wrap.sphere {Riemann}

Prepare Data on Sphere

Description

The unit hypersphere (sphere, for short) is one of the most fundamental curved space in studying geometry. Precisely, we denote (p-1) sphere in \mathbf{R}^p by

\mathcal{S}^{p-1} = \lbrace x \in \mathbf{R}^p ~ \vert ~ x^\top x = \|x\|^2 = 1 \rbrace

where vectors are of unit norm. In wrap.sphere, normalization is applied when each data point is not on the unit sphere.

Usage

wrap.sphere(input)

Arguments

input

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

matrix

an (n \times p) matrix of row observations of unit norm.

list

a length-n list whose elements are length-p vectors of unit norm.

Value

a named riemdata S3 object containing

data

a list of (p\times 1) matrices in \mathcal{S}^{p-1}.

size

dimension of the ambient space.

name

name of the manifold of interests, "sphere"

Examples

#-------------------------------------------------------------------
#                 Checker for Two Types of Inputs
#
#  Generate 5 observations in S^2 embedded in R^3.
#-------------------------------------------------------------------
## DATA GENERATION
d1 = array(0,c(5,3))
d2 = list()
for (i in 1:5){
  single  = stats::rnorm(3)
  d1[i,]  = single
  d2[[i]] = single
}

## RUN
test1 = wrap.sphere(d1)
test2 = wrap.sphere(d2)