\HeaderA{order}{Ordering Permutation}{order}
\aliasA{sort.list}{order}{sort.list}
\keyword{univar}{order}
\keyword{manip}{order}
\begin{Description}\relax
\code{order} returns a permutation which rearranges its first
argument into ascending or descending order, breaking ties by further
arguments. \code{sort.list} is the same, using only one argument.\\
See the examples for how to use these functions to sort data frames,
etc.
\end{Description}
\begin{Usage}
\begin{verbatim}
order(..., na.last = TRUE, decreasing = FALSE)

sort.list(x, partial = NULL, na.last = TRUE, decreasing = FALSE,
          method = c("shell", "quick", "radix"))
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{...}] a sequence of numeric, complex, character or logical
vectors, all of the same length.
\item[\code{x}] a vector.
\item[\code{partial}] vector of indices for partial sorting.
(Non-\code{NULL} values are not implemented.)
\item[\code{decreasing}] logical. Should the sort order be increasing or
decreasing?
\item[\code{na.last}] for controlling the treatment of \code{NA}s.
If \code{TRUE}, missing values in the data are put last; if
\code{FALSE}, they are put first; if \code{NA}, they are removed.

\item[\code{method}] the method to be used: partial matches are allowed.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
In the case of ties in the first vector, values in the second are used
to break the ties.  If the values are still tied, values in the later
arguments are used to break the tie (see the first example).
The sort used is \emph{stable} (except for \code{method = "quick"}),
so any unresolved ties will be left in their original ordering.

Complex values are sorted first by the real part, then the imaginary
part.

The sort order for character vectors will depend on the collating
sequence of the locale in use: see \code{\LinkA{Comparison}{Comparison}}.

The default method for \code{sort.list} is a good compromise.
Method \code{"quick"} is only supported for numeric \code{x} with
\code{na.last=NA}, and is not stable, but will be faster for long vectors.
Method \code{"radix"} is only implemented for integer \code{x} with
a range of less than 100,000.  For such \code{x} it is very
fast (and stable), and hence is ideal for sorting factors.

\code{partial} is supplied for compatibility with other
implementations of S, but no other values are accepted and ordering is
always complete.

Note that these functions are only defined for vectors, so any class
of the object supplied is ignored: this means factors are sorted on
their internal codes and not their printed representation.
\end{Details}
\begin{Note}\relax
\code{sort.list} can get called by mistake as a method for
\code{\LinkA{sort}{sort}} with a list argument, and gives a suitable error
message for list \code{x}.
\end{Note}
\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{sort}{sort}}, \code{\LinkA{rank}{rank}}, \code{\LinkA{xtfrm}{xtfrm}}.
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
require(stats)

(ii <- order(x <- c(1,1,3:1,1:4,3), y <- c(9,9:1), z <-c(2,1:9)))
## 6  5  2  1  7  4 10  8  3  9
rbind(x,y,z)[,ii] # shows the reordering (ties via 2nd & 3rd arg)

## Suppose we wanted descending order on y.
## A simple solution for numeric 'y' is
rbind(x,y,z)[, order(x, -y, z)]
## More generally we can make use of xtfrm
cy <- as.character(y)
rbind(x,y,z)[, order(x, -xtfrm(cy), z)]

## Sorting data frames:
dd <- transform(data.frame(x,y,z),
                z = factor(z, labels=LETTERS[9:1]))
## Either as above {for factor 'z' : using internal coding}:
dd[ order(x, -y, z) ,]
## or along 1st column, ties along 2nd, ... *arbitrary* no.{columns}:
dd[ do.call(order, dd) ,]

set.seed(1)# reproducible example:
d4 <- data.frame(x = round(   rnorm(100)), y = round(10*runif(100)),
                 z = round( 8*rnorm(100)), u = round(50*runif(100)))
(d4s <- d4[ do.call(order, d4) ,])
(i <- which(diff(d4s[,3]) == 0))
#   in 2 places, needed 3 cols to break ties:
d4s[ rbind(i,i+1), ]

## rearrange matched vectors so that the first is in ascending order
x <- c(5:1, 6:8, 12:9)
y <- (x - 5)^2
o <- order(x)
rbind(x[o], y[o])

## tests of na.last
a <- c(4, 3, 2, NA, 1)
b <- c(4, NA, 2, 7, 1)
z <- cbind(a, b)
(o <- order(a, b)); z[o, ]
(o <- order(a, b, na.last = FALSE)); z[o, ]
(o <- order(a, b, na.last = NA)); z[o, ]

## Not run: 
##  speed examples for long vectors:
x <- factor(sample(letters, 1e6, replace=TRUE))
system.time(o <- sort.list(x)) ## 1.2 secs
stopifnot(!is.unsorted(x[o]))
system.time(o <- sort.list(x, method="quick", na.last=NA)) # 0.15 sec
stopifnot(!is.unsorted(x[o]))
system.time(o <- sort.list(x, method="radix")) # 0.02 sec
stopifnot(!is.unsorted(x[o]))
xx <- sample(1:26, 1e7, replace=TRUE)
system.time(o <- sort.list(xx, method="radix")) # 0.2 sec
xx <- sample(1:100000, 1e7, replace=TRUE)
system.time(o <- sort.list(xx, method="radix")) # 0.8 sec
system.time(o <- sort.list(xx, method="quick", na.last=NA)) # 1.4 sec
## End(Not run)\end{ExampleCode}
\end{Examples}

