\HeaderA{Extremes}{Maxima and Minima}{Extremes}
\aliasA{max}{Extremes}{max}
\aliasA{min}{Extremes}{min}
\aliasA{pmax}{Extremes}{pmax}
\aliasA{pmin}{Extremes}{pmin}
\keyword{univar}{Extremes}
\keyword{arith}{Extremes}
\begin{Description}\relax
Returns the (parallel) maxima and minima of the input values.
\end{Description}
\begin{Usage}
\begin{verbatim}
max(..., na.rm=FALSE)
min(..., na.rm=FALSE)

pmax(..., na.rm=FALSE)
pmin(..., na.rm=FALSE)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{...}] numeric arguments.
\item[\code{na.rm}] a logical indicating whether missing values should be
removed.
\end{ldescription}
\end{Arguments}
\begin{Value}
\code{max} and \code{min} return the maximum or minimum of \emph{all}
the  values present in their arguments, as \code{\LinkA{integer}{integer}} if
all are \code{integer}, 
or as \code{\LinkA{double}{double}} otherwise.

The minimum and maximum of an empty set are \code{+Inf} and \code{-Inf}
(in this order!) which ensures \emph{transitivity}, e.g.,
\code{min(x1, min(x2)) == min(x1,x2)}.
In \R{} versions before 1.5, \code{min(integer(0)) == .Machine\$integer.max},
and analogously for \code{max}, preserving argument \emph{type},
whereas from \R{} version 1.5.0, \code{max(x) == -Inf} and
\code{min(x) == +Inf} whenever \code{length(x) == 0} (after removing
missing values if requested).

If \code{na.rm} is \code{FALSE} an \code{NA} value in any of the
arguments will cause a value of \code{NA} to be returned, otherwise
\code{NA} values are ignored.

\code{pmax} and \code{pmin} take several vectors (or matrices) as arguments and
return a single vector giving the \dQuote{parallel} maxima (or minima) of the
vectors.  The first element of the result is the maximum (minimum) of
the first elements of all the arguments, the second element of the
result is the maximum (minimum) of the second elements of all the
arguments and so on.  Shorter vectors are recycled if necessary.  If
\code{na.rm} is \code{FALSE}, \code{NA} values in the input vectors
will produce \code{NA} values in the output.  If \code{na.rm} is
\code{TRUE}, \code{NA} values are ignored.
\code{\LinkA{attributes}{attributes}} (such as \code{\LinkA{names}{names}} or
\code{\LinkA{dim}{dim}}) are transferred from the first argument (if applicable).

\code{max} and \code{min} are generic functions: methods can be defined
for them individually or via the \code{\LinkA{Summary}{Summary}} group generic.
For this to work properly, the arguments \code{...} should be unnamed.

By definition the min/max of any vector containing an \code{NaN} is
\code{NaN}, except that the min/max of any vector containing an \code{NA}
is \code{NA} even if it also contains an \code{NaN}.  Note that
\code{max(NA, Inf) == NA} even though the maximum would be \code{inf}
whatever the missing value actually is.
\end{Value}
\begin{References}\relax
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
\emph{The New S Language}.
Wadsworth \& Brooks/Cole.
\end{References}
\begin{SeeAlso}\relax
\code{\LinkA{range}{range}} (\emph{both} min and max) and
\code{\LinkA{which.min}{which.min}} (\code{which.max}) for the \emph{arg min},
i.e., the location where an extreme value occurs.
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
require(stats)
 min(5:1, pi) #-> one number
pmin(5:1, pi) #->  5  numbers

x <- sort(rnorm(100));  cH <- 1.35
pmin(cH, quantile(x)) # no names
pmin(quantile(x), cH) # has names
plot(x, pmin(cH, pmax(-cH, x)), type='b', main= "Huber's function")
\end{ExampleCode}
\end{Examples}

