disk_integrands_test 19-Apr-2019 09:59:37 disk_integrands_test: MATLAB version Test disk_integrands. disk_integrands_test01 Use a simple Monte Carlo approach to estimate the integral of X^E over the circle of radius 1 centered at the origin. N E Exact Approximate Error 1 2 0.7854 0.6358 1.4962e-01 2 2 0.7854 1.3663 5.8087e-01 4 2 0.7854 1.0196 2.3424e-01 8 2 0.7854 0.8843 9.8867e-02 16 2 0.7854 0.5644 2.2096e-01 32 2 0.7854 0.6681 1.1727e-01 64 2 0.7854 0.6691 1.1631e-01 128 2 0.7854 0.8579 7.2512e-02 256 2 0.7854 0.7583 2.7055e-02 512 2 0.7854 0.8305 4.5077e-02 1024 2 0.7854 0.7848 6.1804e-04 2048 2 0.7854 0.7720 1.3364e-02 4096 2 0.7854 0.7898 4.3850e-03 8192 2 0.7854 0.7868 1.4120e-03 16384 2 0.7854 0.7793 6.0931e-03 32768 2 0.7854 0.7773 8.0715e-03 65536 2 0.7854 0.7823 3.0587e-03 131072 2 0.7854 0.7883 2.9095e-03 262144 2 0.7854 0.7849 5.4647e-04 524288 2 0.7854 0.7838 1.6160e-03 1048576 2 0.7854 0.7845 9.3458e-04 1 4 0.3927 0.1287 2.6403e-01 2 4 0.3927 1.0593 6.6660e-01 4 4 0.3927 0.6114 2.1873e-01 8 4 0.3927 0.4209 2.8170e-02 16 4 0.3927 0.2121 1.8064e-01 32 4 0.3927 0.3412 5.1506e-02 64 4 0.3927 0.2903 1.0236e-01 128 4 0.3927 0.4401 4.7387e-02 256 4 0.3927 0.3890 3.7113e-03 512 4 0.3927 0.4256 3.2912e-02 1024 4 0.3927 0.3961 3.3706e-03 2048 4 0.3927 0.3921 5.9162e-04 4096 4 0.3927 0.3967 4.0431e-03 8192 4 0.3927 0.3945 1.8009e-03 16384 4 0.3927 0.3882 4.5389e-03 32768 4 0.3927 0.3837 8.9951e-03 65536 4 0.3927 0.3897 2.9741e-03 131072 4 0.3927 0.3942 1.5249e-03 262144 4 0.3927 0.3916 1.0822e-03 524288 4 0.3927 0.3913 1.4215e-03 1048576 4 0.3927 0.3918 9.2524e-04 1 6 0.2454 0.0260 2.1940e-01 2 6 0.2454 0.8652 6.1980e-01 4 6 0.2454 0.4355 1.9003e-01 8 6 0.2454 0.2342 1.1198e-02 16 6 0.2454 0.1002 1.4527e-01 32 6 0.2454 0.2151 3.0326e-02 64 6 0.2454 0.1575 8.7911e-02 128 6 0.2454 0.2794 3.3946e-02 256 6 0.2454 0.2487 3.2510e-03 512 6 0.2454 0.2724 2.6957e-02 1024 6 0.2454 0.2477 2.2973e-03 2048 6 0.2454 0.2484 2.9760e-03 4096 6 0.2454 0.2480 2.5142e-03 8192 6 0.2454 0.2469 1.4882e-03 16384 6 0.2454 0.2418 3.6767e-03 32768 6 0.2454 0.2372 8.2618e-03 65536 6 0.2454 0.2429 2.4995e-03 131072 6 0.2454 0.2463 8.6139e-04 262144 6 0.2454 0.2441 1.3438e-03 524288 6 0.2454 0.2442 1.1924e-03 1048576 6 0.2454 0.2446 8.0644e-04 disk_integrands_test02 Use a simple Monte Carlo approach to estimate the integral of R^E over the disk of radius 1 centered at the origin. N E Exact Approximate Error 1 1 2.0944 1.4682 6.2616e-01 2 1 2.0944 2.2702 1.7583e-01 4 1 2.0944 2.4391 3.4466e-01 8 1 2.0944 1.9031 1.9130e-01 16 1 2.0944 1.8081 2.8627e-01 32 1 2.0944 1.8511 2.4333e-01 64 1 2.0944 2.0076 8.6763e-02 128 1 2.0944 2.0655 2.8941e-02 256 1 2.0944 2.0406 5.3807e-02 512 1 2.0944 2.0992 4.8425e-03 1024 1 2.0944 2.0969 2.4875e-03 2048 1 2.0944 2.0838 1.0622e-02 4096 1 2.0944 2.0907 3.7047e-03 8192 1 2.0944 2.0918 2.5538e-03 16384 1 2.0944 2.0842 1.0170e-02 32768 1 2.0944 2.0876 6.7609e-03 65536 1 2.0944 2.0918 2.5786e-03 131072 1 2.0944 2.0909 3.4746e-03 262144 1 2.0944 2.0922 2.1679e-03 524288 1 2.0944 2.0928 1.6368e-03 1048576 1 2.0944 2.0937 6.9466e-04 1 3 1.2566 0.3207 9.3595e-01 2 3 1.2566 1.6293 3.7271e-01 4 3 1.2566 1.7387 4.8203e-01 8 3 1.2566 1.0468 2.0987e-01 16 3 1.2566 1.0049 2.5171e-01 32 3 1.2566 1.0750 1.8159e-01 64 3 1.2566 1.2028 5.3792e-02 128 3 1.2566 1.2677 1.1019e-02 256 3 1.2566 1.2077 4.8919e-02 512 3 1.2566 1.2717 1.5040e-02 1024 3 1.2566 1.2636 7.0042e-03 2048 3 1.2566 1.2464 1.0230e-02 4096 3 1.2566 1.2552 1.4482e-03 8192 3 1.2566 1.2565 1.2546e-04 16384 3 1.2566 1.2447 1.1940e-02 32768 3 1.2566 1.2473 9.3213e-03 65536 3 1.2566 1.2523 4.3187e-03 131072 3 1.2566 1.2518 4.8151e-03 262144 3 1.2566 1.2531 3.5711e-03 524288 3 1.2566 1.2543 2.3196e-03 1048576 3 1.2566 1.2555 1.1260e-03 1 5 0.8976 0.0700 8.2755e-01 2 5 0.8976 1.4399 5.4226e-01 4 5 0.8976 1.3978 5.0024e-01 8 5 0.8976 0.7578 1.3979e-01 16 5 0.8976 0.6972 2.0036e-01 32 5 0.8976 0.7776 1.1995e-01 64 5 0.8976 0.8619 3.5697e-02 128 5 0.8976 0.9254 2.7839e-02 256 5 0.8976 0.8485 4.9143e-02 512 5 0.8976 0.9072 9.5620e-03 1024 5 0.8976 0.9012 3.6239e-03 2048 5 0.8976 0.8885 9.1384e-03 4096 5 0.8976 0.8991 1.4801e-03 8192 5 0.8976 0.8992 1.5564e-03 16384 5 0.8976 0.8865 1.1063e-02 32768 5 0.8976 0.8880 9.5634e-03 65536 5 0.8976 0.8924 5.1640e-03 131072 5 0.8976 0.8925 5.0869e-03 262144 5 0.8976 0.8935 4.0677e-03 524288 5 0.8976 0.8951 2.5097e-03 1048576 5 0.8976 0.8963 1.3068e-03 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 4.9263 1.3753e+00 2 3.5510 2.6002 9.5082e-01 4 3.5510 4.5981 1.0471e+00 8 3.5510 3.5564 5.3735e-03 16 3.5510 4.0237 4.7268e-01 32 3.5510 3.6086 5.7584e-02 64 3.5510 3.6236 7.2605e-02 128 3.5510 3.3051 2.4590e-01 256 3.5510 3.5140 3.7044e-02 512 3.5510 3.5148 3.6160e-02 1024 3.5510 3.5882 3.7169e-02 2048 3.5510 3.6017 5.0727e-02 4096 3.5510 3.5718 2.0827e-02 8192 3.5510 3.5401 1.0858e-02 16384 3.5510 3.5274 2.3568e-02 32768 3.5510 3.5328 1.8161e-02 65536 3.5510 3.5461 4.9253e-03 131072 3.5510 3.5427 8.2794e-03 262144 3.5510 3.5512 1.5888e-04 524288 3.5510 3.5489 2.0620e-03 1048576 3.5510 3.5499 1.1029e-03 disk_integrands_test Normal end of execution. 19-Apr-2019 09:59:39 diary off