power_rule

power_rule, a FORTRAN90 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

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 computer code and data files described and made available on this web page are 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.

Related Data and Programs:

CHEBYSHEV1_RULE, a FORTRAN90 code which can compute and print a Gauss-Chebyshev type 1 quadrature rule.

CHEBYSHEV2_RULE, a FORTRAN90 code which can compute and print a Gauss-Chebyshev type 2 quadrature rule.

CLENSHAW_CURTIS_RULE, a FORTRAN90 code which defines a Clenshaw Curtis quadrature rule.

GEGENBAUER_RULE, a FORTRAN90 code which can compute and print a Gauss-Gegenbauer quadrature rule.

GEN_HERMITE_RULE, a FORTRAN90 code which can compute and print a generalized Gauss-Hermite quadrature rule.

GEN_LAGUERRE_RULE, a FORTRAN90 code which can compute and print a generalized Gauss-Laguerre quadrature rule.

HERMITE_RULE, a FORTRAN90 code which can compute and print a Gauss-Hermite quadrature rule.

JACOBI_RULE, a FORTRAN90 code which can compute and print a Gauss-Jacobi quadrature rule.

LAGUERRE_RULE, a FORTRAN90 code which can compute and print a Gauss-Laguerre quadrature rule.

LEGENDRE_RULE, a FORTRAN90 code which computes a Gauss-Legendre quadrature rule.

LEGENDRE_RULE_FAST, a FORTRAN90 code which uses a fast (order N) algorithm to compute a Gauss-Legendre quadrature rule of given order.

PATTERSON_RULE, a FORTRAN90 code 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_test

PRODUCT_RULE, a FORTRAN90 code 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 FORTRAN90 code which defines quadrature rules on a variety of intervals with different weight functions.

TRUNCATED_NORMAL_RULE, a FORTRAN90 code 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].

Reference:

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

Source Code:

• power_rule.f90, the source code.
• power_rule.sh, compiles the source code.