The R Project SVN R

\name{prcomp}
\alias{prcomp}
\alias{plot.prcomp}
\alias{print.prcomp}
\alias{summary.prcomp}
\alias{print.summary.prcomp}
\title{Principal Components Analysis}
\usage{
prcomp(x, retx = TRUE, center = TRUE, scale. = FALSE, tol = NULL)
}
\arguments{
    \item{x}{a matrix (or data frame) which provides the data for the
    principal components analysis.}
    \item{retx}{a logical value indicating whether the rotated variables
    should be returned.}
    \item{center}{a logical value indicating whether the variables
    should be shifted to be zero centered. Alternately, a vector of
    length equal the number of columns of \code{x} can be supplied.
    The value is passed to \code{scale}.}
    \item{scale}{a logical value indicating whether the variables should
    be scaled to have unit variance before the analysis takes
    place. The default is \code{FALSE} for consistency with S, but
    in general scaling is advisable. Alternately, a vector of length
    equal the number of columns of \code{x} can be supplied.  The
    value is passed to \code{scale}.}
    \item{tol}{a value indicating the magnitude below which components
    should be omitted. With the default null setting, no components
    are omitted.  Other settings for tol could be \code{tol = 0} or
    \code{tol = sqrt(.Machine$double.eps)}.} 
}
\description{
    Performs a principal components analysis on the given data matrix
    and returns the results as a \code{prcomp} object.}
\value{
    \code{prcomp} returns an list with class \code{"prcomp"}
    containing the following components:
    \item{sdev}{the standard deviation of the principal components
    (i.e., the eigenvalues of the cov matrix, though the calculation
    is actually done with the singular values of the data matrix).}
    \item{rotation}{the matrix of variable loadings (i.e., a matrix
    whose olumns contain the eigenvectors).  The function
    \code{princomp} returns this in the element \code{loadings}.}
    \item{x}{if \code{retx} is true the value of the rotated data (the
    data multiplied by the \code{rotation} matrix) is returned.}
}
\details{
    The calculation is done with svd on the data matrix, not by using
    eigen on the covariance matrix.  This is generally the preferred
    method for numerical accuracy.  The print method for the these
    objects prints the results in a nice format and the plot method
    produces a scree plot.
}
\references{
    Mardia, K. V., J. T. Kent, J and M. Bibby (1979),
    \emph{Multivariate Analysis}, London: Academic Press.

    Venables, W. N. and B. D. Ripley (1997),
    \emph{Modern Applied Statistics with S-Plus}, Springer-Verlag.
}
\seealso{
    \code{\link{princomp}}, \code{\link{cor}}, \code{\link{cov}},
    \code{\link{svd}}, \code{\link{eigen}}.
}
\examples{
## the variances of the variables in the
## USArrests data vary by orders of magnitude
data(USArrests)
prcomp(USArrests)
prcomp(USArrests, scale = TRUE)
plot(prcomp(USArrests))
summary(prcomp(USArrests))
}