POWER_RULE is a C++ program 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
For information on the form of these files, see the QUADRATURE_RULES directory listed below.
power_rule prefix dim_numwhere
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_RULE is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.
CLENSHAW_CURTIS_RULE, a C++ program which defines a Clenshaw Curtis quadrature rule.
INTEGRAL_TEST, a FORTRAN90 program which uses some of these test integrals to evaluate sets of quadrature points.
LATTICE_RULE, a C++ library which approximates M-dimensional integrals using lattice rules.
NINT_EXACTNESS, a C++ program which can test a quadrature rule for polynomial exactness.
NINTLIB, a C++ library which numerically estimates integrals in multiple dimensions.
PATTERSON_RULE, a C++ program which computes a Gauss-Patterson quadrature rule.
PRODUCT_RULE, a C++ program which constructs a product quadrature rule from distinct 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 C++ library which defines quadrature rules on a variety of intervals with different weight functions.
STROUD, a C++ library which defines quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and N-dimensions.
TEST_NINT, a C++ library which defines integrand functions for testing multidimensional quadrature routines.
TESTPACK, a C++ library which defines a set of integrands used to test multidimensional quadrature.
TRUNCATED_NORMAL_RULE, a C++ 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 start with a 1D Clenshaw Curtis rule of order 3:
We give the command
power_rule cc3 2to create a Clenshaw Curtis product rule of order 3x3 for a 2D region. The files which are created include:
You can go up one level to the C++ source codes.