14-May-2025 15:53:14 disk_integrals_test(): MATLAB/Octave version 6.4.0 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 12.3944 12.5664 1.72e-01 0 4 24.7268 25.1327 4.06e-01 0 6 61.9686 62.8319 8.63e-01 0 8 174.274 175.929 1.66e+00 2 0 12.6915 12.5664 1.25e-01 2 2 8.4354 8.37758 5.78e-02 2 4 12.5595 12.5664 6.82e-03 2 6 25.0448 25.1327 8.80e-02 2 8 58.6349 58.6431 8.17e-03 4 0 25.3859 25.1327 2.53e-01 4 2 12.669 12.5664 1.03e-01 4 4 15.0485 15.0796 3.11e-02 4 6 24.8057 25.1327 3.27e-01 4 8 49.359 50.2655 9.07e-01 6 0 63.674 62.8319 8.42e-01 6 2 25.3983 25.1327 2.66e-01 6 4 25.1246 25.1327 8.14e-03 6 6 35.2789 35.9039 6.25e-01 6 8 60.8871 62.8319 1.94e+00 8 0 179.518 175.929 3.59e+00 8 2 59.586 58.6431 9.43e-01 8 4 50.5525 50.2655 2.87e-01 8 6 61.859 62.8319 9.73e-01 8 8 94.2433 97.7384 3.50e+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 12.5455 12.5664 2.09e-02 0 4 25.055 25.1327 7.77e-02 0 6 62.6088 62.8319 2.23e-01 0 8 175.375 175.929 5.54e-01 2 0 12.6277 12.5664 6.14e-02 2 2 8.36526 8.37758 1.23e-02 2 4 12.4842 12.5664 8.22e-02 2 6 24.8879 25.1327 2.45e-01 2 8 57.9694 58.6431 6.74e-01 4 0 25.346 25.1327 2.13e-01 4 2 12.5669 12.5664 5.57e-04 4 4 14.9817 15.0796 9.79e-02 4 6 24.8567 25.1327 2.76e-01 4 8 49.5474 50.2655 7.18e-01 6 0 63.5086 62.8319 6.77e-01 6 2 25.1626 25.1327 2.99e-02 6 4 24.9839 25.1327 1.49e-01 6 6 35.5276 35.9039 3.76e-01 6 8 61.9416 62.8319 8.90e-01 8 0 178.12 175.929 2.19e+00 8 2 58.7566 58.6431 1.14e-01 8 4 49.9729 50.2655 2.93e-01 8 6 62.1906 62.8319 6.41e-01 8 8 96.4073 97.7384 1.33e+00 disk_integrals_test(): Normal end of execution. 14-May-2025 15:53:15