quad_rule, a MATLAB code which sets quadrature rules, used to approximate the integral of a function over various domains.

quad_rule returns the abscissas and weights for a variety of one dimensional quadrature rules for approximating the integral of a function. The best rule is generally Gauss-Legendre quadrature, but other rules offer special features, including the ability to handle certain weight functions, to approximate an integral on an infinite integration region, or to estimate the approximation error.


The computer files described and made available on this web page are distributed under the MIT license


quad_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:


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.

clenshaw_curtis_rule, a MATLAB code which defines a multiple dimension clenshaw curtis quadrature rule.

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.

quadmom, a MATLAB code which computes a gaussian quadrature rule for a weight function rho(x) based on the golub-welsch procedure that only requires knowledge of the moments of rho(x).

quadrature_rules, a dataset directory which contains sets of files that define quadrature rules over various 1d intervals or multidimensional hypercubes.

quad_rule_fast, a MATLAB code which defines efficient versions of a few 1d quadrature rules.

test_int, a MATLAB code which defines test integrands for 1d quadrature rules.

toms655, a MATLAB code which computes the weights for interpolatory quadrature rule;
this library is commonly called iqpack;
this is a MATLAB version of acm toms algorithm 655.

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].

Source Code:

Last revised on 02 March 2019.