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.

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.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")