10-Jan-2019 11:55:03 EXACTNESS_TEST MATLAB version Test EXACTNESS. CHEBYSHEV1_EXACTNESS_TEST Test Gauss-Chebyshev1 rules for the Chebyshev1 integral. Density function rho(x) = 1/sqrt(1-x^2). Region: -1 <= x <= +1. Exactness: 2*N-1. Quadrature rule for Chebyshev1 integral. Order N = 1 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 1.0000000000000000 Quadrature rule for Chebyshev1 integral. Order N = 2 Degree Relative Error 0 0.0000000000000003 1 0.0000000000000002 2 0.0000000000000003 3 0.0000000000000003 4 0.3333333333333331 Quadrature rule for Chebyshev1 integral. Order N = 3 Degree Relative Error 0 0.0000000000000003 1 0.0000000000000000 2 0.0000000000000006 3 0.0000000000000000 4 0.0000000000000006 5 0.0000000000000000 6 0.0999999999999992 Quadrature rule for Chebyshev1 integral. 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 Chebyshev1 integral. Order N = 5 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000001 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000002 5 0.0000000000000000 6 0.0000000000000002 7 0.0000000000000000 8 0.0000000000000005 9 0.0000000000000000 10 0.0079365079365082 CHEBYSHEV2_EXACTNESS_TEST Test Gauss-Chebyshev2 rules for the Chebyshev2 integral. Density function rho(x) = sqrt(1-x^2). Region: -1 <= x <= +1. Exactness: 2*N-1. Quadrature rule for Chebyshev2 integral. Order N = 1 Degree Relative Error 0 0.0000000000000003 1 0.0000000000000000 2 1.0000000000000000 Quadrature rule for Chebyshev2 integral. Order N = 2 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000002 2 0.0000000000000000 3 0.0000000000000000 4 0.5000000000000000 Quadrature rule for Chebyshev2 integral. 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 Chebyshev2 integral. Order N = 4 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000003 5 0.0000000000000000 6 0.0000000000000001 7 0.0000000000000000 8 0.0714285714285713 Quadrature rule for Chebyshev2 integral. Order N = 5 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000001 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000000 5 0.0000000000000000 6 0.0000000000000005 7 0.0000000000000000 8 0.0000000000000005 9 0.0000000000000000 10 0.0238095238095231 CHEBYSHEV3_EXACTNESS_TEST Test Gauss-Chebyshev3 rules for the Chebyshev1 integral. Density function rho(x) = 1/sqrt(1-x^2). Region: -1 <= x <= +1. Exactness: 2*N-3. Quadrature rule for Chebyshev1 integral. Order N = 1 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 1.0000000000000000 Quadrature rule for Chebyshev1 integral. Order N = 2 Degree Relative Error 0 0.0000000000000003 1 0.0000000000000000 2 1.0000000000000007 Quadrature rule for Chebyshev1 integral. Order N = 3 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.3333333333333333 Quadrature rule for Chebyshev1 integral. 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 Chebyshev1 integral. Order N = 5 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000001 2 0.0000000000000000 3 0.0000000000000001 4 0.0000000000000000 5 0.0000000000000001 6 0.0000000000000001 7 0.0000000000000001 8 0.0285714285714283 CLENSHAW_CURTIS_EXACTNESS_TEST Test Clenshaw-Curtis rules on Legendre integrals. Density function rho(x) = 1. Region: -1 <= x <= +1. Exactness: N for N odd, N-1 for N even. Quadrature rule for Legendre integral. Rule of order N = 1 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 1.0000000000000000 Quadrature rule for Legendre integral. Rule of order N = 2 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 2.0000000000000004 Quadrature rule for 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 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 Legendre integral. Rule of order N = 5 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 0.0000000000000002 3 0.0000000000000000 4 0.0000000000000000 5 0.0000000000000000 6 0.0666666666666664 FEJER1_EXACTNESS_TEST Test Fejer Type 1 rules on Legendre integrals. Density function rho(x) = 1. Region: -1 <= x <= +1. Exactness: N for N odd, N-1 for N even. Quadrature rule for Legendre integral. Rule of order N = 1 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 1.0000000000000000 Quadrature rule for Legendre integral. Rule of order N = 2 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.4999999999999997 Quadrature rule for Legendre integral. Rule of order N = 3 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 0.0000000000000002 3 0.0000000000000000 4 0.2500000000000002 Quadrature rule for 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 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 0.0208333333333333 FEJER2_EXACTNESS_TEST Test Fejer Type 2 rules on Legendre integrals. Density function rho(x) = 1. Region: -1 <= x <= +1. Exactness: N for N odd, N-1 for N even. Quadrature rule for Legendre integral. Rule of order N = 1 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 1.0000000000000000 Quadrature rule for Legendre integral. Rule of order N = 2 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.2499999999999999 Quadrature rule for Legendre integral. Rule of order N = 3 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000002 3 0.0000000000000000 4 0.1666666666666666 Quadrature rule for Legendre integral. Rule of order N = 4 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000002 3 0.0000000000000000 4 0.0624999999999999 Quadrature rule for Legendre integral. Rule of order N = 5 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 0.0000000000000002 3 0.0000000000000000 4 0.0000000000000001 5 0.0000000000000000 6 0.0374999999999995 GEGENBAUER_EXACTNESS_TEST Test quadrature rules for the Gegenbauer integral. Density function rho(x) = (1-x^2)^(lambda-1/2). Using LAMBDA = 1.75 Region: -1 <= x <= +1. Exactness: 2*N-1. Quadrature rule for Gegenbauer integral. Lambda = 1.75 Rule of order N = 1 Degree Relative Error 0 0.0000000000000004 1 0.0000000000000000 2 1.0000000000000000 Quadrature rule for Gegenbauer integral. Lambda = 1.75 Rule of order N = 2 Degree Relative Error 0 0.0000000000000005 1 0.0000000000000000 2 0.0000000000000010 3 0.0000000000000000 4 0.5454545454545461 Quadrature rule for Gegenbauer integral. Lambda = 1.75 Rule of order N = 3 Degree Relative Error 0 0.0000000000000004 1 0.0000000000000000 2 0.0000000000000002 3 0.0000000000000000 4 0.0000000000000011 5 0.0000000000000000 6 0.2400000000000013 Quadrature rule for Gegenbauer integral. Lambda = 1.75 Rule of order N = 4 Degree Relative Error 0 0.0000000000000004 1 0.0000000000000000 2 0.0000000000000012 3 0.0000000000000001 4 0.0000000000000023 5 0.0000000000000001 6 0.0000000000000028 7 0.0000000000000001 8 0.0938345864661684 Quadrature rule for Gegenbauer integral. Lambda = 1.75 Rule of order N = 5 Degree Relative Error 0 0.0000000000000004 1 0.0000000000000002 2 0.0000000000000007 3 0.0000000000000001 4 0.0000000000000006 5 0.0000000000000000 6 0.0000000000000007 7 0.0000000000000000 8 0.0000000000000012 9 0.0000000000000000 10 0.0339980385746995 HERMITE_EXACTNESS_TEST Test Gauss-Hermite rules on Hermite integrals. Density function rho(x) = exp(-x^2). Region: -oo < x < +oo. Exactness: 2N-1. Quadrature rule for Hermite integral Rule of order N = 1 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 1.0000000000000000 Quadrature rule for Hermite integral Rule of order N = 2 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 0.0000000000000004 3 0.0000000000000000 4 0.6666666666666666 Quadrature rule for Hermite integral Rule of order N = 3 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000003 5 0.0000000000000000 6 0.4000000000000002 Quadrature rule for Hermite integral Rule of order N = 4 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000001 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000002 5 0.0000000000000001 6 0.0000000000000003 7 0.0000000000000000 8 0.2285714285714290 Quadrature rule for 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 0.0000000000000000 9 0.0000000000000000 10 0.1269841269841271 HERMITE_1_EXACTNESS_TEST Test Gauss-Hermite rules on Hermite integrals. Density function rho(x) = 1. Region: -oo < x < +oo. Exactness: 2N-1. Quadrature rule for Hermite integral Rule of order N = 1 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000000 2 1.0000000000000000 Quadrature rule for Hermite integral Rule of order N = 2 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000003 3 0.0000000000000000 4 0.6666666666666666 Quadrature rule for Hermite integral Rule of order N = 3 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000003 3 0.0000000000000000 4 0.0000000000000005 5 0.0000000000000000 6 0.4000000000000003 Quadrature rule for Hermite integral Rule of order N = 4 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000003 5 0.0000000000000001 6 0.0000000000000004 7 0.0000000000000000 8 0.2285714285714290 Quadrature rule for 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 0.0000000000000000 9 0.0000000000000000 10 0.1269841269841271 LAGUERRE_EXACTNESS_TEST Test Gauss-Laguerre rules on Laguerre integrals. Density function rho(x) = exp(-x). Region: 0 <= x < +oo. Exactness: 2N-1. Quadrature rule for Laguerre integral. Rule of order N = 1 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.5000000000000000 Quadrature rule for 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 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 Laguerre integral. Rule of order N = 4 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000001 2 0.0000000000000001 3 0.0000000000000001 4 0.0000000000000001 5 0.0000000000000002 6 0.0000000000000003 7 0.0000000000000002 8 0.0142857142857146 Quadrature rule for 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 0.0000000000000002 7 0.0000000000000002 8 0.0000000000000004 9 0.0000000000000003 10 0.0039682539682544 LAGUERRE_1_EXACTNESS_TEST Test quadrature rules on Laguerre integrals. Density function rho(x) = 1. Region: 0 <= x < +oo. Exactness: 2N-1. Quadrature rule for Laguerre integral. Rule of order N = 1 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.5000000000000000 Quadrature rule for 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 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 Laguerre integral. Rule of order N = 4 Degree Relative Error 0 0.0000000000000001 1 0.0000000000000001 2 0.0000000000000001 3 0.0000000000000001 4 0.0000000000000001 5 0.0000000000000002 6 0.0000000000000003 7 0.0000000000000002 8 0.0142857142857146 Quadrature rule for 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 0.0000000000000002 7 0.0000000000000002 8 0.0000000000000002 9 0.0000000000000003 10 0.0039682539682542 LEGENDRE_EXACTNESS_TEST Test Gauss-Legendre rules on Legendre integrals. Density function rho(x) = 1. Region: -1 <= x <= +1. Exactness: 2*N-1. Quadrature rule for Legendre integral. Rule of order N = 1 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 1.0000000000000000 Quadrature rule for Legendre integral. Rule of order N = 2 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.4444444444444446 Quadrature rule for Legendre integral. Rule of order N = 3 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000002 3 0.0000000000000000 4 0.0000000000000001 5 0.0000000000000000 6 0.1599999999999997 Quadrature rule for 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 0.0000000000000000 7 0.0000000000000000 8 0.0522448979591837 Quadrature rule for Legendre integral. Rule of order N = 5 Degree Relative Error 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000000 5 0.0000000000000000 6 0.0000000000000000 7 0.0000000000000000 8 0.0000000000000001 9 0.0000000000000000 10 0.0161249685059213 EXACTNESS_TEST Normal end of execution. 10-Jan-2019 11:55:03