wrap.sphere: Prepare Data on Sphere

Description Usage Arguments Value Examples

View source: R/wrap01sphere.R

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

1
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

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
#-------------------------------------------------------------------
#                 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)

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