product_rule, a MATLAB 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_o002When 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:
For information on the form of these files, see the QUADRATURE_RULES directory listed below.
product_rule ( list_file, product_prefix )where
If the arguments are not supplied on the command line, the program will prompt for them.
product_rule is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version
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