\HeaderA{mapply}{Apply a function to multiple list or vector arguments}{mapply}
\aliasA{Vectorize}{mapply}{Vectorize}
\keyword{manip}{mapply}
\keyword{utilities}{mapply}
\begin{Description}\relax
\code{mapply} is a multivariate version of \code{\LinkA{sapply}{sapply}}.
\code{mapply} applies \code{FUN} to the first elements of each \dots
argument, the second elements, the third elements, and so on.
Arguments are recycled if necessary. 

\code{Vectorize} returns a new function that acts as if \code{mapply}
was called.
\end{Description}
\begin{Usage}
\begin{verbatim}
mapply(FUN, ..., MoreArgs = NULL, SIMPLIFY = TRUE,
      USE.NAMES = TRUE)

Vectorize(FUN, vectorize.args = arg.names, SIMPLIFY = TRUE,
          USE.NAMES = TRUE)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{FUN}] Function to apply, found via \code{\LinkA{match.fun}{match.fun}}.
\item[\code{...}] Arguments to vectorise over (list or vector).
\item[\code{MoreArgs}] A list of other arguments to \code{FUN}.
\item[\code{SIMPLIFY}] Attempt to reduce the result to a vector or matrix?
\item[\code{USE.NAMES}] If the first \dots argument is character and the
result does not already have names, use it as the names.
\item[\code{vectorize.args}] A character vector of arguments which should be
vectorized.  Defaults to all arguments to \code{FUN}.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
The arguments named in the \code{vectorize.args} argument to
\code{Vectorize} correspond to the arguments passed in the \code{...}
list to \code{mapply}.  However, only those that are actually passed
will be vectorized; default values will not. See the example below.
\end{Details}
\begin{Value}
\code{mapply} returns a list, vector, or matrix.

\code{Vectorize} returns a function with the same arguments as \code{FUN},
but wrapping a call to \code{mapply}.
\end{Value}
\begin{SeeAlso}\relax
\code{\LinkA{sapply}{sapply}},
\code{\LinkA{outer}{outer}}
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
mapply(rep, 1:4, 4:1)

mapply(rep, times=1:4, x=4:1)

mapply(rep, times=1:4, MoreArgs=list(x=42))

# Repeat the same using Vectorize
vrep <- Vectorize(rep)
vrep(1:4, 4:1)
vrep(times=1:4, x=4:1)

vrep <- Vectorize(rep, "times")
vrep(times=1:4, x=42)

f <- function(x=1:3, y) c(x,y)
vf <- Vectorize(f, SIMPLIFY = FALSE)
f(1:3,1:3)
vf(1:3,1:3)
vf(y=1:3) # Only vectorizes y, not x

# Nonlinear regression contour plot, based on nls() example

SS <- function(Vm, K, resp, conc) {
    pred <- (Vm * conc)/(K + conc)
    sum((resp - pred)^2 / pred)
}
vSS <- Vectorize(SS, c("Vm", "K"))
Treated <- subset(Puromycin, state == "treated")

Vm <- seq(140, 310, len=50)
K <- seq(0, 0.15, len=40)
SSvals <- outer(Vm, K, vSS, Treated$rate, Treated$conc)
contour(Vm, K, SSvals, levels=(1:10)^2, xlab="Vm", ylab="K")

\end{ExampleCode}
\end{Examples}

