16 August 2014 11:15:17 PM CUBE_EXACTNESS_PRB C++ version Test the CUBE_EXACTNESS library. TEST01 Product Gauss-Legendre rules for the 3D Legendre integral. Density function rho(x) = 1. Region: -1 <= x <= +1. -1 <= y <= +1. -1 <= z <= +1. Level: L Exactness: 2*L+1 Order: N = (L+1)*(L+1)*(L+1) Quadrature rule for the 3D Legendre integral. Number of points in rule is 1 D I J K Relative Error 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 2 2 0 0 1 1 1 0 0 0 2 0 1 1 0 1 0 0 1 1 0 0 0 2 1 Quadrature rule for the 3D Legendre integral. Number of points in rule is 8 D I J K Relative Error 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 2 2 0 0 0 1 1 0 0 0 2 0 0 1 0 1 0 0 1 1 0 0 0 2 0 3 3 0 0 0 2 1 0 0 1 2 0 0 0 3 0 0 2 0 1 5.55112e-17 1 1 1 0 0 2 1 5.55112e-17 1 0 2 0 0 1 2 0 0 0 3 5.55112e-17 4 4 0 0 0.444444 3 1 0 0 2 2 0 2.498e-16 1 3 0 0 0 4 0 0.444444 3 0 1 0 2 1 1 0 1 2 1 0 0 3 1 0 2 0 2 2.498e-16 1 1 2 0 0 2 2 2.498e-16 1 0 3 0 0 1 3 0 0 0 4 0.444444 Quadrature rule for the 3D Legendre integral. Number of points in rule is 27 D I J K Relative Error 0 0 0 0 2.22045e-16 1 1 0 0 0 0 1 0 2.77556e-17 0 0 1 2.77556e-17 2 2 0 0 1.66533e-16 1 1 0 0 0 2 0 1.66533e-16 1 0 1 0 0 1 1 0 0 0 2 3.33067e-16 3 3 0 0 0 2 1 0 0 1 2 0 0 0 3 0 6.93889e-17 2 0 1 0 1 1 1 0 0 2 1 1.38778e-17 1 0 2 0 0 1 2 1.38778e-17 0 0 3 1.38778e-17 4 4 0 0 2.77556e-16 3 1 0 0 2 2 0 4.996e-16 1 3 0 0 0 4 0 2.77556e-16 3 0 1 0 2 1 1 0 1 2 1 0 0 3 1 2.08167e-17 2 0 2 4.996e-16 1 1 2 0 0 2 2 4.996e-16 1 0 3 0 0 1 3 2.08167e-17 0 0 4 2.77556e-16 5 5 0 0 0 4 1 0 0 3 2 0 0 2 3 0 0 1 4 0 0 0 5 0 1.38778e-17 4 0 1 6.93889e-17 3 1 1 0 2 2 1 0 1 3 1 0 0 4 1 4.16334e-17 3 0 2 0 2 1 2 0 1 2 2 0 0 3 2 1.38778e-17 2 0 3 6.93889e-17 1 1 3 0 0 2 3 4.16334e-17 1 0 4 0 0 1 4 1.38778e-17 0 0 5 4.16334e-17 6 6 0 0 0.16 5 1 0 0 4 2 0 4.16334e-16 3 3 0 0 2 4 0 4.16334e-16 1 5 0 0 0 6 0 0.16 5 0 1 0 4 1 1 0 3 2 1 0 2 3 1 0 1 4 1 0 0 5 1 1.38778e-17 4 0 2 4.16334e-16 3 1 2 0 2 2 2 5.6205e-16 1 3 2 0 0 4 2 4.16334e-16 3 0 3 0 2 1 3 0 1 2 3 0 0 3 3 1.38778e-17 2 0 4 4.16334e-16 1 1 4 0 0 2 4 4.16334e-16 1 0 5 0 0 1 5 1.38778e-17 0 0 6 0.16 Quadrature rule for the 3D Legendre integral. Number of points in rule is 64 D I J K Relative Error 0 0 0 0 2.22045e-16 1 1 0 0 0 0 1 0 2.77556e-17 0 0 1 5.55112e-17 2 2 0 0 8.32667e-16 1 1 0 0 0 2 0 6.66134e-16 1 0 1 2.08167e-17 0 1 1 4.16334e-17 0 0 2 6.66134e-16 3 3 0 0 0 2 1 0 3.1225e-17 1 2 0 3.46945e-18 0 3 0 0 2 0 1 2.42861e-17 1 1 1 3.46945e-18 0 2 1 0 1 0 2 3.46945e-18 0 1 2 5.55112e-17 0 0 3 2.77556e-17 4 4 0 0 1.38778e-15 3 1 0 0 2 2 0 6.245e-16 1 3 0 6.93889e-18 0 4 0 1.38778e-15 3 0 1 0 2 1 1 1.04083e-17 1 2 1 3.46945e-18 0 3 1 3.46945e-18 2 0 2 4.996e-16 1 1 2 3.46945e-18 0 2 2 4.996e-16 1 0 3 6.93889e-18 0 1 3 2.42861e-17 0 0 4 1.249e-15 5 5 0 0 0 4 1 0 1.38778e-17 3 2 0 0 2 3 0 0 1 4 0 6.93889e-18 0 5 0 1.73472e-17 4 0 1 6.93889e-18 3 1 1 0 2 2 1 4.51028e-17 1 3 1 3.46945e-18 0 4 1 1.73472e-17 3 0 2 0 2 1 2 6.93889e-18 1 2 2 3.46945e-18 0 3 2 1.38778e-17 2 0 3 0 1 1 3 0 0 2 3 4.16334e-17 1 0 4 6.93889e-18 0 1 4 2.42861e-17 0 0 5 1.04083e-17 6 6 0 0 1.16573e-15 5 1 0 0 4 2 0 1.249e-15 3 3 0 6.93889e-18 2 4 0 1.04083e-15 1 5 0 6.93889e-18 0 6 0 1.36002e-15 5 0 1 0 4 1 1 0 3 2 1 0 2 3 1 6.93889e-18 1 4 1 0 0 5 1 0 4 0 2 1.45717e-15 3 1 2 3.46945e-18 2 2 2 3.747e-16 1 3 2 3.46945e-18 0 4 2 1.45717e-15 3 0 3 6.93889e-18 2 1 3 0 1 2 3 0 0 3 3 0 2 0 4 1.45717e-15 1 1 4 3.46945e-18 0 2 4 1.66533e-15 1 0 5 6.93889e-18 0 1 5 1.38778e-17 0 0 6 9.71445e-16 7 7 0 0 0 6 1 0 3.46945e-18 5 2 0 0 4 3 0 1.04083e-17 3 4 0 1.73472e-18 2 5 0 1.38778e-17 1 6 0 1.73472e-18 0 7 0 2.08167e-17 6 0 1 4.16334e-17 5 1 1 0 4 2 1 1.73472e-17 3 3 1 0 2 4 1 1.56125e-17 1 5 1 1.73472e-18 0 6 1 5.55112e-17 5 0 2 0 4 1 2 3.46945e-18 3 2 2 1.73472e-18 2 3 2 1.73472e-18 1 4 2 1.73472e-18 0 5 2 0 4 0 3 3.46945e-18 3 1 3 1.73472e-18 2 2 3 0 1 3 3 1.73472e-18 0 4 3 3.46945e-17 3 0 4 1.73472e-18 2 1 4 6.93889e-18 1 2 4 1.73472e-18 0 3 4 6.93889e-18 2 0 5 1.38778e-17 1 1 5 1.73472e-18 0 2 5 1.38778e-17 1 0 6 1.73472e-18 0 1 6 1.38778e-17 0 0 7 6.93889e-18 8 8 0 0 0.0522449 7 1 0 0 6 2 0 1.31145e-15 5 3 0 0 4 4 0 1.56125e-15 3 5 0 0 2 6 0 1.45717e-15 1 7 0 1.73472e-18 0 8 0 0.0522449 7 0 1 0 6 1 1 3.46945e-18 5 2 1 0 4 3 1 1.73472e-18 3 4 1 0 2 5 1 0 1 6 1 0 0 7 1 1.73472e-18 6 0 2 1.60288e-15 5 1 2 0 4 2 2 1.56125e-15 3 3 2 0 2 4 2 1.56125e-15 1 5 2 1.73472e-18 0 6 2 1.60288e-15 5 0 3 0 4 1 3 3.46945e-18 3 2 3 0 2 3 3 5.20417e-18 1 4 3 1.73472e-18 0 5 3 1.21431e-17 4 0 4 1.73472e-15 3 1 4 1.73472e-18 2 2 4 2.18575e-15 1 3 4 0 0 4 4 1.73472e-15 3 0 5 0 2 1 5 3.46945e-18 1 2 5 1.73472e-18 0 3 5 1.21431e-17 2 0 6 1.02002e-15 1 1 6 0 0 2 6 8.74301e-16 1 0 7 1.73472e-18 0 1 7 1.21431e-17 0 0 8 0.0522449 Quadrature rule for the 3D Legendre integral. Number of points in rule is 125 D I J K Relative Error 0 0 0 0 0 1 1 0 0 3.81639e-17 0 1 0 8.67362e-17 0 0 1 3.46945e-18 2 2 0 0 1.66533e-16 1 1 0 1.73472e-18 0 2 0 4.996e-16 1 0 1 1.73472e-18 0 1 1 1.73472e-18 0 0 2 0 3 3 0 0 4.51028e-17 2 1 0 8.67362e-18 1 2 0 5.20417e-18 0 3 0 1.56125e-17 2 0 1 1.73472e-18 1 1 1 8.67362e-18 0 2 1 9.54098e-17 1 0 2 1.73472e-18 0 1 2 5.37764e-17 0 0 3 1.78677e-16 4 4 0 0 2.77556e-16 3 1 0 3.46945e-18 2 2 0 6.245e-16 1 3 0 0 0 4 0 2.77556e-16 3 0 1 3.46945e-18 2 1 1 6.93889e-18 1 2 1 5.20417e-18 0 3 1 1.73472e-17 2 0 2 4.996e-16 1 1 2 0 0 2 2 7.49401e-16 1 0 3 0 0 1 3 3.46945e-18 0 0 4 1.66533e-15 5 5 0 0 3.46945e-18 4 1 0 1.73472e-18 3 2 0 1.73472e-18 2 3 0 1.56125e-17 1 4 0 3.46945e-18 0 5 0 7.45931e-17 4 0 1 4.33681e-17 3 1 1 1.73472e-18 2 2 1 5.20417e-18 1 3 1 0 0 4 1 8.67362e-18 3 0 2 0 2 1 2 8.67362e-18 1 2 2 0 0 3 2 5.20417e-18 2 0 3 8.67362e-18 1 1 3 0 0 2 3 2.25514e-17 1 0 4 3.46945e-18 0 1 4 1.9082e-17 0 0 5 2.25514e-17 6 6 0 0 1.94289e-16 5 1 0 8.67362e-19 4 2 0 6.245e-16 3 3 0 8.67362e-19 2 4 0 8.32667e-16 1 5 0 9.54098e-18 0 6 0 3.88578e-16 5 0 1 8.67362e-19 4 1 1 6.07153e-18 3 2 1 8.67362e-19 2 3 1 1.73472e-18 1 4 1 8.67362e-19 0 5 1 6.07153e-18 4 0 2 8.32667e-16 3 1 2 8.67362e-19 2 2 2 1.31145e-15 1 3 2 2.60209e-18 0 4 2 8.32667e-16 3 0 3 8.67362e-19 2 1 3 8.67362e-18 1 2 3 2.60209e-18 0 3 3 6.07153e-18 2 0 4 6.245e-16 1 1 4 2.60209e-18 0 2 4 8.32667e-16 1 0 5 7.80626e-18 0 1 5 6.07153e-18 0 0 6 1.94289e-16 7 7 0 0 0 6 1 0 6.93889e-18 5 2 0 0 4 3 0 0 3 4 0 0 2 5 0 0 1 6 0 1.73472e-18 0 7 0 1.9082e-17 6 0 1 2.08167e-17 5 1 1 0 4 2 1 1.38778e-17 3 3 1 1.73472e-18 2 4 1 1.12757e-17 1 5 1 1.73472e-18 0 6 1 1.9082e-17 5 0 2 0 4 1 2 0 3 2 2 0 2 3 2 3.46945e-18 1 4 2 1.73472e-18 0 5 2 5.20417e-18 4 0 3 3.46945e-17 3 1 3 1.73472e-18 2 2 3 3.46945e-18 1 3 3 0 0 4 3 3.29597e-17 3 0 4 0 2 1 4 1.04083e-17 1 2 4 0 0 3 4 2.25514e-17 2 0 5 1.04083e-17 1 1 5 1.73472e-18 0 2 5 8.67362e-18 1 0 6 1.73472e-18 0 1 6 2.25514e-17 0 0 7 7.80626e-17 8 8 0 0 2.3731e-15 7 1 0 0 6 2 0 1.7486e-15 5 3 0 1.73472e-18 4 4 0 1.04083e-15 3 5 0 1.73472e-18 2 6 0 1.7486e-15 1 7 0 8.67362e-19 0 8 0 2.1233e-15 7 0 1 0 6 1 1 8.67362e-18 5 2 1 0 4 3 1 3.46945e-18 3 4 1 8.67362e-19 2 5 1 0 1 6 1 4.33681e-18 0 7 1 1.21431e-17 6 0 2 1.16573e-15 5 1 2 8.67362e-19 4 2 2 9.36751e-16 3 3 2 0 2 4 2 9.36751e-16 1 5 2 8.67362e-19 0 6 2 1.02002e-15 5 0 3 1.73472e-18 4 1 3 2.60209e-18 3 2 3 0 2 3 3 8.67362e-19 1 4 3 0 0 5 3 4.33681e-18 4 0 4 1.04083e-15 3 1 4 8.67362e-19 2 2 4 1.249e-15 1 3 4 8.67362e-19 0 4 4 1.04083e-15 3 0 5 1.73472e-18 2 1 5 2.60209e-18 1 2 5 8.67362e-19 0 3 5 4.33681e-18 2 0 6 7.28584e-16 1 1 6 1.73472e-18 0 2 6 1.02002e-15 1 0 7 8.67362e-19 0 1 7 1.56125e-17 0 0 8 1.9984e-15 9 9 0 0 0 8 1 0 6.93889e-18 7 2 0 0 6 3 0 1.04083e-17 5 4 0 0 4 5 0 2.60209e-18 3 6 0 8.67362e-19 2 7 0 1.21431e-17 1 8 0 1.73472e-18 0 9 0 1.47451e-17 8 0 1 3.46945e-18 7 1 1 0 6 2 1 1.73472e-18 5 3 1 0 4 4 1 7.80626e-18 3 5 1 8.67362e-19 2 6 1 6.07153e-18 1 7 1 1.73472e-18 0 8 1 1.30104e-17 7 0 2 0 6 1 2 1.73472e-18 5 2 2 8.67362e-19 4 3 2 8.67362e-19 3 4 2 8.67362e-19 2 5 2 1.73472e-18 1 6 2 8.67362e-19 0 7 2 8.67362e-19 6 0 3 0 5 1 3 0 4 2 3 4.33681e-18 3 3 3 8.67362e-19 2 4 3 1.73472e-18 1 5 3 8.67362e-19 0 6 3 1.30104e-17 5 0 4 0 4 1 4 4.33681e-18 3 2 4 8.67362e-19 2 3 4 1.73472e-18 1 4 4 8.67362e-19 0 5 4 8.67362e-19 4 0 5 1.47451e-17 3 1 5 8.67362e-19 2 2 5 2.60209e-18 1 3 5 8.67362e-19 0 4 5 1.30104e-17 3 0 6 8.67362e-19 2 1 6 1.73472e-18 1 2 6 8.67362e-19 0 3 6 8.67362e-19 2 0 7 1.21431e-17 1 1 7 1.73472e-18 0 2 7 1.30104e-17 1 0 8 1.73472e-18 0 1 8 8.67362e-19 0 0 9 2.86229e-17 10 10 0 0 0.016125 9 1 0 0 8 2 0 1.8735e-16 7 3 0 0 6 4 0 1.09288e-15 5 5 0 0 4 6 0 1.21431e-15 3 7 0 1.73472e-18 2 8 0 3.747e-16 1 9 0 1.73472e-18 0 10 0 0.016125 9 0 1 0 8 1 1 5.20417e-18 7 2 1 0 6 3 1 0 5 4 1 0 4 5 1 1.73472e-18 3 6 1 0 2 7 1 8.67362e-19 1 8 1 0 0 9 1 8.67362e-18 8 0 2 1.1241e-15 7 1 2 0 6 2 2 1.96718e-15 5 3 2 0 4 4 2 2.08167e-15 3 5 2 8.67362e-19 2 6 2 2.18575e-15 1 7 2 0 0 8 2 7.49401e-16 7 0 3 0 6 1 3 0 5 2 3 0 4 3 3 0 3 4 3 0 2 5 3 8.67362e-19 1 6 3 8.67362e-19 0 7 3 1.73472e-18 6 0 4 1.5786e-15 5 1 4 0 4 2 4 2.47198e-15 3 3 4 0 2 4 4 2.34188e-15 1 5 4 0 0 6 4 1.5786e-15 5 0 5 0 4 1 5 1.73472e-18 3 2 5 8.67362e-19 2 3 5 0 1 4 5 0 0 5 5 6.07153e-18 4 0 6 1.21431e-15 3 1 6 1.73472e-18 2 2 6 1.96718e-15 1 3 6 0 0 4 6 9.71445e-16 3 0 7 1.73472e-18 2 1 7 2.60209e-18 1 2 7 0 0 3 7 1.73472e-18 2 0 8 1.8735e-15 1 1 8 0 0 2 8 2.06085e-15 1 0 9 5.20417e-18 0 1 9 8.67362e-18 0 0 10 0.016125 Quadrature rule for the 3D Legendre integral. Number of points in rule is 216 D I J K Relative Error 0 0 0 0 1.11022e-15 1 1 0 0 2.94903e-17 0 1 0 1.07553e-16 0 0 1 1.14492e-16 2 2 0 0 4.996e-16 1 1 0 1.64799e-17 0 2 0 6.66134e-16 1 0 1 2.60209e-18 0 1 1 2.77556e-17 0 0 2 3.33067e-16 3 3 0 0 7.80626e-18 2 1 0 6.93889e-18 1 2 0 6.93889e-18 0 3 0 3.72966e-17 2 0 1 6.93889e-17 1 1 1 1.73472e-18 0 2 1 5.9848e-17 1 0 2 0 0 1 2 2.60209e-18 0 0 3 2.51535e-17 4 4 0 0 1.11022e-15 3 1 0 8.67362e-19 2 2 0 1.249e-15 1 3 0 1.86483e-17 0 4 0 9.71445e-16 3 0 1 3.46945e-18 2 1 1 6.50521e-18 1 2 1 1.30104e-18 0 3 1 6.50521e-18 2 0 2 4.996e-16 1 1 2 1.73472e-18 0 2 2 7.49401e-16 1 0 3 3.03577e-18 0 1 3 7.37257e-18 0 0 4 8.32667e-16 5 5 0 0 3.46945e-18 4 1 0 2.90566e-17 3 2 0 1.04083e-17 2 3 0 6.07153e-18 1 4 0 8.67362e-19 0 5 0 4.25007e-17 4 0 1 3.90313e-18 3 1 1 4.33681e-19 2 2 1 1.99493e-17 1 3 1 3.03577e-18 0 4 1 2.86229e-17 3 0 2 0 2 1 2 2.60209e-18 1 2 2 0 0 3 2 6.07153e-18 2 0 3 8.67362e-19 1 1 3 0 0 2 3 1.30104e-17 1 0 4 7.80626e-18 0 1 4 4.0766e-17 0 0 5 8.41341e-17 6 6 0 0 5.82867e-16 5 1 0 1.73472e-18 4 2 0 0 3 3 0 8.67362e-19 2 4 0 0 1 5 0 8.67362e-19 0 6 0 5.82867e-16 5 0 1 1.73472e-18 4 1 1 1.73472e-18 3 2 1 0 2 3 1 0 1 4 1 0 0 5 1 9.54098e-18 4 0 2 1.04083e-15 3 1 2 1.30104e-18 2 2 2 3.747e-16 1 3 2 1.73472e-18 0 4 2 8.32667e-16 3 0 3 0 2 1 3 3.46945e-18 1 2 3 2.60209e-18 0 3 3 4.33681e-18 2 0 4 2.08167e-16 1 1 4 3.90313e-18 0 2 4 8.32667e-16 1 0 5 2.60209e-18 0 1 5 2.60209e-18 0 0 6 0 7 7 0 0 8.67362e-19 6 1 0 1.73472e-18 5 2 0 8.67362e-19 4 3 0 4.33681e-19 3 4 0 0 2 5 0 1.60462e-17 1 6 0 2.1684e-18 0 7 0 9.97466e-18 6 0 1 8.67362e-18 5 1 1 4.33681e-19 4 2 1 9.1073e-18 3 3 1 0 2 4 1 1.82146e-17 1 5 1 1.73472e-18 0 6 1 3.03577e-18 5 0 2 8.67362e-19 4 1 2 7.37257e-18 3 2 2 4.33681e-19 2 3 2 4.33681e-19 1 4 2 4.33681e-19 0 5 2 9.97466e-18 4 0 3 1.69136e-17 3 1 3 0 2 2 3 9.97466e-18 1 3 3 8.67362e-19 0 4 3 3.07913e-17 3 0 4 0 2 1 4 3.90313e-18 1 2 4 2.1684e-18 0 3 4 1.0842e-17 2 0 5 1.17094e-17 1 1 5 4.33681e-19 0 2 5 3.03577e-18 1 0 6 2.1684e-18 0 1 6 3.90313e-18 0 0 7 1.0842e-17 8 8 0 0 2.498e-16 7 1 0 1.73472e-18 6 2 0 4.3715e-16 5 3 0 2.1684e-18 4 4 0 2.25514e-15 3 5 0 5.63785e-18 2 6 0 2.91434e-16 1 7 0 3.03577e-18 0 8 0 3.747e-16 7 0 1 0 6 1 1 4.33681e-19 5 2 1 4.33681e-19 4 3 1 3.03577e-18 3 4 1 4.33681e-19 2 5 1 4.33681e-18 1 6 1 4.33681e-19 0 7 1 4.33681e-19 6 0 2 2.91434e-16 5 1 2 4.33681e-19 4 2 2 6.245e-16 3 3 2 4.33681e-19 2 4 2 7.80626e-16 1 5 2 1.30104e-18 0 6 2 1.45717e-16 5 0 3 3.03577e-18 4 1 3 4.77049e-18 3 2 3 8.67362e-19 2 3 3 4.33681e-18 1 4 3 4.33681e-19 0 5 3 4.33681e-19 4 0 4 1.56125e-15 3 1 4 4.33681e-19 2 2 4 2.498e-15 1 3 4 4.33681e-19 0 4 4 1.73472e-15 3 0 5 2.1684e-18 2 1 5 4.33681e-18 1 2 5 1.30104e-18 0 3 5 4.33681e-19 2 0 6 1.31145e-15 1 1 6 8.67362e-19 0 2 6 1.31145e-15 1 0 7 1.30104e-18 0 1 7 4.33681e-19 0 0 8 1.1241e-15 9 9 0 0 4.33681e-18 8 1 0 1.73472e-18 7 2 0 0 6 3 0 2.60209e-18 5 4 0 0 4 5 0 1.73472e-18 3 6 0 4.33681e-19 2 7 0 1.73472e-18 1 8 0 0 0 9 0 1.38778e-17 8 0 1 6.07153e-18 7 1 1 8.67362e-19 6 2 1 1.73472e-18 5 3 1 0 4 4 1 3.46945e-18 3 5 1 4.33681e-19 2 6 1 8.67362e-19 1 7 1 1.73472e-18 0 8 1 1.38778e-17 7 0 2 8.67362e-19 6 1 2 8.67362e-19 5 2 2 8.67362e-19 4 3 2 0 3 4 2 4.33681e-19 2 5 2 4.77049e-18 1 6 2 8.67362e-19 0 7 2 4.33681e-18 6 0 3 1.04083e-17 5 1 3 1.30104e-18 4 2 3 5.20417e-18 3 3 3 0 2 4 3 0 1 5 3 4.33681e-19 0 6 3 1.82146e-17 5 0 4 8.67362e-19 4 1 4 0 3 2 4 4.33681e-19 2 3 4 3.46945e-18 1 4 4 8.67362e-19 0 5 4 2.60209e-18 4 0 5 5.20417e-18 3 1 5 0 2 2 5 3.46945e-18 1 3 5 4.33681e-19 0 4 5 4.33681e-18 3 0 6 4.33681e-19 2 1 6 1.73472e-18 1 2 6 8.67362e-19 0 3 6 4.33681e-18 2 0 7 1.38778e-17 1 1 7 0 0 2 7 4.33681e-18 1 0 8 3.46945e-18 0 1 8 6.93889e-18 0 0 9 1.38778e-17 10 10 0 0 1.52656e-15 9 1 0 4.33681e-19 8 2 0 0 7 3 0 1.30104e-18 6 4 0 7.28584e-16 5 5 0 0 4 6 0 9.71445e-16 3 7 0 8.67362e-19 2 8 0 1.8735e-16 1 9 0 0 0 10 0 1.06859e-15 9 0 1 0 8 1 1 8.67362e-19 7 2 1 4.33681e-19 6 3 1 1.30104e-18 5 4 1 4.33681e-19 4 5 1 2.1684e-18 3 6 1 8.67362e-19 2 7 1 4.33681e-19 1 8 1 1.30104e-18 0 9 1 1.64799e-17 8 0 2 5.6205e-16 7 1 2 1.73472e-18 6 2 2 2.18575e-16 5 3 2 4.33681e-19 4 4 2 1.56125e-15 3 5 2 4.33681e-19 2 6 2 2.18575e-16 1 7 2 1.30104e-18 0 8 2 1.8735e-16 7 0 3 4.33681e-19 6 1 3 1.30104e-18 5 2 3 4.33681e-19 4 3 3 2.1684e-18 3 4 3 8.67362e-19 2 5 3 1.73472e-18 1 6 3 1.73472e-18 0 7 3 4.77049e-18 6 0 4 4.85723e-16 5 1 4 1.30104e-18 4 2 4 9.1073e-16 3 3 4 2.1684e-18 2 4 4 1.17094e-15 1 5 4 3.03577e-18 0 6 4 8.50015e-16 5 0 5 8.67362e-19 4 1 5 1.73472e-18 3 2 5 4.33681e-19 2 3 5 1.30104e-18 1 4 5 1.30104e-18 0 5 5 7.80626e-18 4 0 6 1.09288e-15 3 1 6 8.67362e-19 2 2 6 1.31145e-15 1 3 6 2.1684e-18 0 4 6 1.09288e-15 3 0 7 8.67362e-19 2 1 7 2.1684e-18 1 2 7 0 0 3 7 1.30104e-18 2 0 8 1.8735e-16 1 1 8 1.30104e-18 0 2 8 1.8735e-16 1 0 9 1.73472e-18 0 1 9 2.60209e-18 0 0 10 6.10623e-16 11 11 0 0 0 10 1 0 5.20417e-18 9 2 0 4.33681e-19 8 3 0 0 7 4 0 0 6 5 0 8.67362e-19 5 6 0 8.67362e-19 4 7 0 2.1684e-18 3 8 0 4.33681e-19 2 9 0 3.90313e-18 1 10 0 8.67362e-19 0 11 0 4.33681e-19 10 0 1 4.33681e-18 9 1 1 0 8 2 1 8.67362e-19 7 3 1 4.33681e-19 6 4 1 0 5 5 1 0 4 6 1 4.77049e-18 3 7 1 0 2 8 1 5.63785e-18 1 9 1 4.33681e-19 0 10 1 9.97466e-18 9 0 2 1.73472e-18 8 1 2 4.33681e-18 7 2 2 0 6 3 2 0 5 4 2 0 4 5 2 0 3 6 2 0 2 7 2 0 1 8 2 4.33681e-19 0 9 2 6.07153e-18 8 0 3 8.67362e-19 7 1 3 4.33681e-19 6 2 3 8.67362e-18 5 3 3 0 4 4 3 1.30104e-18 3 5 3 0 2 6 3 9.1073e-18 1 7 3 4.33681e-19 0 8 3 4.33681e-19 7 0 4 0 6 1 4 0 5 2 4 4.33681e-19 4 3 4 4.33681e-19 3 4 4 4.33681e-19 2 5 4 4.33681e-19 1 6 4 0 0 7 4 3.03577e-18 6 0 5 1.73472e-18 5 1 5 0 4 2 5 8.67362e-19 3 3 5 0 2 4 5 1.73472e-18 1 5 5 4.33681e-19 0 6 5 7.80626e-18 5 0 6 8.67362e-19 4 1 6 1.73472e-18 3 2 6 0 2 3 6 1.73472e-18 1 4 6 4.33681e-19 0 5 6 8.67362e-19 4 0 7 9.97466e-18 3 1 7 0 2 2 7 4.33681e-19 1 3 7 4.33681e-19 0 4 7 4.33681e-19 3 0 8 4.33681e-19 2 1 8 8.67362e-19 1 2 8 8.67362e-19 0 3 8 4.33681e-19 2 0 9 1.0842e-17 1 1 9 8.67362e-19 0 2 9 1.99493e-17 1 0 10 8.67362e-19 0 1 10 3.07913e-17 0 0 11 8.2833e-17 12 12 0 0 0.00479751 11 1 0 0 10 2 0 2.28983e-16 9 3 0 0 8 4 0 0 7 5 0 8.67362e-19 6 6 0 5.10009e-16 5 7 0 1.30104e-18 4 8 0 1.56125e-16 3 9 0 8.67362e-19 2 10 0 1.14492e-16 1 11 0 3.03577e-18 0 12 0 0.00479751 11 0 1 0 10 1 1 0 9 2 1 0 8 3 1 1.73472e-18 7 4 1 4.33681e-19 6 5 1 2.1684e-18 5 6 1 4.33681e-19 4 7 1 8.67362e-19 3 8 1 0 2 9 1 4.33681e-19 1 10 1 8.67362e-19 0 11 1 8.67362e-18 10 0 2 1.14492e-16 9 1 2 0 8 2 2 0 7 3 2 4.33681e-19 6 4 2 7.28584e-16 5 5 2 0 4 6 2 5.46438e-16 3 7 2 0 2 8 2 2.81025e-16 1 9 2 4.33681e-19 0 10 2 2.28983e-16 9 0 3 0 8 1 3 8.67362e-19 7 2 3 4.33681e-19 6 3 3 8.67362e-19 5 4 3 4.33681e-19 4 5 3 4.33681e-19 3 6 3 8.67362e-19 2 7 3 1.30104e-18 1 8 3 8.67362e-19 0 9 3 1.73472e-18 8 0 4 6.245e-16 7 1 4 4.33681e-19 6 2 4 1.82146e-15 5 3 4 0 4 4 4 4.33681e-16 3 5 4 0 2 6 4 1.63931e-15 1 7 4 4.33681e-19 0 8 4 6.245e-16 7 0 5 8.67362e-19 6 1 5 4.33681e-19 5 2 5 0 4 3 5 4.33681e-19 3 4 5 4.33681e-19 2 5 5 1.30104e-18 1 6 5 4.33681e-19 0 7 5 2.1684e-18 6 0 6 5.10009e-16 5 1 6 4.33681e-19 4 2 6 5.46438e-16 3 3 6 4.33681e-19 2 4 6 1.09288e-15 1 5 6 4.33681e-19 0 6 6 0 5 0 7 4.33681e-19 4 1 7 2.1684e-18 3 2 7 0 2 3 7 3.03577e-18 1 4 7 4.33681e-19 0 5 7 2.1684e-18 4 0 8 4.68375e-16 3 1 8 4.33681e-19 2 2 8 1.1241e-15 1 3 8 8.67362e-19 0 4 8 1.56125e-16 3 0 9 8.67362e-19 2 1 9 2.1684e-18 1 2 9 4.33681e-19 0 3 9 1.73472e-18 2 0 10 4.57967e-16 1 1 10 2.1684e-18 0 2 10 4.57967e-16 1 0 11 2.1684e-18 0 1 11 8.67362e-18 0 0 12 0.00479751 TEST02 Product Gauss-Legendre rules for the 3D Legendre integral. Density function rho(x) = 1. Region: -1 <= x <= +1. -1 <= y <= +1. -1 <= z <= +1. Exactness: 3 = 2 * min ( 2, 3, 4 ) - 1 Order: N = 2 * 3 * 4 Quadrature rule for the 3D Legendre integral. Number of points in rule is 24 D I J K Relative Error 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 3.33067e-16 2 2 0 0 0 1 1 0 0 0 2 0 1.66533e-16 1 0 1 0 0 1 1 0 0 0 2 4.996e-16 3 3 0 0 0 2 1 0 0 1 2 0 0 0 3 0 0 2 0 1 6.93889e-17 1 1 1 0 0 2 1 0 1 0 2 0 0 1 2 0 0 0 3 5.55112e-17 4 4 0 0 0.444444 3 1 0 0 2 2 0 2.498e-16 1 3 0 0 0 4 0 4.16334e-16 3 0 1 0 2 1 1 0 1 2 1 0 0 3 1 0 2 0 2 4.996e-16 1 1 2 0 0 2 2 3.747e-16 1 0 3 0 0 1 3 0 0 0 4 8.32667e-16 CUBE_EXACTNESS_PRB Normal end of execution. 16 August 2014 11:15:17 PM