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 blas have been omitted by default but can be obtained by asking. For example, suppose you already have installed linpack and the blas, but not slatec. Then use a request like "send dqag from quadpack slatec". [see also toms/691]