wrap.rotation {Riemann}

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)

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.

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"

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)