26 February 2020 11:32:49 AM EXACTNESS_TEST C++ version Test the EXACTNESS library. CHEBYSHEV1_EXACTNESS_TEST 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 5.65432e-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 1.88477e-16 5 0 6 2.26173e-16 7 0 8 5.16966e-16 9 0 10 0.00793651 CHEBYSHEV2_EXACTNESS_TEST 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 0 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 2.82716e-16 5 0 6 1.13086e-16 7 2.08167e-17 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 0 5 0 6 4.52346e-16 7 6.93889e-18 8 4.84656e-16 9 0 10 0.0238095 CHEBYSHEV3_EXACTNESS_TEST 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 1.11022e-16 6 1.13086e-16 7 1.11022e-16 8 0.0285714 CLENSHAW_CURTIS_EXACTNESS_TEST 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 0 5 0 6 0.0666667 FEJER1_EXACTNESS_TEST 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 2.77556e-17 4 2.77556e-16 5 2.77556e-17 6 0.0208333 FEJER2_EXACTNESS_TEST 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 1.38778e-16 5 0 6 0.0375 GEGENBAUER_EXACTNESS_TEST Gauss-Gegenbauer rules for the Gegenbauer integral. Density function rho(x) = 1. Region: -1 <= x <= +1. Exactness: 2*N-1. Lambda = 1.75 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 1.38778e-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 0 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 0 5 0 6 0 7 1.38778e-17 8 1.249e-16 9 0 10 0.016125 HERMITE_EXACTNESS_TEST 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 5.55112e-17 4 0.128379 5 0 6 2.38514 7 0 8 12.5406 9 0 10 58.1056 HERMITE_1_EXACTNESS_TEST 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 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 5.55112e-17 4 0.128379 5 0 6 2.38514 7 0 8 12.5406 9 0 10 58.1056 LAGUERRE_EXACTNESS_TEST 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 2.96059e-16 4 0 5 2.36848e-16 6 3.15797e-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 1.57898e-16 7 1.80455e-16 8 3.60911e-16 9 3.20809e-16 10 0.00396825 LAGUERRE_1_EXACTNESS_TEST 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 2.96059e-16 4 0 5 2.36848e-16 6 3.15797e-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 1.57898e-16 7 1.80455e-16 8 1.80455e-16 9 3.20809e-16 10 0.00396825 LEGENDRE_EXACTNESS_TEST 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 1.38778e-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 0 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 0 5 0 6 0 7 1.38778e-17 8 1.249e-16 9 0 10 0.016125 EXACTNESS_TEST Normal end of execution. 26 February 2020 11:32:49 AM