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] 0.5107383 0.9702620 0.9313446 0.7826239 0.9006161 0.9105936 0.2688683
#> [8] 0.6761988 0.5461198 0.9849826 0.7700989 0.6592338 0.9190629 0.8928857
#> [15] 0.9870842 0.8720690 0.7226361 0.7508656 0.9817244 0.9408558