
===== QUADPACK index =====

QUADPACK is a FORTRAN subroutine package for the numerical
computation of definite one-dimensional integrals. It originated
from a joint project of R. Piessens and E. de Doncker (Appl.
Math. and Progr. Div.- K.U.Leuven, Belgium), C. Ueberhuber (Inst.
Fuer Math.- Techn.U.Wien, Austria), and D. Kahaner (Nation. Bur.
of Standards- Washington D.C., U.S.A.).
The routine names for the DOUBLE PRECISION versions are preceded
by the letter D.

- QNG  : Is a simple non-adaptive automatic integrator, based on
         a sequence of rules with increasing degree of algebraic
         precision (Patterson, 1968).

- QAG  : Is a simple globally adaptive integrator using the
         strategy of Aind (Piessens, 1973). It is possible to
         choose between 6 pairs of Gauss-Kronrod quadrature
         formulae for the rule evaluation component. The pairs
         of high degree of precision are suitable for handling
         integration difficulties due to a strongly oscillating
         integrand.

- QAGS : Is an integrator based on globally adaptive interval
         subdivision in connection with extrapolation (de Doncker,
         1978) by the Epsilon algorithm (Wynn, 1956).

- QAGP : Serves the same purposes as QAGS, but also allows
         for eventual user-supplied information, i.e. the
         abscissae of internal singularities, discontinuities
         and other difficulties of the integrand function.
         The algorithm is a modification of that in QAGS.

- QAGI : Handles integration over infinite intervals. The
         infinite range is mapped onto a finite interval and
         then the same strategy as in QAGS is applied.

- QAWO : Is a routine for the integration of COS(OMEGA*X)*F(X)
         or SIN(OMEGA*X)*F(X) over a finite interval (A,B).
         OMEGA is is specified by the user
         The rule evaluation component is based on the
         modified Clenshaw-Curtis technique.
         An adaptive subdivision scheme is used connected with
         an extrapolation procedure, which is a modification
         of that in QAGS and provides the possibility to deal
         even with singularities in F.

- QAWF : Calculates the Fourier cosine or Fourier sine
         transform of F(X), for user-supplied interval (A,
         INFINITY), OMEGA, and F. The procedure of QAWO is
         used on successive finite intervals, and convergence
         acceleration by means of the Epsilon algorithm (Wynn,
         1956) is applied to the series of the integral
         contributions.

- QAWS : Integrates W(X)*F(X) over (A,B) with A.LT.B finite,
         and   W(X) = ((X-A)**ALFA)*((B-X)**BETA)*V(X)
         where V(X) = 1 or LOG(X-A) or LOG(B-X)
                        or LOG(X-A)*LOG(B-X)
         and   ALFA.GT.(-1), BETA.GT.(-1).
         The user specifies A, B, ALFA, BETA and the type of
         the function V.
         A globally adaptive subdivision strategy is applied,
         with modified Clenshaw-Curtis integration on the
         subintervals which contain A or B.

- QAWC : Computes the Cauchy Principal Value of F(X)/(X-C)
         over a finite interval (A,B) and for
         user-determined C.
         The strategy is globally adaptive, and modified
         Clenshaw-Curtis integration is used on the subranges
         which contain the point X = C.

   Each of the routines above also has a "more detailed" version
with a name ending in E, as QAGE.  These provide more
information and control than the easier versions.


   The preceeding routines are all automatic.  That is, the user
inputs his problem and an error tolerance.  The routine
attempts to perform the integration to within the requested
absolute or relative error.
   There are, in addition, a number of non-automatic integrators.
These are most useful when the problem is such that the
user knows that a fixed rule will provide the accuracy
required.  Typically they return an error estimate but make
no attempt to satisfy any particular input error request.

  QK15 QK21 QK31 QK41 QK51 QK61
       Estimate the integral on [a,b] using 15, 21,..., 61
       point rule and return an error estimate.
  QK15I 15 point rule for (semi)infinite interval.
  QK15W 15 point rule for special singular weight functions.
  QC25C 25 point rule for Cauchy Principal Values
  QC25F 25 point rule for sin/cos integrand.
  QMOMO Integrates k-th degree Chebychev polynomial times
        function with various explicit singularities.

(Support functions from linpack, slatec, and core have been omitted.)


[see also toms/691]




file	quadpack/dqc25s
gams	H2a2a2

file	quadpack/qc25s
gams	H2a2a2



file	quadpack/qage
gams	H2a1a1
for	same as (quadpack/qag) but provides more information and control

file	quadpack/dqage
gams	H2a1a1
for	same as (quadpack/dqag) but provides more information and control

file	quadpack/qagie
gams	H2a3a1,H2a4a1
for	same as (quadpack/qagi) but provides more information and control

file	quadpack/dqagie
gams	H2a3a1,H2a4a1
for	same as (quadpack/dqagi) but provides more information and control

file	quadpack/qagpe
gams	H2a2a1
for	same as (quadpack/qagp) but provides more information and control

file	quadpack/dqagpe
gams	H2a2a1
for	same as (quadpack/dqagp) but provides more information and control

file	quadpack/qagse
gams	H2a1a1
for	same as (quadpack/qags) but provides more information and control

file	quadpack/dqagse
gams	H2a1a1
for	same as (quadpack/dqags) but provides more information and control

file	quadpack/qawoe
gams	H2a2a1
for	same as (quadpack/qawo) but provides more information and control

file	quadpack/dqawoe
gams	H2a2a1
for	same as (quadpack/dqawo) but provides more information and control

file	quadpack/qawse
gams	H2a2a1
for	same as (quadpack/qaws) but provides more information and control

file	quadpack/dqawse
gams	H2a2a1
for	same as (quadpack/dqaws) but provides more information and control

file	quadpack/qawce
gams	H2a2a1,J4
for	same as (quadpack/qawc) but provides more information and control

file	quadpack/dqawce
gams	H2a2a1,J4
for	same as (quadpack/dqawc) but provides more information and control

file	quadpack/qnge
for	same as (quadpack/qng) but provides more information and control

file	quadpack/dqnge
for	same as (quadpack/dqng) but provides more information and control

file	quadpack/qawfe
gams	H2a3a1
for	same as (quadpack/qawf) but provides more information and control

file	quadpack/dqawfe
gams	H2a3a1
for	same as (quadpack/dqawf) but provides more information and control

file	quadpack/qag
gams	H2a1a1
for	1D globally adaptive integrator using Gauss-Kronrod quadrature, oscillating integrand
prec	single

file	quadpack/dqag
gams	H2a1a1
for	1D globally adaptive integrator using Gauss-Kronrod quadrature, oscillating integrand
prec	double

file	quadpack/qagi
gams	H2a3a1,H2a4a1
for	1D globally adaptive integrator, infinite intervals
prec	single

file	quadpack/dqagi
gams	H2a3a1,H2a4a1
for	1D globally adaptive integrator, infinite intervals
prec	double

file	quadpack/qagp
gams	H2a2a1
for	1D globally adaptive integrator, singularities or discontinuities
prec	single

file	quadpack/dqagp
gams	H2a2a1
for	1D globally adaptive integrator, singularities or discontinuities
prec	double

file	quadpack/qags
gams	H2a1a1
for	1D globally adaptive integrator using interval subdivision and extrapolation
prec	single

file	quadpack/dqags
gams	H2a1a1
for	1D globally adaptive integrator using interval subdivision and extrapolation
prec	double

file	quadpack/qawo
gams	H2a2a1
for	1D integration of cos(omega*x)*f(x) or sin(omega*x)*f(x) over a finite interval, adaptive subdivision with extrapolation
prec	single

file	quadpack/dqawo
gams	H2a2a1
for	1D integration of cos(omega*x)*f(x) or sin(omega*x)*f(x) over a finite interval, adaptive subdivision with extrapolation
prec	double

file	quadpack/qaws
gams	H2a2a1
for	1D integration of functions with powers and or logs over a finite interval
prec	single

file	quadpack/dqaws
gams	H2a2a1
for	1D integration of functions with powers and or logs over a finite interval
prec	double

file	quadpack/qawc
gams	H2a2a1,J4
for	compute Cauchy principal value of f(x)/(x-c) over a finite interval
prec	single

file	quadpack/dqawc
gams	H2a2a1,J4
for	compute Cauchy principal value of f(x)/(x-c) over a finite interval
prec	double

file	quadpack/qng
gams	H2a1a1
for	1D non-adaptive automatic integrator
prec	single

file	quadpack/dqng
gams	H2a1a1
for	1D non-adaptive automatic integrator
prec	double

file	quadpack/qawf
gams	H2a3a1
for	Fourier sine/cosine transform for user supplied interval a to infinity
prec	single

file	quadpack/dqawf
gams	H2a3a1
for	Fourier sine/cosine transform for user supplied interval a to infinity
prec	double

file	quadpack/qk15
gams	H2a1a2
for	estimate 1D integral on finite interval using a 15 point rule and give error estimate, non-automatic
prec	single

file	quadpack/dqk15
gams	H2a1a2
for	estimate 1D integral on finite interval using a 15 point rule and give error estimate, non-automatic
prec	double

file	quadpack/qk21
gams	H2a1a2
for	estimate 1D integral on finite interval using a 21 point rule and give error estimate, non-automatic
prec	single

file	quadpack/dqk21
gams	H2a1a2
for	estimate 1D integral on finite interval using a 21 point rule and give error estimate, non-automatic
prec	double

file	quadpack/qk31
gams	H2a1a2
for	estimate 1D integral on finite interval using a 31 point rule and give error estimate, non-automatic
prec	single

file	quadpack/dqk31
gams	H2a1a2
for	estimate 1D integral on finite interval using a 31 point rule and give error estimate, non-automatic
prec	double

file	quadpack/qk41
gams	H2a1a2
for	estimate 1D integral on finite interval using a 41 point rule and give error estimate, non-automatic
prec	single

file	quadpack/dqk41
gams	H2a1a2
for	estimate 1D integral on finite interval using a 41 point rule and give error estimate, non-automatic
prec	double

file	quadpack/qk51
gams	H2a1a2
for	estimate 1D integral on finite interval using a 51 point rule and give error estimate, non-automatic
prec	single

file	quadpack/dqk51
gams	H2a1a2
for	estimate 1D integral on finite interval using a 51 point rule and give error estimate, non-automatic
prec	double

file	quadpack/qk61
gams	H2a1a2
for	estimate 1D integral on finite interval using a 61 point rule and give error estimate, non-automatic
prec	single

file	quadpack/dqk61
gams	H2a1a2
for	estimate 1D integral on finite interval using a 61 point rule and give error estimate, non-automatic
prec	double

file	quadpack/qk15i
gams	H2a3a2,H2a4a2
for	estimate 1D integral on (semi)infinite interval using a 15 point quadrature rule,non-automatic
prec	single

file	quadpack/dqk15i
gams	H2a3a2,H2a4a2
for	estimate 1D integral on (semi)infinite interval using a 15 point quadrature rule,non-automatic
prec	double

file	quadpack/qk15w
gams	H2a2a2
for	estimate 1D integral with special singular weight functions using a 15 point quadrature rule
prec	single

file	quadpack/dqk15w
gams	H2a2a2
for	estimate 1D integral with special singular weight functions using a 15 point quadrature rule
prec	double

file	quadpack/qc25c
gams	H2a2a2,J4
for	1D integral for Cauchy principal values using a 25 point quadrature rule
prec	single

file	quadpack/dqc25c
gams	H2a2a2,J4
for	1D integral for Cauchy principal values using a 25 point quadrature rule
prec	double

file	quadpack/qmomo
gams	H2a2a1,C3a2
for	1D integration of k-th degree Chebyshev polynomial times a function with singularities
prec	single

file	quadpack/dqmomo
gams	H2a2a1,C3a2
for	1D integration of k-th degree Chebyshev polynomial times a function with singularities
prec	double

file	quadpack/qc25f
gams	H2a2a2
for	1D integral for sin/cos integrand using a 25 point quadrature rule
prec	single

file	quadpack/dqc25f
gams	H2a2a2
for	1D integral for sin/cos integrand using a 25 point quadrature rule
prec	double

