08-Jan-2022 10:03:36 square_exactness_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test square_exactness(). SQUARE_EXACTNESS_TEST01 Product Gauss-Legendre rules for the 2D Legendre integral. Density function rho(x) = 1. Region: -1 <= x <= +1. Region: -1 <= y <= +1. Level: L Exactness: 2*L+1 Order: N = (L+1)*(L+1) Quadrature rule for the 2D Legendre integral. Number of points in rule is 1 D I J Relative Error 0 0 0 1 1 1 0 0 0 1 0 2 2 0 1 1 1 0 0 2 1 Quadrature rule for the 2D Legendre integral. Number of points in rule is 4 D I J Relative Error 0 0 0 1 1 1 0 0 0 1 0 2 2 0 1 1 1 0 0 2 1 3 3 0 0 2 1 0 1 2 0 0 3 0 4 4 0 1 3 1 0 2 2 1 1 3 0 0 4 1 Quadrature rule for the 2D Legendre integral. Number of points in rule is 9 D I J Relative Error 0 0 0 1 1 1 0 0 0 1 0 2 2 0 1 1 1 0 0 2 1 3 3 0 0 2 1 0 1 2 0 0 3 0 4 4 0 1 3 1 0 2 2 1 1 3 0 0 4 1 5 5 0 0 4 1 0 3 2 0 2 3 0 1 4 0 0 5 8.673617379884035e-19 6 6 0 1 5 1 0 4 2 1 3 3 0 2 4 1 1 5 0 0 6 1 Quadrature rule for the 2D Legendre integral. Number of points in rule is 16 D I J Relative Error 0 0 0 1 1 1 0 0 0 1 0 2 2 0 1 1 1 0 0 2 1 3 3 0 0 2 1 0 1 2 0 0 3 0 4 4 0 1 3 1 0 2 2 1 1 3 0 0 4 1 5 5 0 0 4 1 0 3 2 0 2 3 0 1 4 0 0 5 0 6 6 0 1 5 1 0 4 2 1 3 3 0 2 4 1 1 5 0 0 6 1 7 7 0 0 6 1 0 5 2 0 4 3 0 3 4 0 2 5 0 1 6 0 0 7 0 8 8 0 1 7 1 0 6 2 1 5 3 0 4 4 1 3 5 0 2 6 1 1 7 0 0 8 1 Quadrature rule for the 2D Legendre integral. Number of points in rule is 25 D I J Relative Error 0 0 0 1 1 1 0 0 0 1 0 2 2 0 1 1 1 0 0 2 1 3 3 0 0 2 1 0 1 2 1.734723475976807e-18 0 3 2.168404344971009e-19 4 4 0 1 3 1 0 2 2 1 1 3 3.252606517456513e-19 0 4 1 5 5 0 0 4 1 0 3 2 0 2 3 2.168404344971009e-19 1 4 5.421010862427522e-20 0 5 1.18584612615602e-20 6 6 0 1 5 1 0 4 2 1 3 3 0 2 4 1 1 5 5.082197683525802e-21 0 6 1 7 7 0 0 6 1 0 5 2 0 4 3 0 3 4 2.710505431213761e-20 2 5 1.694065894508601e-21 1 6 2.117582368135751e-22 0 7 1.694065894508601e-21 8 8 0 1 7 1 0 6 2 1 5 3 0 4 4 1 3 5 1.694065894508601e-21 2 6 1 1 7 1.19114008207636e-22 0 8 1 9 9 0 0 8 1 0 7 2 0 6 3 0 5 4 6.776263578034403e-21 4 5 0 3 6 3.176373552203626e-22 2 7 1.19114008207636e-22 1 8 1.588186776101813e-22 0 9 6.203854594147708e-24 10 10 0 1 9 1 0 8 2 1 7 3 0 6 4 1 5 5 8.470329472543003e-22 4 6 1 3 7 6.617444900424221e-23 2 8 1 1 9 5.252596889711726e-23 0 10 1 Quadrature rule for the 2D Legendre integral. Number of points in rule is 36 D I J Relative Error 0 0 0 1 1 1 0 0 0 1 0 2 2 0 1 1 1 0 0 2 1 3 3 0 0 2 1 0 1 2 0 0 3 0 4 4 0 1 3 1 0 2 2 1 1 3 0 0 4 1 5 5 0 0 4 1 0 3 2 0 2 3 0 1 4 0 0 5 0 6 6 0 1 5 1 0 4 2 1 3 3 0 2 4 1 1 5 0 0 6 1 7 7 0 0 6 1 0 5 2 0 4 3 0 3 4 0 2 5 0 1 6 0 0 7 0 8 8 0 1 7 1 0 6 2 1 5 3 0 4 4 1 3 5 0 2 6 1 1 7 0 0 8 1 9 9 0 0 8 1 0 7 2 0 6 3 0 5 4 0 4 5 0 3 6 0 2 7 0 1 8 0 0 9 0 10 10 0 1 9 1 0 8 2 1 7 3 0 6 4 1 5 5 0 4 6 1 3 7 0 2 8 1 1 9 0 0 10 1 11 11 0 0 10 1 0 9 2 0 8 3 0 7 4 0 6 5 0 5 6 0 4 7 0 3 8 0 2 9 0 1 10 0 0 11 0 12 12 0 1 11 1 0 10 2 1 9 3 0 8 4 1 7 5 0 6 6 1 5 7 0 4 8 1 3 9 0 2 10 1 1 11 0 0 12 1 SQUARE_EXACTNESS_TEST02 Padua rule for the 2D Legendre integral. Density function rho(x) = 1. Region: -1 <= x <= +1. Region: -1 <= y <= +1. Level: L Exactness: L+1 when L is 0, L otherwise. Order: N = (L+1)*(L+2)/2 Quadrature rule for the 2D Legendre integral. Number of points in rule is 1 D I J Relative Error 0 0 0 0 1 1 0 0 0 1 0 2 2 0 1 1 1 0 0 2 1 Quadrature rule for the 2D Legendre integral. Number of points in rule is 3 D I J Relative Error 0 0 0 0 1 1 0 0 0 1 0 2 2 0 2 1 1 0 0 2 0.5000000000000001 Quadrature rule for the 2D Legendre integral. Number of points in rule is 6 D I J Relative Error 0 0 0 3.33066907387547e-16 1 1 0 1.110223024625157e-16 0 1 3.885780586188048e-16 2 2 0 4.996003610813204e-16 1 1 5.551115123125783e-17 0 2 3.33066907387547e-16 3 3 0 1.110223024625157e-16 2 1 0.6666666666666665 1 2 2.775557561562891e-17 0 3 0.3333333333333338 Quadrature rule for the 2D Legendre integral. Number of points in rule is 10 D I J Relative Error 0 0 0 0 1 1 0 0 0 1 6.661338147750939e-16 2 2 0 0 1 1 6.938893903907228e-16 0 2 4.996003610813204e-16 3 3 0 2.775557561562891e-17 2 1 7.494005416219807e-16 1 2 3.608224830031759e-16 0 3 9.020562075079397e-16 4 4 0 0.1666666666666666 3 1 1.099814683769296e-15 2 2 0.2499999999999993 1 3 7.077671781985373e-16 0 4 0.04166666666666707 Quadrature rule for the 2D Legendre integral. Number of points in rule is 15 D I J Relative Error 0 0 0 1.110223024625157e-16 1 1 0 7.216449660063518e-16 0 1 2.636779683484747e-16 2 2 0 1.665334536937735e-16 1 1 1.942890293094024e-16 0 2 1.665334536937735e-16 3 3 0 2.775557561562891e-16 2 1 1.179611963664229e-16 1 2 3.608224830031759e-16 0 3 9.367506770274758e-17 4 4 0 1.110223024625157e-15 3 1 3.642919299551295e-16 2 2 9.992007221626409e-16 1 3 1.561251128379126e-16 0 4 2.775557561562891e-16 5 5 0 5.551115123125783e-17 4 1 0.03333333333333315 3 2 3.122502256758253e-16 2 3 0.05555555555555576 1 4 2.151057110211241e-16 0 5 0.01666666666666706 Quadrature rule for the 2D Legendre integral. Number of points in rule is 21 D I J Relative Error 0 0 0 1.110223024625157e-16 1 1 0 8.326672684688674e-17 0 1 1.283695372222837e-16 2 2 0 8.326672684688674e-16 1 1 1.838806884535416e-16 0 2 1.665334536937735e-16 3 3 0 8.604228440844963e-16 2 1 5.793976409762536e-16 1 2 2.081668171172169e-16 0 3 2.51534904016637e-16 4 4 0 1.110223024625157e-15 3 1 4.753142324176451e-16 2 2 0 1 3 2.099015405931937e-16 0 4 2.775557561562891e-16 5 5 0 9.020562075079397e-16 4 1 9.540979117872439e-16 3 2 2.359223927328458e-16 2 3 2.550043509685906e-16 1 4 1.179611963664229e-16 0 5 2.34187669256869e-16 6 6 0 0.008333333333334469 5 1 1.273287031366976e-15 4 2 0.02083333333333305 3 3 4.007211229506424e-16 2 4 0.02083333333333222 1 5 4.041905699025961e-16 0 6 0.006249999999999978 square_exactness_test(): Normal end of execution. 08-Jan-2022 10:03:36