Next: Functions and Variables for QUADPACK, Previous: Functions and Variables for Integration, Up: Integration [Contents][Index]
QUADPACK is a collection of functions for the numerical computation of one-dimensional definite integrals. It originated from a joint project of R. Piessens 1, E. de Doncker 2, C. Ueberhuber 3, and D. Kahaner 4.
The QUADPACK library included in Maxima is an automatic translation (via the
program f2cl) of the Fortran source code of QUADPACK as it appears in
the SLATEC Common Mathematical Library, Version 4.1 5.
The SLATEC library is dated July 1993, but the QUADPACK functions
were written some years before.
There is another version of QUADPACK at Netlib 6;
it is not clear how that version differs from the SLATEC version.
The QUADPACK functions included in Maxima are all automatic, in the sense that these functions attempt to compute a result to a specified accuracy, requiring an unspecified number of function evaluations. Maxima’s Lisp translation of QUADPACK also includes some non-automatic functions, but they are not exposed at the Maxima level.
Further information about QUADPACK can be found in the QUADPACK book 7.
quad_qagIntegration of a general function over a finite interval.
quad_qag implements a simple globally adaptive integrator using the
strategy of Aind (Piessens, 1973).
The caller may choose among 6 pairs of Gauss-Kronrod quadrature
formulae for the rule evaluation component.
The high-degree rules are suitable for strongly oscillating integrands.
quad_qagsIntegration of a general function over a finite interval.
quad_qags implements globally adaptive interval subdivision with
extrapolation (de Doncker, 1978) by the Epsilon algorithm (Wynn, 1956).
quad_qagiIntegration of a general function over an infinite or semi-infinite interval.
The interval is mapped onto a finite interval and
then the same strategy as in quad_qags is applied.
quad_qawoIntegration of
\(\cos(\omega x) f(x)\)
or
\(\sin(\omega x) f(x)\)
over a
finite interval, where
\(\omega\)
is a constant.
The rule evaluation component is based on the modified Clenshaw-Curtis
technique. quad_qawo applies adaptive subdivision with extrapolation,
similar to quad_qags.
quad_qawfCalculates a Fourier cosine or Fourier sine transform on a semi-infinite
interval. The same approach as in quad_qawo is applied on successive
finite intervals, and convergence acceleration by means of the Epsilon algorithm
(Wynn, 1956) is applied to the series of the integral contributions.
quad_qawsIntegration of \(w(x)f(x)\) over a finite interval \([a, b]\), where \(w\) is a function of the form \((x-a)^\alpha (b-x)^\beta v(x)\) and \(v(x)\) is 1 or \(\log(x-a)\) or \(\log(b-x)\) or
\(\log(x-a)\log(b-x)\), and \(\alpha > -1\) and \(\beta > -1\) .
A globally adaptive subdivision strategy is applied, with modified Clenshaw-Curtis integration on the subintervals which contain \(a\) or \(b\).
quad_qawcComputes the Cauchy principal value of \(f(x)/(x - c)\) over a finite interval \((a, b)\) and specified \(c\). The strategy is globally adaptive, and modified Clenshaw-Curtis integration is used on the subranges which contain the point \(x = c\).
quad_qagpBasically the same as quad_qags but points of singularity or
discontinuity of the integrand must be supplied. This makes it easier
for the integrator to produce a good solution.
Applied Mathematics and Programming Division, K.U. Leuven
Applied Mathematics and Programming Division, K.U. Leuven
Institut für Mathematik, T.U. Wien
National Bureau of Standards, Washington, D.C., U.S.A
https://www.netlib.org/quadpack
R. Piessens, E. de Doncker-Kapenga, C.W. Uberhuber, and D.K. Kahaner. QUADPACK: A Subroutine Package for Automatic Integration. Berlin: Springer-Verlag, 1983, ISBN 0387125531.
Next: Functions and Variables for QUADPACK, Previous: Functions and Variables for Integration, Up: Integration [Contents][Index]