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is the only general-purpose routine for infinite intervals, and maps the infinite interval onto the semi-open interval (0,1] using a transformation then uses the same approach as QAGS, except with 15-point rather than 21-point Gauss–Kronrod quadrature. For an integral over the whole real line, the
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and the routine attempts to perform the integration with an error no larger than that requested. There are nine such automatic routines in QUADPACK, in addition to a number of non-automatic routines. All but one of the automatic routines use
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This is not the best approach for all integrands: another transformation may be appropriate, or one might prefer to break up the original interval and use QAGI only on the infinite part.
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The two general-purpose routines most suitable for use without further analysis of the integrand are QAGS for integration over a finite interval and QAGI for
665:{\displaystyle \int _{-\infty }^{+\infty }f(x)dx=\int _{0}^{1}{dt \over t^{2}}\left(f\left({\frac {1-t}{t}}\right)+f\left(-{\frac {1-t}{t}}\right)\right)\;.}
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Each of the adaptive routines also have versions suffixed by E that have an extended parameter list that provides more information and allows more control.
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library offers a 100% type-kind-generic multi-precision implementation of QUADPACK library in modern
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similar to QAGS but allows user to specify locations of internal singularities, discontinuities etc.
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Piessens, Robert; de
Doncker-Kapenga, Elise; Überhuber, Christoph W.; Kahaner, David (1983).
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Fong, Kirby W.; Jefferson, Thomas H.; Suyehiro, Tokihiko; Walton, Lee (July 1993).
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R Development Core Team and contributors worldwide (October 2010).
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Piessens, Robert; De
Doncker, Elise; Kahaner, David (1984-04-17).
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integration routines in which the user inputs the problem and an
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Oscillatory weight function (cos or sin) over a finite interval
1137:"integrate {stats}: Integration of One-Dimensional Functions"
1257:: a package for automatic cubature; framework description".
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QUADPACK: A subroutine package for automatic integration
1051:"scipy.integrate.quad -- SciPy v0.14.0 Reference Guide"
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versions of all routines were released with prefix D.
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Specified points of local difficulty (singularities,
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of one-dimensional functions. It was included in the
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1141:Documentation for package ‘stats’ version 2.13.0
677:Brief overview of the other automatic routines
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1216:Favati, P.; Lotti, G.; Romani, F. (1991).
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299:Weight function of specified form
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400:. These two routines are used in
203:The main focus of QUADPACK is on
180:interface to part of QUADPACK.
1030:Katholieke Universiteit Leuven
685:simple non-adaptive integrator
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895:List of numerical libraries
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691:simple adaptive integrator
209:absolute or relative error
489:{\displaystyle x=(1-t)/t}
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1193:Free Software Foundation
429:Gauss–Kronrod quadrature
392:General-purpose routines
1111:Handbook of integration
450:transformation used is
227:for automatic routines
32:Elise deDoncker-Kapenga
1187:GNU Scientific Library
735:over a finite interval
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373:Cauchy principal value
166:GNU Scientific Library
34:Christoph W. Überhuber
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1306:Numerical software
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26:Original author(s)
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44:May 1981
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36:David Kahaner
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1196:. Retrieved
1189:-- Reference
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1091:. Retrieved
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1054:. Retrieved
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1035:November 13,
1033:. Retrieved
1007:November 13,
1005:. Retrieved
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982:November 13,
980:. Retrieved
978:. netlib.org
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923:November 16,
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423:uses global
416:function).
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66:May 1987
1198:16 November
1146:16 November
1093:16 November
253:Quadrature
241:4th letter
223:Summary of
185:pm_quadpack
176:provides a
1290:Categories
1026:"QUADPACK"
998:"quadpack"
901:References
437:Peter Wynn
402:GNU Octave
238:3rd letter
235:2nd letter
232:1st letter
140:FORTRAN 77
80:FORTRAN 77
76:Written in
637:−
628:−
601:−
547:∫
520:∞
512:∞
509:−
505:∫
470:−
414:integrate
212:tolerance
205:automatic
189:ParaMonte
125:/QUADPACK
123:/software
119:.kuleuven
1246:19675880
1156:cite web
1084:QUADPACK
889:See also
836:= 0 or 1
778:, where
323:handled
276:Adaptive
199:Routines
136:QUADPACK
20:QUADPACK
1279:6855610
1255:CUBPACK
847:> –1
827:, with
193:Fortran
143:library
110:Website
99:License
92:Library
48:1981-05
46: (
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1118:
1088:netlib
1056:1 July
1002:Netlib
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918:Netlib
817:) log(
809:) log(
178:Python
159:netlib
151:SLATEC
1275:S2CID
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793:) = (
766:from
412:(the
404:(the
174:SciPy
138:is a
115:nines
1200:2010
1168:help
1148:2010
1116:ISBN
1095:2010
1058:2014
1037:2010
1009:2010
984:2010
955:ISBN
925:2010
879:and
851:QAWC
838:and
744:QAWS
738:QAWF
721:sin(
705:cos(
700:QAWO
694:QAGP
446:QAGI
420:QAGS
406:quad
183:The
164:The
145:for
87:Type
1267:doi
1232:doi
863:)/(
801:) (
772:to
719:or
688:QAG
682:QNG
439:'s
435:by
335:…)
121:.be
117:.cs
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264:N
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