: 3.10.12 numpy version: 1.26.4 Test disk01_integrands(). disk01_integrands_test00(): 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 0 3.1416 3.1416 0.0000e+00 2 0 3.1416 3.1416 0.0000e+00 4 0 3.1416 3.1416 0.0000e+00 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 0.3994 3.8595e-01 2 2 0.7854 1.8297 1.0443e+00 4 2 0.7854 1.1020 3.1656e-01 8 2 0.7854 0.9237 1.3828e-01 16 2 0.7854 0.8413 5.5944e-02 32 2 0.7854 0.8116 2.6192e-02 64 2 0.7854 0.6725 1.1287e-01 128 2 0.7854 0.8381 5.2674e-02 256 2 0.7854 0.8990 1.1356e-01 512 2 0.7854 0.8209 3.5546e-02 1024 2 0.7854 0.8073 2.1862e-02 2048 2 0.7854 0.7933 7.9324e-03 4096 2 0.7854 0.7874 1.9598e-03 8192 2 0.7854 0.7900 4.6081e-03 16384 2 0.7854 0.7791 6.2983e-03 32768 2 0.7854 0.7910 5.5928e-03 65536 2 0.7854 0.7894 3.9584e-03 131072 2 0.7854 0.7868 1.3905e-03 262144 2 0.7854 0.7868 1.4496e-03 524288 2 0.7854 0.7861 6.6650e-04 1048576 2 0.7854 0.7869 1.5180e-03 1 4 0.3927 0.5278 1.3509e-01 2 4 0.3927 0.8785 4.8579e-01 4 4 0.3927 0.2063 1.8640e-01 8 4 0.3927 0.2888 1.0392e-01 16 4 0.3927 0.4153 2.2558e-02 32 4 0.3927 0.4162 2.3526e-02 64 4 0.3927 0.3476 4.5097e-02 128 4 0.3927 0.4284 3.5664e-02 256 4 0.3927 0.4970 1.0432e-01 512 4 0.3927 0.3897 3.0471e-03 1024 4 0.3927 0.3845 8.1682e-03 2048 4 0.3927 0.4022 9.5304e-03 4096 4 0.3927 0.3881 4.6418e-03 8192 4 0.3927 0.3937 1.0402e-03 16384 4 0.3927 0.3921 5.9749e-04 32768 4 0.3927 0.3846 8.1150e-03 65536 4 0.3927 0.3868 5.8538e-03 131072 4 0.3927 0.3901 2.5652e-03 262144 4 0.3927 0.3924 2.8629e-04 524288 4 0.3927 0.3940 1.3266e-03 1048576 4 0.3927 0.3921 5.7556e-04 1 6 0.2454 0.1037 1.4171e-01 2 6 0.2454 1.0780 8.3255e-01 4 6 0.2454 0.2363 9.0989e-03 8 6 0.2454 0.4161 1.7070e-01 16 6 0.2454 0.4193 1.7391e-01 32 6 0.2454 0.2761 3.0687e-02 64 6 0.2454 0.2777 3.2278e-02 128 6 0.2454 0.2124 3.3040e-02 256 6 0.2454 0.2706 2.5203e-02 512 6 0.2454 0.2885 4.3094e-02 1024 6 0.2454 0.2530 7.5997e-03 2048 6 0.2454 0.2341 1.1381e-02 4096 6 0.2454 0.2524 6.9393e-03 8192 6 0.2454 0.2496 4.1143e-03 16384 6 0.2454 0.2450 4.2876e-04 32768 6 0.2454 0.2498 4.3714e-03 65536 6 0.2454 0.2470 1.5532e-03 131072 6 0.2454 0.2432 2.2232e-03 262144 6 0.2454 0.2454 5.2460e-05 524288 6 0.2454 0.2446 8.8252e-04 1048576 6 0.2454 0.2462 7.5964e-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 EX Exact Approximate Error 1 1 2.0944 1.3195 7.7486e-01 2 1 2.0944 1.0994 9.9501e-01 4 1 2.0944 2.5731 4.7871e-01 8 1 2.0944 2.3048 2.1036e-01 16 1 2.0944 2.0140 8.0404e-02 32 1 2.0944 2.2446 1.5017e-01 64 1 2.0944 1.9119 1.8246e-01 128 1 2.0944 2.2197 1.2528e-01 256 1 2.0944 2.0783 1.6054e-02 512 1 2.0944 2.0808 1.3589e-02 1024 1 2.0944 2.0489 4.5462e-02 2048 1 2.0944 2.0885 5.8836e-03 4096 1 2.0944 2.1097 1.5300e-02 8192 1 2.0944 2.0942 1.7179e-04 16384 1 2.0944 2.0892 5.1752e-03 32768 1 2.0944 2.0960 1.6256e-03 65536 1 2.0944 2.0947 2.7448e-04 131072 1 2.0944 2.0961 1.6762e-03 262144 1 2.0944 2.0963 1.9093e-03 524288 1 2.0944 2.0955 1.1177e-03 1048576 1 2.0944 2.0943 7.0302e-05 1 3 1.2566 0.0163 1.2403e+00 2 3 1.2566 0.3795 8.7713e-01 4 3 1.2566 0.4538 8.0281e-01 8 3 1.2566 1.4221 1.6541e-01 16 3 1.2566 1.2509 5.7180e-03 32 3 1.2566 1.2237 3.2942e-02 64 3 1.2566 1.2327 2.3912e-02 128 3 1.2566 1.2718 1.5186e-02 256 3 1.2566 1.2300 2.6640e-02 512 3 1.2566 1.2638 7.1238e-03 1024 3 1.2566 1.2240 3.2656e-02 2048 3 1.2566 1.2949 3.8257e-02 4096 3 1.2566 1.2765 1.9825e-02 8192 3 1.2566 1.2657 9.0460e-03 16384 3 1.2566 1.2559 7.1531e-04 32768 3 1.2566 1.2511 5.5742e-03 65536 3 1.2566 1.2527 3.9517e-03 131072 3 1.2566 1.2597 3.0568e-03 262144 3 1.2566 1.2569 2.2543e-04 524288 3 1.2566 1.2547 1.9624e-03 1048576 3 1.2566 1.2559 7.0503e-04 1 5 0.8976 0.0375 8.6010e-01 2 5 0.8976 0.6486 2.4895e-01 4 5 0.8976 0.6378 2.5979e-01 8 5 0.8976 0.8951 2.4530e-03 16 5 0.8976 0.9234 2.5836e-02 32 5 0.8976 0.7570 1.4061e-01 64 5 0.8976 0.7592 1.3836e-01 128 5 0.8976 0.8491 4.8546e-02 256 5 0.8976 0.8079 8.9655e-02 512 5 0.8976 0.9217 2.4093e-02 1024 5 0.8976 0.8956 1.9629e-03 2048 5 0.8976 0.8957 1.8657e-03 4096 5 0.8976 0.9288 3.1161e-02 8192 5 0.8976 0.8889 8.7304e-03 16384 5 0.8976 0.8879 9.6913e-03 32768 5 0.8976 0.9054 7.7721e-03 65536 5 0.8976 0.8928 4.8204e-03 131072 5 0.8976 0.9018 4.2204e-03 262144 5 0.8976 0.9003 2.6986e-03 524288 5 0.8976 0.8983 7.2950e-04 1048576 5 0.8976 0.8974 2.1175e-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 1.6759 1.8751e+00 2 3.5510 5.0649 1.5139e+00 4 3.5510 4.3993 8.4833e-01 8 3.5510 4.4682 9.1724e-01 16 3.5510 4.2126 6.6158e-01 32 3.5510 3.2112 3.3976e-01 64 3.5510 3.2771 2.7389e-01 128 3.5510 3.5708 1.9798e-02 256 3.5510 3.4763 7.4668e-02 512 3.5510 3.5130 3.7996e-02 1024 3.5510 3.5749 2.3884e-02 2048 3.5510 3.5892 3.8239e-02 4096 3.5510 3.5612 1.0231e-02 8192 3.5510 3.5619 1.0891e-02 16384 3.5510 3.5479 3.1389e-03 32768 3.5510 3.5520 9.6694e-04 65536 3.5510 3.5665 1.5501e-02 131072 3.5510 3.5472 3.8467e-03 262144 3.5510 3.5480 2.9755e-03 524288 3.5510 3.5520 9.8411e-04 1048576 3.5510 3.5507 3.0625e-04 disk01_integrands_test(): Normal end of execution. Tue May 20 21:35:04 2025