2 April 2023 11:21:46.687 AM gen_hermite_exactness(): FORTRAN90 version Investigate the polynomial exactness of a generalized Gauss-Hermite quadrature rule by integrating exponentially weighted monomials up to a given degree over the (-oo,oo) interval. gen_hermite_exactness: User input: Quadrature rule X file = "gen_herm_o4_a1.0_x.txt". Quadrature rule W file = "gen_herm_o4_a1.0_w.txt". Quadrature rule R file = "gen_herm_o4_a1.0_r.txt". Maximum degree to check = 10 Weighting function exponent ALPHA = 1.00000 OPTION = 0, integrate |x|^alpha*exp(-x*x)*f(x). Spatial dimension = 1 Number of points = 4 The quadrature rule to be tested is a generalized Gauss-Hermite rule ORDER = 4 ALPHA = 1.00000 OPTION = 0, standard rule: Integral ( -oo < x < oo ) |x|^alpha * exp(-x^2) * f(x) dx is to be approximated by sum ( 1 <= I <= ORDER ) w(i) * f(x(i)). Weights W: w( 1) = 0.7322330470336313E-01 w( 2) = 0.4267766952966369 w( 3) = 0.4267766952966369 w( 4) = 0.7322330470336313E-01 Abscissas X: x( 1) = -1.847759065022573 x( 2) = -0.7653668647301796 x( 3) = 0.7653668647301796 x( 4) = 1.847759065022573 Region R: r( 1) = -0.1000000000000000E+31 r( 2) = 0.1000000000000000E+31 A generalized Gauss-Hermite rule would be able to exactly integrate monomials up to and including degree = 7 Error Degree Exponents 0.0000000000000000 0 0.0000000000000000 1 0.0000000000000001 2 0.0000000000000001 3 0.0000000000000009 4 0.0000000000000000 5 0.0000000000000013 6 0.0000000000000000 7 0.1666666666666683 8 0.0000000000000000 9 0.4333333333333348 10 gen_hermite_exactness: Normal end of execution. 2 April 2023 11:21:46.688 AM