quadinf.Rd
\name{quadinf}
\alias{quadinf}
\title{
Infinite Integrals
}
\description{
Adaptive quadrature of functions over an infinite interval.
}
\usage{
quadinf(f, xa, xb, tol = .Machine$double.eps^0.5, ...)
}
\arguments{
\item{f}{univariate function; needs to be vectorized.}
\item{xa}{lower limit of integration; can be infinite}
\item{xb}{upper limit of integration; can be infinite}
\item{tol}{accuracy requested.}
\item{\dots}{additional arguments to be passed to \code{f}.}
}
\details{
\code{quadinf} is simply a wrapper for \code{integrate}. When one of
the integration limits become infinite, the transformed function
\code{(1/x^2)*f(1/x)} is used. This works fine if the new function
does not have a too bad behavior at the limit(s).
The function needs to be vectorized as long as this is required by
\code{integrate}.
}
\value{
A single numeric value, the computed integral.
}
\author{
HwB <hwborchers@googlemail.com>
}
\note{
Based on my remarks on R-help in September 2010 in the thread
``bivariate vector numerical integration with infinite range''
}
\seealso{
\code{\link{integrate}}
}
\examples{
## We will look at the error function exp(-x^2)
f <- function(x) exp(-x^2)
quadinf(f, -Inf, 0) #=> 0.886226925756445 with abs. error 3e-10 (sqrt(pi)/2)
quadinf(f, 0, Inf) # same
quadinf(f, -Inf, -1, tol = 1e-12) - integrate(f, -Inf, -1)$value
quadinf(f, -Inf, 1, tol = 1e-12) - integrate(f, -Inf, 1)$value
quadinf(f, -1, Inf, tol = 1e-12) - integrate(f, -1, Inf)$value
quadinf(f, 1, Inf, tol = 1e-12) - integrate(f, -Inf, -1)$value
}
\keyword{ math }