wrap.grassmann: Prepare Data on Grassmann Manifold

Description Usage Arguments Value Examples

View source: R/wrap05grassmann.R

Description

Grassmann manifold Gr(k,p) is the set of k-planes, or k-dimensional subspaces in R^p, which means that for a given matrix Y \in \mathbf{R}{p\times k}, the column space SPAN(Y) is an element in Grassmann manifold. We use a convention that each element in Gr(k,p) is represented as an orthonormal basis (ONB) X \in \mathbf{R}^{p\times k} where

X^\top X = I_k.

If not provided in such a form, this wrapper takes a QR decomposition of the given data to recover a corresponding ONB.

Usage

1

Arguments

input

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

array

an (p\times k\times n) array where each slice along 3rd dimension is a k-subspace basis in dimension p.

list

a length-n list whose elements are (p\times k) basis for k-subspace.

Value

a named riemdata S3 object containing

data

a list of k-subspace basis matrices.

size

size of each k-subspace basis matrix.

name

name of the manifold of interests, "grassmann"

Examples

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

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

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