\Header{biplot}{Biplot of Multivariate Data}
\alias{biplot.default}{biplot}
\keyword{hplot}{biplot}
\keyword{multivariate}{biplot}
\begin{Usage}
\begin{verbatim}
biplot(x, ...)

biplot.default(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, ...)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\texttt{x}] The \texttt{biplot}, a fitted object. For \texttt{biplot.default},
the first set of points (a two-column matrix), usually associated
with observations.
\item[\texttt{y}] The second set of points (a two-column matrix), usually associated
with variables.
\item[\texttt{var.axes}] If \texttt{TRUE} the second set of points have arrows
representing them as (unscaled) axes.
\item[\texttt{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.
\item[\texttt{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[\texttt{xlabs}] A vector of character strings to label the first set of
points: the default is to use the row dimname of \texttt{x}, or
\texttt{1:n} is the dimname is \texttt{NULL}.
\item[\texttt{ylabs}] A vector of character strings to label the second set of
points: the default is to use the row dimname of \texttt{y}, or
\texttt{1:n} is the dimname is \texttt{NULL}.
\item[\texttt{expand}] An expansion factor to apply when plotting the second set
of points relative to the first. This can be used to get the two sets
on to a physically comparable scale.
\item[\texttt{arrow.len}] The length of the arrow heads on the axes plotted in
\texttt{var.axes} is true. The arrow head can be suppressed by
\texttt{arrow.len = 0}.
\end{ldescription}
\end{Arguments}
\begin{Description}
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 \texttt{\Link{biplot.princomp}}.
The function \texttt{biplot.default} merely provides the
underlying code to plot two sets of variables on the same figure.

Graphical parameters can also be given to \texttt{biplot}.\end{Description}
\begin{Section}{Side Effects}
a plot is produced on the current graphics device.\end{Section}
\begin{Author}
B.D. Ripley\end{Author}
\begin{References}
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}
\texttt{\Link{biplot.princomp}}, also for examples.\end{SeeAlso}

