1
2QUADPACK is a FORTRAN subroutine package for the numerical
3computation of definite one-dimensional integrals. It originated
4from a joint project of R. Piessens and E. de Doncker (Appl.
5Math. and Progr. Div.- K.U.Leuven, Belgium), C. Ueberhuber (Inst.
6Fuer Math.- Techn.U.Wien, Austria), and D. Kahaner (Nation. Bur.
7of Standards- Washington D.C., U.S.A.).
8The routine names for the DOUBLE PRECISION versions are preceded
9by the letter D.
10
11- QNG : Is a simple non-adaptive automatic integrator, based on
12 a sequence of rules with increasing degree of algebraic
13 precision (Patterson, 1968).
14
15- QAG : Is a simple globally adaptive integrator using the
16 strategy of Aind (Piessens, 1973). It is possible to
17 choose between 6 pairs of Gauss-Kronrod quadrature
18 formulae for the rule evaluation component. The pairs
19 of high degree of precision are suitable for handling
20 integration difficulties due to a strongly oscillating
21 integrand.
22
23- QAGS : Is an integrator based on globally adaptive interval
24 subdivision in connection with extrapolation (de Doncker,
25 1978) by the Epsilon algorithm (Wynn, 1956).
26
27- QAGP : Serves the same purposes as QAGS, but also allows
28 for eventual user-supplied information, i.e. the
29 abscissae of internal singularities, discontinuities
30 and other difficulties of the integrand function.
31 The algorithm is a modification of that in QAGS.
32
33- QAGI : Handles integration over infinite intervals. The
34 infinite range is mapped onto a finite interval and
35 then the same strategy as in QAGS is applied.
36
37- QAWO : Is a routine for the integration of COS(OMEGA*X)*F(X)
38 or SIN(OMEGA*X)*F(X) over a finite interval (A,B).
39 OMEGA is is specified by the user
40 The rule evaluation component is based on the
41 modified Clenshaw-Curtis technique.
42 An adaptive subdivision scheme is used connected with
43 an extrapolation procedure, which is a modification
44 of that in QAGS and provides the possibility to deal
45 even with singularities in F.
46
47- QAWF : Calculates the Fourier cosine or Fourier sine
48 transform of F(X), for user-supplied interval (A,
49 INFINITY), OMEGA, and F. The procedure of QAWO is
50 used on successive finite intervals, and convergence
51 acceleration by means of the Epsilon algorithm (Wynn,
52 1956) is applied to the series of the integral
53 contributions.
54
55- QAWS : Integrates W(X)*F(X) over (A,B) with A.LT.B finite,
56 and W(X) = ((X-A)**ALFA)*((B-X)**BETA)*V(X)
57 where V(X) = 1 or LOG(X-A) or LOG(B-X)
58 or LOG(X-A)*LOG(B-X)
59 and ALFA.GT.(-1), BETA.GT.(-1).
60 The user specifies A, B, ALFA, BETA and the type of
61 the function V.
62 A globally adaptive subdivision strategy is applied,
63 with modified Clenshaw-Curtis integration on the
64 subintervals which contain A or B.
65
66- QAWC : Computes the Cauchy Principal Value of F(X)/(X-C)
67 over a finite interval (A,B) and for
68 user-determined C.
69 The strategy is globally adaptive, and modified
70 Clenshaw-Curtis integration is used on the subranges
71 which contain the point X = C.
72
73 Each of the routines above also has a "more detailed" version
74with a name ending in E, as QAGE. These provide more
75information and control than the easier versions.
76
77
78 The preceding routines are all automatic. That is, the user
79inputs his problem and an error tolerance. The routine
80attempts to perform the integration to within the requested
81absolute or relative error.
82 There are, in addition, a number of non-automatic integrators.
83These are most useful when the problem is such that the
84user knows that a fixed rule will provide the accuracy
85required. Typically they return an error estimate but make
86no attempt to satisfy any particular input error request.
87
88 QK15 QK21 QK31 QK41 QK51 QK61
89 Estimate the integral on [a,b] using 15, 21,..., 61
90 point rule and return an error estimate.
91 QK15I 15 point rule for (semi)infinite interval.
92 QK15W 15 point rule for special singular weight functions.
93 QC25C 25 point rule for Cauchy Principal Values
94 QC25F 25 point rule for sin/cos integrand.
95 QMOMO Integrates k-th degree Chebychev polynomial times
96 function with various explicit singularities.
97
98Support functions from linpack, slatec, and blas have been omitted
99by default but can be obtained by asking. For example, suppose you
100already have installed linpack and the blas, but not slatec. Then
101use a request like "send dqag from quadpack slatec".
102
103
104[see also toms/691]
105