g03ehc produces a dendrogram from the results of
g03ecc.
Hierarchical cluster analysis, as performed by
g03ecc can be represented by a tree that shows at which distance the clusters merge. Such a tree is known as a dendrogram. See
Everitt (1974) and
Krzanowski (1990) for examples of dendrograms. A simple example is,
The endpoints of the dendrogram represent the objects that have been clustered. They should be in a suitable order as given by
g03ecc. Object 1 is always the first object. In the example above the height represents the distance at which the clusters merge.
The dendrogram is produced in an array of character pointers using the ordering and distances provided by
g03ecc. Suitable characters are used to represent parts of the tree.
There are four possible orientations for the dendrogram. The example above has the endpoints at the bottom of the diagram which will be referred to as south. If the dendrogram was the other way around with the endpoints at the top of the diagram then the orientation would be north. If the endpoints are at the lefthand or righthand side of the diagram the orientation is west or east. Different symbols are used for east/west and north/south orientations.

1:
$\mathbf{orient}$ – Nag_DendOrient
Input

On entry: indicates which orientation the dendrogram is to take.
 ${\mathbf{orient}}=\mathrm{Nag\_DendNorth}$
 The endpoints of the dendrogram are to the north.
 ${\mathbf{orient}}=\mathrm{Nag\_DendSouth}$
 The endpoints of the dendrogram are to the south.
 ${\mathbf{orient}}=\mathrm{Nag\_DendEast}$
 The endpoints of the dendrogram are to the east.
 ${\mathbf{orient}}=\mathrm{Nag\_DendWest}$
 The endpoints of the dendrogram are to the west.
Constraint:
${\mathbf{orient}}=\mathrm{Nag\_DendNorth}$, $\mathrm{Nag\_DendSouth}$, $\mathrm{Nag\_DendEast}$ or $\mathrm{Nag\_DendWest}$.

2:
$\mathbf{n}$ – Integer
Input

On entry: the number of objects in the cluster analysis.
Constraint:
${\mathbf{n}}\ge 2$.

3:
$\mathbf{dord}\left[{\mathbf{n}}\right]$ – const double
Input

On entry: the array
dord as output by
g03ecc.
dord contains the distances, in dendrogram order, at which clustering takes place.
Constraint:
${\mathbf{dord}}\left[{\mathbf{n}}1\right]\ge {\mathbf{dord}}\left[\mathit{i}1\right]$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}1$.

4:
$\mathbf{dmin}$ – double
Input

On entry: the clustering distance at which the dendrogram begins.
Constraint:
${\mathbf{dmin}}\ge 0.0$.

5:
$\mathbf{dstep}$ – double
Input

On entry: the distance represented by one symbol of the dendrogram.
Constraint:
${\mathbf{dstep}}>0.0$.

6:
$\mathbf{nsym}$ – Integer
Input

On entry: the number of character positions used in the dendrogram. Hence the clustering distance at which the dendrogram terminates is given by ${\mathbf{dmin}}+{\mathbf{nsym}}\times {\mathbf{dstep}}$.
Constraint:
${\mathbf{nsym}}\ge 1$.

7:
$\mathbf{c}$ – char ***
Input/Output

On entry/exit: a pointer to an array of character pointers, containing consecutive lines of the dendrogram. The memory to which
c points is allocated internally.
 ${\mathbf{orient}}=\mathrm{Nag\_DendNorth}$ or $\mathrm{Nag\_DendSouth}$
 The number of lines in the dendrogram is nsym.
 ${\mathbf{orient}}=\mathrm{Nag\_DendEast}$ or $\mathrm{Nag\_DendWest}$
 The number of lines in the dendrogram is n.
The storage pointed to by this pointer must be freed using
g03xzc.

8:
$\mathbf{fail}$ – NagError *
Input/Output

The NAG error argument (see
Section 7 in the Introduction to the NAG Library CL Interface).
Not applicable.
Background information to multithreading can be found in the
Multithreading documentation.
The scale of the dendrogram is controlled by
dstep. The smaller the value of
dstep the greater the amount of detail that will be given. However,
nsym will have to be larger to give the full dendrogram. The range of distances represented by the dendrogram is
dmin to
${\mathbf{nsym}}\times {\mathbf{dstep}}$. The values of
dmin,
dstep and
nsym can thus be set so that only part of the dendrogram is produced.
The dendrogram does not include any labelling of the objects. You can print suitable labels using the ordering given by the array
iord returned by
g03ecc.
Data consisting of three variables on five objects are read in. Euclidean squared distances are computed using
g03eac and median clustering performed by
g03ecc.
g03ehc is used to produce a dendrogram with orientation east and a dendrogram with orientation south. The two dendrograms are printed.
Note the use of
g03xzc to free the memory allocated internally to the character array pointed to by
c.