\name{Extract}
\title{Extract or Replace Parts of an Object}
\alias{Extract}
\alias{Subscript}
\alias{[}
\alias{[[}
\alias{$}
\alias{[<-}
\alias{[[<-}
\alias{$<-}
\concept{delete}
\description{
  Operators acting on vectors, matrices, arrays and lists to extract or
  replace parts.
}
\usage{
x[i]
x[i, j, \dots , drop = TRUE]
x[[i]]
x[[i, j, \dots]]
x$name
}
\arguments{
  \item{x}{
    object from which to extract element(s) or in which to replace element(s).
  }
  \item{i, j, \dots, name}{
    indices specifying elements to extract or replace.  \code{i, j} are
    \code{numeric} or \code{character} vectors or empty (missing) or
    \code{NULL} whereas \code{name} must be a character string or an
    (unquoted or backtick quoted) name.  Numeric values are coerced to
    integer as by \code{\link{as.integer}}.  For extraction with
    \code{[[} and \code{$} character strings are normally (see under
    Environments) partially matched to the \code{\link{names}} of the
    object if exact matching does not succeed.

    For \code{[}-indexing only: \code{i, j, \dots} can be logical
    vectors, indicating elements/slices to select.  Such vectors are
    recycled if necessary to match the corresponding extent. \code{i, j,
      \dots} can also be negative integers, indicating elements/slices
    to leave out of the selection.

    When indexing arrays by \code{[} a single argument \code{i} can be a
    matrix with as many columns as there are dimensions of \code{x}; the
    result is then a vector with elements corresponding to the sets of
    indices in each row of \code{i}.

    An index value of \code{NULL} is treated as if it were \code{integer(0)}.
  }
  \item{drop}{For matrices and arrays.  If \code{TRUE} the result is
    coerced to the lowest possible dimension (see the examples).  This
    only works for extracting elements, not for the replacement.}
}
\details{
  These operators are generic.  You can write methods to handle indexing
  of specific classes of objects, see \link{InternalMethods} as well as
  \code{\link{[.data.frame}} and \code{\link{[.factor}}.  The
  descriptions here apply only to the default methods.  Note that
  separate methods are required for the replacement functions
  \code{[<-}, \code{[[<-} and \code{$<-} for use when indexing occurs on
  the assignment side of an expression.

  The most important distinction between \code{[}, \code{[[} and
  \code{$} is that the \code{[} can select more than one element whereas
  the other two select a single element.

  The default methods work somewhat differently for atomic vectors,
  matrices/arrays and for recursive (list-like, see
  \code{\link{is.recursive}}) objects.  \code{$} returns \code{NULL}
  except for recursive objects, and is only discussed in the section
  below on recursive objects.

  Subsetting (except by an empty index) will drop all attributes except
  \code{names}, \code{dim} and \code{dimnames}.

  Indexing can occur on the right-hand-side of an expression for
  extraction, or on the left-hand-side for replacement. When an index
  expression appears on the left side of an assignment (known as
  \emph{subassignment}) then that part of \code{x} is set to the value
  of the right hand side of the assignment.  In this case no partial
  matching of indices is done, and the left-hand-side is coerced as
  needed to accept the values.  Attributes are preserved (although
  \code{names}, \code{dim} and \code{dinmanes} will be adjusted
  suitably).
}
\section{Atomic vectors}{
  The usual form of indexing is \code{"["}.  \code{"[["} can be used to
  select a single element, but \code{"["} can also do so (but will not
  partially match a character index).

  The index object \code{i} can be numeric, logical, character or empty.
  Indexing by factors is allowed and is equivalent to indexing by the
  numeric codes (see \code{\link{factor}}) and not by the character
  values which are printed (for which use \code{[as.character(i)]}).

  An empty index selects all values: this is most often used to replace
  all the entries but keep the \code{\link{attributes}}.
}
\section{Matrices and arrays}{
  Matrices and arrays are vectors with a dimension attribute and so all
  the vector forms of indexing can be used with a single index.  The
  result will be an unnamed vector unless \code{x} is one-dimensional
  when it will be a one-dimensional array.

  The most common form of indexing a \eqn{k}-dimensional array is to
  specify \eqn{k} indices to \code{[}.  As for vector indexing, the
  indices can be numeric, logical, character, empty or even factor.
  An empty index (a comma separated blank) indicates that all entries in
  that dimension are selected.
  The argument \code{drop} applies to this form of indexing.
  
  A third form of indexing is via a numeric matrix with the one column
  for each dimension: each row of the index matrix then selects a single
  element of the array, and the result is a vector.  Negative indices are
  not allowed in the index matrix.  \code{NA} and zero values are allowed:
  rows of an index matrix containing a zero are ignored, whereas rows
  containing an \code{NA} produce an \code{NA} in the result.

  A vector obtained by matrix indexing will be unnamed unless \code{x}
  is one-dimensional when the row names (if any) will be indexed to
  provide names for the result.
}
\section{Recursive (list-like) objects}{
  Indexing by \code{[} is similar to atomic vectors and selects a list
  of the specified element(s).

  Both \code{[[} and \code{$} select a single element of the list.  The
  main difference is that \code{$} does not allow computed indices,
  whereas \code{[[} does.  \code{x$name} is equivalent to
  \code{x[["name"]]}.

  \code{[} and \code{[[} are sometimes applied to other recursive
  objects such as \link{call}s and \link{expression}s.  Pairlists are
  coerced to lists for extraction by \code{[}, but all three operators
  can be used for replacement.

  \code{[[} can be applied recursively to lists, so that if the single
  index \code{i} is a vector of length \code{p}, \code{alist[[i]]} is
  equivalent to \code{alist[[i1]]\dots[[ip]]} providing all but the
  final indexing results in a list.

  When \code{$<-} is applied to a \code{NULL} \code{x}, it first coerces
  \code{x} to \code{list()}.  This is what also happens with \code{[[<-}
  if the replacement value \code{value} is of length greater than one:
  if \code{value} has length 1 or 0, \code{x} is first coerced to a
  zero-length vector of the type of \code{value}.
}
\section{Environments}{
  Both \code{$} and \code{[[} can be applied to environments.  Only
  character arguments are allowed and no partial matching is done. The
  semantics of these operations are those of \code{get(i, env=x,
    inherits=FALSE)}.  If no match is found then \code{NULL} is
  returned.  The assignment versions, \code{$<-} and \code{[[<-}, can
  also be used.  Again, only character arguments are allowed.  The
  semantics in this case are those of \code{assign(i, value, env=x,
    inherits=FALSE)}.  Such an assignment will either create a new
  binding or change the existing binding in \code{x}.
}
\section{NAs in indexing}{
  When extracting, a numerical, logical or character \code{NA} index picks
  an unknown element and so returns \code{NA} in the corresponding
  element of a logical, integer, numeric, complex or character result,
  and \code{NULL} for a list.  (It returns \code{00} for a raw result.]

  When replacing (that is using indexing on the lhs of an
  assignment) \code{NA} does not select any element to be replaced.  As
  there is ambiguity as to whether an element of the rhs should
  be used or not, this is only allowed if the rhs value is of length one
  (so the two interpretations would have the same outcome).
}
\section{Argument matching}{
  Note that these operations do not match their index arguments in the
  standard way: argument names are ignored and positional matching only is
  used.  So \code{m[j=2,i=1]} is equivalent to \code{m[2,1]} and
  \strong{not} to \code{m[1,2]}.

  This may not be true for methods defined for them; for example it is
  not true for the \code{data.frame} methods described in
  \code{\link{[.data.frame}}.

  To avoid confusion, do not name index arguments (but \code{drop} must
  be named).
}
\note{
  S uses partial matching when extracting by \code{[}
  (Becker \emph{et al} p. 358) whereas \R does not.

  The documented behaviour of S is that an \code{NA} replacement index
  \sQuote{goes nowhere} but uses up an element of \code{value}
  (Becker \emph{et al} p. 359).  However, that is not the current
  behaviour of S-PLUS.
}
\references{
  Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
  \emph{The New S Language}.
  Wadsworth \& Brooks/Cole.
}
\seealso{
  \code{\link{list}}, \code{\link{array}}, \code{\link{matrix}}.

  \code{\link{[.data.frame}} and \code{\link{[.factor}} for the
  behaviour when applied to data.frame and factors.

  \code{\link{Syntax}} for operator precedence, and the
  \emph{R Language} reference manual about indexing details.
  %% Fixme: Link (to html in 'help.start()', pdf from 'ref manual',
  %% 'info' from ESS, see \url{http://cran.R-project.org/manuals.html}.
}
\examples{
x <- 1:12; m <- matrix(1:6,nr=2); li <- list(pi=pi, e = exp(1))
x[10]                 # the tenth element of x
x <- x[-1]	      # delete the 1st element of x
m[1,]                 # the first row of matrix m
m[1, , drop = FALSE]  # is a 1-row matrix
m[,c(TRUE,FALSE,TRUE)]# logical indexing
m[cbind(c(1,2,1),3:1)]# matrix index
m <- m[,-1]	      # delete the first column of m
li[[1]]               # the first element of list li
y <- list(1,2,a=4,5)
y[c(3,4)]             # a list containing elements 3 and 4 of y
y$a                   # the element of y named a

## non-integer indices are truncated:
(i <- 3.999999999) # "4" is printed
(1:5)[i]  # 3

## recursive indexing into lists
z <- list( a=list( b=9, c='hello'), d=1:5)
unlist(z)
z[[c(1, 2)]]
z[[c(1, 2, 1)]]  # both "hello"
z[[c("a", "b")]] <- "new"
unlist(z)

## check $ and [[ for environments
e1 <- new.env()
e1$a <- 10
e1[["a"]]
e1[["b"]] <- 20
e1$b
ls(e1)
}
\keyword{array}
\keyword{list}