Re: [R] two-dimensional integration?

From: Prof Brian Ripley <>
Date: Thu 10 Mar 2005 - 18:56:34 EST


For 2D, see package 'adapt' on CRAN. e.g.

adapt(2, c(0,0), c(1,1), functn=function(x) sin(prod(x))*exp(x[1]-x[2]))

Package `adapt' will do larger numbers of dimensions, but numerical quadrature is often no more effective than Monte-Carlo methods in more than a few dimensions. For very smooth functions, quasi-random numbers can help.

A good reference aimed at statisticians is


   author =       {Michael Evans and Tim Swartz},
   title =        {Approximating Integrals via Monte Carlo and
                   Deterministic Methods},
   publisher =    {Oxford University Press},
   year =         2000,
   address =      {Oxford},
   ISBN =         "0-19-850278-8",


BTW, we are not good are predicting to 2014, but fairly good at the present. In this case I could not guess a good search term on, but it often gets you there. It has a `complete' list of packages, as does CRAN, and searching those pages for `integrate' works.


On Thu, 10 Mar 2005, Nils-at-Duke Lid Hjort wrote:

> I find the one-dimensional "integrate" very helpful,
> but often enough I stumble into problems that require
> two (or more)-dimensional integrals. I suppose there
> are no R functions that can do this for me, "directly"?
> The ideal thing would be to be able to define say
> f <- function(x)
> {
> x1 <- x[1]
> x2 <- x[2]
> sin(x1*x2)*exp(x1-x2)
> }
> and then write say
> integrate(f, xlim=c(0,1), ylim=c(0,1)) .
> (a) No such thing exists, as of today, right?
> (b) There *are* general numerical routines "out there"
> for doing such things, right? (Importance sampling
> or adaptive important sampling would often do the
> job, but it would be difficult to find something that
> "always" works -- at least in higher dimension?
> Also, iterated one-dimensional integrations could
> be attempted, but I find that messy, also because
> things lose the g(many) = many(g) property, and
> then R refuses to integrate g.)
> (c) Will a thing like the above exist in R before
> the Tromsoe Olympics in 2014? For which dimensions?
> Nils Lid Hjort
> [Professor of statistics at Oslo, but currently at Duke]

Brian D. Ripley,        
Professor of Applied Statistics,
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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