gegenbauer_rule, a FORTRAN90 code which generates a specific Gauss-Gegenbauer quadrature rule, based on user input.
The rule is written to three files for easy use as input to other programs.
The Gauss-Gegenbauer quadrature rule is used as follows:
Integral ( A <= x <= B ) ((x-A)(B-X))^alpha f(x) dxis to be approximated by
Sum ( 1 <= i <= order ) w(i) * f(x(i))where alpha is a real parameter greater than -1.
gegenbauer_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.
gegenbauer_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_CC, a FORTRAN90 code which estimates the Gegenbauer weighted integral of a function f(x) using a Clenshaw-Curtis approach.
GEGENBAUER_EXACTNESS, a FORTRAN90 code which checks the polynomial exactness of a Gauss-Gegenbauer rule.
GEN_HERMITE_RULE, a FORTRAN90 code which can compute and print a generalized Gauss-Hermite quadrature rule.
GEN_LAGUERRE_RULE, a FORTRAN90 code which can compute and print a generalized Gauss-Laguerre quadrature rule.
HERMITE_RULE, a FORTRAN90 code which can compute and print a Gauss-Hermite quadrature rule.
JACOBI_RULE, a FORTRAN90 code which can compute and print a Gauss-Jacobi quadrature rule.
LAGUERRE_RULE, a FORTRAN90 code which can compute and print 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.
LINE_NCO_RULE, a FORTRAN90 code which computes a Newton Cotes Open (NCO) quadrature rule, using equally spaced points, over the interior of a line segment in 1D.
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_GEGENBAUER, a dataset directory which contains triples of files defining Gauss-Gegenbauer quadrature rules.
QUADRULE, a FORTRAN90 code which contains 1-dimensional quadrature rules.
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].