power_rule, an Octave code which creates a power rule, that is, a multidimensional quadrature rule formed as a repeated product of a single one-dimensional quadrature rule.

Note that the three files that define the quadrature rule are assumed to have related names, of the form

When running the program, the user only enters the common prefix part of the file names, which is enough information for the program to find all three files.

For information on the form of these files, see the QUADRATURE_RULES directory listed below.


power_rule prefix dim_num

If the arguments are not supplied on the command line, the program will prompt for them.

The program will create these output files, which define the multidimensional quadrature rule:

a file containing the abscissas of the power rule;
a file containing the weights of the power rule;
a file containing the range of the power rule;


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


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

Related Data and Programs:


alpert_rule, an Octave code which sets up an Alpert quadrature rule for functions which are regular, log(x) singular, or 1/sqrt(x) singular.

nintlib, an Octave code which numerically estimates integrals in multiple dimensions.

patterson_rule, an Octave code which computes a gauss-patterson quadrature rule.

product_rule, an Octave code which constructs a product quadrature rule from distinct 1d factor rules.

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

quadrule, an Octave code which defines quadrature rules on a variety of intervals with different weight functions.

stroud, an Octave code which contains quadrature rules for a variety of unusual areas, surfaces and volumes in 2d, 3d and n-dimensions.

test_nint, an Octave code which defines integrand functions for testing multidimensional quadrature routines.

truncated_normal_rule, an Octave 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].


  1. Philip Davis, Philip Rabinowitz,
    Methods of Numerical Integration,
    Second Edition,
    Dover, 2007,
    ISBN: 0486453391,
    LC: QA299.3.D28.

Source Code:

Last revised on 06 March 2019.