Tue Oct 11 19:57:31 2022 disk_integrands_test(): Python version: 3.6.9 Test disk_integrands(). disk_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 0.0012 7.8422e-01 2 2 0.7854 0.4399 3.4549e-01 4 2 0.7854 0.4766 3.0882e-01 8 2 0.7854 0.4103 3.7507e-01 16 2 0.7854 0.5182 2.6717e-01 32 2 0.7854 0.8983 1.1291e-01 64 2 0.7854 0.8757 9.0274e-02 128 2 0.7854 0.9204 1.3500e-01 256 2 0.7854 0.7010 8.4350e-02 512 2 0.7854 0.8305 4.5057e-02 1024 2 0.7854 0.7443 4.1063e-02 2048 2 0.7854 0.8087 2.3350e-02 4096 2 0.7854 0.8023 1.6858e-02 8192 2 0.7854 0.8029 1.7526e-02 16384 2 0.7854 0.7854 3.5290e-05 32768 2 0.7854 0.7833 2.0877e-03 65536 2 0.7854 0.7848 5.8938e-04 131072 2 0.7854 0.7878 2.4318e-03 262144 2 0.7854 0.7829 2.4766e-03 524288 2 0.7854 0.7866 1.1540e-03 1048576 2 0.7854 0.7850 4.4563e-04 1 4 0.3927 1.0307 6.3803e-01 2 4 0.3927 0.1081 2.8456e-01 4 4 0.3927 0.3752 1.7546e-02 8 4 0.3927 0.0669 3.2578e-01 16 4 0.3927 0.6583 2.6563e-01 32 4 0.3927 0.5302 1.3751e-01 64 4 0.3927 0.3812 1.1535e-02 128 4 0.3927 0.4263 3.3587e-02 256 4 0.3927 0.3583 3.4392e-02 512 4 0.3927 0.3789 1.3774e-02 1024 4 0.3927 0.4455 5.2822e-02 2048 4 0.3927 0.3808 1.1927e-02 4096 4 0.3927 0.3976 4.8554e-03 8192 4 0.3927 0.3887 4.0079e-03 16384 4 0.3927 0.3916 1.1218e-03 32768 4 0.3927 0.3945 1.8387e-03 65536 4 0.3927 0.3867 6.0311e-03 131072 4 0.3927 0.3931 4.0147e-04 262144 4 0.3927 0.3926 6.4275e-05 524288 4 0.3927 0.3915 1.1920e-03 1048576 4 0.3927 0.3922 4.8306e-04 1 6 0.2454 1.3961 1.1506e+00 2 6 0.2454 0.4792 2.3378e-01 4 6 0.2454 0.0827 1.6271e-01 8 6 0.2454 0.2490 3.5631e-03 16 6 0.2454 0.2809 3.5478e-02 32 6 0.2454 0.2771 3.1674e-02 64 6 0.2454 0.1741 7.1336e-02 128 6 0.2454 0.3192 7.3791e-02 256 6 0.2454 0.2274 1.8032e-02 512 6 0.2454 0.2322 1.3199e-02 1024 6 0.2454 0.2636 1.8201e-02 2048 6 0.2454 0.2439 1.5042e-03 4096 6 0.2454 0.2429 2.5019e-03 8192 6 0.2454 0.2455 1.0301e-04 16384 6 0.2454 0.2425 2.9204e-03 32768 6 0.2454 0.2470 1.5560e-03 65536 6 0.2454 0.2479 2.4441e-03 131072 6 0.2454 0.2464 9.1784e-04 262144 6 0.2454 0.2447 7.0424e-04 524288 6 0.2454 0.2456 1.5881e-04 1048576 6 0.2454 0.2450 3.9413e-04 disk_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 1.8961 1.9826e-01 2 1 2.0944 2.6100 5.1558e-01 4 1 2.0944 2.4787 3.8434e-01 8 1 2.0944 2.2772 1.8284e-01 16 1 2.0944 1.9487 1.4567e-01 32 1 2.0944 2.1752 8.0819e-02 64 1 2.0944 2.1085 1.4147e-02 128 1 2.0944 2.0352 5.9173e-02 256 1 2.0944 2.1427 4.8257e-02 512 1 2.0944 2.0466 4.7783e-02 1024 1 2.0944 2.0769 1.7448e-02 2048 1 2.0944 2.1064 1.2033e-02 4096 1 2.0944 2.0852 9.2285e-03 8192 1 2.0944 2.0915 2.9319e-03 16384 1 2.0944 2.0959 1.5161e-03 32768 1 2.0944 2.1017 7.2699e-03 65536 1 2.0944 2.0948 3.7640e-04 131072 1 2.0944 2.0890 5.4175e-03 262144 1 2.0944 2.0966 2.2469e-03 524288 1 2.0944 2.0973 2.8989e-03 1048576 1 2.0944 2.0942 2.2134e-04 1 3 1.2566 0.1178 1.1389e+00 2 3 1.2566 2.2889 1.0323e+00 4 3 1.2566 0.7418 5.1485e-01 8 3 1.2566 1.4755 2.1884e-01 16 3 1.2566 1.3275 7.0906e-02 32 3 1.2566 1.3308 7.4211e-02 64 3 1.2566 1.1331 1.2352e-01 128 3 1.2566 1.1384 1.1819e-01 256 3 1.2566 1.2511 5.5274e-03 512 3 1.2566 1.3035 4.6888e-02 1024 3 1.2566 1.2460 1.0629e-02 2048 3 1.2566 1.2841 2.7441e-02 4096 3 1.2566 1.2452 1.1465e-02 8192 3 1.2566 1.2659 9.2950e-03 16384 3 1.2566 1.2577 1.1106e-03 32768 3 1.2566 1.2565 1.0774e-04 65536 3 1.2566 1.2601 3.4210e-03 131072 3 1.2566 1.2530 3.6180e-03 262144 3 1.2566 1.2549 1.6973e-03 524288 3 1.2566 1.2564 2.2961e-04 1048576 3 1.2566 1.2563 3.1448e-04 1 5 0.8976 1.3651 4.6755e-01 2 5 0.8976 0.6130 2.8457e-01 4 5 0.8976 0.4827 4.1493e-01 8 5 0.8976 1.1779 2.8028e-01 16 5 0.8976 1.0348 1.3720e-01 32 5 0.8976 0.7281 1.6949e-01 64 5 0.8976 0.9016 3.9558e-03 128 5 0.8976 0.9812 8.3623e-02 256 5 0.8976 0.9499 5.2317e-02 512 5 0.8976 0.8736 2.3969e-02 1024 5 0.8976 0.9132 1.5563e-02 2048 5 0.8976 0.9154 1.7760e-02 4096 5 0.8976 0.8829 1.4652e-02 8192 5 0.8976 0.8855 1.2056e-02 16384 5 0.8976 0.8846 1.3015e-02 32768 5 0.8976 0.8961 1.5422e-03 65536 5 0.8976 0.8964 1.2156e-03 131072 5 0.8976 0.8954 2.2364e-03 262144 5 0.8976 0.9005 2.8686e-03 524288 5 0.8976 0.8978 1.6466e-04 1048576 5 0.8976 0.8971 5.0633e-04 disk_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 7.4683 3.9173e+00 2 3.5510 2.4269 1.1241e+00 4 3.5510 3.5122 3.8840e-02 8 3.5510 5.1114 1.5604e+00 16 3.5510 3.5808 2.9825e-02 32 3.5510 3.9326 3.8160e-01 64 3.5510 3.2772 2.7378e-01 128 3.5510 3.6731 1.2214e-01 256 3.5510 3.4507 1.0026e-01 512 3.5510 3.6073 5.6259e-02 1024 3.5510 3.6444 9.3430e-02 2048 3.5510 3.6026 5.1629e-02 4096 3.5510 3.5113 3.9735e-02 8192 3.5510 3.5655 1.4526e-02 16384 3.5510 3.5487 2.2995e-03 32768 3.5510 3.5377 1.3274e-02 65536 3.5510 3.5547 3.6818e-03 131072 3.5510 3.5527 1.7167e-03 262144 3.5510 3.5494 1.5626e-03 524288 3.5510 3.5474 3.5984e-03 1048576 3.5510 3.5535 2.5257e-03 disk_integrands_test(): Normal end of execution. Tue Oct 11 19:57:32 2022