gen_hermite_rule, a FORTRAN90 code which generates a specific generalized Gauss-Hermite quadrature rule, based on user input.
The rule is written to three files for easy use as input to other programs.
The generalized Gauss Hermite quadrature rule is used as follows:
Integral ( -oo < x < +oo ) |x-a|^alpha * exp( - b * ( x - a)^2 ) f(x) dxis to be approximated by
Sum ( 1 <= i <= order ) w(i) * f(x(i))
gen_hermite_rule order alpha a b filenamewhere
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
gen_hermite_rule is available in a C++ version and a FORTRAN90 version and a MATLAB version
ALPERT_RULE, a FORTRAN90 code which can set up an Alpert quadrature rule for functions which are regular, log(x) singular, or 1/sqrt(x) singular.
CCN_RULE, a FORTRAN90 code which defines a nested Clenshaw Curtis quadrature rule.
CHEBYSHEV1_RULE, a FORTRAN90 code which can compute and print a Gauss-Chebyshev type 1 quadrature rule.
CHEBYSHEV2_RULE, a FORTRAN90 code which can compute and print a Gauss-Chebyshev type 2 quadrature rule.
CLENSHAW_CURTIS_RULE, a FORTRAN90 code which defines a Clenshaw Curtis quadrature rule.
GEGENBAUER_RULE, a FORTRAN90 code which can compute and print a Gauss-Gegenbauer quadrature rule.
GEN_LAGUERRE_RULE, a FORTRAN90 code which computes a generalized Gauss-Laguerre quadrature rule.
HERMITE_RULE, a FORTRAN90 code which computes a generalized Gauss-Hermite quadrature rule.
INT_EXACTNESS_GEN_HERMITE, a FORTRAN90 code which checks the polynomial exactness of a generalized Gauss-Hermite quadrature rule.
JACOBI_RULE, a FORTRAN90 code which computes a generalized Gauss-Jacobi quadrature rule.
LAGUERRE_RULE, a FORTRAN90 code which computes a Gauss-Laguerre quadrature rule.
LEGENDRE_RULE, a FORTRAN90 code which computes a Gauss-Legendre quadrature rule.
LEGENDRE_RULE_FAST, a FORTRAN90 code which uses a fast (order N) algorithm to compute a Gauss-Legendre quadrature rule of given order.
LOGNORMAL_RULE, a FORTRAN90 code which can compute and print a quadrature rule for functions of a variable whose logarithm is normally distributed.
PATTERSON_RULE, a FORTRAN90 code which returns the points and weights of a 1D Gauss-Patterson quadrature rule of order 1, 3, 7, 15, 31, 63, 127, 255 or 511.
PATTERSON_RULE_COMPUTE, a FORTRAN90 code which computes the points and weights of a 1D Gauss-Patterson quadrature rule of order 1, 3, 7, 15, 31, 63, 127, 255 or 511.
QUADRATURE_RULES_GEN_HERMITE, a dataset directory which contains triples of files defining generalized Gauss-Hermite quadrature rules.
QUADRULE, a FORTRAN90 code which contains 1-dimensional quadrature rules.
TEST_INT_HERMITE, a FORTRAN90 code which defines test integrands that can be approximated using a Gauss-Hermite rule.
TRUNCATED_NORMAL_RULE, a FORTRAN90 code which computes a quadrature rule for a normal distribution that has been truncated to [A,+oo), (-oo,B] or [A,B].