Wed Oct 8 07:43:41 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 3.0204 2.2350e+00 2 2 0.7854 0.0277 7.5770e-01 4 2 0.7854 0.3911 3.9427e-01 8 2 0.7854 0.9736 1.8819e-01 16 2 0.7854 0.9414 1.5597e-01 32 2 0.7854 0.8154 2.9969e-02 64 2 0.7854 0.6823 1.0309e-01 128 2 0.7854 0.7104 7.4990e-02 256 2 0.7854 0.7735 1.1932e-02 512 2 0.7854 0.8422 5.6794e-02 1024 2 0.7854 0.7644 2.0995e-02 2048 2 0.7854 0.8054 2.0010e-02 4096 2 0.7854 0.7880 2.5786e-03 8192 2 0.7854 0.7818 3.5631e-03 16384 2 0.7854 0.7842 1.2331e-03 32768 2 0.7854 0.7853 1.1663e-04 65536 2 0.7854 0.7826 2.8119e-03 131072 2 0.7854 0.7845 8.8468e-04 262144 2 0.7854 0.7876 2.2484e-03 524288 2 0.7854 0.7852 1.5469e-04 1048576 2 0.7854 0.7859 4.5801e-04 1 4 0.3927 0.0041 3.8856e-01 2 4 0.3927 0.0167 3.7595e-01 4 4 0.3927 0.1903 2.0237e-01 8 4 0.3927 0.2486 1.4406e-01 16 4 0.3927 0.1893 2.0341e-01 32 4 0.3927 0.5107 1.1805e-01 64 4 0.3927 0.5252 1.3249e-01 128 4 0.3927 0.4305 3.7767e-02 256 4 0.3927 0.3066 8.6082e-02 512 4 0.3927 0.3491 4.3568e-02 1024 4 0.3927 0.3697 2.3001e-02 2048 4 0.3927 0.4253 3.2648e-02 4096 4 0.3927 0.4102 1.7491e-02 8192 4 0.3927 0.3986 5.9034e-03 16384 4 0.3927 0.3951 2.4052e-03 32768 4 0.3927 0.3942 1.5123e-03 65536 4 0.3927 0.3918 8.8664e-04 131072 4 0.3927 0.3963 3.5914e-03 262144 4 0.3927 0.3940 1.2648e-03 524288 4 0.3927 0.3929 2.2191e-04 1048576 4 0.3927 0.3917 1.0322e-03 1 6 0.2454 0.2104 3.5085e-02 2 6 0.2454 0.0880 1.5748e-01 4 6 0.2454 0.0640 1.8141e-01 8 6 0.2454 0.0310 2.1440e-01 16 6 0.2454 0.0781 1.6731e-01 32 6 0.2454 0.3892 1.4379e-01 64 6 0.2454 0.2562 1.0768e-02 128 6 0.2454 0.2537 8.2359e-03 256 6 0.2454 0.1757 6.9754e-02 512 6 0.2454 0.2801 3.4672e-02 1024 6 0.2454 0.2712 2.5772e-02 2048 6 0.2454 0.2516 6.1390e-03 4096 6 0.2454 0.2437 1.7136e-03 8192 6 0.2454 0.2478 2.3996e-03 16384 6 0.2454 0.2467 1.3044e-03 32768 6 0.2454 0.2447 7.7820e-04 65536 6 0.2454 0.2448 6.5718e-04 131072 6 0.2454 0.2446 8.0864e-04 262144 6 0.2454 0.2448 6.4442e-04 524288 6 0.2454 0.2447 7.0575e-04 1048576 6 0.2454 0.2453 1.4433e-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 2.6296 5.3517e-01 2 1 2.0944 2.0573 3.7111e-02 4 1 2.0944 2.3759 2.8152e-01 8 1 2.0944 2.0080 8.6387e-02 16 1 2.0944 2.1637 6.9338e-02 32 1 2.0944 2.0809 1.3539e-02 64 1 2.0944 2.2481 1.5369e-01 128 1 2.0944 2.0681 2.6341e-02 256 1 2.0944 2.1149 2.0530e-02 512 1 2.0944 2.1005 6.1484e-03 1024 1 2.0944 2.0915 2.9166e-03 2048 1 2.0944 2.0860 8.3969e-03 4096 1 2.0944 2.0815 1.2909e-02 8192 1 2.0944 2.0777 1.6740e-02 16384 1 2.0944 2.0942 1.6329e-04 32768 1 2.0944 2.0896 4.8132e-03 65536 1 2.0944 2.0938 6.1105e-04 131072 1 2.0944 2.0928 1.6407e-03 262144 1 2.0944 2.0989 4.5331e-03 524288 1 2.0944 2.0956 1.1841e-03 1048576 1 2.0944 2.0947 3.4612e-04 1 3 1.2566 0.3779 8.7869e-01 2 3 1.2566 1.5346 2.7801e-01 4 3 1.2566 1.6763 4.1965e-01 8 3 1.2566 0.6977 5.5891e-01 16 3 1.2566 1.5118 2.5519e-01 32 3 1.2566 1.1860 7.0634e-02 64 3 1.2566 1.2730 1.6330e-02 128 3 1.2566 1.3249 6.8230e-02 256 3 1.2566 1.3773 1.2067e-01 512 3 1.2566 1.2259 3.0765e-02 1024 3 1.2566 1.2874 3.0807e-02 2048 3 1.2566 1.2327 2.3911e-02 4096 3 1.2566 1.2619 5.2930e-03 8192 3 1.2566 1.2749 1.8230e-02 16384 3 1.2566 1.2547 1.9107e-03 32768 3 1.2566 1.2555 1.1503e-03 65536 3 1.2566 1.2585 1.9095e-03 131072 3 1.2566 1.2599 3.2644e-03 262144 3 1.2566 1.2547 1.9050e-03 524288 3 1.2566 1.2582 1.5332e-03 1048576 3 1.2566 1.2567 2.8070e-05 1 5 0.8976 2.4579 1.5603e+00 2 5 0.8976 0.2436 6.5400e-01 4 5 0.8976 0.4301 4.6748e-01 8 5 0.8976 0.6795 2.1807e-01 16 5 0.8976 0.8990 1.4394e-03 32 5 0.8976 0.6767 2.2093e-01 64 5 0.8976 0.9933 9.5736e-02 128 5 0.8976 0.7973 1.0026e-01 256 5 0.8976 0.9060 8.3824e-03 512 5 0.8976 0.8583 3.9340e-02 1024 5 0.8976 0.8881 9.5322e-03 2048 5 0.8976 0.8672 3.0364e-02 4096 5 0.8976 0.8739 2.3738e-02 8192 5 0.8976 0.8856 1.1954e-02 16384 5 0.8976 0.9019 4.2736e-03 32768 5 0.8976 0.8969 6.8447e-04 65536 5 0.8976 0.9007 3.1264e-03 131072 5 0.8976 0.8960 1.5700e-03 262144 5 0.8976 0.8959 1.7224e-03 524288 5 0.8976 0.8963 1.3154e-03 1048576 5 0.8976 0.8972 3.9819e-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 1.7912 1.7598e+00 2 3.5510 4.6705 1.1195e+00 4 3.5510 3.4640 8.6967e-02 8 3.5510 2.6418 9.0925e-01 16 3.5510 3.6799 1.2891e-01 32 3.5510 3.6533 1.0234e-01 64 3.5510 3.4676 8.3370e-02 128 3.5510 3.7100 1.5898e-01 256 3.5510 3.4544 9.6639e-02 512 3.5510 3.4683 8.2738e-02 1024 3.5510 3.5763 2.5347e-02 2048 3.5510 3.5729 2.1868e-02 4096 3.5510 3.5088 4.2249e-02 8192 3.5510 3.5871 3.6103e-02 16384 3.5510 3.5378 1.3206e-02 32768 3.5510 3.5491 1.9394e-03 65536 3.5510 3.5564 5.4210e-03 131072 3.5510 3.5585 7.5244e-03 262144 3.5510 3.5508 1.7022e-04 524288 3.5510 3.5490 2.0004e-03 1048576 3.5510 3.5511 1.3338e-04 disk01_integrands_test(): Normal end of execution. Wed Oct 8 07:43:42 2025