Nils,
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
@Book{Evans.Swartz.00,
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
http://search.r-project.org, but it often gets you there. It has a `complete' list of packages, as does CRAN, and searching those pages for `integrate' works.
Brian
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, [EMAIL PROTECTED] 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
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