PRODUCT_RULE is a FORTRAN90 program 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 FORTRAN77 version and a FORTRAN90 version and a MATLAB version
CHEBYSHEV1_RULE, a FORTRAN90 program which can compute and print a Gauss-Chebyshev type 1 quadrature rule.
CHEBYSHEV2_RULE, a FORTRAN90 program which can compute and print a Gauss-Chebyshev type 2 quadrature rule.
CLENSHAW_CURTIS_RULE, a FORTRAN90 program which defines a Clenshaw Curtis quadrature rule.
GEGENBAUER_RULE, a FORTRAN90 program which can compute and print a Gauss-Gegenbauer quadrature rule.
GEN_HERMITE_RULE, a FORTRAN90 program which can compute and print a generalized Gauss-Hermite quadrature rule.
GEN_LAGUERRE_RULE, a FORTRAN90 program which can compute and print a generalized Gauss-Laguerre quadrature rule.
HERMITE_RULE, a FORTRAN90 program which can compute and print a Gauss-Hermite quadrature rule.
JACOBI_RULE, a FORTRAN90 program which can compute and print a Gauss-Jacobi quadrature rule.
LAGUERRE_RULE, a FORTRAN90 program which can compute and print a Gauss-Laguerre quadrature rule.
LEGENDRE_RULE, a FORTRAN90 program which computes a Gauss-Legendre quadrature rule.
LOGNORMAL_RULE, a FORTRAN90 program which can compute and print a quadrature rule for functions of a variable whose logarithm is normally distributed.
PATTERSON_RULE, a FORTRAN90 program which returns the points and weights of a 1D Gauss-Patterson quadrature rule of order 1, 3, 7, 15, 31, 63, 127, 255 or 511.
POWER_RULE, a FORTRAN90 program 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, a FORTRAN90 library which defines quadrature rules on a variety of intervals with different weight functions.
TANH_SINH_RULE, a FORTRAN90 program which computes and writes out a tanh-sinh quadrature rule of given order.
TRUNCATED_NORMAL_RULE, a FORTRAN90 program 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].
As an example, we make a 2D product rule.
The first factor is a 1D Clenshaw Curtis rule of order 3:
The second factor is a 1D Gauss Legendre rule of order 2:
We give the command
The resulting product rule files:
You can go up one level to the FORTRAN90 source codes.