30 July 2014 08:02:17 AM SQUARE_EXACTNESS_PRB C++ version Test the SQUARE_EXACTNESS library. 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 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 4 D I J Relative Error 0 0 0 0 1 1 0 0 0 1 0 2 2 0 0 1 1 0 0 2 0 3 3 0 0 2 1 0 1 2 0 0 3 0 4 4 0 0.4444444444444445 3 1 0 2 2 0 1 3 0 0 4 0.4444444444444445 Quadrature rule for the 2D Legendre integral. Number of points in rule is 9 D I J Relative Error 0 0 0 0 1 1 0 0 0 1 0 2 2 0 1.665334536937735e-16 1 1 0 0 2 1.665334536937735e-16 3 3 0 0 2 1 0 1 2 0 0 3 5.551115123125783e-17 4 4 0 2.775557561562891e-16 3 1 0 2 2 4.996003610813204e-16 1 3 0 0 4 2.775557561562891e-16 5 5 0 0 4 1 0 3 2 0 2 3 0 1 4 0 0 5 1.387778780781446e-17 6 6 0 0.1599999999999996 5 1 0 4 2 4.163336342344337e-16 3 3 0 2 4 4.163336342344337e-16 1 5 0 0 6 0.1599999999999996 Quadrature rule for the 2D Legendre integral. Number of points in rule is 16 D I J Relative Error 0 0 0 2.220446049250313e-16 1 1 0 1.387778780781446e-17 0 1 1.387778780781446e-17 2 2 0 1.665334536937735e-16 1 1 0 0 2 3.33066907387547e-16 3 3 0 0 2 1 2.775557561562891e-17 1 2 1.387778780781446e-17 0 3 0 4 4 0 8.326672684688674e-16 3 1 0 2 2 4.996003610813204e-16 1 3 0 0 4 8.326672684688674e-16 5 5 0 0 4 1 1.387778780781446e-17 3 2 6.938893903907228e-18 2 3 1.387778780781446e-17 1 4 0 0 5 1.387778780781446e-17 6 6 0 9.71445146547012e-16 5 1 0 4 2 1.040834085586084e-15 3 3 0 2 4 1.040834085586084e-15 1 5 0 0 6 1.165734175856414e-15 7 7 0 0 6 1 1.387778780781446e-17 5 2 0 4 3 0 3 4 0 2 5 6.938893903907228e-18 1 6 0 0 7 1.387778780781446e-17 8 8 0 0.05224489795918474 7 1 0 6 2 1.165734175856414e-15 5 3 0 4 4 1.214306433183765e-15 3 5 0 2 6 1.020017403874363e-15 1 7 6.938893903907228e-18 0 8 0.05224489795918474 Quadrature rule for the 2D Legendre integral. Number of points in rule is 25 D I J Relative Error 0 0 0 0 1 1 0 3.469446951953614e-17 0 1 3.469446951953614e-17 2 2 0 1.665334536937735e-16 1 1 6.938893903907228e-18 0 2 3.33066907387547e-16 3 3 0 1.387778780781446e-17 2 1 8.326672684688674e-17 1 2 0 0 3 2.775557561562891e-17 4 4 0 8.326672684688674e-16 3 1 0 2 2 8.743006318923108e-16 1 3 0 0 4 8.326672684688674e-16 5 5 0 0 4 1 1.387778780781446e-17 3 2 0 2 3 6.938893903907228e-18 1 4 6.938893903907228e-18 0 5 6.938893903907228e-18 6 6 0 7.771561172376096e-16 5 1 3.469446951953614e-18 4 2 1.040834085586084e-15 3 3 0 2 4 1.040834085586084e-15 1 5 0 0 6 9.71445146547012e-16 7 7 0 0 6 1 0 5 2 0 4 3 3.469446951953614e-18 3 4 0 2 5 6.938893903907228e-18 1 6 0 0 7 3.469446951953614e-17 8 8 0 9.992007221626409e-16 7 1 0 6 2 1.457167719820518e-15 5 3 3.469446951953614e-18 4 4 1.214306433183765e-15 3 5 3.469446951953614e-18 2 6 1.311450947838466e-15 1 7 0 0 8 8.743006318923108e-16 9 9 0 0 8 1 6.938893903907228e-18 7 2 0 6 3 0 5 4 0 4 5 0 3 6 0 2 7 0 1 8 3.469446951953614e-18 0 9 3.469446951953614e-17 10 10 0 0.01612496850592232 9 1 0 8 2 1.311450947838466e-15 7 3 0 6 4 1.578598363138894e-15 5 5 0 4 6 1.700029006457271e-15 3 7 0 2 8 1.311450947838466e-15 1 9 0 0 10 0.01612496850592232 Quadrature rule for the 2D Legendre integral. Number of points in rule is 36 D I J Relative Error 0 0 0 2.220446049250313e-16 1 1 0 3.469446951953614e-18 0 1 1.040834085586084e-17 2 2 0 1.665334536937735e-16 1 1 1.040834085586084e-17 0 2 0 3 3 0 1.734723475976807e-17 2 1 3.469446951953614e-18 1 2 3.469446951953614e-18 0 3 1.040834085586084e-17 4 4 0 0 3 1 3.469446951953614e-18 2 2 0 1 3 3.469446951953614e-18 0 4 1.387778780781446e-16 5 5 0 0 4 1 1.387778780781446e-17 3 2 3.469446951953614e-18 2 3 2.081668171172169e-17 1 4 6.938893903907228e-18 0 5 3.469446951953614e-17 6 6 0 1.942890293094024e-16 5 1 3.469446951953614e-18 4 2 0 3 3 0 2 4 2.081668171172169e-16 1 5 0 0 6 0 7 7 0 0 6 1 6.938893903907228e-18 5 2 3.469446951953614e-18 4 3 3.469446951953614e-18 3 4 3.469446951953614e-18 2 5 1.040834085586084e-17 1 6 3.469446951953614e-18 0 7 3.469446951953614e-18 8 8 0 3.747002708109903e-16 7 1 0 6 2 1.457167719820518e-16 5 3 0 4 4 0 3 5 0 2 6 0 1 7 0 0 8 1.249000902703301e-16 9 9 0 0 8 1 6.938893903907228e-18 7 2 0 6 3 0 5 4 0 4 5 6.938893903907228e-18 3 6 0 2 7 3.469446951953614e-18 1 8 0 0 9 1.040834085586084e-17 10 10 0 0 9 1 5.204170427930421e-18 8 2 3.747002708109903e-16 7 3 0 6 4 1.214306433183765e-16 5 5 1.734723475976807e-18 4 6 1.214306433183765e-16 3 7 0 2 8 3.747002708109903e-16 1 9 5.204170427930421e-18 0 10 0 11 11 0 0 10 1 3.469446951953614e-18 9 2 1.734723475976807e-18 8 3 0 7 4 1.734723475976807e-18 6 5 3.469446951953614e-18 5 6 1.734723475976807e-18 4 7 5.204170427930421e-18 3 8 1.734723475976807e-18 2 9 3.469446951953614e-18 1 10 0 0 11 6.938893903907228e-18 12 12 0 0.004797511291018436 11 1 0 10 2 1.144917494144693e-16 9 3 0 8 4 3.122502256758253e-16 7 5 0 6 6 1.700029006457271e-16 5 7 0 4 8 1.561251128379126e-16 3 9 0 2 10 2.289834988289385e-16 1 11 0 0 12 0.004797511291018075 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 1.110223024625157e-16 1 1 0 1.110223024625157e-16 0 1 4.440892098500626e-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 1.110223024625157e-16 1 1 0 8.326672684688674e-17 0 1 6.38378239159465e-16 2 2 0 0 1 1 6.800116025829084e-16 0 2 3.33066907387547e-16 3 3 0 2.775557561562891e-17 2 1 7.494005416219807e-16 1 2 4.163336342344337e-16 0 3 9.020562075079397e-16 4 4 0 0.1666666666666668 3 1 1.096345236817342e-15 2 2 0.2499999999999993 1 3 7.216449660063518e-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 0 1 1 0 8.604228440844963e-16 0 1 3.05311331771918e-16 2 2 0 1.665334536937735e-16 1 1 1.942890293094024e-16 0 2 1.665334536937735e-16 3 3 0 2.498001805406602e-16 2 1 1.249000902703301e-16 1 2 4.163336342344337e-16 0 3 2.081668171172169e-17 4 4 0 1.249000902703301e-15 3 1 3.608224830031759e-16 2 2 1.124100812432971e-15 1 3 1.595945597898663e-16 0 4 1.387778780781446e-16 5 5 0 5.551115123125783e-17 4 1 0.03333333333333316 3 2 3.05311331771918e-16 2 3 0.05555555555555579 1 4 2.046973701652632e-16 0 5 0.01666666666666697 Quadrature rule for the 2D Legendre integral. Number of points in rule is 21 D I J Relative Error 0 0 0 0 1 1 0 4.163336342344337e-16 0 1 7.28583859910259e-17 2 2 0 8.326672684688674e-16 1 1 1.908195823574488e-16 0 2 1.665334536937735e-16 3 3 0 7.771561172376096e-16 2 1 5.93275428784068e-16 1 2 2.0643209364124e-16 0 3 2.445960101127298e-16 4 4 0 8.326672684688674e-16 3 1 4.961309141293668e-16 2 2 1.249000902703301e-16 1 3 2.099015405931937e-16 0 4 0 5 5 0 7.494005416219807e-16 4 1 9.71445146547012e-16 3 2 2.203098814490545e-16 2 3 2.584737979205443e-16 1 4 1.023486850826316e-16 0 5 2.688821387764051e-16 6 6 0 0.008333333333334275 5 1 1.269817584415023e-15 4 2 0.02083333333333263 3 3 4.007211229506424e-16 2 4 0.02083333333333243 1 5 4.041905699025961e-16 0 6 0.006250000000000172 SQUARE_EXACTNESS_PRB Normal end of execution. 30 July 2014 08:02:17 AM