Riemann (version 0.1.6)

wrap.rotation: Prepare Data on Rotation Group

Description

Rotation group, also known as special orthogonal group, is a Riemannian manifold $$SO(p) = \lbrace Q \in \mathbf{R}^{p\times p}~\vert~ Q^\top Q = I, \textrm{det}(Q)=1 \rbrace $$ where the name originates from an observation that when \(p=2,3\) these matrices are rotation of shapes/configurations.

Usage

wrap.rotation(input)

Value

a named riemdata S3 object containing

data

a list of \((p\times p)\) rotation matrices.

size

size of each rotation matrix.

name

name of the manifold of interests, "rotation"

Arguments

input

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

array

a \((p\times p\times n)\) array where each slice along 3rd dimension is a rotation matrix.

list

a length-\(n\) list whose elements are \((p\times p)\) rotation matrices.

Examples

#-------------------------------------------------------------------
#                 Checker for Two Types of Inputs
#-------------------------------------------------------------------
## DATA GENERATION
d1 = array(0,c(3,3,5))
d2 = list()
for (i in 1:5){
  single  = qr.Q(qr(matrix(rnorm(9),nrow=3)))
  d1[,,i] = single
  d2[[i]] = single
}

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