hermite_rule, a FORTRAN77 code which generates a specific Gauss-Hermite quadrature rule.
The rule is written to three files for easy use as input to other programs.
The Gauss-Hermite quadrature rule is used as follows:
c * Integral ( -oo < x < +oo ) f(x) exp ( - b * ( x - a )^2 ) dx
is to be approximated by
Sum ( 1 <= i <= order ) w(i) * f(x(i))
Generally, a Gauss-Hermite quadrature rule of n points will
produce the exact integral when f(x) is a polynomial of degree
2n-1 or less.
The value of C in front of the integral depends on the user's choice of the SCALE parameter:
hermite_rule n a b scale filenamewhere
The computer code and data files made available on this web page are distributed under the GNU LGPL license.
hermite_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and a Octave version and a Python version.
ccn_rule, a FORTRAN77 program which defines one of a set of nested Clenshaw Curtis quadrature rules of any order.
clenshaw_curtis_rule, a FORTRAN77 program which defines a Clenshaw Curtis quadrature rule.
hermite_exactness, a FORTRAN77 program which tests the polynomial exactness of Gauss-Hermite quadrature rules for estimating the integral of a function with density exp(-x^2) over the interval (-oo,+oo).
HERMITE_POLYNOMIAL, a FORTRAN77 library which evaluates the physicist's Hermite polynomial, the probabilist's Hermite polynomial, the Hermite function, and related functions.
HERMITE_TEST_INT, a FORTRAN77 library which defines test integrands for Hermite integrals with interval (-oo,+oo) and density exp(-x^2).
LAGUERRE_RULE, a FORTRAN77 program which can compute and print a Gauss-Laguerre quadrature rule for estimating the integral of a function with density exp(-x) over the interval [0,+oo).
LEGENDRE_RULE, a FORTRAN77 program which computes a Gauss-Legendre quadrature rule.
PATTERSON_RULE, a FORTRAN77 program 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.
QUADRATURE_RULES_HERMITE_PHYSICIST, a dataset directory which contains Gauss-Hermite quadrature rules, for integration on the interval (-oo,+oo), with weight function exp(-x^2).
QUADRATURE_RULES_HERMITE_PROBABILIST, a dataset directory which contains Gauss-Hermite quadrature rules, for integration on the interval (-oo,+oo), with weight function exp(-x^2/2).
QUADRATURE_RULES_HERMITE_UNWEIGHTED, a dataset directory which contains Gauss-Hermite quadrature rules, for integration on the interval (-oo,+oo), with weight function 1.
QUADRULE, a FORTRAN77 library which contains 1-dimensional quadrature rules.
TRUNCATED_NORMAL_RULE, a FORTRAN77 program which computes a quadrature rule for a normal distribution that has been truncated to [A,+oo), (-oo,B] or [A,B].