legendre_rule, a MATLAB code which generates a specific Gauss-Legendre quadrature rule, based on user input.
The Gauss-Legendre quadrature rule is used as follows:
Integral ( A <= x <= B ) f(x) dxis to be approximated by
Sum ( 1 <= i <= order ) w(i) * f(x(i))
legendre_rule ( order, a, b, 'filename' )where
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
legendre_rule is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.
alpert_rule, a MATLAB 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 MATLAB code which defines a nested clenshaw curtis quadrature rule.
chebyshev1_rule, a MATLAB code which can compute and print a gauss-chebyshev type 1 quadrature rule.
chebyshev2_rule, a MATLAB code which can compute and print a gauss-chebyshev type 2 quadrature rule.
clenshaw_curtis_rule, a MATLAB code which defines a clenshaw curtis quadrature rule.
gegenbauer_rule, a MATLAB code which can compute and print a gauss-gegenbauer quadrature rule.
gen_hermite_rule, a MATLAB code which can compute and print a generalized gauss-hermite quadrature rule.
gen_laguerre_rule, a MATLAB code which can compute and print a generalized gauss-laguerre quadrature rule.
hermite_rule, a MATLAB code which can compute and print a gauss-hermite quadrature rule.
jacobi_rule, a MATLAB code which can compute and print a gauss-jacobi quadrature rule.
laguerre_rule, a MATLAB code which can compute and print a gauss-laguerre quadrature rule.
legendre_rule_fast, a MATLAB code which uses a fast (order n) algorithm to compute a gauss-legendre quadrature rule of given order.
line_felippa_rule, a MATLAB code which returns the points and weights of a felippa quadrature rule over the interior of a line segment in 1d.
patterson_rule, a MATLAB code which computes a gauss-patterson quadrature rule.
quadrature_rules, a dataset directory which contains sets of files that define quadrature rules over various 1d intervals or multidimensional hypercubes.
quadrature_rules_legendre, a dataset directory which contains triples of files defining standard gauss-legendre quadrature rules.
quadrule, a MATLAB code which defines 1-dimensional quadrature rules.
truncated_normal_rule, a MATLAB code which computes a quadrature rule for a normal probability density function (pdf), also called a gaussian distribution, that has been truncated to [a,+oo), (-oo,b] or [a,b].