# Multivariate integration with infinite limits

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## Multivariate integration with infinite limits

 Dear All, Can R perform multivariate integration with infinite limits of integration? Thanks in advance, Paul ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Multivariate integration with infinite limits

 Paul Smith wrote: > Dear All, > > Can R perform multivariate integration with infinite limits of integration? No, R does numerical (not symbolical) calculations, hence it can never perform integration (not even univariate) with infinite limits. Uwe Ligges > Thanks in advance, > > Paul > > ______________________________________________ > [hidden email] mailing list > https://stat.ethz.ch/mailman/listinfo/r-help> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html> and provide commented, minimal, self-contained, reproducible code. ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Multivariate integration with infinite limits

 On Nov 10, 2007 12:43 PM, Uwe Ligges <[hidden email]> wrote: > > Can R perform multivariate integration with infinite limits of integration? > > No, R does numerical (not symbolical) calculations, hence it can never > perform integration (not even univariate) with infinite limits. Not entirely true in the one-dimensional case: > f <- function(x) {exp(-x)} > integrate(f,0,Inf) 1 with absolute error < 5.7e-05 > Paul ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Multivariate integration with infinite limits

 In reply to this post by Uwe Ligges On Sat, 10 Nov 2007, Uwe Ligges wrote: > > > Paul Smith wrote: >> Dear All, >> >> Can R perform multivariate integration with infinite limits of integration? > > No, R does numerical (not symbolical) calculations, hence it can never > perform integration (not even univariate) with infinite limits. Not really true, as I managed to implement it in integrate().  There is nothing to stop a numerical integration routine working on an infinite interval if some assumptions are made about the rate of decay of the integrand at infinity: several of the classical numerical quadrature formulae (e.g. Gauss-Hermite) are for infinite intervals.  (You can think of these as making a particular pre-assigned transformation to e.g. [-1, 1].) dqagi is adaptive, but at the heart is a Gauss-Kronrod rule done on a half-infinite interval. -- Brian D. Ripley,                  [hidden email] Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/University of Oxford,             Tel:  +44 1865 272861 (self) 1 South Parks Road,                     +44 1865 272866 (PA) Oxford OX1 3TG, UK                Fax:  +44 1865 272595 ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Multivariate integration with infinite limits

 In reply to this post by paul smith-6 Ermmm... from ?integrate "Description:      Adaptive quadrature of functions of one variable over a finite or      infinite interval." R maps infinite intervals to a finite interval before numerical integration, provided that you tell it that the limits are infinite. Using integrate() over multivariate intervals will get very slow, though; I wouldn't do that... Steve E >>> Uwe Ligges <[hidden email]> 11/10/07 12:43 PM >>> Paul Smith wrote: > Dear All, > > Can R perform multivariate integration with infinite limits of integration? No, R does numerical (not symbolical) calculations, hence it can never perform integration (not even univariate) with infinite limits. Uwe Ligges > Thanks in advance, > > Paul > > ______________________________________________ > [hidden email] mailing list > https://stat.ethz.ch/mailman/listinfo/r-help> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html> and provide commented, minimal, self-contained, reproducible code. ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code. ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.