6 March 2018 2:21:49.306 PM SQUARE_EXACTNESS_TEST FORTRAN90 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 0.0000000000000000 1 1 0 0.0000000000000000 0 1 0.0000000000000000 2 2 0 1.0000000000000000 1 1 0.0000000000000000 0 2 1.0000000000000000 Quadrature rule for the 2D Legendre integral. Number of points in rule is 4 D I J Relative Error 0 0 0 0.0000000000000000 1 1 0 0.0000000000000000 0 1 0.0000000000000000 2 2 0 0.0000000000000000 1 1 0.0000000000000000 0 2 0.0000000000000000 3 3 0 0.0000000000000000 2 1 0.0000000000000000 1 2 0.0000000000000000 0 3 0.0000000000000000 4 4 0 0.4444444444444445 3 1 0.0000000000000000 2 2 0.0000000000000000 1 3 0.0000000000000000 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 0.0000000000000000 1 1 0 0.0000000000000000 0 1 0.0000000000000000 2 2 0 0.0000000000000002 1 1 0.0000000000000000 0 2 0.0000000000000002 3 3 0 0.0000000000000000 2 1 0.0000000000000000 1 2 0.0000000000000000 0 3 0.0000000000000001 4 4 0 0.0000000000000003 3 1 0.0000000000000000 2 2 0.0000000000000005 1 3 0.0000000000000000 0 4 0.0000000000000003 5 5 0 0.0000000000000000 4 1 0.0000000000000000 3 2 0.0000000000000000 2 3 0.0000000000000000 1 4 0.0000000000000000 0 5 0.0000000000000000 6 6 0 0.1599999999999996 5 1 0.0000000000000000 4 2 0.0000000000000004 3 3 0.0000000000000000 2 4 0.0000000000000004 1 5 0.0000000000000000 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 0.0000000000000002 1 1 0 0.0000000000000000 0 1 0.0000000000000000 2 2 0 0.0000000000000002 1 1 0.0000000000000000 0 2 0.0000000000000003 3 3 0 0.0000000000000000 2 1 0.0000000000000000 1 2 0.0000000000000000 0 3 0.0000000000000000 4 4 0 0.0000000000000008 3 1 0.0000000000000000 2 2 0.0000000000000005 1 3 0.0000000000000000 0 4 0.0000000000000008 5 5 0 0.0000000000000000 4 1 0.0000000000000000 3 2 0.0000000000000000 2 3 0.0000000000000000 1 4 0.0000000000000000 0 5 0.0000000000000000 6 6 0 0.0000000000000010 5 1 0.0000000000000000 4 2 0.0000000000000010 3 3 0.0000000000000000 2 4 0.0000000000000010 1 5 0.0000000000000000 0 6 0.0000000000000012 7 7 0 0.0000000000000000 6 1 0.0000000000000000 5 2 0.0000000000000000 4 3 0.0000000000000000 3 4 0.0000000000000000 2 5 0.0000000000000000 1 6 0.0000000000000000 0 7 0.0000000000000000 8 8 0 0.0522448979591847 7 1 0.0000000000000000 6 2 0.0000000000000012 5 3 0.0000000000000000 4 4 0.0000000000000012 3 5 0.0000000000000000 2 6 0.0000000000000010 1 7 0.0000000000000000 0 8 0.0522448979591847 Quadrature rule for the 2D Legendre integral. Number of points in rule is 25 D I J Relative Error 0 0 0 0.0000000000000000 1 1 0 0.0000000000000000 0 1 0.0000000000000000 2 2 0 0.0000000000000002 1 1 0.0000000000000000 0 2 0.0000000000000003 3 3 0 0.0000000000000000 2 1 0.0000000000000001 1 2 0.0000000000000000 0 3 0.0000000000000000 4 4 0 0.0000000000000008 3 1 0.0000000000000000 2 2 0.0000000000000009 1 3 0.0000000000000000 0 4 0.0000000000000008 5 5 0 0.0000000000000000 4 1 0.0000000000000000 3 2 0.0000000000000000 2 3 0.0000000000000000 1 4 0.0000000000000000 0 5 0.0000000000000000 6 6 0 0.0000000000000008 5 1 0.0000000000000000 4 2 0.0000000000000010 3 3 0.0000000000000000 2 4 0.0000000000000010 1 5 0.0000000000000000 0 6 0.0000000000000010 7 7 0 0.0000000000000000 6 1 0.0000000000000000 5 2 0.0000000000000000 4 3 0.0000000000000000 3 4 0.0000000000000000 2 5 0.0000000000000000 1 6 0.0000000000000000 0 7 0.0000000000000000 8 8 0 0.0000000000000010 7 1 0.0000000000000000 6 2 0.0000000000000015 5 3 0.0000000000000000 4 4 0.0000000000000012 3 5 0.0000000000000000 2 6 0.0000000000000013 1 7 0.0000000000000000 0 8 0.0000000000000009 9 9 0 0.0000000000000000 8 1 0.0000000000000000 7 2 0.0000000000000000 6 3 0.0000000000000000 5 4 0.0000000000000000 4 5 0.0000000000000000 3 6 0.0000000000000000 2 7 0.0000000000000000 1 8 0.0000000000000000 0 9 0.0000000000000000 10 10 0 0.0161249685059223 9 1 0.0000000000000000 8 2 0.0000000000000013 7 3 0.0000000000000000 6 4 0.0000000000000016 5 5 0.0000000000000000 4 6 0.0000000000000017 3 7 0.0000000000000000 2 8 0.0000000000000013 1 9 0.0000000000000000 0 10 0.0161249685059223 Quadrature rule for the 2D Legendre integral. Number of points in rule is 36 D I J Relative Error 0 0 0 0.0000000000000002 1 1 0 0.0000000000000000 0 1 0.0000000000000000 2 2 0 0.0000000000000002 1 1 0.0000000000000000 0 2 0.0000000000000000 3 3 0 0.0000000000000000 2 1 0.0000000000000000 1 2 0.0000000000000000 0 3 0.0000000000000000 4 4 0 0.0000000000000000 3 1 0.0000000000000000 2 2 0.0000000000000000 1 3 0.0000000000000000 0 4 0.0000000000000001 5 5 0 0.0000000000000000 4 1 0.0000000000000000 3 2 0.0000000000000000 2 3 0.0000000000000000 1 4 0.0000000000000000 0 5 0.0000000000000000 6 6 0 0.0000000000000002 5 1 0.0000000000000000 4 2 0.0000000000000000 3 3 0.0000000000000000 2 4 0.0000000000000002 1 5 0.0000000000000000 0 6 0.0000000000000000 7 7 0 0.0000000000000000 6 1 0.0000000000000000 5 2 0.0000000000000000 4 3 0.0000000000000000 3 4 0.0000000000000000 2 5 0.0000000000000000 1 6 0.0000000000000000 0 7 0.0000000000000000 8 8 0 0.0000000000000004 7 1 0.0000000000000000 6 2 0.0000000000000001 5 3 0.0000000000000000 4 4 0.0000000000000000 3 5 0.0000000000000000 2 6 0.0000000000000000 1 7 0.0000000000000000 0 8 0.0000000000000001 9 9 0 0.0000000000000000 8 1 0.0000000000000000 7 2 0.0000000000000000 6 3 0.0000000000000000 5 4 0.0000000000000000 4 5 0.0000000000000000 3 6 0.0000000000000000 2 7 0.0000000000000000 1 8 0.0000000000000000 0 9 0.0000000000000000 10 10 0 0.0000000000000000 9 1 0.0000000000000000 8 2 0.0000000000000004 7 3 0.0000000000000000 6 4 0.0000000000000001 5 5 0.0000000000000000 4 6 0.0000000000000001 3 7 0.0000000000000000 2 8 0.0000000000000004 1 9 0.0000000000000000 0 10 0.0000000000000000 11 11 0 0.0000000000000000 10 1 0.0000000000000000 9 2 0.0000000000000000 8 3 0.0000000000000000 7 4 0.0000000000000000 6 5 0.0000000000000000 5 6 0.0000000000000000 4 7 0.0000000000000000 3 8 0.0000000000000000 2 9 0.0000000000000000 1 10 0.0000000000000000 0 11 0.0000000000000000 12 12 0 0.0047975112910184 11 1 0.0000000000000000 10 2 0.0000000000000001 9 3 0.0000000000000000 8 4 0.0000000000000003 7 5 0.0000000000000000 6 6 0.0000000000000002 5 7 0.0000000000000000 4 8 0.0000000000000002 3 9 0.0000000000000000 2 10 0.0000000000000002 1 11 0.0000000000000000 0 12 0.0047975112910181 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 0.0000000000000000 1 1 0 0.0000000000000000 0 1 0.0000000000000000 2 2 0 1.0000000000000000 1 1 0.0000000000000000 0 2 1.0000000000000000 Quadrature rule for the 2D Legendre integral. Number of points in rule is 3 D I J Relative Error 0 0 0 0.0000000000000000 1 1 0 0.0000000000000000 0 1 0.0000000000000000 2 2 0 2.0000000000000004 1 1 0.0000000000000000 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 0.0000000000000001 1 1 0 0.0000000000000001 0 1 0.0000000000000004 2 2 0 0.0000000000000005 1 1 0.0000000000000001 0 2 0.0000000000000003 3 3 0 0.0000000000000001 2 1 0.6666666666666665 1 2 0.0000000000000000 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 0.0000000000000001 1 1 0 0.0000000000000001 0 1 0.0000000000000006 2 2 0 0.0000000000000000 1 1 0.0000000000000007 0 2 0.0000000000000003 3 3 0 0.0000000000000000 2 1 0.0000000000000007 1 2 0.0000000000000004 0 3 0.0000000000000009 4 4 0 0.1666666666666668 3 1 0.0000000000000011 2 2 0.2499999999999993 1 3 0.0000000000000007 0 4 0.0416666666666671 Quadrature rule for the 2D Legendre integral. Number of points in rule is 15 D I J Relative Error 0 0 0 0.0000000000000000 1 1 0 0.0000000000000009 0 1 0.0000000000000003 2 2 0 0.0000000000000002 1 1 0.0000000000000002 0 2 0.0000000000000002 3 3 0 0.0000000000000002 2 1 0.0000000000000001 1 2 0.0000000000000004 0 3 0.0000000000000000 4 4 0 0.0000000000000012 3 1 0.0000000000000004 2 2 0.0000000000000011 1 3 0.0000000000000002 0 4 0.0000000000000001 5 5 0 0.0000000000000001 4 1 0.0333333333333332 3 2 0.0000000000000003 2 3 0.0555555555555558 1 4 0.0000000000000002 0 5 0.0166666666666670 Quadrature rule for the 2D Legendre integral. Number of points in rule is 21 D I J Relative Error 0 0 0 0.0000000000000000 1 1 0 0.0000000000000004 0 1 0.0000000000000001 2 2 0 0.0000000000000008 1 1 0.0000000000000002 0 2 0.0000000000000002 3 3 0 0.0000000000000008 2 1 0.0000000000000006 1 2 0.0000000000000002 0 3 0.0000000000000002 4 4 0 0.0000000000000008 3 1 0.0000000000000005 2 2 0.0000000000000001 1 3 0.0000000000000002 0 4 0.0000000000000000 5 5 0 0.0000000000000007 4 1 0.0000000000000010 3 2 0.0000000000000002 2 3 0.0000000000000003 1 4 0.0000000000000001 0 5 0.0000000000000003 6 6 0 0.0083333333333343 5 1 0.0000000000000013 4 2 0.0208333333333326 3 3 0.0000000000000004 2 4 0.0208333333333324 1 5 0.0000000000000004 0 6 0.0062500000000002 SQUARE_EXACTNESS_TEST Normal end of execution. 6 March 2018 2:21:49.306 PM