quadv.Rd
\name{quadv}
\alias{quadv}
\title{
Vectorized Integration
}
\description{
Vectorized adaptive Simpson integration.
}
\usage{
quadv(f, a, b, tol = .Machine$double.eps^(1/2), ...)
}
\arguments{
\item{f}{univariate, vector-valued function; need not be vectorized.}
\item{a, b}{endpoints of the integration interval.}
\item{tol}{acuracy required for the recursion step.}
\item{\dots}{further parameters to be passed to the function \code{f}.}
}
\details{
Recursive version of the adaptive Simpson quadrature, recursion is based
on the maximum of all components of the function calls.
\code{quad} is not suitable for functions with singularities in the
interval or at end points.
}
\value{
Returns a list with components \code{Q} the integral value, \code{fcnt}
the number of function calls, and \code{estim.prec} the estimated precision
that normally will be much too high.
}
\seealso{
\code{\link{quad}}
}
\examples{
## Examples
f1 <- function(x) c(sin(x), cos(x))
quadv(f1, 0, pi)
# $Q
# [1] 2.000000e+00 1.110223e-16
# $fcnt
# [1] 65
# $estim.prec
# [1] 4.321337e-07
f2 <- function(x) x^c(1:10)
quadv(f2, 0, 1, tol = 1e-12)
# $Q
# [1] 0.50000000 0.33333333 0.25000000 0.20000000 0.16666667
# [6] 0.14285714 0.12500000 0.11111111 0.10000000 0.09090909
# $fcnt
# [1] 505
# $estim.prec
# [1] 2.49e-10
}
\keyword{ math }