Fri Nov 4 10:14:24 2022 disk01_integrands_test(): Python version: 3.6.9 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 0.3687 4.1668e-01 2 2 0.7854 0.1843 6.0106e-01 4 2 0.7854 0.4302 3.5519e-01 8 2 0.7854 0.6667 1.1872e-01 16 2 0.7854 0.7573 2.8065e-02 32 2 0.7854 0.7901 4.6824e-03 64 2 0.7854 0.6752 1.1022e-01 128 2 0.7854 0.9352 1.4976e-01 256 2 0.7854 0.7669 1.8482e-02 512 2 0.7854 0.7292 5.6238e-02 1024 2 0.7854 0.8029 1.7512e-02 2048 2 0.7854 0.8017 1.6320e-02 4096 2 0.7854 0.7848 6.3389e-04 8192 2 0.7854 0.7823 3.1453e-03 16384 2 0.7854 0.7845 8.8598e-04 32768 2 0.7854 0.7910 5.5837e-03 65536 2 0.7854 0.7908 5.3881e-03 131072 2 0.7854 0.7855 5.7760e-05 262144 2 0.7854 0.7840 1.3902e-03 524288 2 0.7854 0.7842 1.1835e-03 1048576 2 0.7854 0.7857 3.2341e-04 1 4 0.3927 3.0462 2.6535e+00 2 4 0.3927 0.2495 1.4324e-01 4 4 0.3927 0.5203 1.2755e-01 8 4 0.3927 0.7771 3.8439e-01 16 4 0.3927 0.7001 3.0739e-01 32 4 0.3927 0.4398 4.7129e-02 64 4 0.3927 0.5054 1.1271e-01 128 4 0.3927 0.4000 7.3035e-03 256 4 0.3927 0.4161 2.3404e-02 512 4 0.3927 0.4196 2.6855e-02 1024 4 0.3927 0.4032 1.0521e-02 2048 4 0.3927 0.4218 2.9097e-02 4096 4 0.3927 0.3880 4.6694e-03 8192 4 0.3927 0.3919 8.3149e-04 16384 4 0.3927 0.3867 5.9709e-03 32768 4 0.3927 0.3885 4.2044e-03 65536 4 0.3927 0.3936 8.5815e-04 131072 4 0.3927 0.3904 2.3121e-03 262144 4 0.3927 0.3926 1.2849e-04 524288 4 0.3927 0.3911 1.6053e-03 1048576 4 0.3927 0.3932 5.3787e-04 1 6 0.2454 0.0062 2.3927e-01 2 6 0.2454 0.2623 1.6903e-02 4 6 0.2454 0.3625 1.1709e-01 8 6 0.2454 0.1289 1.1654e-01 16 6 0.2454 0.1947 5.0746e-02 32 6 0.2454 0.1255 1.1996e-01 64 6 0.2454 0.1719 7.3560e-02 128 6 0.2454 0.2696 2.4198e-02 256 6 0.2454 0.2258 1.9593e-02 512 6 0.2454 0.2378 7.6409e-03 1024 6 0.2454 0.2454 3.9624e-05 2048 6 0.2454 0.2608 1.5333e-02 4096 6 0.2454 0.2375 7.9290e-03 8192 6 0.2454 0.2523 6.8154e-03 16384 6 0.2454 0.2455 4.2701e-05 32768 6 0.2454 0.2502 4.7818e-03 65536 6 0.2454 0.2452 2.0369e-04 131072 6 0.2454 0.2427 2.7609e-03 262144 6 0.2454 0.2460 6.0229e-04 524288 6 0.2454 0.2459 4.9633e-04 1048576 6 0.2454 0.2449 5.8344e-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 2.4531 3.5868e-01 2 1 2.0944 2.0629 3.1521e-02 4 1 2.0944 2.0274 6.7024e-02 8 1 2.0944 1.5821 5.1234e-01 16 1 2.0944 2.4033 3.0888e-01 32 1 2.0944 2.0412 5.3207e-02 64 1 2.0944 2.0539 4.0471e-02 128 1 2.0944 2.1689 7.4544e-02 256 1 2.0944 2.0619 3.2480e-02 512 1 2.0944 2.1479 5.3513e-02 1024 1 2.0944 2.0984 3.9755e-03 2048 1 2.0944 2.1103 1.5905e-02 4096 1 2.0944 2.0851 9.2755e-03 8192 1 2.0944 2.0960 1.6062e-03 16384 1 2.0944 2.0943 1.4343e-04 32768 1 2.0944 2.0996 5.2369e-03 65536 1 2.0944 2.0957 1.3453e-03 131072 1 2.0944 2.0967 2.3546e-03 262144 1 2.0944 2.0955 1.1184e-03 524288 1 2.0944 2.0929 1.5232e-03 1048576 1 2.0944 2.0943 5.6694e-05 1 3 1.2566 2.1029 8.4626e-01 2 3 1.2566 0.6811 5.7551e-01 4 3 1.2566 1.1740 8.2604e-02 8 3 1.2566 1.1571 9.9574e-02 16 3 1.2566 1.8353 5.7867e-01 32 3 1.2566 1.2899 3.3296e-02 64 3 1.2566 1.3012 4.4548e-02 128 3 1.2566 1.2707 1.4058e-02 256 3 1.2566 1.2393 1.7330e-02 512 3 1.2566 1.2597 3.0510e-03 1024 3 1.2566 1.1786 7.8066e-02 2048 3 1.2566 1.2481 8.5279e-03 4096 3 1.2566 1.2415 1.5107e-02 8192 3 1.2566 1.2774 2.0765e-02 16384 3 1.2566 1.2504 6.2586e-03 32768 3 1.2566 1.2618 5.1529e-03 65536 3 1.2566 1.2546 2.0006e-03 131072 3 1.2566 1.2548 1.7890e-03 262144 3 1.2566 1.2556 1.0289e-03 524288 3 1.2566 1.2579 1.2709e-03 1048576 3 1.2566 1.2566 1.1478e-05 1 5 0.8976 1.4289 5.3127e-01 2 5 0.8976 0.4638 4.3378e-01 4 5 0.8976 0.0874 8.1023e-01 8 5 0.8976 0.7378 1.5977e-01 16 5 0.8976 0.8095 8.8073e-02 32 5 0.8976 0.9917 9.4138e-02 64 5 0.8976 0.7754 1.2221e-01 128 5 0.8976 0.7931 1.0445e-01 256 5 0.8976 0.9089 1.1325e-02 512 5 0.8976 0.8613 3.6309e-02 1024 5 0.8976 0.9381 4.0532e-02 2048 5 0.8976 0.9282 3.0593e-02 4096 5 0.8976 0.8820 1.5596e-02 8192 5 0.8976 0.9179 2.0287e-02 16384 5 0.8976 0.8932 4.3598e-03 32768 5 0.8976 0.8985 8.9302e-04 65536 5 0.8976 0.9017 4.1082e-03 131072 5 0.8976 0.9005 2.9475e-03 262144 5 0.8976 0.8946 3.0155e-03 524288 5 0.8976 0.8973 3.0036e-04 1048576 5 0.8976 0.8986 9.9420e-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 4.0874 5.3637e-01 2 3.5510 2.2369 1.3141e+00 4 3.5510 2.4997 1.0513e+00 8 3.5510 3.3845 1.6650e-01 16 3.5510 3.2862 2.6479e-01 32 3.5510 3.7570 2.0604e-01 64 3.5510 3.3953 1.5571e-01 128 3.5510 3.6854 1.3443e-01 256 3.5510 3.2600 2.9096e-01 512 3.5510 3.6371 8.6062e-02 1024 3.5510 3.6133 6.2326e-02 2048 3.5510 3.5538 2.7930e-03 4096 3.5510 3.5632 1.2249e-02 8192 3.5510 3.5749 2.3876e-02 16384 3.5510 3.5585 7.4722e-03 32768 3.5510 3.5645 1.3492e-02 65536 3.5510 3.5522 1.2232e-03 131072 3.5510 3.5434 7.5905e-03 262144 3.5510 3.5484 2.6022e-03 524288 3.5510 3.5506 3.7242e-04 1048576 3.5510 3.5487 2.2616e-03 disk01_integrands_test(): Normal end of execution. Fri Nov 4 10:14:25 2022