wrap.stiefel: Prepare Data on (Compact) Stiefel Manifold

Description Usage Arguments Value Examples

View source: R/wrap04stiefel.R

Description

Stiefel manifold St(k,p) is the set of k-frames in \mathbf{R}^p, which is indeed a Riemannian manifold. For usage in Riemann package, each data point is represented as a matrix by the convention

St(k,p) = \lbrace X \in \mathbf{R}^{p\times k} ~\vert~ X^\top X = I_k \rbrace

which means that columns are orthonormal. When the provided matrix is not an orthonormal basis as above, wrap.stiefel applies orthogonalization to extract valid basis information.

Usage

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wrap.stiefel(input)

Arguments

input

data matrices to be wrapped as riemdata class. Following inputs are considered,

array

a (p\times k\times n) array where each slice along 3rd dimension is a k-frame.

list

a length-n list whose elements are (p\times k) k-frames.

Value

a named riemdata S3 object containing

data

a list of k-frame orthonormal matrices.

size

size of each k-frame basis matrix.

name

name of the manifold of interests, "stiefel"

Examples

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#-------------------------------------------------------------------
#                 Checker for Two Types of Inputs
#
#  Generate 5 observations in St(2,4)
#-------------------------------------------------------------------
#  Data Generation by QR Decomposition
d1 = array(0,c(4,2,5))
d2 = list()
for (i in 1:5){
  d1[,,i] = qr.Q(qr(matrix(rnorm(4*2),ncol=2)))
  d2[[i]] = d1[,,i]
}

#  Run
test1 = wrap.stiefel(d1)
test2 = wrap.stiefel(d2)

Riemann documentation built on June 20, 2021, 5:07 p.m.