07-Jan-2022 19:16:02 ellipse_monte_carlo_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test ELLIPSE_MONTE_CARLO(). ELLIPSE_AREA1_TEST ELLIPSE_AREA1 computes the area of an ellipse. R = 10 Matrix A in ellipse definition x*A*x=r^2 Col: 1 2 Row 1 : 5 1 2 : 1 2 Area = 104.72 ELLIPSE_AREA1_TEST Normal end of execution. ELLIPSE_AREA2_TEST ELLIPSE_AREA2 computes the area of an ellipse. Ellipse: 5 * x^2 + 2 * xy + 2 * y^2 = 10 Area = 104.72 ELLIPSE_AREA2_TEST Normal end of execution. ellipse_monte_carlo_test01(): Use ELLIPSE01_SAMPLE to estimate integrals in the ellipse x' * A * x <= r^2. N 1 X Y X^2 XY Y^2 X^3 1 2.1241 0.0071697 0.361385 2.42006e-05 0.00121982 0.0614843 8.16868e-08 2 2.1241 -0.158656 0.419339 0.0508271 -0.0769157 0.13612 -0.00961901 4 2.1241 0.198683 -0.164009 0.0688399 -0.0117255 0.1035 0.00937666 8 2.1241 -0.0309805 -0.0400103 0.0284909 -0.0390769 0.201429 -0.00260555 16 2.1241 -0.0395731 0.0269707 0.0348913 -0.012789 0.125329 -0.000532494 32 2.1241 -0.0147526 -0.0401729 0.0321129 -0.0362544 0.142571 0.000829042 64 2.1241 -0.0594489 0.025608 0.0282135 -0.0205013 0.147672 -0.0019236 128 2.1241 -0.00463452 -0.0144758 0.0327859 -0.0158738 0.125436 0.000640402 256 2.1241 0.00748272 0.0261459 0.028039 -0.0288348 0.157206 0.000165603 512 2.1241 -0.00135406 0.00874308 0.0302541 -0.023288 0.145532 -0.000205052 1024 2.1241 0.00311187 -0.006573 0.0293315 -0.0215144 0.139812 0.000110314 2048 2.1241 -0.000773975 0.0227805 0.0270963 -0.0203142 0.141704 3.76982e-05 4096 2.1241 0.00111607 0.00257545 0.0289795 -0.0218403 0.144805 0.000119649 8192 2.1241 0.00263684 -0.00778273 0.0299835 -0.0226374 0.140742 4.53299e-05 16384 2.1241 -0.0010917 0.00206759 0.0296011 -0.0227181 0.142259 -3.32389e-05 32768 2.1241 -0.00135252 0.00508284 0.0295386 -0.0223628 0.141757 -3.57709e-05 65536 2.1241 -0.000154078 -0.00344291 0.0294088 -0.0227947 0.142942 4.59301e-06 ELLIPSE_MONTE_CARLO_TEST Normal end of execution. 07-Jan-2022 19:16:04