product_rule


product_rule, an Octave code which creates a multidimensional quadrature rule by using a product of distinct one-dimensional quadrature rules.

The program reads a single input file, which contains a list that defines the 1D rules to be used as factors.

Each 1D rule is stored in three files, an "X", "W", and "R" file, which are assumed to share a common filename prefix, so that the files defined by a given prefix have the form:

For instance, let us suppose we want to compute a 2D product rule formed from a 3 point Clenshaw Curtis rule and a 2 point Gauss-Legendre rule. If the prefixes for these files were "cc_d1_o003" and "gl_d1_o002" respectively, then the input file to the program would read as follows:

        cc_d1_o003
        gl_d1_o002
      
When the program read the first 1D rule, it would be searching for three files: and similarly for the second file.

Once the program has computed the multidimensional product rule, it again writes out three files describing the product rule, with a common filename prefix specified by the user, which might be, for instance, product, in which case the files would be:

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

Usage:

product_rule ( list_file, product_prefix )
where

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

Licensing:

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

Languages:

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

product_rule_test

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.

nint_exactness_mixed, an Octave code which measures the polynomial exactness of a multidimensional quadrature rule based on a mixture of 1D quadrature rule factors.

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

power_rule, an Octave code which constructs a power rule, that is, a product quadrature rule from identical 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].

Reference:

  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.