testpack
testpack,
a C++ code 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.
With M denoting the spatial dimension, R a parameter,
C a scaling vector, and X0 a displacement vector,
the test functions can be summarized as:
-
f(x) = cos ( 2 * pi * r + sum ( c(1:m) * x(1:m) ) ),
Genz "Oscillatory";
-
f(x) = 1 / product ( c(1:m)^2 + (x(1:m) - x0(1:m))^2),
Genz "Product Peak";
-
f(x) = 1 / ( 1 + sum ( c(1:m) * x(1:m) ) )^(m+r),
Genz "Corner Peak";
-
f(x) = exp(-sum(c(1:m)^2 * ( x(1:m) - x0(1:m))^2 ) ),
Genz "Gaussian";
-
f(x) = exp ( - sum ( c(1:m) * abs ( x(1:m) - x0(1:m) ) ) ),
Genz "Continuous";
-
f(x) = exp(sum(c(1:m)*x(1:m)) for x(1:m) <= x0(1:m), 0 otherwise,
Genz "Discontinuous";
Licensing:
The information on this web page is distributed under the MIT license.
Languages:
testpack is available in
a C version and
a C++ version and
a FORTRAN90 version and
a MATLAB version.
Related Data and Programs:
testpack_test
nintlib,
a C++ code which
estimates the integral of a function over a one-dimensional interval.
product_rule,
a C++ code which
can create a multidimensional quadrature rule as a product of
one dimensional rules.
quad_rule,
a C++ code which
defines a variety of
(mostly 1-dimensional) quadrature rules.
stroud_rule,
a C++ code which
defines a variety of quadrature rules over various "interesting" geometric shapes.
test_nint,
a C++ code which
can be used to test N-dimensional quadrature routines.
Reference:
-
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.
-
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
-
John Hart, Ward Cheney, Charles Lawson, Hans Maehly,
Charles Mesztenyi, John Rice, Henry Thatcher,
Christoph Witzgall,
Computer Approximations,
Wiley, 1968,
LC: QA297.C64.
-
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:
Last revised on 24 April 2020.