28 May 2014 11:09:13 PM EXACTNESS_PRB C++ 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 1 0 2 1 Quadrature rule for the Legendre integral. Rule of order N = 2 Degree Relative Error 0 0 1 0 2 0 3 0 4 0.444444 Quadrature rule for the Legendre integral. Rule of order N = 3 Degree Relative Error 0 0 1 0 2 1.66533e-16 3 0 4 2.77556e-16 5 0 6 0.16 Quadrature rule for the Legendre integral. Rule of order N = 4 Degree Relative Error 0 0 1 0 2 0 3 0 4 0 5 0 6 1.94289e-16 7 0 8 0.0522449 Quadrature rule for the Legendre integral. Rule of order N = 5 Degree Relative Error 0 0 1 2.77556e-17 2 0 3 2.77556e-17 4 1.38778e-16 5 0 6 0 7 1.38778e-17 8 1.249e-16 9 0 10 0.016125 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 1 0 2 1 Quadrature rule for the Legendre integral. Rule of order N = 2 Degree Relative Error 0 0 1 0 2 0.5 Quadrature rule for the Legendre integral. Rule of order N = 3 Degree Relative Error 0 1.11022e-16 1 0 2 1.66533e-16 3 0 4 0.25 Quadrature rule for the Legendre integral. Rule of order N = 4 Degree Relative Error 0 1.11022e-16 1 5.55112e-17 2 1.66533e-16 3 2.77556e-17 4 0.0416667 Quadrature rule for the Legendre integral. Rule of order N = 5 Degree Relative Error 0 0 1 5.55112e-17 2 1.66533e-16 3 8.32667e-17 4 2.77556e-16 5 2.77556e-17 6 0.0208333 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 1 0 2 1 Quadrature rule for the Legendre integral. Rule of order N = 2 Degree Relative Error 0 0 1 0 2 0.25 Quadrature rule for the Legendre integral. Rule of order N = 3 Degree Relative Error 0 0 1 0 2 1.66533e-16 3 0 4 0.166667 Quadrature rule for the Legendre integral. Rule of order N = 4 Degree Relative Error 0 0 1 0 2 1.66533e-16 3 0 4 0.0625 Quadrature rule for the Legendre integral. Rule of order N = 5 Degree Relative Error 0 1.11022e-16 1 0 2 1.66533e-16 3 2.77556e-17 4 2.77556e-16 5 0 6 0.0375 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 1 0 2 1 Quadrature rule for the Legendre integral. Rule of order N = 2 Degree Relative Error 0 0 1 0 2 2 Quadrature rule for the Legendre integral. Rule of order N = 3 Degree Relative Error 0 1.11022e-16 1 0 2 0 3 0 4 0.666667 Quadrature rule for the Legendre integral. Rule of order N = 4 Degree Relative Error 0 0 1 5.55112e-17 2 1.66533e-16 3 0 4 0.166667 Quadrature rule for the Legendre integral. Rule of order N = 5 Degree Relative Error 0 1.11022e-16 1 1.38778e-17 2 1.66533e-16 3 1.38778e-17 4 2.77556e-16 5 1.38778e-17 6 0.0666667 TEST04 Gauss-Laguerre rules for the Laguerre integral. Density function rho(x) = exp(-x). Region: 0 <= x < +oo. Exactness: 2N-1. Quadrature rule for the Laguerre integral. Rule of order N = 1 Degree Relative Error 0 0 1 0 2 0.5 Quadrature rule for the Laguerre integral. Rule of order N = 2 Degree Relative Error 0 0 1 0 2 0 3 0 4 0.166667 Quadrature rule for the Laguerre integral. Rule of order N = 3 Degree Relative Error 0 0 1 0 2 0 3 0 4 1.4803e-16 5 2.36848e-16 6 0.05 Quadrature rule for the Laguerre integral. Rule of order N = 4 Degree Relative Error 0 0 1 1.11022e-16 2 1.11022e-16 3 1.4803e-16 4 0 5 1.18424e-16 6 1.57898e-16 7 1.80455e-16 8 0.0142857 Quadrature rule for the Laguerre integral. Rule of order N = 5 Degree Relative Error 0 1.11022e-16 1 0 2 1.11022e-16 3 1.4803e-16 4 1.4803e-16 5 2.36848e-16 6 0 7 1.80455e-16 8 3.60911e-16 9 1.60405e-16 10 0.00396825 TEST05 Gauss-Laguerre rules for the Laguerre integral. Density function rho(x) = 1. Region: 0 <= x < +oo. Exactness: 2N-1. Quadrature rule for the Laguerre integral. Rule of order N = 1 Degree Relative Error 0 0 1 0 2 0.5 Quadrature rule for the Laguerre integral. Rule of order N = 2 Degree Relative Error 0 0 1 0 2 0 3 0 4 0.166667 Quadrature rule for the Laguerre integral. Rule of order N = 3 Degree Relative Error 0 0 1 0 2 0 3 0 4 0 5 0 6 0.05 Quadrature rule for the Laguerre integral. Rule of order N = 4 Degree Relative Error 0 1.11022e-16 1 1.11022e-16 2 1.11022e-16 3 1.4803e-16 4 0 5 1.18424e-16 6 1.57898e-16 7 1.80455e-16 8 0.0142857 Quadrature rule for the Laguerre integral. Rule of order N = 5 Degree Relative Error 0 1.11022e-16 1 0 2 2.22045e-16 3 1.4803e-16 4 1.4803e-16 5 2.36848e-16 6 0 7 1.80455e-16 8 1.80455e-16 9 1.60405e-16 10 0.00396825 TEST06 Gauss-Hermite rules for the Hermite integral. Density function rho(x) = exp(-x^2). Region: -oo < x < +oo. Exactness: 2N-1. Quadrature rule for the Hermite integral. Rule of order N = 1 Degree Relative Error 0 0.43581 1 0 2 1 Quadrature rule for the Hermite integral. Rule of order N = 2 Degree Relative Error 0 0.43581 1 0 2 0.43581 3 0 4 0.623874 Quadrature rule for the Hermite integral. Rule of order N = 3 Degree Relative Error 0 0.43581 1 0 2 0.43581 3 0 4 0.128379 5 0 6 1.03108 Quadrature rule for the Hermite integral. Rule of order N = 4 Degree Relative Error 0 0.43581 1 5.55112e-17 2 0.43581 3 0 4 0.128379 5 1.11022e-16 6 2.38514 7 0 8 9.44557 Quadrature rule for the Hermite integral. Rule of order N = 5 Degree Relative Error 0 0.43581 1 2.77556e-17 2 0.43581 3 2.77556e-17 4 0.128379 5 0 6 2.38514 7 0 8 12.5406 9 0 10 58.1056 TEST07 Gauss-Hermite rules for the Hermite integral. Density function rho(x) = 1. Region: -oo < x < +oo. Exactness: 2N-1. Quadrature rule for the Hermite integral. Rule of order N = 1 Degree Relative Error 0 0.43581 1 0 2 1 Quadrature rule for the Hermite integral. Rule of order N = 2 Degree Relative Error 0 0.43581 1 0 2 0.43581 3 0 4 0.623874 Quadrature rule for the Hermite integral. Rule of order N = 3 Degree Relative Error 0 0.43581 1 0 2 0.43581 3 0 4 0.128379 5 0 6 1.03108 Quadrature rule for the Hermite integral. Rule of order N = 4 Degree Relative Error 0 0.43581 1 2.77556e-17 2 0.43581 3 0 4 0.128379 5 0 6 2.38514 7 0 8 9.44557 Quadrature rule for the Hermite integral. Rule of order N = 5 Degree Relative Error 0 0.43581 1 2.77556e-17 2 0.43581 3 2.77556e-17 4 0.128379 5 0 6 2.38514 7 0 8 12.5406 9 0 10 58.1056 TEST08 Gauss-Chebyshev1 rules for the Chebyshev1 integral. Density function rho(x) = 1/sqrt(1-x^2). Region: -1 <= x <= +1. Exactness: 2N-1. Quadrature rule for the Chebyshev1 integral. Rule of order N = 1 Degree Relative Error 0 0 1 0 2 1 Quadrature rule for the Chebyshev1 integral. Rule of order N = 2 Degree Relative Error 0 2.82716e-16 1 2.22045e-16 2 2.82716e-16 3 3.33067e-16 4 0.333333 Quadrature rule for the Chebyshev1 integral. Rule of order N = 3 Degree Relative Error 0 2.82716e-16 1 0 2 5.65432e-16 3 0 4 7.53909e-16 5 0 6 0.1 Quadrature rule for the Chebyshev1 integral. Rule of order N = 4 Degree Relative Error 0 0 1 1.11022e-16 2 0 3 0 4 0 5 0 6 1.13086e-16 7 0 8 0.0285714 Quadrature rule for the Chebyshev1 integral. Rule of order N = 5 Degree Relative Error 0 0 1 1.11022e-16 2 0 3 0 4 3.76955e-16 5 0 6 3.39259e-16 7 0 8 6.46208e-16 9 0 10 0.00793651 TEST085 Gauss-Chebyshev3 rules for the Chebyshev1 integral. Density function rho(x) = 1/sqrt(1-x^2). Region: -1 <= x <= +1. Exactness: 2N-3. Quadrature rule for the Chebyshev1 integral. Rule of order N = 1 Degree Relative Error 0 0 1 0 2 1 Quadrature rule for the Chebyshev1 integral. Rule of order N = 2 Degree Relative Error 0 2.82716e-16 1 0 2 1 Quadrature rule for the Chebyshev1 integral. Rule of order N = 3 Degree Relative Error 0 1.41358e-16 1 0 2 0 3 0 4 0.333333 Quadrature rule for the Chebyshev1 integral. Rule of order N = 4 Degree Relative Error 0 1.41358e-16 1 0 2 0 3 0 4 0 5 0 6 0.1 Quadrature rule for the Chebyshev1 integral. Rule of order N = 5 Degree Relative Error 0 0 1 5.55112e-17 2 0 3 1.11022e-16 4 0 5 1.66533e-16 6 1.13086e-16 7 1.11022e-16 8 0.0285714 TEST09 Gauss-Chebyshev2 rules for the Chebyshev2 integral. Density function rho(x) = sqrt(1-x^2). Region: -1 <= x <= +1. Exactness: 2N-1. Quadrature rule for the Chebyshev2 integral. Rule of order N = 1 Degree Relative Error 0 2.82716e-16 1 0 2 1 Quadrature rule for the Chebyshev2 integral. Rule of order N = 2 Degree Relative Error 0 0 1 1.66533e-16 2 0 3 4.16334e-17 4 0.5 Quadrature rule for the Chebyshev2 integral. Rule of order N = 3 Degree Relative Error 0 0 1 2.22045e-16 2 0 3 5.55112e-17 4 0 5 2.77556e-17 6 0.2 Quadrature rule for the Chebyshev2 integral. Rule of order N = 4 Degree Relative Error 0 1.41358e-16 1 2.77556e-17 2 0 3 1.38778e-17 4 1.41358e-16 5 1.38778e-17 6 2.26173e-16 7 6.93889e-18 8 0.0714286 Quadrature rule for the Chebyshev2 integral. Rule of order N = 5 Degree Relative Error 0 0 1 1.11022e-16 2 0 3 2.77556e-17 4 2.82716e-16 5 0 6 5.65432e-16 7 6.93889e-18 8 8.0776e-16 9 0 10 0.0238095 EXACTNESS_PRB Normal end of execution. 28 May 2014 11:09:13 PM