Home License -- for personal use only. Not for government, academic, research, commercial, or other organizational use. 13-May-2025 13:09:53 disk_integrals_test(): MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7 Test disk_integrals(). disk_integrals_test01(): Estimate monomial integrals using Monte Carlo over the interior of the unit disk in 2D. Disk radius is 2 Number of sample points is 4192 If any exponent is odd, the integral is zero. We will restrict this test to randomly chosen even exponents. Ex Ey MC-Estimate Exact Error 0 0 12.5664 12.5664 1.78e-15 0 2 12.6616 12.5664 9.52e-02 0 4 25.4433 25.1327 3.11e-01 0 6 63.521 62.8319 6.89e-01 0 8 177.424 175.929 1.49e+00 2 0 12.3059 12.5664 2.60e-01 2 2 8.43923 8.37758 6.16e-02 2 4 12.9724 12.5664 4.06e-01 2 6 26.2497 25.1327 1.12e+00 2 8 61.4196 58.6431 2.78e+00 4 0 24.3629 25.1327 7.70e-01 4 2 12.4613 12.5664 1.05e-01 4 4 15.4182 15.0796 3.39e-01 4 6 26.3303 25.1327 1.20e+00 4 8 53.4463 50.2655 3.18e+00 6 0 60.7539 62.8319 2.08e+00 6 2 24.6381 25.1327 4.95e-01 6 4 25.3196 25.1327 1.87e-01 6 6 37.2215 35.9039 1.32e+00 6 8 66.6156 62.8319 3.78e+00 8 0 170.409 175.929 5.52e+00 8 2 57.2042 58.6431 1.44e+00 8 4 50.0656 50.2655 2.00e-01 8 6 64.3054 62.8319 1.47e+00 8 8 102.555 97.7384 4.82e+00 disk_integrals_test01(): Estimate monomial integrals using Monte Carlo over the interior of the unit disk in 2D. Disk radius is 2 Number of sample points is 67072 If any exponent is odd, the integral is zero. We will restrict this test to randomly chosen even exponents. Ex Ey MC-Estimate Exact Error 0 0 12.5664 12.5664 1.78e-15 0 2 12.5863 12.5664 1.99e-02 0 4 25.1093 25.1327 2.35e-02 0 6 62.6905 62.8319 1.41e-01 0 8 175.482 175.929 4.47e-01 2 0 12.6015 12.5664 3.51e-02 2 2 8.46559 8.37758 8.80e-02 2 4 12.6305 12.5664 6.41e-02 2 6 25.1136 25.1327 1.91e-02 2 8 58.3175 58.6431 3.26e-01 4 0 25.1864 25.1327 5.36e-02 4 2 12.7945 12.5664 2.28e-01 4 4 15.3156 15.0796 2.36e-01 4 6 25.3743 25.1327 2.42e-01 4 8 50.3997 50.2655 1.34e-01 6 0 62.7571 62.8319 7.47e-02 6 2 25.6545 25.1327 5.22e-01 6 4 25.7055 25.1327 5.73e-01 6 6 36.6087 35.9039 7.05e-01 6 8 63.6833 62.8319 8.51e-01 8 0 174.959 175.929 9.70e-01 8 2 59.7954 58.6431 1.15e+00 8 4 51.5505 50.2655 1.29e+00 8 6 64.4818 62.8319 1.65e+00 8 8 99.9564 97.7384 2.22e+00 disk_integrals_test(): Normal end of execution. 13-May-2025 13:09:53