JACOBI_RULE is a FORTRAN90 program which generates a specific Gauss-Jacobi quadrature rule, based on user input.
The rule is written to three files for easy use as input to other programs.
The Gauss-Jacobi quadrature rule is used as follows:
Integral ( A <= x <= B ) (B-x)^alpha (x-A)^beta f(x) dxis to be approximated by
Sum ( 1 <= i <= order ) w(i) * f(x(i))
jacobi_rule order alpha beta a b filenamewhere
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
JACOBI_RULE is available in a C++ version and a FORTRAN90 version and a MATLAB version.
ALPERT_RULE, a FORTRAN90 library 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 program which defines a nested Clenshaw Curtis quadrature rule.
CHEBYSHEV1_RULE, a FORTRAN90 program which can compute and print a Gauss-Chebyshev type 1 quadrature rule.
CHEBYSHEV2_RULE, a FORTRAN90 program which can compute and print a Gauss-Chebyshev type 2 quadrature rule.
CLENSHAW_CURTIS_RULE, a FORTRAN90 program which defines a Clenshaw Curtis quadrature rule.
GEGENBAUER_RULE, a FORTRAN90 program which can compute and print a Gauss-Gegenbauer quadrature rule.
GEN_HERMITE_RULE, a FORTRAN90 program which can compute and print a generalized Gauss-Hermite quadrature rule.
GEN_LAGUERRE_RULE, a FORTRAN90 program which can compute and print a generalized Gauss-Laguerre quadrature rule.
HERMITE_RULE, a FORTRAN90 program which can compute and print a Gauss-Hermite quadrature rule.
INT_EXACTNESS, a FORTRAN90 program which checks the polynomial exactness of a 1-dimensional quadrature rule for a finite interval.
INT_EXACTNESS_JACOBI, a FORTRAN90 program which checks the polynomial exactness of a Gauss-Jacobi rule.
INTLIB, a FORTRAN90 library which contains a variety of routines for numerical estimation of integrals in 1D.
JACOBI_POLYNOMIAL, a FORTRAN90 library which evaluates the Jacobi polynomial and associated functions.
LAGUERRE_RULE, a FORTRAN90 program which can compute and print a Gauss-Laguerre quadrature rule.
LEGENDRE_RULE, a FORTRAN90 program which computes a Gauss-Legendre quadrature rule.
LEGENDRE_RULE_FAST, a FORTRAN90 program which uses a fast (order N) algorithm to compute a Gauss-Legendre quadrature rule of given order.
LINE_NCC_RULE, a FORTRAN90 library which computes a Newton Cotes Closed (NCC) quadrature rule for the line, that is, for an interval of the form [A,B], using equally spaced points which include the endpoints.
LINE_NCO_RULE, a FORTRAN90 library 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 program which can compute and print a quadrature rule for functions of a variable whose logarithm is normally distributed.
PATTERSON_RULE, a FORTRAN90 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.
PATTERSON_RULE_COMPUTE, a FORTRAN90 program 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_JACOBI, a dataset directory which contains triples of files defining Gauss-Jacobi quadrature rules.
QUADRULE, a FORTRAN90 library which contains 1-dimensional quadrature rules.
TANH_SINH_RULE, a FORTRAN90 program which computes and writes out a tanh-sinh quadrature rule of given order.
TRUNCATED_NORMAL_RULE, a FORTRAN90 program which computes a quadrature rule for a normal distribution that has been truncated to [A,+oo), (-oo,B] or [A,B].
jacobi_rule 4 0.5 1.5 -1.0 +1.0 jac_o4_a0.5_b1.5
jacobi_rule 4 0.5 1.5 -1.0 +1.0 jac_o4_a0.5_b1.5
jacobi_rule 4 0.5 1.5 -1.0 +1.0 jac_o4_a0.5_b1.5
You can go up one level to the FORTRAN90 source codes.