\HeaderA{dendrogram}{General Tree Structures}{dendrogram}
\aliasA{as.dendrogram}{dendrogram}{as.dendrogram}
\methaliasA{as.dendrogram.dendrogram}{dendrogram}{as.dendrogram.dendrogram}
\methaliasA{as.dendrogram.hclust}{dendrogram}{as.dendrogram.hclust}
\aliasA{cut.dendrogram}{dendrogram}{cut.dendrogram}
\aliasA{is.leaf}{dendrogram}{is.leaf}
\aliasA{plot.dendrogram}{dendrogram}{plot.dendrogram}
\aliasA{print.dendrogram}{dendrogram}{print.dendrogram}
\aliasA{rev.dendrogram}{dendrogram}{rev.dendrogram}
\aliasA{str.dendrogram}{dendrogram}{str.dendrogram}
\aliasA{[[.dendrogram}{dendrogram}{[[.dendrogram}
\keyword{multivariate}{dendrogram}
\keyword{tree}{dendrogram}
\keyword{hplot}{dendrogram}
\begin{Description}\relax
Class \code{"dendrogram"} provides general functions for handling
tree-like structures.  It is intended as a replacement for similar
functions in hierarchical clustering and classification/regression
trees, such that all of these can use the same engine for plotting or
cutting trees.

The code is still in testing stage and the API may
change in the future.
\end{Description}
\begin{Usage}
\begin{verbatim}
as.dendrogram(object, ...)
## S3 method for class 'hclust':
as.dendrogram(object, hang = -1, ...)

## S3 method for class 'dendrogram':
plot(x, type = c("rectangle", "triangle"),
      center = FALSE,
      edge.root = is.leaf(x) || !is.null(attr(x,"edgetext")),
      nodePar = NULL, edgePar = list(),
      leaflab = c("perpendicular", "textlike", "none"),
      dLeaf = NULL, xlab = "", ylab = "", xaxt = "n", yaxt = "s",
      horiz = FALSE, frame.plot = FALSE, xlim, ylim, ...)

## S3 method for class 'dendrogram':
cut(x, h, ...)

## S3 method for class 'dendrogram':
print(x, digits, ...)

## S3 method for class 'dendrogram':
rev(x)

## S3 method for class 'dendrogram':
str(object, max.level = NA, digits.d = 3,
    give.attr = FALSE, wid = getOption("width"),
    nest.lev = 0, indent.str = "", stem = "--", ...)

is.leaf(object)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{object}] any \R{} object that can be made into one of class
\code{"dendrogram"}.
\item[\code{x}] object of class \code{"dendrogram"}.
\item[\code{hang}] numeric scalar indicating how the \emph{height} of leaves
should be computed from the heights of their parents; see
\code{\LinkA{plot.hclust}{plot.hclust}}.
\item[\code{type}] type of plot.
\item[\code{center}] logical; if \code{TRUE}, nodes are plotted centered with
respect to the leaves in the branch.  Otherwise (default), plot them
in the middle of all direct child nodes.
\item[\code{edge.root}] logical; if true, draw an edge to the root node.
\item[\code{nodePar}] a \code{list} of plotting parameters to use for the
nodes (see \code{\LinkA{points}{points}}) or \code{NULL} by default which
does not draw symbols at the nodes.  The list may contain components
named \code{pch}, \code{cex}, \code{col}, and/or \code{bg} each of
which can have length two for specifying separate attributes for
\emph{inner} nodes and \emph{leaves}.
\item[\code{edgePar}] a \code{list} of plotting parameters to use for the
edge \code{\LinkA{segments}{segments}} and labels (if there's an
\code{edgetext}).  The list may contain components
named \code{col}, \code{lty} and \code{lwd} (for the segments),
\code{p.col}, \code{p.lwd}, and \code{p.lty} (for the
\code{\LinkA{polygon}{polygon}} around the text) and \code{t.col} for the text
color.  As with \code{nodePar}, each can have length two for
differentiating leaves and inner nodes.

\item[\code{leaflab}] a string specifying how leaves are labeled.  The
default \code{"perpendicular"} write text vertically (by default).\\
\code{"textlike"} writes text horizontally (in a rectangle), and \\
\code{"none"} suppresses leaf labels.
\item[\code{dLeaf}] a number specifying the \bold{d}istance in user
coordinates between the tip of a leaf and its label.  If \code{NULL}
as per default, 3/4 of a letter width or height is used.
\item[\code{horiz}] logical indicating if the dendrogram should be drawn
\emph{horizontally} or not.
\item[\code{frame.plot}] logical indicating if a box around the plot should
be drawn, see \code{\LinkA{plot.default}{plot.default}}.
\item[\code{h}] height at which the tree is cut.
\item[\code{xlim, ylim}] optional x- and y-limits of the plot, passed to
\code{\LinkA{plot.default}{plot.default}}.  The defaults for these show the full
dendrogram.
\item[\code{..., xlab, ylab, xaxt, yaxt}] graphical parameters, or arguments for
other methods.
\item[\code{digits}] integer specifying the precision for printing, see
\code{\LinkA{print.default}{print.default}}.
\item[\code{max.level, digits.d, give.attr, wid, nest.lev, indent.str}] arguments to \code{str}, see \code{\LinkA{str.default}{str.default}()}.  Note that
\code{give.attr = FALSE} still shows \code{height} and \code{members}
attributes for each node.
\item[\code{stem}] a string used for \code{str()} specifying the \emph{stem}
to use for each dendrogram branch.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
Warning: This documentation is preliminary.

The dendrogram is directly represented as a nested list where each
component corresponds to a branch of the tree.  Hence, the first
branch of tree \code{z} is \code{z[[1]]}, the second branch of the
corresponding subtree is \code{z[[1]][[2]]} etc.. Each node of the tree
carries some information needed for efficient plotting or cutting as
attributes, of which only \code{members}, \code{height} and
\code{leaf} for leaves are compulsory:
\describe{
\item[\code{members}] total number of leaves in the branch
\item[\code{height}] numeric non-negative height at which the node
is plotted.
\item[\code{midpoint}] numeric horizontal distance of the node from
the left border (the leftmost leaf) of the branch (unit 1 between
all leaves).  This is used for \code{plot(*, center=FALSE)}.
\item[\code{label}] character; the label of the node
\item[\code{x.member}] for \code{cut()\$upper},
the number of \emph{former} members; more generally a substitute
for the \code{members} component used for \sQuote{horizontal}
(when \code{horiz = FALSE}, else \sQuote{vertical}) alignment.
\item[\code{edgetext}] character; the label for the edge leading to
the node
\item[\code{nodePar}] a named list (of length-1 components)
specifying node-specific attributes for \code{\LinkA{points}{points}}
plotting, see the \code{nodePar} argument above.
\item[\code{edgePar}] a named list (of length-1 components)
specifying attributes for \code{\LinkA{segments}{segments}} plotting of the
edge leading to the node, and drawing of the \code{edgetext} if
available, see the \code{edgePar} argument above.
\item[\code{leaf}] logical, if \code{TRUE}, the node is a leaf of
the tree.
}

\code{cut.dendrogram()} returns a list with components \code{\$upper}
and \code{\$lower}, the first is a truncated version of the original
tree, also of class \code{dendrogram}, the latter a list with the
branches obtained from cutting the tree, each a \code{dendrogram}.

There are \code{\LinkA{[[}{[[}}, \code{\LinkA{print}{print}}, and \code{\LinkA{str}{str}}
methods for \code{"dendrogram"} objects where the first one
(extraction) ensures that selecting sub-branches keeps the class.

Objects of class \code{"hclust"} can be converted to class
\code{"dendrogram"} using method \code{as.dendrogram}.

\code{rev.dendrogram} simply returns the dendrogram \code{x} with
reversed nodes, see also \code{\LinkA{reorder.dendrogram}{reorder.dendrogram}}.

\code{is.leaf(object)} is logical indicating if \code{object} is a
leaf (the most simple dendrogram).
\code{plotNode()} and \code{plotNodeLimit()} are helper functions.
\end{Details}
\begin{Section}{Warning}
Some operations on dendrograms (including plotting) make use of
recursion.  For very deep trees It may be necessary to increase
\code{\LinkA{options}{options}("expressions")}: if you do you are likely to need
to set the C stack size larger than the OS default if possible
(which it is not on Windows).
\end{Section}
\begin{Note}\relax
When using \code{type = "triangle"}, \code{center = TRUE} often looks
better.
\end{Note}
\begin{SeeAlso}\relax
\code{\LinkA{order.dendrogram}{order.dendrogram}} also on the \code{\LinkA{labels}{labels}} method
for dendrograms.
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
require(graphics); require(utils)

hc <- hclust(dist(USArrests), "ave")
(dend1 <- as.dendrogram(hc)) # "print()" method
str(dend1)          # "str()" method
str(dend1, max = 2) # only the first two sub-levels

op <- par(mfrow= c(2,2), mar = c(5,2,1,4))
plot(dend1)
## "triangle" type and show inner nodes:
plot(dend1, nodePar=list(pch = c(1,NA), cex=0.8, lab.cex = 0.8),
      type = "t", center=TRUE)
plot(dend1, edgePar=list(col = 1:2, lty = 2:3),
     dLeaf=1, edge.root = TRUE)
plot(dend1, nodePar=list(pch = 2:1,cex=.4*2:1, col = 2:3),
     horiz=TRUE)

dend2 <- cut(dend1, h=70)
plot(dend2$upper)
## leafs are wrong horizontally:
plot(dend2$upper, nodePar=list(pch = c(1,7), col = 2:1))
##  dend2$lower is *NOT* a dendrogram, but a list of .. :
plot(dend2$lower[[3]], nodePar=list(col=4), horiz = TRUE, type = "tr")
## "inner" and "leaf" edges in different type & color :
plot(dend2$lower[[2]], nodePar=list(col=1),# non empty list
     edgePar = list(lty=1:2, col=2:1), edge.root=TRUE)
par(op)
str(d3 <- dend2$lower[[2]][[2]][[1]])

## "Zoom" in to the first dendrogram :
plot(dend1, xlim = c(1,20), ylim = c(1,50))

nP <- list(col=3:2, cex=c(2.0, 0.75), pch= 21:22,
           bg= c("light blue", "pink"),
           lab.cex = 0.75, lab.col = "tomato")
plot(d3, nodePar= nP, edgePar = list(col="gray", lwd=2), horiz = TRUE)
addE <- function(n) {
      if(!is.leaf(n)) {
        attr(n, "edgePar") <- list(p.col="plum")
        attr(n, "edgetext") <- paste(attr(n,"members"),"members")
      }
      n
}
d3e <- dendrapply(d3, addE)
plot(d3e, nodePar= nP)
plot(d3e, nodePar= nP, leaflab = "textlike")

\end{ExampleCode}
\end{Examples}

