28 May 2014 8:59:37.450 PM EXACTNESS_PRB FORTRAN77 version Test the EXACTNESS library. TEST01 Gauss-Legendre rules for the Legendre integral. Density function rho(x) = 1. Region: -1 <= x <= +1. Exactness: 2*N-1. Quadrature rule for the Legendre integral Rule of order N = 1 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 1.0000000000000000 Quadrature rule for the Legendre integral Rule of order N = 2 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.4444444444444445 Quadrature rule for the Legendre integral Rule of order N = 3 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000002 3 0.0000000000000000 4 0.0000000000000003 5 0.0000000000000000 6 0.1599999999999996 Quadrature rule for the Legendre integral Rule of order N = 4 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000000 5 0.0000000000000000 6 0.0000000000000002 7 0.0000000000000000 8 0.0522448979591837 Quadrature rule for the Legendre integral Rule of order N = 5 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000001 5 0.0000000000000000 6 0.0000000000000000 7 0.0000000000000000 8 0.0000000000000001 9 0.0000000000000000 10 0.0161249685059213 TEST015 Fejer Type 1 rules for the Legendre integral. Density function rho(x) = 1. Region: -1 <= x <= +1. Exactness: N for N odd, N-1 for N even. Quadrature rule for the Legendre integral Rule of order N = 1 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 1.0000000000000000 Quadrature rule for the Legendre integral Rule of order N = 2 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.4999999999999997 Quadrature rule for the Legendre integral Rule of order N = 3 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000002 3 0.0000000000000000 4 0.2500000000000005 Quadrature rule for the Legendre integral Rule of order N = 4 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000001 2 0.0000000000000002 3 0.0000000000000000 4 0.0416666666666664 Quadrature rule for the Legendre integral Rule of order N = 5 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000001 2 0.0000000000000002 3 0.0000000000000001 4 0.0000000000000003 5 0.0000000000000000 6 0.0208333333333331 TEST02 Fejer Type 2 rules for the Legendre integral. Density function rho(x) = 1. Region: -1 <= x <= +1. Exactness: N for N odd, N-1 for N even. Quadrature rule for the Legendre integral Rule of order N = 1 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 1.0000000000000000 Quadrature rule for the Legendre integral Rule of order N = 2 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.2499999999999999 Quadrature rule for the Legendre integral Rule of order N = 3 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000002 3 0.0000000000000000 4 0.1666666666666664 Quadrature rule for the Legendre integral Rule of order N = 4 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000002 3 0.0000000000000000 4 0.0625000000000001 Quadrature rule for the Legendre integral Rule of order N = 5 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 0.0000000000000002 3 0.0000000000000000 4 0.0000000000000003 5 0.0000000000000000 6 0.0374999999999995 TEST03 Clenshaw-Curtis rules for the Legendre integral. Density function rho(x) = 1. Region: -1 <= x <= +1. Exactness: N for N odd, N-1 for N even. Quadrature rule for the Legendre integral Rule of order N = 1 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 1.0000000000000000 Quadrature rule for the Legendre integral Rule of order N = 2 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 2.0000000000000004 Quadrature rule for the Legendre integral Rule of order N = 3 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.6666666666666665 Quadrature rule for the Legendre integral Rule of order N = 4 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000001 2 0.0000000000000002 3 0.0000000000000000 4 0.1666666666666668 Quadrature rule for the Legendre integral Rule of order N = 5 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 0.0000000000000002 3 0.0000000000000000 4 0.0000000000000003 5 0.0000000000000000 6 0.0666666666666664 TEST04 Gauss-Laguerre rules for the Laguerre integral. Density function rho(x) = exp(-x). Region: 0 <= x .lt. +oo. Exactness: 2N-1. Quadrature rule for the Laguerre integral Rule of order N = 1 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.5000000000000000 Quadrature rule for the Laguerre integral Rule of order N = 2 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.1666666666666667 Quadrature rule for the Laguerre integral Rule of order N = 3 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000001 5 0.0000000000000002 6 0.0499999999999998 Quadrature rule for the Laguerre integral Rule of order N = 4 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000001 2 0.0000000000000001 3 0.0000000000000001 4 0.0000000000000000 5 0.0000000000000001 6 0.0000000000000002 7 0.0000000000000002 8 0.0142857142857145 Quadrature rule for the Laguerre integral Rule of order N = 5 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 0.0000000000000001 3 0.0000000000000001 4 0.0000000000000001 5 0.0000000000000002 6 0.0000000000000000 7 0.0000000000000002 8 0.0000000000000004 9 0.0000000000000002 10 0.0039682539682541 TEST05 Gauss-Laguerre quadrature rules for the Laguerre integral. Density function rho(x) = 1. Region: 0 <= x .lt. +oo. Exactness: 2N-1. Quadrature rule for the Laguerre integral Rule of order N = 1 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.5000000000000000 Quadrature rule for the Laguerre integral Rule of order N = 2 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.1666666666666667 Quadrature rule for the Laguerre integral Rule of order N = 3 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000000 5 0.0000000000000000 6 0.0500000000000000 Quadrature rule for the Laguerre integral Rule of order N = 4 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000001 2 0.0000000000000001 3 0.0000000000000001 4 0.0000000000000000 5 0.0000000000000001 6 0.0000000000000002 7 0.0000000000000002 8 0.0142857142857145 Quadrature rule for the Laguerre integral Rule of order N = 5 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 0.0000000000000002 3 0.0000000000000001 4 0.0000000000000001 5 0.0000000000000002 6 0.0000000000000000 7 0.0000000000000002 8 0.0000000000000002 9 0.0000000000000002 10 0.0039682539682540 TEST06 Gauss-Hermite rules for the Hermite integral. Density function rho(x) = exp(-x^2). Region: -oo .lt. x .lt. +oo. Exactness: 2N-1. Quadrature rule for the Hermite integral Rule of order N = 1 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 1.0000000000000000 Quadrature rule for the Hermite integral Rule of order N = 2 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 0.0000000000000004 3 0.0000000000000000 4 0.6666666666666664 Quadrature rule for the Hermite integral Rule of order N = 3 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000002 5 0.0000000000000000 6 0.4000000000000001 Quadrature rule for the Hermite integral Rule of order N = 4 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000001 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000005 5 0.0000000000000001 6 0.0000000000000005 7 0.0000000000000000 8 0.2285714285714293 Quadrature rule for the Hermite integral Rule of order N = 5 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000001 3 0.0000000000000000 4 0.0000000000000000 5 0.0000000000000000 6 0.0000000000000001 7 0.0000000000000000 8 0.0000000000000006 9 0.0000000000000000 10 0.1269841269841276 TEST07 Gauss-Hermite rules for the Hermite integral. Density function rho(x) = 1. Region: -oo .lt. x .lt. +oo. Exactness: 2N-1. Quadrature rule for the Hermite integral Rule of order N = 1 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 1.0000000000000000 Quadrature rule for the Hermite integral Rule of order N = 2 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000003 3 0.0000000000000000 4 0.6666666666666665 Quadrature rule for the Hermite integral Rule of order N = 3 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000003 3 0.0000000000000000 4 0.0000000000000003 5 0.0000000000000000 6 0.4000000000000002 Quadrature rule for the Hermite integral Rule of order N = 4 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000007 5 0.0000000000000000 6 0.0000000000000008 7 0.0000000000000000 8 0.2285714285714293 Quadrature rule for the Hermite integral Rule of order N = 5 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000001 3 0.0000000000000000 4 0.0000000000000000 5 0.0000000000000000 6 0.0000000000000001 7 0.0000000000000000 8 0.0000000000000006 9 0.0000000000000000 10 0.1269841269841276 TEST08 Gauss-Chebyshev1 rules for the Chebyshev1 integral. Density function rho(x) = 1/sqrt(1-x^2). Region: -1 .lt. x .lt. +1. Exactness: 2N-1. Quadrature rule for the Chebyshev1 integral Rule of order N = 1 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 1.0000000000000000 Quadrature rule for the Chebyshev1 integral Rule of order N = 2 Degree Relative Error 0 0.0000000000000003 1 0.0000000000000002 2 0.0000000000000003 3 0.0000000000000003 4 0.3333333333333331 Quadrature rule for the Chebyshev1 integral Rule of order N = 3 Degree Relative Error 0 0.0000000000000003 1 0.0000000000000000 2 0.0000000000000006 3 0.0000000000000000 4 0.0000000000000008 5 0.0000000000000000 6 0.0999999999999991 Quadrature rule for the Chebyshev1 integral Rule of order N = 4 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000001 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000000 5 0.0000000000000000 6 0.0000000000000001 7 0.0000000000000000 8 0.0285714285714287 Quadrature rule for the Chebyshev1 integral Rule of order N = 5 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000001 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000004 5 0.0000000000000000 6 0.0000000000000003 7 0.0000000000000000 8 0.0000000000000006 9 0.0000000000000000 10 0.0079365079365085 TEST085 Gauss-Chebyshev3 rules for the Chebyshev1 integral. Density function rho(x) = 1/sqrt(1-x^2). Region: -1 .lt. x .lt. +1. Exactness: 2N-3. Quadrature rule for the Chebyshev1 integral Rule of order N = 1 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 1.0000000000000000 Quadrature rule for the Chebyshev1 integral Rule of order N = 2 Degree Relative Error 0 0.0000000000000003 1 0.0000000000000000 2 1.0000000000000007 Quadrature rule for the Chebyshev1 integral Rule of order N = 3 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.3333333333333333 Quadrature rule for the Chebyshev1 integral Rule of order N = 4 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000000 5 0.0000000000000000 6 0.1000000000000000 Quadrature rule for the Chebyshev1 integral Rule of order N = 5 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000001 2 0.0000000000000000 3 0.0000000000000001 4 0.0000000000000000 5 0.0000000000000002 6 0.0000000000000001 7 0.0000000000000001 8 0.0285714285714283 TEST09 Gauss-Chebyshev1 rules for the Chebyshev2 integral. Density function rho(x) = sqrt(1-x^2). Region: -1 .lt. x .lt. +1. Exactness: 2N-1. Quadrature rule for the Chebyshev2 integral Rule of order N = 1 Degree Relative Error 0 0.0000000000000003 1 0.0000000000000000 2 1.0000000000000000 Quadrature rule for the Chebyshev2 integral Rule of order N = 2 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000002 2 0.0000000000000000 3 0.0000000000000000 4 0.5000000000000000 Quadrature rule for the Chebyshev2 integral Rule of order N = 3 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000002 2 0.0000000000000000 3 0.0000000000000001 4 0.0000000000000000 5 0.0000000000000000 6 0.1999999999999999 Quadrature rule for the Chebyshev2 integral Rule of order N = 4 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000001 5 0.0000000000000000 6 0.0000000000000002 7 0.0000000000000000 8 0.0714285714285715 Quadrature rule for the Chebyshev2 integral Rule of order N = 5 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000001 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000003 5 0.0000000000000000 6 0.0000000000000006 7 0.0000000000000000 8 0.0000000000000008 9 0.0000000000000000 10 0.0238095238095227 EXACTNESS_PRB Normal end of execution. 28 May 2014 8:59:37.452 PM