\HeaderA{biplot}{Biplot of Multivariate Data}{biplot}
\methaliasA{biplot.default}{biplot}{biplot.default}
\keyword{hplot}{biplot}
\keyword{multivariate}{biplot}
\begin{Description}\relax
Plot a biplot on the current graphics device.
\end{Description}
\begin{Usage}
\begin{verbatim}
biplot(x, ...)

## Default S3 method:
biplot(x, y, var.axes = TRUE, col, cex = rep(par("cex"), 2),
       xlabs = NULL, ylabs = NULL, expand = 1,
       xlim  = NULL, ylim  = NULL, arrow.len = 0.1,
       main = NULL, sub = NULL, xlab = NULL, ylab = NULL, ...)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{x}] The \code{biplot}, a fitted object. For \code{biplot.default},
the first set of points (a two-column matrix), usually associated
with observations.
\item[\code{y}] The second set of points (a two-column matrix), usually associated
with variables.
\item[\code{var.axes}] If \code{TRUE} the second set of points have arrows
representing them as (unscaled) axes.
\item[\code{col}] A vector of length 2 giving the colours for the first and
second set of points respectively (and the corresponding axes). If a
single colour is specified it will be used for both sets.  If
missing the default colour is looked for in the
\code{\LinkA{palette}{palette}}: if there it and the next colour as used,
otherwise the first two colours of the paletter are used.
\item[\code{cex}] The character expansion factor used for labelling the
points. The labels can be of different sizes for the two sets by
supplying a vector of length two.
\item[\code{xlabs}] A vector of character strings to label the first set of
points: the default is to use the row dimname of \code{x}, or
\code{1:n} is the dimname is \code{NULL}.
\item[\code{ylabs}] A vector of character strings to label the second set of
points: the default is to use the row dimname of \code{y}, or
\code{1:n} is the dimname is \code{NULL}.
\item[\code{expand}] An expansion factor to apply when plotting the second set
of points relative to the first. This can be used to tweak the
scaling of the two sets to a physically comparable scale.
\item[\code{arrow.len}] The length of the arrow heads on the axes plotted in
\code{var.axes} is true. The arrow head can be suppressed by
\code{arrow.len = 0}.
\item[\code{xlim, ylim}] Limits for the x and y axes in the units of the
first set of variables.
\item[\code{main, sub, xlab, ylab, ...}] graphical parameters.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
A biplot is plot which aims to represent both the observations and
variables of a matrix of multivariate data on the same plot. There are
many variations on biplots (see the references) and perhaps the most
widely used one is implemented by \code{\LinkA{biplot.princomp}{biplot.princomp}}.
The function \code{biplot.default} merely provides the
underlying code to plot two sets of variables on the same figure.

Graphical parameters can also be given to \code{biplot}: the size of
\code{xlabs} and \code{ylabs} is controlled by \code{cex}.
\end{Details}
\begin{Section}{Side Effects}
a plot is produced on the current graphics device.
\end{Section}
\begin{References}\relax
K. R. Gabriel (1971).  The biplot graphical display of matrices with
application to principal component analysis. \emph{Biometrika}
\bold{58}, 453--467.

J.C. Gower and D. J. Hand (1996). \emph{Biplots}. Chapman \& Hall.
\end{References}
\begin{SeeAlso}\relax
\code{\LinkA{biplot.princomp}{biplot.princomp}}, also for examples.
\end{SeeAlso}

