16 August 2014 08:51:46 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 0.0000000000000000 1 1 0 0 0.0000000000000000 0 1 0 0.0000000000000000 0 0 1 0.0000000000000000 2 2 0 0 1.0000000000000000 1 1 0 0.0000000000000000 0 2 0 1.0000000000000000 1 0 1 0.0000000000000000 0 1 1 0.0000000000000000 0 0 2 1.0000000000000000 Quadrature rule for the 3D Legendre integral. Number of points in rule is 8 D I J K Relative Error 0 0 0 0 0.0000000000000000 1 1 0 0 0.0000000000000000 0 1 0 0.0000000000000000 0 0 1 0.0000000000000000 2 2 0 0 0.0000000000000000 1 1 0 0.0000000000000000 0 2 0 0.0000000000000000 1 0 1 0.0000000000000000 0 1 1 0.0000000000000000 0 0 2 0.0000000000000000 3 3 0 0 0.0000000000000000 2 1 0 0.0000000000000000 1 2 0 0.0000000000000000 0 3 0 0.0000000000000000 2 0 1 0.0000000000000001 1 1 1 0.0000000000000000 0 2 1 0.0000000000000001 1 0 2 0.0000000000000000 0 1 2 0.0000000000000000 0 0 3 0.0000000000000001 4 4 0 0 0.4444444444444446 3 1 0 0.0000000000000000 2 2 0 0.0000000000000002 1 3 0 0.0000000000000000 0 4 0 0.4444444444444446 3 0 1 0.0000000000000000 2 1 1 0.0000000000000000 1 2 1 0.0000000000000000 0 3 1 0.0000000000000000 2 0 2 0.0000000000000002 1 1 2 0.0000000000000000 0 2 2 0.0000000000000002 1 0 3 0.0000000000000000 0 1 3 0.0000000000000000 0 0 4 0.4444444444444446 Quadrature rule for the 3D Legendre integral. Number of points in rule is 27 D I J K Relative Error 0 0 0 0 0.0000000000000002 1 1 0 0 0.0000000000000000 0 1 0 0.0000000000000000 0 0 1 0.0000000000000000 2 2 0 0 0.0000000000000002 1 1 0 0.0000000000000000 0 2 0 0.0000000000000002 1 0 1 0.0000000000000000 0 1 1 0.0000000000000000 0 0 2 0.0000000000000003 3 3 0 0 0.0000000000000000 2 1 0 0.0000000000000000 1 2 0 0.0000000000000000 0 3 0 0.0000000000000000 2 0 1 0.0000000000000000 1 1 1 0.0000000000000000 0 2 1 0.0000000000000000 1 0 2 0.0000000000000000 0 1 2 0.0000000000000000 0 0 3 0.0000000000000001 4 4 0 0 0.0000000000000001 3 1 0 0.0000000000000000 2 2 0 0.0000000000000005 1 3 0 0.0000000000000000 0 4 0 0.0000000000000001 3 0 1 0.0000000000000000 2 1 1 0.0000000000000000 1 2 1 0.0000000000000000 0 3 1 0.0000000000000000 2 0 2 0.0000000000000005 1 1 2 0.0000000000000000 0 2 2 0.0000000000000005 1 0 3 0.0000000000000000 0 1 3 0.0000000000000000 0 0 4 0.0000000000000001 5 5 0 0 0.0000000000000000 4 1 0 0.0000000000000000 3 2 0 0.0000000000000000 2 3 0 0.0000000000000000 1 4 0 0.0000000000000000 0 5 0 0.0000000000000000 4 0 1 0.0000000000000000 3 1 1 0.0000000000000000 2 2 1 0.0000000000000000 1 3 1 0.0000000000000000 0 4 1 0.0000000000000000 3 0 2 0.0000000000000000 2 1 2 0.0000000000000000 1 2 2 0.0000000000000000 0 3 2 0.0000000000000000 2 0 3 0.0000000000000001 1 1 3 0.0000000000000000 0 2 3 0.0000000000000000 1 0 4 0.0000000000000000 0 1 4 0.0000000000000000 0 0 5 0.0000000000000000 6 6 0 0 0.1599999999999997 5 1 0 0.0000000000000000 4 2 0 0.0000000000000004 3 3 0 0.0000000000000000 2 4 0 0.0000000000000004 1 5 0 0.0000000000000000 0 6 0 0.1599999999999997 5 0 1 0.0000000000000000 4 1 1 0.0000000000000000 3 2 1 0.0000000000000000 2 3 1 0.0000000000000000 1 4 1 0.0000000000000000 0 5 1 0.0000000000000000 4 0 2 0.0000000000000004 3 1 2 0.0000000000000000 2 2 2 0.0000000000000006 1 3 2 0.0000000000000000 0 4 2 0.0000000000000004 3 0 3 0.0000000000000000 2 1 3 0.0000000000000000 1 2 3 0.0000000000000000 0 3 3 0.0000000000000000 2 0 4 0.0000000000000004 1 1 4 0.0000000000000000 0 2 4 0.0000000000000004 1 0 5 0.0000000000000000 0 1 5 0.0000000000000000 0 0 6 0.1599999999999998 Quadrature rule for the 3D Legendre integral. Number of points in rule is 64 D I J K Relative Error 0 0 0 0 0.0000000000000002 1 1 0 0 0.0000000000000000 0 1 0 0.0000000000000000 0 0 1 0.0000000000000001 2 2 0 0 0.0000000000000008 1 1 0 0.0000000000000000 0 2 0 0.0000000000000007 1 0 1 0.0000000000000000 0 1 1 0.0000000000000000 0 0 2 0.0000000000000007 3 3 0 0 0.0000000000000000 2 1 0 0.0000000000000000 1 2 0 0.0000000000000000 0 3 0 0.0000000000000000 2 0 1 0.0000000000000000 1 1 1 0.0000000000000000 0 2 1 0.0000000000000000 1 0 2 0.0000000000000000 0 1 2 0.0000000000000001 0 0 3 0.0000000000000000 4 4 0 0 0.0000000000000014 3 1 0 0.0000000000000000 2 2 0 0.0000000000000006 1 3 0 0.0000000000000000 0 4 0 0.0000000000000014 3 0 1 0.0000000000000000 2 1 1 0.0000000000000000 1 2 1 0.0000000000000000 0 3 1 0.0000000000000000 2 0 2 0.0000000000000005 1 1 2 0.0000000000000000 0 2 2 0.0000000000000005 1 0 3 0.0000000000000000 0 1 3 0.0000000000000000 0 0 4 0.0000000000000012 5 5 0 0 0.0000000000000000 4 1 0 0.0000000000000000 3 2 0 0.0000000000000000 2 3 0 0.0000000000000000 1 4 0 0.0000000000000000 0 5 0 0.0000000000000000 4 0 1 0.0000000000000000 3 1 1 0.0000000000000000 2 2 1 0.0000000000000000 1 3 1 0.0000000000000000 0 4 1 0.0000000000000000 3 0 2 0.0000000000000000 2 1 2 0.0000000000000000 1 2 2 0.0000000000000000 0 3 2 0.0000000000000000 2 0 3 0.0000000000000000 1 1 3 0.0000000000000000 0 2 3 0.0000000000000000 1 0 4 0.0000000000000000 0 1 4 0.0000000000000000 0 0 5 0.0000000000000001 6 6 0 0 0.0000000000000012 5 1 0 0.0000000000000000 4 2 0 0.0000000000000012 3 3 0 0.0000000000000000 2 4 0 0.0000000000000010 1 5 0 0.0000000000000000 0 6 0 0.0000000000000012 5 0 1 0.0000000000000000 4 1 1 0.0000000000000000 3 2 1 0.0000000000000000 2 3 1 0.0000000000000000 1 4 1 0.0000000000000000 0 5 1 0.0000000000000000 4 0 2 0.0000000000000015 3 1 2 0.0000000000000000 2 2 2 0.0000000000000004 1 3 2 0.0000000000000000 0 4 2 0.0000000000000015 3 0 3 0.0000000000000000 2 1 3 0.0000000000000000 1 2 3 0.0000000000000000 0 3 3 0.0000000000000000 2 0 4 0.0000000000000015 1 1 4 0.0000000000000000 0 2 4 0.0000000000000017 1 0 5 0.0000000000000000 0 1 5 0.0000000000000000 0 0 6 0.0000000000000006 7 7 0 0 0.0000000000000000 6 1 0 0.0000000000000000 5 2 0 0.0000000000000000 4 3 0 0.0000000000000000 3 4 0 0.0000000000000000 2 5 0 0.0000000000000000 1 6 0 0.0000000000000000 0 7 0 0.0000000000000000 6 0 1 0.0000000000000000 5 1 1 0.0000000000000000 4 2 1 0.0000000000000000 3 3 1 0.0000000000000000 2 4 1 0.0000000000000000 1 5 1 0.0000000000000000 0 6 1 0.0000000000000000 5 0 2 0.0000000000000000 4 1 2 0.0000000000000000 3 2 2 0.0000000000000000 2 3 2 0.0000000000000000 1 4 2 0.0000000000000000 0 5 2 0.0000000000000000 4 0 3 0.0000000000000000 3 1 3 0.0000000000000000 2 2 3 0.0000000000000000 1 3 3 0.0000000000000000 0 4 3 0.0000000000000001 3 0 4 0.0000000000000000 2 1 4 0.0000000000000000 1 2 4 0.0000000000000000 0 3 4 0.0000000000000000 2 0 5 0.0000000000000000 1 1 5 0.0000000000000000 0 2 5 0.0000000000000000 1 0 6 0.0000000000000000 0 1 6 0.0000000000000000 0 0 7 0.0000000000000000 8 8 0 0 0.0522448979591846 7 1 0 0.0000000000000000 6 2 0 0.0000000000000007 5 3 0 0.0000000000000000 4 4 0 0.0000000000000016 3 5 0 0.0000000000000000 2 6 0 0.0000000000000009 1 7 0 0.0000000000000000 0 8 0 0.0522448979591847 7 0 1 0.0000000000000000 6 1 1 0.0000000000000000 5 2 1 0.0000000000000000 4 3 1 0.0000000000000000 3 4 1 0.0000000000000000 2 5 1 0.0000000000000000 1 6 1 0.0000000000000000 0 7 1 0.0000000000000000 6 0 2 0.0000000000000010 5 1 2 0.0000000000000000 4 2 2 0.0000000000000016 3 3 2 0.0000000000000000 2 4 2 0.0000000000000016 1 5 2 0.0000000000000000 0 6 2 0.0000000000000010 5 0 3 0.0000000000000000 4 1 3 0.0000000000000000 3 2 3 0.0000000000000000 2 3 3 0.0000000000000000 1 4 3 0.0000000000000000 0 5 3 0.0000000000000000 4 0 4 0.0000000000000017 3 1 4 0.0000000000000000 2 2 4 0.0000000000000022 1 3 4 0.0000000000000000 0 4 4 0.0000000000000017 3 0 5 0.0000000000000000 2 1 5 0.0000000000000000 1 2 5 0.0000000000000000 0 3 5 0.0000000000000000 2 0 6 0.0000000000000007 1 1 6 0.0000000000000000 0 2 6 0.0000000000000006 1 0 7 0.0000000000000000 0 1 7 0.0000000000000000 0 0 8 0.0522448979591847 Quadrature rule for the 3D Legendre integral. Number of points in rule is 125 D I J K Relative Error 0 0 0 0 0.0000000000000000 1 1 0 0 0.0000000000000000 0 1 0 0.0000000000000001 0 0 1 0.0000000000000000 2 2 0 0 0.0000000000000002 1 1 0 0.0000000000000000 0 2 0 0.0000000000000005 1 0 1 0.0000000000000000 0 1 1 0.0000000000000000 0 0 2 0.0000000000000000 3 3 0 0 0.0000000000000000 2 1 0 0.0000000000000000 1 2 0 0.0000000000000000 0 3 0 0.0000000000000000 2 0 1 0.0000000000000000 1 1 1 0.0000000000000000 0 2 1 0.0000000000000001 1 0 2 0.0000000000000000 0 1 2 0.0000000000000001 0 0 3 0.0000000000000002 4 4 0 0 0.0000000000000003 3 1 0 0.0000000000000000 2 2 0 0.0000000000000006 1 3 0 0.0000000000000000 0 4 0 0.0000000000000003 3 0 1 0.0000000000000000 2 1 1 0.0000000000000000 1 2 1 0.0000000000000000 0 3 1 0.0000000000000000 2 0 2 0.0000000000000005 1 1 2 0.0000000000000000 0 2 2 0.0000000000000007 1 0 3 0.0000000000000000 0 1 3 0.0000000000000000 0 0 4 0.0000000000000017 5 5 0 0 0.0000000000000000 4 1 0 0.0000000000000000 3 2 0 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Number of points in rule is 216 D I J K Relative Error 0 0 0 0 0.0000000000000011 1 1 0 0 0.0000000000000000 0 1 0 0.0000000000000001 0 0 1 0.0000000000000001 2 2 0 0 0.0000000000000005 1 1 0 0.0000000000000000 0 2 0 0.0000000000000007 1 0 1 0.0000000000000000 0 1 1 0.0000000000000000 0 0 2 0.0000000000000003 3 3 0 0 0.0000000000000000 2 1 0 0.0000000000000000 1 2 0 0.0000000000000000 0 3 0 0.0000000000000000 2 0 1 0.0000000000000001 1 1 1 0.0000000000000000 0 2 1 0.0000000000000001 1 0 2 0.0000000000000000 0 1 2 0.0000000000000000 0 0 3 0.0000000000000000 4 4 0 0 0.0000000000000011 3 1 0 0.0000000000000000 2 2 0 0.0000000000000012 1 3 0 0.0000000000000000 0 4 0 0.0000000000000010 3 0 1 0.0000000000000000 2 1 1 0.0000000000000000 1 2 1 0.0000000000000000 0 3 1 0.0000000000000000 2 0 2 0.0000000000000005 1 1 2 0.0000000000000000 0 2 2 0.0000000000000007 1 0 3 0.0000000000000000 0 1 3 0.0000000000000000 0 0 4 0.0000000000000010 5 5 0 0 0.0000000000000000 4 1 0 0.0000000000000000 3 2 0 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0.0000000000000000 4 1 7 0.0000000000000000 3 2 7 0.0000000000000000 2 3 7 0.0000000000000000 1 4 7 0.0000000000000000 0 5 7 0.0000000000000000 4 0 8 0.0000000000000005 3 1 8 0.0000000000000000 2 2 8 0.0000000000000013 1 3 8 0.0000000000000000 0 4 8 0.0000000000000008 3 0 9 0.0000000000000000 2 1 9 0.0000000000000000 1 2 9 0.0000000000000000 0 3 9 0.0000000000000000 2 0 10 0.0000000000000011 1 1 10 0.0000000000000000 0 2 10 0.0000000000000011 1 0 11 0.0000000000000000 0 1 11 0.0000000000000000 0 0 12 0.0047975112910181 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 0.0000000000000000 1 1 0 0 0.0000000000000000 0 1 0 0.0000000000000000 0 0 1 0.0000000000000003 2 2 0 0 0.0000000000000000 1 1 0 0.0000000000000000 0 2 0 0.0000000000000002 1 0 1 0.0000000000000000 0 1 1 0.0000000000000000 0 0 2 0.0000000000000005 3 3 0 0 0.0000000000000000 2 1 0 0.0000000000000000 1 2 0 0.0000000000000000 0 3 0 0.0000000000000000 2 0 1 0.0000000000000001 1 1 1 0.0000000000000000 0 2 1 0.0000000000000000 1 0 2 0.0000000000000000 0 1 2 0.0000000000000000 0 0 3 0.0000000000000001 4 4 0 0 0.4444444444444447 3 1 0 0.0000000000000000 2 2 0 0.0000000000000002 1 3 0 0.0000000000000000 0 4 0 0.0000000000000003 3 0 1 0.0000000000000000 2 1 1 0.0000000000000000 1 2 1 0.0000000000000000 0 3 1 0.0000000000000000 2 0 2 0.0000000000000005 1 1 2 0.0000000000000000 0 2 2 0.0000000000000004 1 0 3 0.0000000000000000 0 1 3 0.0000000000000000 0 0 4 0.0000000000000008 CUBE_EXACTNESS_PRB Normal end of execution. 16 August 2014 08:51:46 PM