product_rule, a Fortran90 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:
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:
product_rule ( list_file, product_prefix )where
If the arguments are not supplied on the command line, the program will prompt for them.
The information on this web page is distributed under the MIT license.
product_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version.
f90_rule, a Fortran90 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).