Tue May 20 22:32:45 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 0 5 0.169424 0.166667 0.0028 7 4 0.0251635 0.025 0.00016 1 0 0.505533 0.5 0.0055 2 3 0.0847875 0.0833333 0.0015 4 7 0.0254277 0.025 0.00043 0 5 0.169424 0.166667 0.0028 3 6 0.0364815 0.0357143 0.00077 3 5 0.042533 0.0416667 0.00087 0 2 0.334279 0.333333 0.00095 2 7 0.0426972 0.0416667 0.001 4 2 0.0677215 0.0666667 0.0011 5 5 0.0281494 0.0277778 0.00037 4 2 0.0677215 0.0666667 0.0011 6 7 0.0179682 0.0178571 0.00011 5 5 0.0281494 0.0277778 0.00037 5 2 0.0563608 0.0555556 0.00081 5 5 0.0281494 0.0277778 0.00037 1 2 0.168299 0.166667 0.0016 2 2 0.112706 0.111111 0.0016 7 4 0.0251635 0.025 0.00016 square01_sample_test(): square01_sample() samples the unit square. Sample points in the unit square. Row: 0 1 Col 0 : 0.845553 0.130457 1 : 0.616366 0.663625 2 : 0.144043 0.955628 3 : 0.162576 0.998421 4 : 0.64603 0.248618 5 : 0.89531 0.99521 6 : 0.368262 0.410498 7 : 0.708823 0.208424 8 : 0.460145 0.363285 9 : 0.475715 0.809298 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 1 2 0.0297292 0 0.03 6 6 0.0864035 0.0816327 0.0048 1 5 -0.00306496 0 0.0031 6 7 -0.00392202 0 0.0039 1 5 -0.00306496 0 0.0031 5 5 0.00131358 0 0.0013 1 0 0.0992331 0 0.099 0 0 4 4 0 4 4 0.161332 0.16 0.0013 2 4 0.264031 0.266667 0.0026 1 5 -0.00306496 0 0.0031 2 0 1.31981 1.33333 0.014 5 4 0.00340249 0 0.0034 0 0 4 4 0 2 0 1.31981 1.33333 0.014 5 2 0.00721317 0 0.0072 1 3 -0.00379983 0 0.0038 6 3 -0.00427378 0 0.0043 7 0 0.00733919 0 0.0073 6 0 0.562342 0.571429 0.0091 squaresym_sample_test(): squaresym_sample samples the symmeric unit square. Sample points in the symmetric unit square. Row: 0 1 Col 0 : 0.623622 0.631408 1 : -0.767528 0.868172 2 : 0.286134 0.0624489 3 : 0.771778 0.0824742 4 : 0.0218173 0.0310874 5 : 0.216788 -0.804547 6 : 0.279158 -0.0325001 7 : -0.772404 -0.848517 8 : 0.736602 -0.462627 9 : -0.266204 0.125463 square_integrals_test(): Normal end of execution. Tue May 20 22:32:45 2025