# volume.ellipsoid: Compute the Volume (of an Ellipsoid) In cluster: "Finding Groups in Data": Cluster Analysis Extended Rousseeuw et al.

## Description

Compute the volume of geometric R object. This is a generic function and has a method for `ellipsoid` objects (typically resulting from `ellipsoidhull()`.

## Usage

 ```1 2 3``` ```volume(object, ...) ## S3 method for class 'ellipsoid' volume(object, log = FALSE, ...) ```

## Arguments

 `object` an R object the volume of which is wanted; for the `ellipsoid` method, an object of that class (see `ellipsoidhull` or the example below). `log` `logical` indicating if the volume should be returned in log scale. Maybe needed in largish dimensions. `...` potential further arguments of methods, e.g. `log`.

## Value

a number, the volume V (or \log(V) if `log = TRUE`) of the given `object`.

## Author(s)

Martin Maechler (2002, extracting from former `clusplot` code); Keefe Murphy (2019) provided code for dimensions d > 2.

`ellipsoidhull` for spanning ellipsoid computation.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```## example(ellipsoidhull) # which defines 'ellipsoid' object myEl <- structure(list(cov = rbind(c(3,1),1:2), loc = c(0,0), d2 = 10), class = "ellipsoid") volume(myEl)# i.e. "area" here (d = 2) myEl # also mentions the "volume" set.seed(1) d5 <- matrix(rt(500, df=3), 100,5) e5 <- ellipsoidhull(d5) ```

### Example output

``` 70.24815
'ellipsoid' in 2 dimensions:
center = ( 0 0 ); squared ave.radius d^2 =  10
and shape matrix =
[,1] [,2]
[1,]    3    1
[2,]    1    2
hence, area  =  70.248
```

cluster documentation built on April 17, 2021, 9:07 a.m.