TESTPACK
Testing Multidimensional Integration Routines

TESTPACK is a FORTRAN77 library which demonstrates the testing of a routine for multidimensional integration.

In this case, the code being tested is a subroutine known as ADAPT, written by Genz. The code is tested on six test integrand functions, also defined by Genz. The test is done with a variety of spatial dimensions, parameter values, and difficulty factors.

Languages:

TESTPACK is available in a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

INTEGRAL_TEST, a FORTRAN90 program which tests the suitability of a set of N points for use in an equal-weight quadrature rule over the M-dimensional unit hypercube.

INTLIB, a FORTRAN90 library which estimate the integral of a function over a one-dimensional interval.

KRONROD, a FORTRAN77 library which can compute a Gauss and Gauss-Kronrod pair of quadrature rules of arbitrary order, by Robert Piessens, Maria Branders.

NINTLIB, a FORTRAN77 library which estimates the integral of a function over a one-dimensional interval.

QUADRULE, a FORTRAN90 library which defines a variety of (mostly 1-dimensional) quadrature rules.

SMOLPACK, a C library which uses the Genz test functions to demonstrate quadrature in multiple dimensions using a sparse grid.

SPINTERP, a MATLAB library which uses the Genz test functions to demonstrate multilinear interpolation on a sparse grid.

STROUD, a FORTRAN90 library which defines a variety of quadrature rules over various "interesting" geometric shapes.

TEST_NINT, a FORTRAN90 library which can be used to test N-dimensional quadrature routines.

Reference:

1. Alan Genz,
   Testing Multidimensional Integration Routines,
   in Tools, Methods, and Languages for Scientific and Engineering Computation,
   edited by B Ford, JC Rault, F Thomasset,
   North-Holland, 1984, pages 81-94,
   ISBN: 0444875700,
   LC: Q183.9.I53.
2. Alan Genz,
   A Package for Testing Multiple Integration Subroutines,
   in Numerical Integration: Recent Developments, Software and Applications,
   edited by Patrick Keast, Graeme Fairweather,
   Reidel, 1987, pages 337-340,
   ISBN: 9027725144,
   LC: QA299.3.N38
3. John Hart, Ward Cheney, Charles Lawson, Hans Maehly, Charles Mesztenyi, John Rice, Henry Thatcher, Christoph Witzgall,
   Computer Approximations,
   Wiley, 1968,
   LC: QA297.C64.
4. Linus Schrage,
   A More Portable Fortran Random Number Generator,
   ACM Transactions on Mathematical Software,
   Volume 5, Number 2, June 1979, pages 132-138.

Source Code:

• testpack.f, the source code.
• testpack.sh, commands to compile the source code.
• testpack_output.txt, the output file.

List of Routines:

• MAIN is the main program for testing TESTPACK.
• ADAPT carries out adaptive multidimensional quadrature.
• FUNCTN evaluates one of the test integrand functions.
• MEDIAN computes the median of an array of reals.
• MULTST tests a multidimensional integration routine.
• PHI estimates the normal cumulative density function.
• RANDOM is a portable random number generator
• TIMESTAMP prints out the current YMDHMS date as a timestamp.
• VALINT computes the exact integrals of the test functions.

You can go up one level to the FORTRAN77 source codes.