Generate Uniform Samples on Grassmann Manifold

It generates \(n\) random samples from Grassmann manifold \(Gr(k,p)\).

Usage

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

Arguments

n

number of samples to be generated.

k

dimension of the subspace.

p

original dimension (of the ambient space).

type

return type;

"list"

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

"array"

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

"riemdata"

a S3 object. See wrap.grassmann 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

stiefel.runif, wrap.grassmann

Examples

#-------------------------------------------------------------------
#                 Draw Samples on Grassmann Manifold 
#-------------------------------------------------------------------
#  Multiple Return Types with 3 Observations of 5-dim subspaces in R^10
dat.list = grassmann.runif(n=3, k=5, p=10, type="list")
dat.arr3 = grassmann.runif(n=3, k=5, p=10, type="array")
dat.riem = grassmann.runif(n=3, k=5, p=10, type="riemdata")