Sample finite-dimensional vectors to use as latent position vectors in random dot product graphs

## Arguments

- dim
Integer scalar, the dimension of the random vectors.

- n
Integer scalar, the sample size.

- radius
Numeric scalar, the radius of the sphere to sample.

- positive
Logical scalar, whether to sample from the positive orthant of the sphere.

## Value

A `dim`

(length of the `alpha`

vector for
`sample_dirichlet()`

) times `n`

matrix, whose columns are the sample
vectors.

## Details

`sample_sphere_volume()`

generates uniform samples from \(S^{dim-1}\)
(the `(dim-1)`

-sphere) i.e. the Euclidean norm of the samples is
smaller or equal to `radius`

.

## See also

Other latent position vector samplers:
`sample_dirichlet()`

,
`sample_sphere_surface()`

## Examples

```
lpvs.sph.vol <- sample_sphere_volume(dim = 10, n = 20, radius = 1)
RDP.graph.4 <- sample_dot_product(lpvs.sph.vol)
vec.norm <- apply(lpvs.sph.vol, 2, function(x) {
sum(x^2)
})
vec.norm
#> [1] 0.7688058 0.6585114 0.9551110 0.8593609 0.9989740 0.9987677 0.8974146
#> [8] 0.9730082 0.9656196 0.9356756 0.7363652 0.9339241 0.9183260 0.9686613
#> [15] 0.8277614 0.9508361 0.9275304 0.6914062 0.8031998 0.9770563
```