Wed Oct 8 08:56:23 2025 square_integrals_test(): python version: 3.10.12 numpy version: 1.26.4 Test square_integrals(). square01_area_test(): square01_area returns the area of the unit square. square01_area() = 1 square01_monomial_integral_test(): square01_monomial_integral() returns the integral of a monomial over the interior of the unit square in 2D. Compare with a Monte Carlo estimate. Number of sample points used is 4192 Ex Ey MC-Estimate Exact Error 3 7 0.0298284 0.03125 0.0014 4 5 0.0320057 0.0333333 0.0013 4 3 0.0485156 0.05 0.0015 0 2 0.327151 0.333333 0.0062 4 4 0.0386073 0.04 0.0014 2 0 0.328116 0.333333 0.0052 5 2 0.0541406 0.0555556 0.0014 7 2 0.0405028 0.0416667 0.0012 7 3 0.0301591 0.03125 0.0011 5 3 0.0403759 0.0416667 0.0013 5 5 0.0265863 0.0277778 0.0012 4 4 0.0386073 0.04 0.0014 3 0 0.24596 0.25 0.004 7 2 0.0405028 0.0416667 0.0012 0 7 0.120742 0.125 0.0043 3 3 0.0606548 0.0625 0.0018 7 5 0.0197785 0.0208333 0.0011 7 5 0.0197785 0.0208333 0.0011 6 5 0.0226985 0.0238095 0.0011 1 2 0.162291 0.166667 0.0044 square01_sample_test(): square01_sample() samples the unit square. Sample points in the unit square. Row: 0 1 Col 0 : 0.495519 0.0332717 1 : 0.429578 0.304518 2 : 0.0298354 0.416739 3 : 0.344488 0.699737 4 : 0.592863 0.909411 5 : 0.470899 0.833374 6 : 0.106998 0.345924 7 : 0.380703 0.886715 8 : 0.865056 0.48775 9 : 0.0678796 0.291032 squaresym_area_test(): Python version: 3.10.12 squaresym_area returns the area of the symmetric unit square. squaresym_area() = 4 squaresym_monomial_integral_test(): squaresym_monomial_integral() returns the integral of a monomial over the interior of the unit square in 2D. Compare with a Monte Carlo estimate. Number of sample points used is 4192 Ex Ey MC-Estimate Exact Error 2 1 0.0136654 0 0.014 2 2 0.452771 0.444444 0.0083 7 3 -0.0104608 0 0.01 4 0 0.81399 0.8 0.014 7 3 -0.0104608 0 0.01 1 1 -0.0450297 0 0.045 6 3 0.00599364 0 0.006 6 3 0.00599364 0 0.006 2 2 0.452771 0.444444 0.0083 3 4 0.0113445 0 0.011 4 0 0.81399 0.8 0.014 1 2 0.0201333 0 0.02 6 5 0.00361353 0 0.0036 5 3 -0.0132464 0 0.013 7 1 -0.0170134 0 0.017 0 0 4 4 0 3 5 -0.0130833 0 0.013 7 7 -0.00587162 0 0.0059 1 6 0.00350958 0 0.0035 1 0 0.0500967 0 0.05 squaresym_sample_test(): squaresym_sample samples the symmeric unit square. Sample points in the symmetric unit square. Row: 0 1 Col 0 : 0.697325 -0.0852319 1 : 0.0241916 0.658538 2 : -0.935081 0.124688 3 : 0.63797 0.289123 4 : 0.644185 0.834985 5 : -0.0288343 0.290445 6 : -0.0975842 0.280927 7 : -0.314278 -0.846422 8 : -0.764199 -0.611709 9 : 0.391188 0.0553112 square_integrals_test(): Normal end of execution. Wed Oct 8 08:56:23 2025