Sample vectors uniformly from the surface of a sphere

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

Usage

sample_sphere_surface(dim, n = 1, ..., radius = 1, positive = TRUE)

Arguments

dim

Integer scalar, the dimension of the random vectors.

n

Integer scalar, the sample size.

...

These dots are for future extensions and must be empty.

radius

Numeric scalar, the radius of the sphere to sample.

positive

Logical, 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_surface() generates uniform samples from \(S^{dim-1}\) (the (dim-1)-sphere) with radius radius, i.e. the Euclidean norm of the samples equal radius.

Related documentation in the C library

sample_sphere_surface()

See also

Other latent position vector samplers: sample_dirichlet(), sample_sphere_volume()

Examples

lpvs.sph <- sample_sphere_surface(dim = 10, n = 20, radius = 1)
RDP.graph.3 <- sample_dot_product(lpvs.sph)
vec.norm <- apply(lpvs.sph, 2, function(x) {
  sum(x^2)
})
vec.norm
#>  [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1