29-Jul-2021 16:19:57 square_integrals_test(): MATLAB/Octave version 9.9.0.1467703 (R2020b) Test square_integrals(). SQUARE01_MONOMIAL_INTEGRAL_TEST SQUARE01_MONOMIAL_INTEGRAL reports the integral of a monomial over the unit square. Compare exact and estimated integrals over the interior of the unit square in 2D. Number of sample points used is 4192 Ex Ey MC-Estimate Exact Error 0 0 1 1 0.00e+00 1 1 0.250518 0.25 5.18e-04 4 4 0.0395067 0.04 4.93e-04 3 1 0.12377 0.125 1.23e-03 5 0 0.162365 0.166667 4.30e-03 6 1 0.0696073 0.0714286 1.82e-03 6 3 0.034845 0.0357143 8.69e-04 0 7 0.124939 0.125 6.07e-05 2 7 0.0419597 0.0416667 2.93e-04 4 4 0.0395067 0.04 4.93e-04 6 2 0.0464663 0.047619 1.15e-03 5 1 0.0816061 0.0833333 1.73e-03 4 0 0.195557 0.2 4.44e-03 2 3 0.0832931 0.0833333 4.02e-05 3 2 0.082733 0.0833333 6.00e-04 4 2 0.0657738 0.0666667 8.93e-04 5 7 0.0206775 0.0208333 1.56e-04 2 4 0.0666707 0.0666667 4.04e-06 6 1 0.0696073 0.0714286 1.82e-03 5 3 0.0408713 0.0416667 7.95e-04 SQUARESYM_MONOMIAL_INTEGRAL_TEST SQUARESYM_MONOMIAL_INTEGRAL reports the integral of a monomial over the symmetric unit square. Compare exact and estimated integrals over the interior of the symmetric unit square in 2D. Number of sample points used is 4192 Ex Ey MC-Estimate Exact Error 0 6 0.562318 0.571429 9.11e-03 5 0 -0.0279524 0 2.80e-02 0 0 4 4 0.00e+00 1 3 0.0164293 0 1.64e-02 2 6 0.188225 0.190476 2.25e-03 4 4 0.160378 0.16 3.78e-04 1 6 -0.0179502 0 1.80e-02 6 5 -0.00384083 0 3.84e-03 5 5 0.00653193 0 6.53e-03 6 4 0.116003 0.114286 1.72e-03 1 0 -0.0148145 0 1.48e-02 1 1 0.0364771 0 3.65e-02 6 1 -0.00780515 0 7.81e-03 2 2 0.444139 0.444444 3.05e-04 3 3 0.0117177 0 1.17e-02 5 5 0.00653193 0 6.53e-03 5 4 -0.0156381 0 1.56e-02 6 2 0.194792 0.190476 4.32e-03 5 7 0.00460055 0 4.60e-03 5 7 0.00460055 0 4.60e-03 square_integrals_test(): Normal end of execution. 29-Jul-2021 16:19:57