power_rule

power_rule, a Fortran77 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

• prefix_x.txt
• prefix_w.txt
• prefix_r.txt

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

Usage:

power_rule prefix dim_num

• prefix is the common prefix for the files containing the abscissa, weight and region information of the quadrature rule;
• dim_num is the dimension of the product space.

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:

power_x.txt

a file containing the abscissas of the power rule;

power_w.txt

a file containing the weights of the power rule;

power_r.txt

a file containing the range of the power rule;

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

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:

power_rule_test

f77_rule, a Fortran77 code which computes a quadrature rule which estimates the integral of a function f(x), which might be defined over a one dimensional region (a line) or more complex shapes such as a circle, a triangle, a quadrilateral, a polygon, or a higher dimensional region, and which might include an associated weight function w(x).

Reference:

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

Source Code:

• power_rule.f, the source code.
• power_rule.sh, commands to compile the source code.