C 代码 研究 f（x，y） 正交规则的多项式精度 在 2D 矩形的内部.rar

21 January 2020 08:59:41 AM SQUARE_EXACTNESS_TEST 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 0.0000000000000000 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 0.4444444444444446 3 1 0.0000000000000000 2 2 0.0000000000000000 1 3 0.0000000000000000 0 4 0.4444444444444446 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 0.0000000000000000 4 4 0 0.0000000000000001 3 1 0.0000000000000000 2 2 0.0000000000000005 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 0.1599999999999996 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 0.0000000000000006 5 1 0.0000000000000000 4 2 0.0000000000000010 3 3 0.0000000000000000 2 4 0.0000000000000010 1 5 0.0000000000000000 0 6 0.0000000000000008 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 0.0000000000000010 5 3 0.0000000000000000 4 4 0.0000000000000012 3 5 0.0000000000000000 2 6 0.0000000000000009 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 t