Generate Uniform Samples on Stiefel Manifold

It generates \(n\) random samples from Stiefel manifold \(St(k,p)\).

Usage

stiefel.runif(n, k, p, type = c("list", "array", "riemdata"))

Arguments

n

number of samples to be generated.

k

dimension of the frame.

p

original dimension (of the ambient space).

type

return type;

"list"

a length-\(n\) list of \((p\times k)\) basis of \(k\)-frames.

"array"

a \((p\times k\times n)\) 3D array whose slices are \(k\)-frame basis.

"riemdata"

a S3 object. See wrap.stiefel for more details.

Value

an object from one of the above by type option.

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.stiefel

Examples

#-------------------------------------------------------------------
#                 Draw Samples on Stiefel Manifold 
#
# Try Different Return Types with 3 Observations of 5-frames in R^10
#-------------------------------------------------------------------
#  GENERATION
dat.list = stiefel.runif(n=3, k=5, p=10, type="list")
dat.arr3 = stiefel.runif(n=3, k=5, p=10, type="array")
dat.riem = stiefel.runif(n=3, k=5, p=10, type="riemdata")