\name{Extremes}
\alias{max}
\alias{min}
\alias{pmax}
\alias{pmin}
\title{Maxima and Minima}
\description{
  Returns the (parallel) maxima and minima of the input values.
}
\usage{
max(\dots, na.rm=FALSE)
min(\dots, na.rm=FALSE)

pmax(\dots, na.rm=FALSE)
pmin(\dots, na.rm=FALSE)
}
\arguments{
  \item{\dots}{numeric arguments (see Note).}
  \item{na.rm}{a logical indicating whether missing values should be
    removed.}
}
\value{
  \code{max} and \code{min} return the maximum or minimum of \emph{all}
  the  values present in their arguments, as \code{\link{integer}} if
  all are \code{integer}, % and at least one is nonempty
  or as \code{\link{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)}.  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{\link{attributes}} (such as \code{\link{names}} or
  \code{\link{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{\link[base:groupGeneric]{Summary}}
  group generic.
  For this to work properly, the arguments \code{\dots} should be
  unnamed, and dispatch is on the first argument.

  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.
}
\references{
  Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
  \emph{The New S Language}.
  Wadsworth \& Brooks/Cole.
}
\note{
  \sQuote{Numeric} arguments are vectors of type integer and numeric,
  and logical (coerced to integer).  For historical reasons, \code{NULL}
  is accepted as equivalent to \code{integer(0)}.% PR#1283
}
\seealso{
  \code{\link{range}} (\emph{both} min and max) and
  \code{\link{which.min}} (\code{which.max}) for the \emph{arg min},
  i.e., the location where an extreme value occurs.
}
\examples{
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")
}
\keyword{univar}
\keyword{arith}