Generate Uniform Samples on Sphere

It generates \(n\) random samples from \(\mathcal{S}^{p-1}\). For convenient usage of users, we provide a number of options in terms of the return type.

Usage

sphere.runif(n, p, type = c("list", "matrix", "riemdata"))

Arguments

n

number of samples to be generated.

p

original dimension (of the ambient space).

type

return type;

"list"

a length-\(n\) list of length-\(p\) vectors.

"matrix"

a \((n\times p)\) where rows are unit vectors.

"riemdata"

a S3 object. See wrap.sphere for more details (Default).

Value

an object from one of the above by type option.

Validation status

This retained legacy interface is experimental. Its full numerical and statistical contract has not been independently verified across supported inputs. See riem-method-contracts and the installed contract table for method-specific assumptions, restrictions, and evidence scope.

References

Chikuse Y (2003). Statistics on Special Manifolds, volume 174 of Lecture Notes in Statistics. Springer New York, New York, NY. ISBN 978-0-387-00160-9 978-0-387-21540-2.

See also

wrap.sphere

Examples

#-------------------------------------------------------------------
#                       Draw Samples on Sphere
#
# Multiple return types on S^4 in R^5
#-------------------------------------------------------------------
dat.list = sphere.runif(n=10, p=5, type="list")
dat.matx = sphere.runif(n=10, p=5, type="matrix")
dat.riem = sphere.runif(n=10, p=5, type="riemdata")